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

Percentage Accurate: 99.9% → 99.9%

Time: 11.9s

Alternatives: 12

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+23} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-17}\right):\\ \;\;\;\;t\_1 - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (or (<= t_1 -2e+23) (not (<= t_1 2e-17)))
     (- t_1 z)
     (- (log t) (+ y z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if ((t_1 <= -2e+23) || !(t_1 <= 2e-17)) {
		tmp = t_1 - 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) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) - y
    if ((t_1 <= (-2d+23)) .or. (.not. (t_1 <= 2d-17))) then
        tmp = t_1 - 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 t_1 = (x * Math.log(y)) - y;
	double tmp;
	if ((t_1 <= -2e+23) || !(t_1 <= 2e-17)) {
		tmp = t_1 - z;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if (t_1 <= -2e+23) or not (t_1 <= 2e-17):
		tmp = t_1 - z
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if ((t_1 <= -2e+23) || !(t_1 <= 2e-17))
		tmp = Float64(t_1 - z);
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - y;
	tmp = 0.0;
	if ((t_1 <= -2e+23) || ~((t_1 <= 2e-17)))
		tmp = t_1 - z;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+23], N[Not[LessEqual[t$95$1, 2e-17]], $MachinePrecision]], N[(t$95$1 - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -1.9999999999999998e23 or 2.00000000000000014e-17 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 89.1%

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

   7. Simplified 88.9%

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

      1. clear-num 88.8%

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

      2. un-div-inv 88.9%

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

   9. Applied egg-rr 88.9%

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

   10. Taylor expanded in z around inf 88.9%

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

   11. Taylor expanded in y around 0 99.8%

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

   if -1.9999999999999998e23 < (-.f64 (*.f64 x (log.f64 y)) y) < 2.00000000000000014e-17

   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. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -2 \cdot 10^{+23} \lor \neg \left(x \cdot \log y - y \leq 2 \cdot 10^{-17}\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 112:\\ \;\;\;\;\left(t\_1 + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 - y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= y 112.0) (- (+ t_1 (log t)) 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 <= 112.0) {
		tmp = (t_1 + log(t)) - 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 <= 112.0d0) then
        tmp = (t_1 + log(t)) - 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 <= 112.0) {
		tmp = (t_1 + Math.log(t)) - 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 <= 112.0:
		tmp = (t_1 + math.log(t)) - 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 <= 112.0)
		tmp = Float64(Float64(t_1 + log(t)) - 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 <= 112.0)
		tmp = (t_1 + log(t)) - 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, 112.0], N[(N[(t$95$1 + N[Log[t], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(t$95$1 - y), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 112

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 98.8%

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

   if 112 < 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%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 99.8%

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

   7. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   9. Applied egg-rr 99.8%

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

   10. Taylor expanded in z around inf 99.8%

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

   11. Taylor expanded in y around 0 99.9%

       \[\leadsto \color{blue}{\left(-1 \cdot y + x \cdot \log y\right) - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 112:\\ \;\;\;\;\left(x \cdot \log y + \log t\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+63} \lor \neg \left(x \leq 2.8 \cdot 10^{+49}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.3e+63) (not (<= x 2.8e+49)))
   (- (* x (log y)) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.3e+63) || !(x <= 2.8e+49)) {
		tmp = (x * log(y)) - 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 <= (-2.3d+63)) .or. (.not. (x <= 2.8d+49))) then
        tmp = (x * log(y)) - 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 <= -2.3e+63) || !(x <= 2.8e+49)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.3e+63) or not (x <= 2.8e+49):
		tmp = (x * math.log(y)) - y
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.3e+63) || !(x <= 2.8e+49))
		tmp = Float64(Float64(x * log(y)) - 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 <= -2.3e+63) || ~((x <= 2.8e+49)))
		tmp = (x * log(y)) - y;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.3e+63], N[Not[LessEqual[x, 2.8e+49]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.29999999999999993e63 or 2.7999999999999998e49 < x

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 88.1%

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

   if -2.29999999999999993e63 < x < 2.7999999999999998e49

   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. Simplified 100.0%

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

   5. Taylor expanded in x around 0 98.5%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+63} \lor \neg \left(x \leq 2.8 \cdot 10^{+49}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+64} \lor \neg \left(x \leq 1.95 \cdot 10^{+86}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.8e+64) (not (<= x 1.95e+86)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.8e+64) || !(x <= 1.95e+86)) {
		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 <= (-8.8d+64)) .or. (.not. (x <= 1.95d+86))) 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 <= -8.8e+64) || !(x <= 1.95e+86)) {
		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 <= -8.8e+64) or not (x <= 1.95e+86):
		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 <= -8.8e+64) || !(x <= 1.95e+86))
		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 <= -8.8e+64) || ~((x <= 1.95e+86)))
		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, -8.8e+64], N[Not[LessEqual[x, 1.95e+86]], $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 < -8.80000000000000007e64 or 1.9500000000000001e86 < x

