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

Percentage Accurate: 99.9% → 99.9%

Time: 11.1s

Alternatives: 8

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 99.8%

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

Alternative 2: 90.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+158}:\\ \;\;\;\;t\_2 + \log t\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-14}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t + \left(t\_1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -1e+158)
     (+ t_2 (log t))
     (if (<= t_2 -1e-14) (- (- (log t) y) z) (+ (log t) (- 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 <= -1e+158) {
		tmp = t_2 + log(t);
	} else if (t_2 <= -1e-14) {
		tmp = (log(t) - y) - z;
	} else {
		tmp = log(t) + (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 <= (-1d+158)) then
        tmp = t_2 + log(t)
    else if (t_2 <= (-1d-14)) then
        tmp = (log(t) - y) - z
    else
        tmp = log(t) + (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 <= -1e+158) {
		tmp = t_2 + Math.log(t);
	} else if (t_2 <= -1e-14) {
		tmp = (Math.log(t) - y) - z;
	} else {
		tmp = Math.log(t) + (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 <= -1e+158:
		tmp = t_2 + math.log(t)
	elif t_2 <= -1e-14:
		tmp = (math.log(t) - y) - z
	else:
		tmp = math.log(t) + (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 <= -1e+158)
		tmp = Float64(t_2 + log(t));
	elseif (t_2 <= -1e-14)
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = Float64(log(t) + 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 <= -1e+158)
		tmp = t_2 + log(t);
	elseif (t_2 <= -1e-14)
		tmp = (log(t) - y) - z;
	else
		tmp = log(t) + (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, -1e+158], N[(t$95$2 + N[Log[t], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-14], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] + N[(t$95$1 - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -9.99999999999999953e157

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot \log y - y\right)}, \mathsf{log.f64}\left(t\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot \log y\right), y\right), \mathsf{log.f64}\left(\color{blue}{t}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log y\right), y\right), \mathsf{log.f64}\left(t\right)\right) \]

      3. log-lowering-log.f64 87.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), y\right), \mathsf{log.f64}\left(t\right)\right) \]

   5. Simplified 87.2%

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

   if -9.99999999999999953e157 < (-.f64 (*.f64 x (log.f64 y)) y) < -9.99999999999999999e-15

   1. Initial program 99.9%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}\right)\right) \]

      5. flip3-+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\left(\left(x \cdot \log y - y\right) - z\right) + \color{blue}{\log t}}\right)\right) \]

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\log t - y\right), \color{blue}{z}\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, y\right), z\right) \]

      4. log-lowering-log.f64 86.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), y\right), z\right) \]

   7. Simplified 86.9%

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

   if -9.99999999999999999e-15 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot \log y - z\right)}, \mathsf{log.f64}\left(t\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot \log y\right), z\right), \mathsf{log.f64}\left(\color{blue}{t}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log y\right), z\right), \mathsf{log.f64}\left(t\right)\right) \]

      3. log-lowering-log.f64 99.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), z\right), \mathsf{log.f64}\left(t\right)\right) \]

