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

Percentage Accurate: 99.9% → 99.9%

Time: 12.9s

Alternatives: 14

Speedup: 1.0×

• could not determine a ground truth

  1. x = -6.1543290027713455e-214
  2. y = 2.522259885655154e+149
  3. z = 4.557069646684376e+146
  4. t = 5.888416345631519e+65

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * log(y)) - y) - z) + log(t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x * log(y)) - y) - z) + log(t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l- 99.8%

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

   2. sub-neg 99.8%

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

   3. associate--l+ 99.8%

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

   4. fma-define 99.9%

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

   5. sub-neg 99.9%

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

   6. distribute-neg-in 99.9%

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

   7. sub-neg 99.9%

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

   8. associate-+r+ 99.9%

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

   9. +-commutative 99.9%

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

   10. distribute-neg-in 99.9%

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

   11. remove-double-neg 99.9%

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

   12. unsub-neg 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(t\_1 - y\right) - z\\ \mathbf{if}\;t\_2 \leq -2000000 \lor \neg \left(t\_2 \leq 10^{+17}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\log t + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- t_1 y) z)))
   (if (or (<= t_2 -2000000.0) (not (<= t_2 1e+17))) 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 <= -2000000.0) || !(t_2 <= 1e+17)) {
		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 <= (-2000000.0d0)) .or. (.not. (t_2 <= 1d+17))) 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 <= -2000000.0) || !(t_2 <= 1e+17)) {
		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 <= -2000000.0) or not (t_2 <= 1e+17):
		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 <= -2000000.0) || !(t_2 <= 1e+17))
		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 <= -2000000.0) || ~((t_2 <= 1e+17)))
		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, -2000000.0], N[Not[LessEqual[t$95$2, 1e+17]], $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) < -2e6 or 1e17 < (-.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. Add Preprocessing

   5. Taylor expanded in z around inf 99.1%

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

   if -2e6 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 1e17

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. associate--l+ 99.8%

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

      4. fma-define 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. sub-neg 99.9%

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

      8. associate-+r+ 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. remove-double-neg 99.9%

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

      12. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in y around 0 99.8%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \log y - y\right) - z \leq -2000000 \lor \neg \left(\left(x \cdot \log y - y\right) - z \leq 10^{+17}\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t + x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -50000 \lor \neg \left(z \leq 8.8 \cdot 10^{-18}\right):\\ \;\;\;\;\left(t\_1 - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + t\_1\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (or (<= z -50000.0) (not (<= z 8.8e-18)))
     (- (- t_1 y) z)
     (- (+ (log t) t_1) y))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if ((z <= -50000.0) || !(z <= 8.8e-18)) {
		tmp = (t_1 - y) - z;
	} else {
		tmp = (log(t) + t_1) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if ((z <= (-50000.0d0)) .or. (.not. (z <= 8.8d-18))) then
        tmp = (t_1 - y) - z
    else
        tmp = (log(t) + t_1) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if ((z <= -50000.0) || !(z <= 8.8e-18)) {
		tmp = (t_1 - y) - z;
	} else {
		tmp = (Math.log(t) + t_1) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if (z <= -50000.0) or not (z <= 8.8e-18):
		tmp = (t_1 - y) - z
	else:
		tmp = (math.log(t) + t_1) - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if ((z <= -50000.0) || !(z <= 8.8e-18))
		tmp = Float64(Float64(t_1 - y) - z);
	else
		tmp = Float64(Float64(log(t) + t_1) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if ((z <= -50000.0) || ~((z <= 8.8e-18)))
		tmp = (t_1 - y) - z;
	else
		tmp = (log(t) + t_1) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -50000.0], N[Not[LessEqual[z, 8.8e-18]], $MachinePrecision]], N[(N[(t$95$1 - y), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5e4 or 8.7999999999999994e-18 < z

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.7%

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

   if -5e4 < z < 8.7999999999999994e-18

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.8%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -50000 \lor \neg \left(z \leq 8.8 \cdot 10^{-18}\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 0.0085:\\ \;\;\;\;\left(\log t + t\_1\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= y 0.0085) (- (+ (log t) t_1) z) (- (- t_1 y) z))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (y <= 0.0085) {
		tmp = (log(t) + t_1) - z;
	} else {
		tmp = (t_1 - y) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (y <= 0.0085d0) then
        tmp = (log(t) + t_1) - z
    else
        tmp = (t_1 - y) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (y <= 0.0085) {
		tmp = (Math.log(t) + t_1) - z;
	} else {
		tmp = (t_1 - y) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if y <= 0.0085:
		tmp = (math.log(t) + t_1) - z
	else:
		tmp = (t_1 - y) - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 0.0085)
		tmp = Float64(Float64(log(t) + t_1) - z);
	else
		tmp = Float64(Float64(t_1 - y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (y <= 0.0085)
		tmp = (log(t) + t_1) - z;
	else
		tmp = (t_1 - y) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 0.0085], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - z), $MachinePrecision], N[(N[(t$95$1 - y), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 0.0085000000000000006

