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

Percentage Accurate: 99.9% → 99.9%

Time: 12.0s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[Log[y], $MachinePrecision] + N[((-y) - z), $MachinePrecision]), $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. Step-by-step derivation

   1. sub-neg 99.9%

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

   2. associate--l+ 99.9%

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

   3. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 99.9%

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

   1. associate--l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. +-commutative 99.9%

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

   4. associate--r- 99.9%

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

   5. fma-neg 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+r- 99.9%

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

   8. associate-+r- 99.9%

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

   9. +-commutative 99.9%

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

   10. sub-neg 99.9%

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

   11. log-rec 99.9%

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

   12. distribute-neg-in 99.9%

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

   13. +-commutative 99.9%

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

   14. log-rec 99.9%

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

   15. remove-double-neg 99.9%

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

   16. +-commutative 99.9%

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

   17. sub-neg 99.9%

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

4. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 3: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+62} \lor \neg \left(x \leq 2.5 \cdot 10^{+105}\right):\\ \;\;\;\;\log t + \left(x \cdot \log y - y\right)\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.8e+62) (not (<= x 2.5e+105)))
   (+ (log t) (- (* x (log y)) y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.8e+62) || !(x <= 2.5e+105)) {
		tmp = log(t) + ((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 <= (-5.8d+62)) .or. (.not. (x <= 2.5d+105))) then
        tmp = log(t) + ((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 <= -5.8e+62) || !(x <= 2.5e+105)) {
		tmp = Math.log(t) + ((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 <= -5.8e+62) or not (x <= 2.5e+105):
		tmp = math.log(t) + ((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 <= -5.8e+62) || !(x <= 2.5e+105))
		tmp = Float64(log(t) + 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 <= -5.8e+62) || ~((x <= 2.5e+105)))
		tmp = log(t) + ((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, -5.8e+62], N[Not[LessEqual[x, 2.5e+105]], $MachinePrecision]], N[(N[Log[t], $MachinePrecision] + N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.79999999999999968e62 or 2.50000000000000023e105 < 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 86.4%

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

      1. associate--l+ 86.4%

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

      2. +-commutative 86.4%

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

   4. Simplified 86.4%

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

   if -5.79999999999999968e62 < x < 2.50000000000000023e105

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 94.0%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+62} \lor \neg \left(x \leq 2.5 \cdot 10^{+105}\right):\\ \;\;\;\;\log t + \left(x \cdot \log y - y\right)\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 4: 89.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+63}:\\ \;\;\;\;\log t + \left(t_1 - y\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+24}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + t_1\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -5.5e+63)
     (+ (log t) (- t_1 y))
     (if (<= x 8.6e+24) (- (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 tmp;
	if (x <= -5.5e+63) {
		tmp = log(t) + (t_1 - y);
	} else if (x <= 8.6e+24) {
		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) :: tmp
    t_1 = x * log(y)
    if (x <= (-5.5d+63)) then
        tmp = log(t) + (t_1 - y)
    else if (x <= 8.6d+24) 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 tmp;
	if (x <= -5.5e+63) {
		tmp = Math.log(t) + (t_1 - y);
	} else if (x <= 8.6e+24) {
		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)
	tmp = 0
	if x <= -5.5e+63:
		tmp = math.log(t) + (t_1 - y)
	elif x <= 8.6e+24:
		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))
	tmp = 0.0
	if (x <= -5.5e+63)
		tmp = Float64(log(t) + Float64(t_1 - y));
	elseif (x <= 8.6e+24)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(Float64(log(t) + t_1) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -5.5e+63)
		tmp = log(t) + (t_1 - y);
	elseif (x <= 8.6e+24)
		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]}, If[LessEqual[x, -5.5e+63], N[(N[Log[t], $MachinePrecision] + N[(t$95$1 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.6e+24], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.50000000000000004e63

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 86.8%

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

      1. associate--l+ 86.8%

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

      2. +-commutative 86.8%

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

   4. Simplified 86.8%

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

   if -5.50000000000000004e63 < x < 8.59999999999999975e24

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 97.9%

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

   if 8.59999999999999975e24 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 86.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+63}:\\ \;\;\;\;\log t + \left(x \cdot \log y - y\right)\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+24}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \end{array} \]