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 87.9%

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

   6. Taylor expanded in x around inf 87.9%

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

      1. mul-1-neg 87.9%

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

      2. unsub-neg 87.9%

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

   8. Simplified 87.9%

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

   9. Taylor expanded in z around 0 75.6%

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

   if -8.80000000000000007e64 < x < 1.9500000000000001e86

   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. Simplified 100.0%

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

   5. Taylor expanded in x around 0 96.8%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+64} \lor \neg \left(x \leq 1.95 \cdot 10^{+86}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(\log y - \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+50}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.5e+63)
   (* x (- (log y) (/ z x)))
   (if (<= x 5.2e+50) (- (log t) (+ y z)) (- (* x (log y)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.5e+63) {
		tmp = x * (log(y) - (z / x));
	} else if (x <= 5.2e+50) {
		tmp = log(t) - (y + z);
	} else {
		tmp = (x * log(y)) - 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+63)) then
        tmp = x * (log(y) - (z / x))
    else if (x <= 5.2d+50) then
        tmp = log(t) - (y + z)
    else
        tmp = (x * log(y)) - 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+63) {
		tmp = x * (Math.log(y) - (z / x));
	} else if (x <= 5.2e+50) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = (x * Math.log(y)) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.5e+63:
		tmp = x * (math.log(y) - (z / x))
	elif x <= 5.2e+50:
		tmp = math.log(t) - (y + z)
	else:
		tmp = (x * math.log(y)) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.5e+63)
		tmp = Float64(x * Float64(log(y) - Float64(z / x)));
	elseif (x <= 5.2e+50)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(Float64(x * log(y)) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.5e+63)
		tmp = x * (log(y) - (z / x));
	elseif (x <= 5.2e+50)
		tmp = log(t) - (y + z);
	else
		tmp = (x * log(y)) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.5e+63], N[(x * N[(N[Log[y], $MachinePrecision] - N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+50], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.50000000000000029e63

   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. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 90.2%

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

   6. Taylor expanded in x around inf 90.3%

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

      1. mul-1-neg 90.3%

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

      2. unsub-neg 90.3%

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

   8. Simplified 90.3%

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

   if -3.50000000000000029e63 < x < 5.2000000000000004e50

   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. Simplified 100.0%

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

   5. Taylor expanded in x around 0 98.5%

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

   if 5.2000000000000004e50 < 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%

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

      2. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 91.2%

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

Alternative 7: 89.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+63}:\\ \;\;\;\;t\_1 - z\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+52}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -3.5e+63)
     (- t_1 z)
     (if (<= x 1.12e+52) (- (log t) (+ y z)) (- t_1 y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -3.5e+63) {
		tmp = t_1 - z;
	} else if (x <= 1.12e+52) {
		tmp = log(t) - (y + z);
	} else {
		tmp = 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 (x <= (-3.5d+63)) then
        tmp = t_1 - z
    else if (x <= 1.12d+52) then
        tmp = log(t) - (y + z)
    else
        tmp = 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 (x <= -3.5e+63) {
		tmp = t_1 - z;
	} else if (x <= 1.12e+52) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1 - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -3.5e+63:
		tmp = t_1 - z
	elif x <= 1.12e+52:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1 - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -3.5e+63)
		tmp = Float64(t_1 - z);
	elseif (x <= 1.12e+52)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(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 (x <= -3.5e+63)
		tmp = t_1 - z;
	elseif (x <= 1.12e+52)
		tmp = log(t) - (y + z);
	else
		tmp = 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[LessEqual[x, -3.5e+63], N[(t$95$1 - z), $MachinePrecision], If[LessEqual[x, 1.12e+52], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.50000000000000029e63

   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. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 90.2%

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

   if -3.50000000000000029e63 < x < 1.12000000000000002e52

   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. Simplified 100.0%

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

   5. Taylor expanded in x around 0 98.5%

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

   if 1.12000000000000002e52 < 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%

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

      2. associate--l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 91.2%

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

Alternative 8: 63.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+64} \lor \neg \left(x \leq 1.15 \cdot 10^{+86}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-1 - \frac{z}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.3e+64) (not (<= x 1.15e+86)))
   (* x (log y))
   (* y (- -1.0 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.3e+64) || !(x <= 1.15e+86)) {
		tmp = x * log(y);
	} else {
		tmp = y * (-1.0 - (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 <= (-2.3d+64)) .or. (.not. (x <= 1.15d+86))) then
        tmp = x * log(y)
    else
        tmp = y * ((-1.0d0) - (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 <= -2.3e+64) || !(x <= 1.15e+86)) {
		tmp = x * Math.log(y);
	} else {
		tmp = y * (-1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.3e+64) or not (x <= 1.15e+86):
		tmp = x * math.log(y)
	else:
		tmp = y * (-1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.3e+64) || !(x <= 1.15e+86))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(y * Float64(-1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.3e+64) || ~((x <= 1.15e+86)))
		tmp = x * log(y);
	else
		tmp = y * (-1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.3e+64], N[Not[LessEqual[x, 1.15e+86]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(y * N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e64 or 1.14999999999999995e86 < x

