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

Percentage Accurate: 99.9% → 99.9%

Time: 17.7s

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. Final simplification 99.9%

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

Alternative 2: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+16} \lor \neg \left(x \leq 7.8 \cdot 10^{+43}\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.25e+16) (not (<= x 7.8e+43)))
   (- (+ (log t) (* x (log y))) y)
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.25e+16) || !(x <= 7.8e+43)) {
		tmp = (log(t) + (x * log(y))) - y;
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.25d+16)) .or. (.not. (x <= 7.8d+43))) then
        tmp = (log(t) + (x * log(y))) - y
    else
        tmp = (log(t) - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.25e+16) || !(x <= 7.8e+43)) {
		tmp = (Math.log(t) + (x * Math.log(y))) - y;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.25e+16) or not (x <= 7.8e+43):
		tmp = (math.log(t) + (x * math.log(y))) - y
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.25e+16) || !(x <= 7.8e+43))
		tmp = Float64(Float64(log(t) + Float64(x * log(y))) - y);
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.25e+16) || ~((x <= 7.8e+43)))
		tmp = (log(t) + (x * log(y))) - y;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.25e+16], N[Not[LessEqual[x, 7.8e+43]], $MachinePrecision]], N[(N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e16 or 7.8000000000000001e43 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 84.3%

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

   if -1.25e16 < x < 7.8000000000000001e43

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 98.6%

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

      1. +-commutative 98.6%

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

      2. associate--r+ 98.6%

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

   4. Simplified 98.6%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+16} \lor \neg \left(x \leq 7.8 \cdot 10^{+43}\right):\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 3: 89.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t + x \cdot \log y\\ \mathbf{if}\;z \leq -1.52 \cdot 10^{+122}:\\ \;\;\;\;t_1 - z\\ \mathbf{elif}\;z \leq 1600:\\ \;\;\;\;t_1 - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (log t) (* x (log y)))))
   (if (<= z -1.52e+122)
     (- t_1 z)
     (if (<= z 1600.0) (- t_1 y) (- (- (log t) z) y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) + (x * log(y));
	double tmp;
	if (z <= -1.52e+122) {
		tmp = t_1 - z;
	} else if (z <= 1600.0) {
		tmp = t_1 - y;
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) + (x * log(y))
    if (z <= (-1.52d+122)) then
        tmp = t_1 - z
    else if (z <= 1600.0d0) then
        tmp = t_1 - y
    else
        tmp = (log(t) - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) + (x * Math.log(y));
	double tmp;
	if (z <= -1.52e+122) {
		tmp = t_1 - z;
	} else if (z <= 1600.0) {
		tmp = t_1 - y;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) + (x * math.log(y))
	tmp = 0
	if z <= -1.52e+122:
		tmp = t_1 - z
	elif z <= 1600.0:
		tmp = t_1 - y
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) + Float64(x * log(y)))
	tmp = 0.0
	if (z <= -1.52e+122)
		tmp = Float64(t_1 - z);
	elseif (z <= 1600.0)
		tmp = Float64(t_1 - y);
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) + (x * log(y));
	tmp = 0.0;
	if (z <= -1.52e+122)
		tmp = t_1 - z;
	elseif (z <= 1600.0)
		tmp = t_1 - y;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.52e+122], N[(t$95$1 - z), $MachinePrecision], If[LessEqual[z, 1600.0], N[(t$95$1 - y), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.52e122