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

   if 0.0085000000000000006 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 98.8%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.0085:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 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 99.8%

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

3. Final simplification 99.8%

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

Alternative 6: 60.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - y\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+93}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 19000000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) y)))
   (if (<= z -1.65e+93)
     (- z)
     (if (<= z -1.9e-171)
       t_1
       (if (<= z -6.8e-216)
         (* x (log y))
         (if (<= z 19000000000000.0) t_1 (- z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - y;
	double tmp;
	if (z <= -1.65e+93) {
		tmp = -z;
	} else if (z <= -1.9e-171) {
		tmp = t_1;
	} else if (z <= -6.8e-216) {
		tmp = x * log(y);
	} else if (z <= 19000000000000.0) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) - y
    if (z <= (-1.65d+93)) then
        tmp = -z
    else if (z <= (-1.9d-171)) then
        tmp = t_1
    else if (z <= (-6.8d-216)) then
        tmp = x * log(y)
    else if (z <= 19000000000000.0d0) then
        tmp = t_1
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) - y;
	double tmp;
	if (z <= -1.65e+93) {
		tmp = -z;
	} else if (z <= -1.9e-171) {
		tmp = t_1;
	} else if (z <= -6.8e-216) {
		tmp = x * Math.log(y);
	} else if (z <= 19000000000000.0) {
		tmp = t_1;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - y
	tmp = 0
	if z <= -1.65e+93:
		tmp = -z
	elif z <= -1.9e-171:
		tmp = t_1
	elif z <= -6.8e-216:
		tmp = x * math.log(y)
	elif z <= 19000000000000.0:
		tmp = t_1
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - y)
	tmp = 0.0
	if (z <= -1.65e+93)
		tmp = Float64(-z);
	elseif (z <= -1.9e-171)
		tmp = t_1;
	elseif (z <= -6.8e-216)
		tmp = Float64(x * log(y));
	elseif (z <= 19000000000000.0)
		tmp = t_1;
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - y;
	tmp = 0.0;
	if (z <= -1.65e+93)
		tmp = -z;
	elseif (z <= -1.9e-171)
		tmp = t_1;
	elseif (z <= -6.8e-216)
		tmp = x * log(y);
	elseif (z <= 19000000000000.0)
		tmp = t_1;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[z, -1.65e+93], (-z), If[LessEqual[z, -1.9e-171], t$95$1, If[LessEqual[z, -6.8e-216], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 19000000000000.0], t$95$1, (-z)]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000004e93 or 1.9e13 < z

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 69.2%

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

      1. neg-mul-1 69.2%

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

   7. Simplified 69.2%

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

   if -1.65000000000000004e93 < z < -1.90000000000000011e-171 or -6.7999999999999995e-216 < z < 1.9e13

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. associate--l+ 99.8%

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

      4. fma-define 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. sub-neg 99.9%

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

      8. associate-+r+ 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. remove-double-neg 99.9%

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

      12. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 97.1%

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

   6. Taylor expanded in x around 0 61.4%

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

   if -1.90000000000000011e-171 < z < -6.7999999999999995e-216

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 78.2%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+93}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-171}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 19000000000000:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \lor \neg \left(x \leq 0.000435\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.5) (not (<= x 0.000435)))
   (- (- (* x (log y)) y) z)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.5) || !(x <= 0.000435)) {
		tmp = ((x * log(y)) - y) - z;
	} 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 <= (-1.5d0)) .or. (.not. (x <= 0.000435d0))) then
        tmp = ((x * log(y)) - y) - z
    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 <= -1.5) || !(x <= 0.000435)) {
		tmp = ((x * Math.log(y)) - y) - z;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.5) or not (x <= 0.000435):
		tmp = ((x * math.log(y)) - y) - z
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.5) || !(x <= 0.000435))
		tmp = Float64(Float64(Float64(x * log(y)) - y) - z);
	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 <= -1.5) || ~((x <= 0.000435)))
		tmp = ((x * log(y)) - y) - z;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.5], N[Not[LessEqual[x, 0.000435]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5 or 4.35000000000000003e-4 < x