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 6: 46.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -8 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-37}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-146}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-153}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-49}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+131}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -8e+39)
     t_1
     (if (<= x -3.7e-37)
       (- z)
       (if (<= x -4e-146)
         (log t)
         (if (<= x 1.35e-153)
           (- z)
           (if (<= x 2.6e-49) (- y) (if (<= x 1.1e+131) (- z) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -8e+39) {
		tmp = t_1;
	} else if (x <= -3.7e-37) {
		tmp = -z;
	} else if (x <= -4e-146) {
		tmp = log(t);
	} else if (x <= 1.35e-153) {
		tmp = -z;
	} else if (x <= 2.6e-49) {
		tmp = -y;
	} else if (x <= 1.1e+131) {
		tmp = -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 <= (-8d+39)) then
        tmp = t_1
    else if (x <= (-3.7d-37)) then
        tmp = -z
    else if (x <= (-4d-146)) then
        tmp = log(t)
    else if (x <= 1.35d-153) then
        tmp = -z
    else if (x <= 2.6d-49) then
        tmp = -y
    else if (x <= 1.1d+131) then
        tmp = -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 <= -8e+39) {
		tmp = t_1;
	} else if (x <= -3.7e-37) {
		tmp = -z;
	} else if (x <= -4e-146) {
		tmp = Math.log(t);
	} else if (x <= 1.35e-153) {
		tmp = -z;
	} else if (x <= 2.6e-49) {
		tmp = -y;
	} else if (x <= 1.1e+131) {
		tmp = -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -8e+39:
		tmp = t_1
	elif x <= -3.7e-37:
		tmp = -z
	elif x <= -4e-146:
		tmp = math.log(t)
	elif x <= 1.35e-153:
		tmp = -z
	elif x <= 2.6e-49:
		tmp = -y
	elif x <= 1.1e+131:
		tmp = -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 <= -8e+39)
		tmp = t_1;
	elseif (x <= -3.7e-37)
		tmp = Float64(-z);
	elseif (x <= -4e-146)
		tmp = log(t);
	elseif (x <= 1.35e-153)
		tmp = Float64(-z);
	elseif (x <= 2.6e-49)
		tmp = Float64(-y);
	elseif (x <= 1.1e+131)
		tmp = Float64(-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 <= -8e+39)
		tmp = t_1;
	elseif (x <= -3.7e-37)
		tmp = -z;
	elseif (x <= -4e-146)
		tmp = log(t);
	elseif (x <= 1.35e-153)
		tmp = -z;
	elseif (x <= 2.6e-49)
		tmp = -y;
	elseif (x <= 1.1e+131)
		tmp = -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, -8e+39], t$95$1, If[LessEqual[x, -3.7e-37], (-z), If[LessEqual[x, -4e-146], N[Log[t], $MachinePrecision], If[LessEqual[x, 1.35e-153], (-z), If[LessEqual[x, 2.6e-49], (-y), If[LessEqual[x, 1.1e+131], (-z), t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.99999999999999952e39 or 1.0999999999999999e131 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--r- 99.7%

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

      5. fma-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+r- 99.8%

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

      8. associate-+r- 99.8%

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

      9. +-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. log-rec 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. +-commutative 99.8%

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

      14. log-rec 99.8%

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

      15. remove-double-neg 99.8%

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

      16. +-commutative 99.8%

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

      17. sub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in x around inf 72.3%

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

   if -7.99999999999999952e39 < x < -3.7e-37 or -4.0000000000000001e-146 < x < 1.35000000000000005e-153 or 2.59999999999999995e-49 < x < 1.0999999999999999e131

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--r- 99.9%

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

      5. fma-neg 99.9%

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

      6. +-commutative 99.9%

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

      7. associate-+r- 99.9%

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

      8. associate-+r- 99.9%

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

      9. +-commutative 99.9%

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

      10. sub-neg 99.9%

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

      11. log-rec 99.9%

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

      12. distribute-neg-in 99.9%

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

      13. +-commutative 99.9%

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

      14. log-rec 99.9%

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

      15. remove-double-neg 99.9%

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

      16. +-commutative 99.9%

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

      17. sub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 50.6%

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

      1. neg-mul-1 50.6%

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

   7. Simplified 50.6%

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

   if -3.7e-37 < x < -4.0000000000000001e-146

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 77.4%

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

      1. remove-double-neg 77.4%

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

      2. log-rec 77.4%

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

      3. mul-1-neg 77.4%

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

      4. mul-1-neg 77.4%

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

      5. log-rec 77.4%

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

      6. remove-double-neg 77.4%

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

      7. log-pow 77.4%

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

      8. log-prod 77.4%

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

   4. Simplified 77.4%

      \[\leadsto \color{blue}{\log \left(t \cdot {y}^{x}\right) - y} \]
   5. Step-by-step derivation

      1. add-log-exp 47.2%

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

      2. diff-log 47.2%

         \[\leadsto \color{blue}{\log \left(\frac{t \cdot {y}^{x}}{e^{y}}\right)} \]