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.3%

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

   if -1.52e122 < z < 1600

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 97.0%

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

   if 1600 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 84.7%

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

      1. +-commutative 84.7%

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

      2. associate--r+ 84.7%

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

   4. Simplified 84.7%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+122}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{elif}\;z \leq 1600:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 4: 83.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+148} \lor \neg \left(x \leq 6 \cdot 10^{+63} \lor \neg \left(x \leq 1.55 \cdot 10^{+103}\right) \land x \leq 2.55 \cdot 10^{+169}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.2e+148)
         (not (or (<= x 6e+63) (and (not (<= x 1.55e+103)) (<= x 2.55e+169)))))
   (* x (log y))
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e+148) || !((x <= 6e+63) || (!(x <= 1.55e+103) && (x <= 2.55e+169)))) {
		tmp = x * log(y);
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.2d+148)) .or. (.not. (x <= 6d+63) .or. (.not. (x <= 1.55d+103)) .and. (x <= 2.55d+169))) then
        tmp = x * log(y)
    else
        tmp = (log(t) - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e+148) || !((x <= 6e+63) || (!(x <= 1.55e+103) && (x <= 2.55e+169)))) {
		tmp = x * Math.log(y);
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.2e+148) or not ((x <= 6e+63) or (not (x <= 1.55e+103) and (x <= 2.55e+169))):
		tmp = x * math.log(y)
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.2e+148) || !((x <= 6e+63) || (!(x <= 1.55e+103) && (x <= 2.55e+169))))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.2e+148) || ~(((x <= 6e+63) || (~((x <= 1.55e+103)) && (x <= 2.55e+169)))))
		tmp = x * log(y);
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.2e+148], N[Not[Or[LessEqual[x, 6e+63], And[N[Not[LessEqual[x, 1.55e+103]], $MachinePrecision], LessEqual[x, 2.55e+169]]]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.20000000000000013e148 or 5.99999999999999998e63 < x < 1.5500000000000001e103 or 2.55000000000000004e169 < x

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-+r+ 99.7%

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

      4. sub-neg 99.7%

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

      5. fma-udef 99.7%

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

      6. add-cbrt-cube 16.4%

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

      7. pow3 16.5%

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

   3. Applied egg-rr 14.6%

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

   4. Taylor expanded in x around inf 14.3%

      \[\leadsto \sqrt[3]{\color{blue}{{x}^{3} \cdot {\log y}^{3}}} \]
   5. Step-by-step derivation

      1. pow-prod-down 14.3%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(x \cdot \log y\right)}^{3}}} \]

      2. rem-cbrt-cube 80.6%

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

      3. *-commutative 80.6%

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

   6. Applied egg-rr 80.6%

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

   if -7.20000000000000013e148 < x < 5.99999999999999998e63 or 1.5500000000000001e103 < x < 2.55000000000000004e169

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 88.5%

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

      1. +-commutative 88.5%

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

      2. associate--r+ 88.5%

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

   4. Simplified 88.5%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+148} \lor \neg \left(x \leq 6 \cdot 10^{+63} \lor \neg \left(x \leq 1.55 \cdot 10^{+103}\right) \land x \leq 2.55 \cdot 10^{+169}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 5: 61.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t - y\\ \mathbf{if}\;x \leq -9.8 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-171}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (log t) y)))
   (if (<= x -9.8e+54)
     t_1
     (if (<= x -4.7e-253)
       t_2
       (if (<= x 3.2e-171) (- (log t) z) (if (<= x 4.2e+63) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = log(t) - y;
	double tmp;
	if (x <= -9.8e+54) {
		tmp = t_1;
	} else if (x <= -4.7e-253) {
		tmp = t_2;
	} else if (x <= 3.2e-171) {
		tmp = log(t) - z;
	} else if (x <= 4.2e+63) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = log(t) - y
    if (x <= (-9.8d+54)) then
        tmp = t_1
    else if (x <= (-4.7d-253)) then
        tmp = t_2
    else if (x <= 3.2d-171) then
        tmp = log(t) - z
    else if (x <= 4.2d+63) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = Math.log(t) - y;
	double tmp;
	if (x <= -9.8e+54) {
		tmp = t_1;
	} else if (x <= -4.7e-253) {
		tmp = t_2;
	} else if (x <= 3.2e-171) {
		tmp = Math.log(t) - z;
	} else if (x <= 4.2e+63) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = math.log(t) - y
	tmp = 0
	if x <= -9.8e+54:
		tmp = t_1
	elif x <= -4.7e-253:
		tmp = t_2
	elif x <= 3.2e-171:
		tmp = math.log(t) - z
	elif x <= 4.2e+63:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(log(t) - y)
	tmp = 0.0
	if (x <= -9.8e+54)
		tmp = t_1;
	elseif (x <= -4.7e-253)
		tmp = t_2;
	elseif (x <= 3.2e-171)
		tmp = Float64(log(t) - z);
	elseif (x <= 4.2e+63)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = log(t) - y;
	tmp = 0.0;
	if (x <= -9.8e+54)
		tmp = t_1;
	elseif (x <= -4.7e-253)
		tmp = t_2;
	elseif (x <= 3.2e-171)
		tmp = log(t) - z;
	elseif (x <= 4.2e+63)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -9.8e+54], t$95$1, If[LessEqual[x, -4.7e-253], t$95$2, If[LessEqual[x, 3.2e-171], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, 4.2e+63], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.80000000000000002e54 or 4.2000000000000004e63 < x