   5. Simplified 99.3%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -1 \cdot 10^{+158}:\\ \;\;\;\;\left(x \cdot \log y - y\right) + \log t\\ \mathbf{elif}\;x \cdot \log y - y \leq -1 \cdot 10^{-14}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t + \left(x \cdot \log y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \log y - y\right) + \log t\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+25}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- (* x (log y)) y) (log t))))
   (if (<= x -2.8e+40) t_1 (if (<= x 1.7e+25) (- (- (log t) y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * log(y)) - y) + log(t);
	double tmp;
	if (x <= -2.8e+40) {
		tmp = t_1;
	} else if (x <= 1.7e+25) {
		tmp = (log(t) - y) - z;
	} 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) :: tmp
    t_1 = ((x * log(y)) - y) + log(t)
    if (x <= (-2.8d+40)) then
        tmp = t_1
    else if (x <= 1.7d+25) then
        tmp = (log(t) - y) - z
    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)) - y) + Math.log(t);
	double tmp;
	if (x <= -2.8e+40) {
		tmp = t_1;
	} else if (x <= 1.7e+25) {
		tmp = (Math.log(t) - y) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x * math.log(y)) - y) + math.log(t)
	tmp = 0
	if x <= -2.8e+40:
		tmp = t_1
	elif x <= 1.7e+25:
		tmp = (math.log(t) - y) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * log(y)) - y) + log(t))
	tmp = 0.0
	if (x <= -2.8e+40)
		tmp = t_1;
	elseif (x <= 1.7e+25)
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x * log(y)) - y) + log(t);
	tmp = 0.0;
	if (x <= -2.8e+40)
		tmp = t_1;
	elseif (x <= 1.7e+25)
		tmp = (log(t) - y) - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] + N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+40], t$95$1, If[LessEqual[x, 1.7e+25], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000001e40 or 1.69999999999999992e25 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot \log y - y\right)}, \mathsf{log.f64}\left(t\right)\right) \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\left(x \cdot \log y\right), y\right), \mathsf{log.f64}\left(\color{blue}{t}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \log y\right), y\right), \mathsf{log.f64}\left(t\right)\right) \]

      3. log-lowering-log.f64 82.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right), y\right), \mathsf{log.f64}\left(t\right)\right) \]

   5. Simplified 82.2%

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

   if -2.8000000000000001e40 < x < 1.69999999999999992e25

   1. Initial program 100.0%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}\right)\right) \]

      5. flip3-+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\left(\left(x \cdot \log y - y\right) - z\right) + \color{blue}{\log t}}\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\log t - y\right), \color{blue}{z}\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, y\right), z\right) \]

      4. log-lowering-log.f64 98.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), y\right), z\right) \]

   7. Simplified 98.9%

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

Alternative 4: 83.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{+164}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2.8e+100) t_1 (if (<= x 9.6e+164) (- (- (log t) y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -2.8e+100) {
		tmp = t_1;
	} else if (x <= 9.6e+164) {
		tmp = (log(t) - y) - z;
	} 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) :: tmp
    t_1 = x * log(y)
    if (x <= (-2.8d+100)) then
        tmp = t_1
    else if (x <= 9.6d+164) then
        tmp = (log(t) - y) - z
    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 tmp;
	if (x <= -2.8e+100) {
		tmp = t_1;
	} else if (x <= 9.6e+164) {
		tmp = (Math.log(t) - y) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -2.8e+100:
		tmp = t_1
	elif x <= 9.6e+164:
		tmp = (math.log(t) - y) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -2.8e+100)
		tmp = t_1;
	elseif (x <= 9.6e+164)
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -2.8e+100)
		tmp = t_1;
	elseif (x <= 9.6e+164)
		tmp = (log(t) - y) - z;
	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]}, If[LessEqual[x, -2.8e+100], t$95$1, If[LessEqual[x, 9.6e+164], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7999999999999998e100 or 9.60000000000000043e164 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\log y}\right) \]

      2. log-lowering-log.f64 78.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right) \]

   5. Simplified 78.6%

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

   if -2.7999999999999998e100 < x < 9.60000000000000043e164

   1. Initial program 99.9%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}\right)\right) \]

      5. flip3-+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\left(\left(x \cdot \log y - y\right) - z\right) + \color{blue}{\log t}}\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\log t - y\right), \color{blue}{z}\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, y\right), z\right) \]

      4. log-lowering-log.f64 90.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), y\right), z\right) \]