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.1%

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

   if -1.5 < x < 4.35000000000000003e-4

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \lor \neg \left(x \leq 0.000435\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+91}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-197}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-267}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.55e+91)
   (- z)
   (if (<= z -7e-197)
     (- y)
     (if (<= z -1.45e-267) (log t) (if (<= z 13000000000000.0) (- y) (- z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e+91) {
		tmp = -z;
	} else if (z <= -7e-197) {
		tmp = -y;
	} else if (z <= -1.45e-267) {
		tmp = log(t);
	} else if (z <= 13000000000000.0) {
		tmp = -y;
	} else {
		tmp = -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 (z <= (-1.55d+91)) then
        tmp = -z
    else if (z <= (-7d-197)) then
        tmp = -y
    else if (z <= (-1.45d-267)) then
        tmp = log(t)
    else if (z <= 13000000000000.0d0) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e+91) {
		tmp = -z;
	} else if (z <= -7e-197) {
		tmp = -y;
	} else if (z <= -1.45e-267) {
		tmp = Math.log(t);
	} else if (z <= 13000000000000.0) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.55e+91:
		tmp = -z
	elif z <= -7e-197:
		tmp = -y
	elif z <= -1.45e-267:
		tmp = math.log(t)
	elif z <= 13000000000000.0:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.55e+91)
		tmp = Float64(-z);
	elseif (z <= -7e-197)
		tmp = Float64(-y);
	elseif (z <= -1.45e-267)
		tmp = log(t);
	elseif (z <= 13000000000000.0)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.55e+91)
		tmp = -z;
	elseif (z <= -7e-197)
		tmp = -y;
	elseif (z <= -1.45e-267)
		tmp = log(t);
	elseif (z <= 13000000000000.0)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.55e+91], (-z), If[LessEqual[z, -7e-197], (-y), If[LessEqual[z, -1.45e-267], N[Log[t], $MachinePrecision], If[LessEqual[z, 13000000000000.0], (-y), (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999999e91 or 1.3e13 < z

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 69.2%

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

      1. neg-mul-1 69.2%

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

   7. Simplified 69.2%

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

   if -1.54999999999999999e91 < z < -6.9999999999999996e-197 or -1.45000000000000011e-267 < z < 1.3e13

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 44.3%

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

      1. neg-mul-1 44.3%

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

   7. Simplified 44.3%

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

   if -6.9999999999999996e-197 < z < -1.45000000000000011e-267

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. associate--l+ 99.8%

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

      4. fma-define 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. sub-neg 99.9%

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

      8. associate-+r+ 99.9%

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

      9. +-commutative 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. remove-double-neg 99.9%

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

      12. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in y around 0 84.0%

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

      1. +-commutative 84.0%

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

      2. *-commutative 84.0%

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

      3. fma-undefine 84.0%

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

   8. Simplified 84.0%

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

   9. Taylor expanded in x around 0 34.0%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+91}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-197}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-267}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+139} \lor \neg \left(x \leq 1.5 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.8e+139) (not (<= x 1.5e+125)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.8e+139) || !(x <= 1.5e+125)) {
		tmp = x * log(y);
	} 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 <= (-5.8d+139)) .or. (.not. (x <= 1.5d+125))) then
        tmp = x * log(y)
    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 <= -5.8e+139) || !(x <= 1.5e+125)) {
		tmp = x * Math.log(y);
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.8e+139) or not (x <= 1.5e+125):
		tmp = x * math.log(y)
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.8e+139) || !(x <= 1.5e+125))
		tmp = Float64(x * log(y));
	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 <= -5.8e+139) || ~((x <= 1.5e+125)))
		tmp = x * log(y);
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.8e+139], N[Not[LessEqual[x, 1.5e+125]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.7999999999999998e139 or 1.50000000000000008e125 < x

