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

Percentage Accurate: 99.9% → 99.9%

Time: 10.3s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 89.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+206}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{-12}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -5e+206)
     t_2
     (if (<= t_2 1e-12) (- (log t) (+ y z)) (- t_1 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -5e+206) {
		tmp = t_2;
	} else if (t_2 <= 1e-12) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-5d+206)) then
        tmp = t_2
    else if (t_2 <= 1d-12) then
        tmp = log(t) - (y + z)
    else
        tmp = t_1 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -5e+206) {
		tmp = t_2;
	} else if (t_2 <= 1e-12) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - y
	tmp = 0
	if t_2 <= -5e+206:
		tmp = t_2
	elif t_2 <= 1e-12:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - y)
	tmp = 0.0
	if (t_2 <= -5e+206)
		tmp = t_2;
	elseif (t_2 <= 1e-12)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - y;
	tmp = 0.0;
	if (t_2 <= -5e+206)
		tmp = t_2;
	elseif (t_2 <= 1e-12)
		tmp = log(t) - (y + z);
	else
		tmp = t_1 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+206], t$95$2, If[LessEqual[t$95$2, 1e-12], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -5.0000000000000002e206

   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 89.2%

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

   if -5.0000000000000002e206 < (-.f64 (*.f64 x (log.f64 y)) y) < 9.9999999999999998e-13

   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 x around 0 87.5%

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

   if 9.9999999999999998e-13 < (-.f64 (*.f64 x (log.f64 y)) y)

   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 z around inf 98.8%

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

Alternative 3: 64.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := z \cdot \left(-1 - \frac{y}{z}\right)\\ \mathbf{if}\;x \leq -2.55 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.6:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-76}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+83}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (* z (- -1.0 (/ y z)))))
   (if (<= x -2.55e+171)
     t_1
     (if (<= x -2.6)
       t_2
       (if (<= x 6e-76) (- (log t) z) (if (<= x 1.5e+83) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = z * (-1.0 - (y / z));
	double tmp;
	if (x <= -2.55e+171) {
		tmp = t_1;
	} else if (x <= -2.6) {
		tmp = t_2;
	} else if (x <= 6e-76) {
		tmp = log(t) - z;
	} else if (x <= 1.5e+83) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = z * ((-1.0d0) - (y / z))
    if (x <= (-2.55d+171)) then
        tmp = t_1
    else if (x <= (-2.6d0)) then
        tmp = t_2
    else if (x <= 6d-76) then
        tmp = log(t) - z
    else if (x <= 1.5d+83) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = z * (-1.0 - (y / z));
	double tmp;
	if (x <= -2.55e+171) {
		tmp = t_1;
	} else if (x <= -2.6) {
		tmp = t_2;
	} else if (x <= 6e-76) {
		tmp = Math.log(t) - z;
	} else if (x <= 1.5e+83) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = z * (-1.0 - (y / z))
	tmp = 0
	if x <= -2.55e+171:
		tmp = t_1
	elif x <= -2.6:
		tmp = t_2
	elif x <= 6e-76:
		tmp = math.log(t) - z
	elif x <= 1.5e+83:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(z * Float64(-1.0 - Float64(y / z)))
	tmp = 0.0
	if (x <= -2.55e+171)
		tmp = t_1;
	elseif (x <= -2.6)
		tmp = t_2;
	elseif (x <= 6e-76)
		tmp = Float64(log(t) - z);
	elseif (x <= 1.5e+83)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = z * (-1.0 - (y / z));
	tmp = 0.0;
	if (x <= -2.55e+171)
		tmp = t_1;
	elseif (x <= -2.6)
		tmp = t_2;
	elseif (x <= 6e-76)
		tmp = log(t) - z;
	elseif (x <= 1.5e+83)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(-1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.55e+171], t$95$1, If[LessEqual[x, -2.6], t$95$2, If[LessEqual[x, 6e-76], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 1.5e+83], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.55000000000000011e171 or 1.5e83 < 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. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. add-cube-cbrt 98.8%

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

      3. associate-*l* 98.7%

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

      4. fma-neg 98.7%

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

      5. pow2 98.7%

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

      6. associate-+r- 98.7%

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

   6. Applied egg-rr 98.7%

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

   7. Taylor expanded in x around inf 68.9%

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

      1. *-commutative 68.9%

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

   9. Simplified 68.9%

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

   if -2.55000000000000011e171 < x < -2.60000000000000009 or 6.00000000000000048e-76 < x < 1.5e83