   7. Simplified 90.8%

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

Alternative 5: 71.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+164}:\\ \;\;\;\;0 - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.55e+100) t_1 (if (<= x 9.2e+164) (- 0.0 (+ y z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.55e+100) {
		tmp = t_1;
	} else if (x <= 9.2e+164) {
		tmp = 0.0 - (y + z);
	} 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) :: tmp
    t_1 = x * log(y)
    if (x <= (-1.55d+100)) then
        tmp = t_1
    else if (x <= 9.2d+164) then
        tmp = 0.0d0 - (y + z)
    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 tmp;
	if (x <= -1.55e+100) {
		tmp = t_1;
	} else if (x <= 9.2e+164) {
		tmp = 0.0 - (y + z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.55e+100:
		tmp = t_1
	elif x <= 9.2e+164:
		tmp = 0.0 - (y + z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.55e+100)
		tmp = t_1;
	elseif (x <= 9.2e+164)
		tmp = Float64(0.0 - Float64(y + z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.55e+100)
		tmp = t_1;
	elseif (x <= 9.2e+164)
		tmp = 0.0 - (y + z);
	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]}, If[LessEqual[x, -1.55e+100], t$95$1, If[LessEqual[x, 9.2e+164], N[(0.0 - N[(y + z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000003e100 or 9.1999999999999998e164 < x

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\log y}\right) \]

      2. log-lowering-log.f64 78.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{log.f64}\left(y\right)\right) \]

   5. Simplified 78.6%

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

   if -1.55000000000000003e100 < x < 9.1999999999999998e164

   1. Initial program 99.9%

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

      1. flip3-+ N/A

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

      2. clear-num N/A

         \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}\right)}\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}\right)\right) \]

      5. flip3-+ N/A

         \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\left(\left(x \cdot \log y - y\right) - z\right) + \color{blue}{\log t}}\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\log t - y\right), \color{blue}{z}\right) \]

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, y\right), z\right) \]

      4. log-lowering-log.f64 90.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), y\right), z\right) \]

   7. Simplified 90.8%

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

   8. Taylor expanded in y around inf

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot y\right)}, z\right) \]
   9. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(y\right)\right), z\right) \]

      2. neg-sub0 N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(0 - y\right), z\right) \]

      3. --lowering--.f64 74.8%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, y\right), z\right) \]

   10. Simplified 74.8%

       \[\leadsto \color{blue}{\left(0 - y\right)} - z \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+164}:\\ \;\;\;\;0 - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.5% accurate, 16.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5000000:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+72}:\\ \;\;\;\;0 - y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5000000.0) (- 0.0 z) (if (<= z 4.2e+72) (- 0.0 y) (- 0.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5000000.0) {
		tmp = 0.0 - z;
	} else if (z <= 4.2e+72) {
		tmp = 0.0 - y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5000000.0d0)) then
        tmp = 0.0d0 - z
    else if (z <= 4.2d+72) then
        tmp = 0.0d0 - y
    else
        tmp = 0.0d0 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5000000.0) {
		tmp = 0.0 - z;
	} else if (z <= 4.2e+72) {
		tmp = 0.0 - y;
	} else {
		tmp = 0.0 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5000000.0:
		tmp = 0.0 - z
	elif z <= 4.2e+72:
		tmp = 0.0 - y
	else:
		tmp = 0.0 - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5000000.0)
		tmp = Float64(0.0 - z);
	elseif (z <= 4.2e+72)
		tmp = Float64(0.0 - y);
	else
		tmp = Float64(0.0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5000000.0)
		tmp = 0.0 - z;
	elseif (z <= 4.2e+72)
		tmp = 0.0 - y;
	else
		tmp = 0.0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5000000.0], N[(0.0 - z), $MachinePrecision], If[LessEqual[z, 4.2e+72], N[(0.0 - y), $MachinePrecision], N[(0.0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5e6 or 4.2000000000000003e72 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-sub0 N/A

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

      3. --lowering--.f64 63.9%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{z}\right) \]

   5. Simplified 63.9%

      \[\leadsto \color{blue}{0 - z} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. neg-lowering-neg.f64 63.9%

         \[\leadsto \mathsf{neg.f64}\left(z\right) \]