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 77.1%

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

   if -5.7999999999999998e139 < x < 1.50000000000000008e125

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 91.0%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+139} \lor \neg \left(x \leq 1.5 \cdot 10^{+125}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+75}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 15000000000000:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.4e+75)
   (- z)
   (if (<= z -3.1e-267)
     (* x (log y))
     (if (<= z 15000000000000.0) (- y) (- z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.4e+75) {
		tmp = -z;
	} else if (z <= -3.1e-267) {
		tmp = x * log(y);
	} else if (z <= 15000000000000.0) {
		tmp = -y;
	} else {
		tmp = -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 (z <= (-5.4d+75)) then
        tmp = -z
    else if (z <= (-3.1d-267)) then
        tmp = x * log(y)
    else if (z <= 15000000000000.0d0) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.4e+75) {
		tmp = -z;
	} else if (z <= -3.1e-267) {
		tmp = x * Math.log(y);
	} else if (z <= 15000000000000.0) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.4e+75:
		tmp = -z
	elif z <= -3.1e-267:
		tmp = x * math.log(y)
	elif z <= 15000000000000.0:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.4e+75)
		tmp = Float64(-z);
	elseif (z <= -3.1e-267)
		tmp = Float64(x * log(y));
	elseif (z <= 15000000000000.0)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.4e+75)
		tmp = -z;
	elseif (z <= -3.1e-267)
		tmp = x * log(y);
	elseif (z <= 15000000000000.0)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.4e+75], (-z), If[LessEqual[z, -3.1e-267], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 15000000000000.0], (-y), (-z)]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.39999999999999996e75 or 1.5e13 < z

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 67.9%

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

      1. neg-mul-1 67.9%

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

   7. Simplified 67.9%

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

   if -5.39999999999999996e75 < z < -3.1000000000000001e-267

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 46.3%

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

   if -3.1000000000000001e-267 < z < 1.5e13

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 47.3%

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

      1. neg-mul-1 47.3%

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

   7. Simplified 47.3%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+75}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 15000000000000:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{-18}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.2e-18) (- (log t) z) (if (<= y 1.85e+94) (* x (log y)) (- y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.2e-18) {
		tmp = log(t) - z;
	} else if (y <= 1.85e+94) {
		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 (y <= 1.2d-18) then
        tmp = log(t) - z
    else if (y <= 1.85d+94) 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 (y <= 1.2e-18) {
		tmp = Math.log(t) - z;
	} else if (y <= 1.85e+94) {
		tmp = x * Math.log(y);
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.2e-18:
		tmp = math.log(t) - z
	elif y <= 1.85e+94:
		tmp = x * math.log(y)
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.2e-18)
		tmp = Float64(log(t) - z);
	elseif (y <= 1.85e+94)
		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 (y <= 1.2e-18)
		tmp = log(t) - z;
	elseif (y <= 1.85e+94)
		tmp = x * log(y);
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.2e-18], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], If[LessEqual[y, 1.85e+94], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], (-y)]]

Derivation

1. Split input into 3 regimes

2. if y < 1.19999999999999997e-18

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

   6. Taylor expanded in x around 0 67.7%

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

   if 1.19999999999999997e-18 < y < 1.8500000000000001e94

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 49.9%

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

   if 1.8500000000000001e94 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 65.5%

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

      1. neg-mul-1 65.5%

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

   7. Simplified 65.5%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{-18}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.9% accurate, 17.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+92} \lor \neg \left(z \leq 5500000000000\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.5e+92) (not (<= z 5500000000000.0))) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.5e+92) || !(z <= 5500000000000.0)) {
		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 <= (-6.5d+92)) .or. (.not. (z <= 5500000000000.0d0))) 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 <= -6.5e+92) || !(z <= 5500000000000.0)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.5e+92) or not (z <= 5500000000000.0):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.5e+92) || !(z <= 5500000000000.0))
		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 <= -6.5e+92) || ~((z <= 5500000000000.0)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.5e+92], N[Not[LessEqual[z, 5500000000000.0]], $MachinePrecision]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999999e92 or 5.5e12 < z

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 69.2%

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

      1. neg-mul-1 69.2%

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

   7. Simplified 69.2%

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

   if -6.49999999999999999e92 < z < 5.5e12

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 39.6%

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

      1. neg-mul-1 39.6%

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

   7. Simplified 39.6%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+92} \lor \neg \left(z \leq 5500000000000\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.8% 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 99.8%

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

   1. associate-+l- 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 29.4%

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

   1. neg-mul-1 29.4%

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

7. Simplified 29.4%

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

8. Final simplification 29.4%

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

Alternative 14: 2.2% accurate, 209.0× 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 y
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-+l- 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 29.4%

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

   1. neg-mul-1 29.4%

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

7. Simplified 29.4%

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

   1. neg-sub0 29.4%

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

   2. sub-neg 29.4%

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

   3. add-sqr-sqrt 0.0%

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

   4. sqrt-unprod 2.3%

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

   5. sqr-neg 2.3%

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

   6. sqrt-unprod 2.3%

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

   7. add-sqr-sqrt 2.3%

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

9. Applied egg-rr 2.3%

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

    1. +-lft-identity 2.3%

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

11. Simplified 2.3%

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

12. Final simplification 2.3%

    \[\leadsto y \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024052 
(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)))