   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 85.2%

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

   6. Taylor expanded in z around -inf 85.2%

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

   8. Simplified 74.8%

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

   9. Taylor expanded in y around inf 63.9%

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

       1. mul-1-neg 63.9%

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

       2. distribute-neg-frac2 63.9%

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

   11. Simplified 63.9%

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

   if -2.60000000000000009 < x < 6.00000000000000048e-76

   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 0 76.2%

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

   6. Taylor expanded in x around 0 76.2%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -2.6:\\ \;\;\;\;z \cdot \left(-1 - \frac{y}{z}\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-76}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \left(-1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -12500 \lor \neg \left(x \leq 1.1 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(\log y - \left(\frac{y}{x} + \frac{z}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -12500.0) (not (<= x 1.1e-9)))
   (* x (- (log y) (+ (/ y x) (/ z x))))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -12500.0) || !(x <= 1.1e-9)) {
		tmp = x * (log(y) - ((y / x) + (z / x)));
	} 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 <= (-12500.0d0)) .or. (.not. (x <= 1.1d-9))) then
        tmp = x * (log(y) - ((y / x) + (z / x)))
    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 <= -12500.0) || !(x <= 1.1e-9)) {
		tmp = x * (Math.log(y) - ((y / x) + (z / x)));
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -12500.0) or not (x <= 1.1e-9):
		tmp = x * (math.log(y) - ((y / x) + (z / x)))
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -12500.0) || !(x <= 1.1e-9))
		tmp = Float64(x * Float64(log(y) - Float64(Float64(y / x) + Float64(z / x))));
	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 <= -12500.0) || ~((x <= 1.1e-9)))
		tmp = x * (log(y) - ((y / x) + (z / x)));
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -12500.0], N[Not[LessEqual[x, 1.1e-9]], $MachinePrecision]], N[(x * N[(N[Log[y], $MachinePrecision] - N[(N[(y / x), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -12500 or 1.0999999999999999e-9 < 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 x around inf 99.6%

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

   6. Taylor expanded in x around inf 98.7%

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

   if -12500 < x < 1.0999999999999999e-9

   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 99.8%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -12500 \lor \neg \left(x \leq 1.1 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot \left(\log y - \left(\frac{y}{x} + \frac{z}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+120} \lor \neg \left(x \leq 1.05 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7e+120) (not (<= x 1.05e-5)))
   (- (* x (log y)) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7e+120) || !(x <= 1.05e-5)) {
		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 <= (-7d+120)) .or. (.not. (x <= 1.05d-5))) 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 <= -7e+120) || !(x <= 1.05e-5)) {
		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 <= -7e+120) or not (x <= 1.05e-5):
		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 <= -7e+120) || !(x <= 1.05e-5))
		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 <= -7e+120) || ~((x <= 1.05e-5)))
		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, -7e+120], N[Not[LessEqual[x, 1.05e-5]], $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 < -7.00000000000000015e120 or 1.04999999999999994e-5 < 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 79.8%

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

   if -7.00000000000000015e120 < x < 1.04999999999999994e-5

   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 x around 0 94.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+120} \lor \neg \left(x \leq 1.05 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+174} \lor \neg \left(x \leq 2.15 \cdot 10^{+83}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.8e+174) (not (<= x 2.15e+83)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.8e+174) || !(x <= 2.15e+83)) {
		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+174)) .or. (.not. (x <= 2.15d+83))) 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+174) || !(x <= 2.15e+83)) {
		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+174) or not (x <= 2.15e+83):
		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+174) || !(x <= 2.15e+83))
		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+174) || ~((x <= 2.15e+83)))
		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+174], N[Not[LessEqual[x, 2.15e+83]], $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 < -5.7999999999999999e174 or 2.15e83 < 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. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. add-cube-cbrt 98.8%

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

      3. associate-*l* 98.7%

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

      4. fma-neg 98.7%

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

      5. pow2 98.7%

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

      6. associate-+r- 98.7%

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

   6. Applied egg-rr 98.7%

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

   7. Taylor expanded in x around inf 70.3%

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

      1. *-commutative 70.3%

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

   9. Simplified 70.3%

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

   if -5.7999999999999999e174 < x < 2.15e83

   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 x around 0 89.2%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+174} \lor \neg \left(x \leq 2.15 \cdot 10^{+83}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+171} \lor \neg \left(x \leq 1.05 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.55e+171) (not (<= x 1.05e+82)))
   (* x (log y))
   (* z (- -1.0 (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.55e+171) || !(x <= 1.05e+82)) {
		tmp = x * log(y);
	} else {
		tmp = z * (-1.0 - (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 <= (-2.55d+171)) .or. (.not. (x <= 1.05d+82))) then
        tmp = x * log(y)
    else
        tmp = z * ((-1.0d0) - (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 <= -2.55e+171) || !(x <= 1.05e+82)) {
		tmp = x * Math.log(y);
	} else {
		tmp = z * (-1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.55e+171) or not (x <= 1.05e+82):
		tmp = x * math.log(y)
	else:
		tmp = z * (-1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.55e+171) || !(x <= 1.05e+82))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(z * Float64(-1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.55e+171) || ~((x <= 1.05e+82)))
		tmp = x * log(y);
	else
		tmp = z * (-1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.55e+171], N[Not[LessEqual[x, 1.05e+82]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(z * N[(-1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.55000000000000011e171 or 1.05e82 < 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. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. add-cube-cbrt 98.8%