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-+r+ 99.7%

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

      4. sub-neg 99.7%

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

      5. fma-udef 99.7%

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

      6. add-cbrt-cube 17.6%

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

      7. pow3 17.7%

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

   3. Applied egg-rr 15.8%

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

   4. Taylor expanded in x around inf 15.7%

      \[\leadsto \sqrt[3]{\color{blue}{{x}^{3} \cdot {\log y}^{3}}} \]
   5. Step-by-step derivation

      1. pow-prod-down 15.7%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(x \cdot \log y\right)}^{3}}} \]

      2. rem-cbrt-cube 66.1%

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

      3. *-commutative 66.1%

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

   6. Applied egg-rr 66.1%

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

   if -9.80000000000000002e54 < x < -4.69999999999999981e-253 or 3.2000000000000001e-171 < x < 4.2000000000000004e63

   1. Initial program 100.0%

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

      1. add-cube-cbrt 99.9%

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

      2. pow3 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around inf 69.2%

      \[\leadsto \color{blue}{-1 \cdot y} + \log t \]
   5. Step-by-step derivation

      1. mul-1-neg 69.2%

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

   6. Simplified 69.2%

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

   if -4.69999999999999981e-253 < x < 3.2000000000000001e-171

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 68.7%

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

   3. Taylor expanded in x around 0 68.7%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-253}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-171}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+63}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 6: 60.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+15} \lor \neg \left(x \leq 4.4 \cdot 10^{+63}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.4e+15) (not (<= x 4.4e+63))) (* x (log y)) (- (log t) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.4e+15) || !(x <= 4.4e+63)) {
		tmp = x * log(y);
	} else {
		tmp = log(t) - 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 <= (-4.4d+15)) .or. (.not. (x <= 4.4d+63))) then
        tmp = x * log(y)
    else
        tmp = log(t) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.4e+15) || !(x <= 4.4e+63)) {
		tmp = x * Math.log(y);
	} else {
		tmp = Math.log(t) - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.4e+15) or not (x <= 4.4e+63):
		tmp = x * math.log(y)
	else:
		tmp = math.log(t) - z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.4e+15) || !(x <= 4.4e+63))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(log(t) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.4e+15) || ~((x <= 4.4e+63)))
		tmp = x * log(y);
	else
		tmp = log(t) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.4e+15], N[Not[LessEqual[x, 4.4e+63]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4e15 or 4.3999999999999997e63 < x

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. sub-neg 99.7%

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

      3. associate-+r+ 99.7%

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

      4. sub-neg 99.7%

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

      5. fma-udef 99.7%

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

      6. add-cbrt-cube 20.2%

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

      7. pow3 20.3%

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

   3. Applied egg-rr 17.4%

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

   4. Taylor expanded in x around inf 16.7%

      \[\leadsto \sqrt[3]{\color{blue}{{x}^{3} \cdot {\log y}^{3}}} \]
   5. Step-by-step derivation

      1. pow-prod-down 16.7%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(x \cdot \log y\right)}^{3}}} \]

      2. rem-cbrt-cube 64.1%

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

      3. *-commutative 64.1%

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

   6. Applied egg-rr 64.1%

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

   if -4.4e15 < x < 4.3999999999999997e63

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 51.3%

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

   3. Taylor expanded in x around 0 50.3%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+15} \lor \neg \left(x \leq 4.4 \cdot 10^{+63}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - z\\ \end{array} \]

Alternative 7: 47.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1600:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e+122) (- z) (if (<= z 1600.0) (* x (log y)) (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+122) {
		tmp = -z;
	} else if (z <= 1600.0) {
		tmp = x * log(y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.6d+122)) then
        tmp = -z
    else if (z <= 1600.0d0) then
        tmp = x * log(y)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+122) {
		tmp = -z;
	} else if (z <= 1600.0) {
		tmp = x * Math.log(y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e+122:
		tmp = -z
	elif z <= 1600.0:
		tmp = x * math.log(y)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e+122)
		tmp = Float64(-z);
	elseif (z <= 1600.0)
		tmp = Float64(x * log(y));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e+122)
		tmp = -z;
	elseif (z <= 1600.0)
		tmp = x * log(y);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e+122], (-z), If[LessEqual[z, 1600.0], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000006e122 or 1600 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 63.1%

