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

Percentage Accurate: 99.9% → 99.9%

Time: 11.5s

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, 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. Final simplification 99.9%

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

Alternative 2: 88.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+36} \lor \neg \left(z \leq 1.65 \cdot 10^{+140}\right):\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.15e+36) (not (<= z 1.65e+140)))
   (- (- (log t) z) y)
   (- (+ (* x (log y)) (log t)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.15e+36) || !(z <= 1.65e+140)) {
		tmp = (log(t) - z) - y;
	} else {
		tmp = ((x * log(y)) + 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 <= (-2.15d+36)) .or. (.not. (z <= 1.65d+140))) then
        tmp = (log(t) - z) - y
    else
        tmp = ((x * log(y)) + 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 <= -2.15e+36) || !(z <= 1.65e+140)) {
		tmp = (Math.log(t) - z) - y;
	} else {
		tmp = ((x * Math.log(y)) + Math.log(t)) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.15e+36) or not (z <= 1.65e+140):
		tmp = (math.log(t) - z) - y
	else:
		tmp = ((x * math.log(y)) + math.log(t)) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.15e+36) || !(z <= 1.65e+140))
		tmp = Float64(Float64(log(t) - z) - y);
	else
		tmp = Float64(Float64(Float64(x * log(y)) + log(t)) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.15e+36) || ~((z <= 1.65e+140)))
		tmp = (log(t) - z) - y;
	else
		tmp = ((x * log(y)) + log(t)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.15e+36], N[Not[LessEqual[z, 1.65e+140]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15000000000000002e36 or 1.6500000000000001e140 < z

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l- 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--r+ 100.0%

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

      5. fma-neg 100.0%

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

      6. neg-sub0 100.0%

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

      7. associate-+l- 100.0%

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

      8. neg-sub0 100.0%

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

      9. +-commutative 100.0%

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

      10. 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 84.2%

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

   if -2.15000000000000002e36 < z < 1.6500000000000001e140

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 93.8%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+36} \lor \neg \left(z \leq 1.65 \cdot 10^{+140}\right):\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - y\\ \end{array} \]

Alternative 3: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-12} \lor \neg \left(x \leq 8 \cdot 10^{+71}\right):\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.5e-12) (not (<= x 8e+71)))
   (- (+ (* x (log y)) (log t)) z)
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.5e-12) || !(x <= 8e+71)) {
		tmp = ((x * log(y)) + log(t)) - 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 <= (-3.5d-12)) .or. (.not. (x <= 8d+71))) then
        tmp = ((x * log(y)) + log(t)) - 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 <= -3.5e-12) || !(x <= 8e+71)) {
		tmp = ((x * Math.log(y)) + Math.log(t)) - z;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.5e-12) or not (x <= 8e+71):
		tmp = ((x * math.log(y)) + math.log(t)) - z
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.5e-12) || !(x <= 8e+71))
		tmp = Float64(Float64(Float64(x * log(y)) + log(t)) - 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 <= -3.5e-12) || ~((x <= 8e+71)))
		tmp = ((x * log(y)) + log(t)) - z;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.5e-12], N[Not[LessEqual[x, 8e+71]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5e-12 or 8.0000000000000003e71 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 89.9%

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

   if -3.5e-12 < x < 8.0000000000000003e71

   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. associate--l- 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--r+ 100.0%