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

      3. associate-*l* 98.7%

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

      4. fma-neg 98.7%

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

      5. pow2 98.7%

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

      6. associate-+r- 98.7%

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

   6. Applied egg-rr 98.7%

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

   7. Taylor expanded in x around inf 68.9%

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

      1. *-commutative 68.9%

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

   9. Simplified 68.9%

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

   if -2.55000000000000011e171 < x < 1.05e82

   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 84.6%

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

   6. Taylor expanded in z around -inf 88.6%

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

   8. Simplified 77.6%

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

   9. Taylor expanded in y around inf 63.9%

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

       1. mul-1-neg 63.9%

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

       2. distribute-neg-frac2 63.9%

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

   11. Simplified 63.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+171} \lor \neg \left(x \leq 1.05 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.7% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-59} \lor \neg \left(z \leq 7.8 \cdot 10^{-60}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.8e-59) (not (<= z 7.8e-60))) (* z (- -1.0 (/ y z))) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.8e-59) || !(z <= 7.8e-60)) {
		tmp = z * (-1.0 - (y / 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 <= (-2.8d-59)) .or. (.not. (z <= 7.8d-60))) then
        tmp = z * ((-1.0d0) - (y / 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 <= -2.8e-59) || !(z <= 7.8e-60)) {
		tmp = z * (-1.0 - (y / z));
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.8e-59) or not (z <= 7.8e-60):
		tmp = z * (-1.0 - (y / z))
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.8e-59) || !(z <= 7.8e-60))
		tmp = Float64(z * Float64(-1.0 - Float64(y / z)));
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.8e-59) || ~((z <= 7.8e-60)))
		tmp = z * (-1.0 - (y / z));
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.8e-59], N[Not[LessEqual[z, 7.8e-60]], $MachinePrecision]], N[(z * N[(-1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -2.79999999999999981e-59 or 7.8000000000000004e-60 < z

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. 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 70.6%

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

   6. Taylor expanded in z around -inf 84.2%

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

   8. Simplified 84.2%

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

   9. Taylor expanded in y around inf 68.1%

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

       1. mul-1-neg 68.1%

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

       2. distribute-neg-frac2 68.1%

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

   11. Simplified 68.1%

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

   if -2.79999999999999981e-59 < z < 7.8000000000000004e-60

   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 35.8%

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

      1. mul-1-neg 35.8%

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

   7. Simplified 35.8%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-59} \lor \neg \left(z \leq 7.8 \cdot 10^{-60}\right):\\ \;\;\;\;z \cdot \left(-1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.1% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.42 \cdot 10^{+64}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 2.42e+64) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.42e+64) {
		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 <= 2.42d+64) 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 <= 2.42e+64) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.42e+64:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.42e+64)
		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 <= 2.42e+64)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.42e+64], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.41999999999999993e64

   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 45.5%

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

      1. mul-1-neg 45.5%

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

   7. Simplified 45.5%

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

   if 2.41999999999999993e64 < 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 58.5%

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

      1. mul-1-neg 58.5%

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

   7. Simplified 58.5%

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

Alternative 10: 29.1% 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 23.2%

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

   1. mul-1-neg 23.2%

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

7. Simplified 23.2%

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

Alternative 11: 2.2% 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 y around inf 78.4%

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

6. Taylor expanded in z around inf 24.0%

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

   1. associate-*r/ 24.0%

      \[\leadsto y \cdot \color{blue}{\frac{-1 \cdot z}{y}} \]

   2. mul-1-neg 24.0%

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

8. Simplified 24.0%

   \[\leadsto y \cdot \color{blue}{\frac{-z}{y}} \]
9. Step-by-step derivation

   1. clear-num 24.0%

      \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{y}{-z}}} \]

   2. un-div-inv 25.4%

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

   3. add-sqr-sqrt 12.8%

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

   4. sqrt-unprod 7.8%

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

   5. sqr-neg 7.8%

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

   6. sqrt-unprod 1.0%

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

   7. add-sqr-sqrt 2.1%

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

10. Applied egg-rr 2.1%

    \[\leadsto \color{blue}{\frac{y}{\frac{y}{z}}} \]
11. Step-by-step derivation

    1. associate-/r/ 2.2%

       \[\leadsto \color{blue}{\frac{y}{y} \cdot z} \]

    2. *-inverses 2.2%

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

    3. *-lft-identity 2.2%

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

12. Simplified 2.2%

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

Reproduce

herbie shell --seed 2024087 
(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)))