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

      1. neg-mul-1 63.1%

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

   4. Simplified 63.1%

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

   if -1.60000000000000006e122 < z < 1600

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. sub-neg 99.8%

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

      3. associate-+r+ 99.8%

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

      4. sub-neg 99.8%

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

      5. fma-udef 99.8%

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

      6. add-cbrt-cube 41.0%

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

      7. pow3 41.0%

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

   3. Applied egg-rr 27.4%

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

   4. Taylor expanded in x around inf 12.7%

      \[\leadsto \sqrt[3]{\color{blue}{{x}^{3} \cdot {\log y}^{3}}} \]
   5. Step-by-step derivation

      1. pow-prod-down 12.7%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(x \cdot \log y\right)}^{3}}} \]

      2. rem-cbrt-cube 38.6%

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

      3. *-commutative 38.6%

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

   6. Applied egg-rr 38.6%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+122}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 1600:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 40.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+32}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 0.44:\\ \;\;\;\;\log t\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.5e+32) (- z) (if (<= z 0.44) (log t) (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e+32) {
		tmp = -z;
	} else if (z <= 0.44) {
		tmp = log(t);
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.5d+32)) then
        tmp = -z
    else if (z <= 0.44d0) then
        tmp = log(t)
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e+32) {
		tmp = -z;
	} else if (z <= 0.44) {
		tmp = Math.log(t);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.5e+32:
		tmp = -z
	elif z <= 0.44:
		tmp = math.log(t)
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.5e+32)
		tmp = Float64(-z);
	elseif (z <= 0.44)
		tmp = log(t);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.5e+32)
		tmp = -z;
	elseif (z <= 0.44)
		tmp = log(t);
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.5e+32], (-z), If[LessEqual[z, 0.44], N[Log[t], $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000001e32 or 0.440000000000000002 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 55.4%

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

      1. neg-mul-1 55.4%

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

   4. Simplified 55.4%

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

   if -3.5000000000000001e32 < z < 0.440000000000000002

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 54.7%

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

   3. Taylor expanded in x around 0 18.6%

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

   4. Taylor expanded in z around 0 18.1%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+32}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 0.44:\\ \;\;\;\;\log t\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9: 29.1% accurate, 104.5× 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 Float64(-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. Taylor expanded in z around inf 25.2%

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

   1. neg-mul-1 25.2%

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

4. Simplified 25.2%

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

5. Final simplification 25.2%

   \[\leadsto -z \]

Alternative 10: 2.2% accurate, 209.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. sub-neg 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-+r+ 99.9%

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

   4. sub-neg 99.9%

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

   5. fma-udef 99.9%

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

   6. add-cbrt-cube 32.3%

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

   7. pow3 32.3%

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

3. Applied egg-rr 22.7%

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

4. Taylor expanded in y around inf 2.0%

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

5. Final simplification 2.0%

   \[\leadsto y \]

Alternative 11: 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. sub-neg 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-+r+ 99.9%

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

   4. sub-neg 99.9%

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

   5. fma-udef 99.9%

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

   6. add-cbrt-cube 32.3%

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

   7. pow3 32.3%

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

3. Applied egg-rr 22.7%

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

4. Taylor expanded in z around inf 7.5%

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

   1. mul-1-neg 7.5%

      \[\leadsto \sqrt[3]{\color{blue}{-{z}^{3}}} \]

   2. cube-neg 7.5%

      \[\leadsto \sqrt[3]{\color{blue}{{\left(-z\right)}^{3}}} \]

6. Simplified 7.5%

   \[\leadsto \sqrt[3]{\color{blue}{{\left(-z\right)}^{3}}} \]
7. Step-by-step derivation

   1. rem-cbrt-cube 25.2%

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

   2. add-sqr-sqrt 10.8%

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

   3. sqrt-unprod 4.4%

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

   4. sqr-neg 4.4%

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

   5. sqrt-prod 1.0%

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

   6. add-sqr-sqrt 2.3%

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

   7. add-log-exp 2.1%

      \[\leadsto \color{blue}{\log \left(e^{z}\right)} \]

   8. *-un-lft-identity 2.1%

      \[\leadsto \log \color{blue}{\left(1 \cdot e^{z}\right)} \]

   9. log-prod 2.1%

      \[\leadsto \color{blue}{\log 1 + \log \left(e^{z}\right)} \]

   10. metadata-eval 2.1%

       \[\leadsto \color{blue}{0} + \log \left(e^{z}\right) \]

   11. add-log-exp 2.3%

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

8. Applied egg-rr 2.3%

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

   1. +-lft-identity 2.3%

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

10. Simplified 2.3%

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

11. Final simplification 2.3%

    \[\leadsto z \]

Reproduce

herbie shell --seed 2023275 
(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)))