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

      5. fma-neg 100.0%

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

      6. neg-sub0 100.0%

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

      7. associate-+l- 100.0%

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

      8. neg-sub0 100.0%

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

      9. +-commutative 100.0%

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

      10. 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 97.4%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-12} \lor \neg \left(x \leq 8 \cdot 10^{+71}\right):\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 4: 60.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t - y\\ \mathbf{if}\;x \leq -24.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-226}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (log t) y)))
   (if (<= x -24.5)
     t_1
     (if (<= x 1.4e-295)
       t_2
       (if (<= x 6.8e-226) (- (log t) z) (if (<= x 2.2e+66) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = log(t) - y;
	double tmp;
	if (x <= -24.5) {
		tmp = t_1;
	} else if (x <= 1.4e-295) {
		tmp = t_2;
	} else if (x <= 6.8e-226) {
		tmp = log(t) - z;
	} else if (x <= 2.2e+66) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = log(t) - y
    if (x <= (-24.5d0)) then
        tmp = t_1
    else if (x <= 1.4d-295) then
        tmp = t_2
    else if (x <= 6.8d-226) then
        tmp = log(t) - z
    else if (x <= 2.2d+66) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = Math.log(t) - y;
	double tmp;
	if (x <= -24.5) {
		tmp = t_1;
	} else if (x <= 1.4e-295) {
		tmp = t_2;
	} else if (x <= 6.8e-226) {
		tmp = Math.log(t) - z;
	} else if (x <= 2.2e+66) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = math.log(t) - y
	tmp = 0
	if x <= -24.5:
		tmp = t_1
	elif x <= 1.4e-295:
		tmp = t_2
	elif x <= 6.8e-226:
		tmp = math.log(t) - z
	elif x <= 2.2e+66:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(log(t) - y)
	tmp = 0.0
	if (x <= -24.5)
		tmp = t_1;
	elseif (x <= 1.4e-295)
		tmp = t_2;
	elseif (x <= 6.8e-226)
		tmp = Float64(log(t) - z);
	elseif (x <= 2.2e+66)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = log(t) - y;
	tmp = 0.0;
	if (x <= -24.5)
		tmp = t_1;
	elseif (x <= 1.4e-295)
		tmp = t_2;
	elseif (x <= 6.8e-226)
		tmp = log(t) - z;
	elseif (x <= 2.2e+66)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -24.5], t$95$1, If[LessEqual[x, 1.4e-295], t$95$2, If[LessEqual[x, 6.8e-226], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 2.2e+66], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -24.5 or 2.1999999999999998e66 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 65.6%

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

   if -24.5 < x < 1.4e-295 or 6.80000000000000014e-226 < x < 2.1999999999999998e66

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 74.4%

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

      1. log-pow 65.8%

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

      2. log-prod 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in x around 0 71.3%

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

   if 1.4e-295 < x < 6.80000000000000014e-226

   1. Initial program 100.0%

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

      1. flip-- 83.0%

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

      2. clear-num 83.0%

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

      3. fma-def 83.0%

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

      4. pow2 83.0%

         \[\leadsto \left(\frac{1}{\frac{\mathsf{fma}\left(x, \log y, y\right)}{\color{blue}{{\left(x \cdot \log y\right)}^{2}} - y \cdot y}} - z\right) + \log t \]

   3. Applied egg-rr 83.0%

      \[\leadsto \left(\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, \log y, y\right)}{{\left(x \cdot \log y\right)}^{2} - y \cdot y}}} - z\right) + \log t \]

   4. Taylor expanded in x around inf 82.7%

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

      1. associate-/r* 82.7%

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

   6. Simplified 82.7%

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

   7. Taylor expanded in x around 0 82.7%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -24.5:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-295}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-226}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+66}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 5: 83.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+58} \lor \neg \left(x \leq 2.1 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.8e+58) (not (<= x 2.1e+82)))
   (* x (log y))
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e+58) || !(x <= 2.1e+82)) {
		tmp = x * log(y);
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.8d+58)) .or. (.not. (x <= 2.1d+82))) then
        tmp = x * log(y)
    else
        tmp = (log(t) - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.8e+58) || !(x <= 2.1e+82)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.8e+58) or not (x <= 2.1e+82):
		tmp = x * math.log(y)
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.8e+58) || !(x <= 2.1e+82))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.8e+58) || ~((x <= 2.1e+82)))
		tmp = x * log(y);
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.8e+58], N[Not[LessEqual[x, 2.1e+82]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999999e58 or 2.1e82 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 71.9%

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

   if -3.7999999999999999e58 < x < 2.1e82

   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. associate--l- 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--r+ 100.0%

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

      5. fma-neg 100.0%

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

      6. neg-sub0 100.0%

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

      7. associate-+l- 100.0%

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

      8. neg-sub0 100.0%

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

      9. +-commutative 100.0%

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

      10. 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 94.3%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+58} \lor \neg \left(x \leq 2.1 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 6: 48.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -24.5 \lor \neg \left(x \leq 3.4 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -24.5) (not (<= x 3.4e+67))) (* x (log y)) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -24.5) || !(x <= 3.4e+67)) {
		tmp = x * log(y);
	} 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 ((x <= (-24.5d0)) .or. (.not. (x <= 3.4d+67))) then
        tmp = x * log(y)
    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 ((x <= -24.5) || !(x <= 3.4e+67)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -24.5) or not (x <= 3.4e+67):
		tmp = x * math.log(y)
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -24.5) || !(x <= 3.4e+67))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -24.5) || ~((x <= 3.4e+67)))
		tmp = x * log(y);
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -24.5], N[Not[LessEqual[x, 3.4e+67]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if x < -24.5 or 3.4000000000000002e67 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 65.6%