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. associate--l- 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 87.9%

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

   6. Taylor expanded in x around inf 87.9%

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

      1. mul-1-neg 87.9%

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

      2. unsub-neg 87.9%

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

   8. Simplified 87.9%

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

   9. Taylor expanded in z around 0 75.6%

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

   if -2.3e64 < x < 1.14999999999999995e86

   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. Simplified 100.0%

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

   5. Taylor expanded in y around inf 90.4%

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

   7. Simplified 71.1%

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

      1. clear-num 71.1%

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

      2. un-div-inv 71.1%

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

   9. Applied egg-rr 71.1%

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

   10. Taylor expanded in z around inf 71.8%

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

   11. Taylor expanded in x around 0 68.6%

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

       1. mul-1-neg 68.6%

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

       2. distribute-rgt-neg-in 68.6%

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

       3. distribute-neg-in 68.6%

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

       4. metadata-eval 68.6%

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

       5. sub-neg 68.6%

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

   13. Simplified 68.6%

       \[\leadsto \color{blue}{y \cdot \left(-1 - \frac{z}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+64} \lor \neg \left(x \leq 1.15 \cdot 10^{+86}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-1 - \frac{z}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.5% accurate, 17.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.8:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-1 - \frac{z}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 6.8) (- z) (* y (- -1.0 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6.8) {
		tmp = -z;
	} else {
		tmp = y * (-1.0 - (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 6.8d0) then
        tmp = -z
    else
        tmp = y * ((-1.0d0) - (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6.8) {
		tmp = -z;
	} else {
		tmp = y * (-1.0 - (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 6.8:
		tmp = -z
	else:
		tmp = y * (-1.0 - (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6.8)
		tmp = Float64(-z);
	else
		tmp = Float64(y * Float64(-1.0 - Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 6.8)
		tmp = -z;
	else
		tmp = y * (-1.0 - (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6.8], (-z), N[(y * N[(-1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.79999999999999982

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 37.7%

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

      1. mul-1-neg 37.7%

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

   7. Simplified 37.7%

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

   if 6.79999999999999982 < 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%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 99.8%

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

   7. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   9. Applied egg-rr 99.8%

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

   10. Taylor expanded in z around inf 99.8%

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

   11. Taylor expanded in x around 0 75.3%

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

       1. mul-1-neg 75.3%

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

       2. distribute-rgt-neg-in 75.3%

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

       3. distribute-neg-in 75.3%

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

       4. metadata-eval 75.3%

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

       5. sub-neg 75.3%

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

   13. Simplified 75.3%

       \[\leadsto \color{blue}{y \cdot \left(-1 - \frac{z}{y}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 48.7% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{+69}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 4e+69) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4e+69) {
		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 <= 4d+69) 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 <= 4e+69) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 4e+69:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 4e+69)
		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 <= 4e+69)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 4e+69], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 4.0000000000000003e69

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 38.3%

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

      1. mul-1-neg 38.3%

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

   7. Simplified 38.3%

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

   if 4.0000000000000003e69 < 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%

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

      2. associate--l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 64.8%

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

      1. mul-1-neg 64.8%

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

   7. Simplified 64.8%

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

Alternative 11: 30.5% accurate, 104.5× speedup

Math

\[\begin{array}{l} \\ -y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := (-y)

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

   2. associate--l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in y around inf 31.7%

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

   1. mul-1-neg 31.7%

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

7. Simplified 31.7%

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

Alternative 12: 2.3% accurate, 209.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

   2. associate--l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 29.3%

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

   1. mul-1-neg 29.3%

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

7. Simplified 29.3%

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

   1. add-sqr-sqrt 13.4%

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

   2. sqrt-unprod 6.7%

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

   3. sqr-neg 6.7%

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

   4. sqrt-unprod 1.1%

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

   5. add-sqr-sqrt 2.3%

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

   6. *-un-lft-identity 2.3%

      \[\leadsto \color{blue}{1 \cdot z} \]

9. Applied egg-rr 2.3%

   \[\leadsto \color{blue}{1 \cdot z} \]

10. Taylor expanded in z around 0 2.3%

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

Reproduce

herbie shell --seed 2024157 
(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)))