   7. Applied egg-rr 63.9%

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

   if -5e6 < z < 4.2000000000000003e72

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y\right) \]

      2. neg-sub0 N/A

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

      3. --lowering--.f64 40.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{y}\right) \]

   5. Simplified 40.3%

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

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(y\right) \]

      2. neg-lowering-neg.f64 40.3%

         \[\leadsto \mathsf{neg.f64}\left(y\right) \]

   7. Applied egg-rr 40.3%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5000000:\\ \;\;\;\;0 - z\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+72}:\\ \;\;\;\;0 - y\\ \mathbf{else}:\\ \;\;\;\;0 - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.1% accurate, 41.8× speedup

Math

\[\begin{array}{l} \\ 0 - \left(y + z\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- 0.0 (+ y z)))

C

double code(double x, double y, double z, double t) {
	return 0.0 - (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 = 0.0d0 - (y + z)
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.0 - (y + z);
}

Python

def code(x, y, z, t):
	return 0.0 - (y + z)

Julia

function code(x, y, z, t)
	return Float64(0.0 - Float64(y + z))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.0 - (y + z);
end

Wolfram

code[x_, y_, z_, t_] := N[(0.0 - N[(y + z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. flip3-+ N/A

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

   2. clear-num N/A

      \[\leadsto \frac{1}{\color{blue}{\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}}} \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}\right)}\right) \]

   4. clear-num N/A

      \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\color{blue}{\frac{{\left(\left(x \cdot \log y - y\right) - z\right)}^{3} + {\log t}^{3}}{\left(\left(x \cdot \log y - y\right) - z\right) \cdot \left(\left(x \cdot \log y - y\right) - z\right) + \left(\log t \cdot \log t - \left(\left(x \cdot \log y - y\right) - z\right) \cdot \log t\right)}}}\right)\right) \]

   5. flip3-+ N/A

      \[\leadsto \mathsf{/.f64}\left(1, \left(\frac{1}{\left(\left(x \cdot \log y - y\right) - z\right) + \color{blue}{\log t}}\right)\right) \]

4. Applied egg-rr 99.6%

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

5. Taylor expanded in x around 0

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

   1. associate--r+ N/A

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

   2. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\log t - y\right), \color{blue}{z}\right) \]

   3. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\log t, y\right), z\right) \]

   4. log-lowering-log.f64 70.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{log.f64}\left(t\right), y\right), z\right) \]

7. Simplified 70.0%

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

8. Taylor expanded in y around inf

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot y\right)}, z\right) \]
9. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(y\right)\right), z\right) \]

   2. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(0 - y\right), z\right) \]

   3. --lowering--.f64 58.7%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, y\right), z\right) \]

10. Simplified 58.7%

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

11. Final simplification 58.7%

    \[\leadsto 0 - \left(y + z\right) \]
12. Add Preprocessing

Alternative 8: 30.4% accurate, 69.7× speedup

Math

\[\begin{array}{l} \\ 0 - y \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- 0.0 y))

C

double code(double x, double y, double z, double t) {
	return 0.0 - 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 = 0.0d0 - y
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.0 - y;
}

Python

def code(x, y, z, t):
	return 0.0 - y

Julia

function code(x, y, z, t)
	return Float64(0.0 - y)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.0 - y;
end

Wolfram

code[x_, y_, z_, t_] := N[(0.0 - y), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around inf

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(y\right) \]

   2. neg-sub0 N/A

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

   3. --lowering--.f64 28.9%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{y}\right) \]

5. Simplified 28.9%

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

   1. sub0-neg N/A

      \[\leadsto \mathsf{neg}\left(y\right) \]

   2. neg-lowering-neg.f64 28.9%

      \[\leadsto \mathsf{neg.f64}\left(y\right) \]

7. Applied egg-rr 28.9%

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

8. Final simplification 28.9%

   \[\leadsto 0 - y \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024160 
(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)))