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

   if -24.5 < x < 3.4000000000000002e67

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 48.4%

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

      1. neg-mul-1 48.4%

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

   4. Simplified 48.4%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -24.5 \lor \neg \left(x \leq 3.4 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 7: 60.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -24.5 \lor \neg \left(x \leq 1.55 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -24.5) (not (<= x 1.55e+66))) (* x (log y)) (- (log t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -24.5) || !(x <= 1.55e+66)) {
		tmp = x * log(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 ((x <= (-24.5d0)) .or. (.not. (x <= 1.55d+66))) then
        tmp = x * log(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 ((x <= -24.5) || !(x <= 1.55e+66)) {
		tmp = x * Math.log(y);
	} else {
		tmp = Math.log(t) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -24.5) or not (x <= 1.55e+66):
		tmp = x * math.log(y)
	else:
		tmp = math.log(t) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -24.5) || !(x <= 1.55e+66))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(log(t) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -24.5) || ~((x <= 1.55e+66)))
		tmp = x * log(y);
	else
		tmp = log(t) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -24.5], N[Not[LessEqual[x, 1.55e+66]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -24.5 or 1.55000000000000009e66 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 65.6%

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

   if -24.5 < x < 1.55000000000000009e66

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 72.3%

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

      1. log-pow 64.4%

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

      2. log-prod 64.4%

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

   4. Simplified 64.4%

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

   5. Taylor expanded in x around 0 69.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -24.5 \lor \neg \left(x \leq 1.55 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - y\\ \end{array} \]

Alternative 8: 47.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.5 \cdot 10^{-246}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-191}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+25}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 9.5e-246)
   (- z)
   (if (<= y 2.1e-191) (log t) (if (<= y 2e+25) (- z) (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 9.5e-246) {
		tmp = -z;
	} else if (y <= 2.1e-191) {
		tmp = log(t);
	} else if (y <= 2e+25) {
		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 <= 9.5d-246) then
        tmp = -z
    else if (y <= 2.1d-191) then
        tmp = log(t)
    else if (y <= 2d+25) 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 <= 9.5e-246) {
		tmp = -z;
	} else if (y <= 2.1e-191) {
		tmp = Math.log(t);
	} else if (y <= 2e+25) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 9.5e-246:
		tmp = -z
	elif y <= 2.1e-191:
		tmp = math.log(t)
	elif y <= 2e+25:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 9.5e-246)
		tmp = Float64(-z);
	elseif (y <= 2.1e-191)
		tmp = log(t);
	elseif (y <= 2e+25)
		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 <= 9.5e-246)
		tmp = -z;
	elseif (y <= 2.1e-191)
		tmp = log(t);
	elseif (y <= 2e+25)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 9.5e-246], (-z), If[LessEqual[y, 2.1e-191], N[Log[t], $MachinePrecision], If[LessEqual[y, 2e+25], (-z), (-y)]]]

Derivation

1. Split input into 3 regimes

2. if y < 9.5000000000000002e-246 or 2.09999999999999985e-191 < y < 2.00000000000000018e25

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 35.7%

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

      1. neg-mul-1 35.7%

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

   4. Simplified 35.7%

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

   if 9.5000000000000002e-246 < y < 2.09999999999999985e-191

   1. Initial program 99.9%

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

      1. flip-- 92.3%

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

      2. clear-num 92.3%

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

      3. fma-def 92.3%

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

      4. pow2 92.3%

         \[\leadsto \left(\frac{1}{\frac{\mathsf{fma}\left(x, \log y, y\right)}{\color{blue}{{\left(x \cdot \log y\right)}^{2}} - y \cdot y}} - z\right) + \log t \]

   3. Applied egg-rr 92.3%

      \[\leadsto \left(\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(x, \log y, y\right)}{{\left(x \cdot \log y\right)}^{2} - y \cdot y}}} - z\right) + \log t \]

   4. Taylor expanded in x around inf 99.8%

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

   5. Taylor expanded in z around 0 72.5%

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

      1. *-commutative 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in x around 0 49.3%

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

   if 2.00000000000000018e25 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 66.5%

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

      1. neg-mul-1 66.5%

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

   4. Simplified 66.5%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9.5 \cdot 10^{-246}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-191}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+25}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 9: 48.6% accurate, 51.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{+25}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 1.65e+25) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.65e+25) {
		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 <= 1.65d+25) 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 <= 1.65e+25) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.65e+25:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.65e+25)
		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 <= 1.65e+25)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.65e+25], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 1.6500000000000001e25

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 34.5%

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

      1. neg-mul-1 34.5%

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

   4. Simplified 34.5%

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

   if 1.6500000000000001e25 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 66.5%

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

      1. neg-mul-1 66.5%

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

   4. Simplified 66.5%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{+25}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 10: 29.6% 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 y around inf 32.8%

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

   1. neg-mul-1 32.8%

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

4. Simplified 32.8%

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

5. Final simplification 32.8%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023271 
(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)))