   6. Applied egg-rr 47.2%

      \[\leadsto \color{blue}{\log \left(\frac{t \cdot {y}^{x}}{e^{y}}\right)} \]

   7. Taylor expanded in x around 0 47.2%

      \[\leadsto \color{blue}{\log \left(\frac{t}{e^{y}}\right)} \]

   8. Taylor expanded in y around 0 46.5%

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

   if 1.35000000000000005e-153 < x < 2.59999999999999995e-49

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--r- 100.0%

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

      5. fma-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+r- 100.0%

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

      8. associate-+r- 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

      11. log-rec 100.0%

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

      12. distribute-neg-in 100.0%

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

      13. +-commutative 100.0%

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

      14. log-rec 100.0%

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

      15. remove-double-neg 100.0%

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

      16. +-commutative 100.0%

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

      17. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 70.1%

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

      1. neg-mul-1 70.1%

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

   7. Simplified 70.1%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-37}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-146}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-153}:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-49}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+131}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 7: 59.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \log t - z\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-49}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (log t) z)))
   (if (<= x -1.7e+40)
     t_1
     (if (<= x 1.9e-155)
       t_2
       (if (<= x 4.3e-49) (- (log t) y) (if (<= x 1.1e+131) 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) - z;
	double tmp;
	if (x <= -1.7e+40) {
		tmp = t_1;
	} else if (x <= 1.9e-155) {
		tmp = t_2;
	} else if (x <= 4.3e-49) {
		tmp = log(t) - y;
	} else if (x <= 1.1e+131) {
		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) - z
    if (x <= (-1.7d+40)) then
        tmp = t_1
    else if (x <= 1.9d-155) then
        tmp = t_2
    else if (x <= 4.3d-49) then
        tmp = log(t) - y
    else if (x <= 1.1d+131) 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) - z;
	double tmp;
	if (x <= -1.7e+40) {
		tmp = t_1;
	} else if (x <= 1.9e-155) {
		tmp = t_2;
	} else if (x <= 4.3e-49) {
		tmp = Math.log(t) - y;
	} else if (x <= 1.1e+131) {
		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) - z
	tmp = 0
	if x <= -1.7e+40:
		tmp = t_1
	elif x <= 1.9e-155:
		tmp = t_2
	elif x <= 4.3e-49:
		tmp = math.log(t) - y
	elif x <= 1.1e+131:
		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) - z)
	tmp = 0.0
	if (x <= -1.7e+40)
		tmp = t_1;
	elseif (x <= 1.9e-155)
		tmp = t_2;
	elseif (x <= 4.3e-49)
		tmp = Float64(log(t) - y);
	elseif (x <= 1.1e+131)
		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) - z;
	tmp = 0.0;
	if (x <= -1.7e+40)
		tmp = t_1;
	elseif (x <= 1.9e-155)
		tmp = t_2;
	elseif (x <= 4.3e-49)
		tmp = log(t) - y;
	elseif (x <= 1.1e+131)
		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] - z), $MachinePrecision]}, If[LessEqual[x, -1.7e+40], t$95$1, If[LessEqual[x, 1.9e-155], t$95$2, If[LessEqual[x, 4.3e-49], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 1.1e+131], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.69999999999999994e40 or 1.0999999999999999e131 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--r- 99.7%

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

      5. fma-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+r- 99.8%

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

      8. associate-+r- 99.8%

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

      9. +-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. log-rec 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. +-commutative 99.8%

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

      14. log-rec 99.8%

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

      15. remove-double-neg 99.8%

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

      16. +-commutative 99.8%

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

      17. sub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in x around inf 72.3%

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

   if -1.69999999999999994e40 < x < 1.8999999999999999e-155 or 4.30000000000000016e-49 < x < 1.0999999999999999e131

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 63.7%

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

      1. neg-mul-1 63.7%

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

   4. Simplified 63.7%

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

   if 1.8999999999999999e-155 < x < 4.30000000000000016e-49

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 93.4%

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

      1. remove-double-neg 93.4%

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

      2. log-rec 93.4%

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

      3. mul-1-neg 93.4%

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

      4. mul-1-neg 93.4%

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

      5. log-rec 93.4%

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

      6. remove-double-neg 93.4%

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

      7. log-pow 93.4%

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

      8. log-prod 93.4%

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

   4. Simplified 93.4%

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

   5. Taylor expanded in x around 0 93.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-155}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-49}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+131}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 8: 59.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-49}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+131}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -2.3e+68)
     t_1
     (if (<= x 2.35e-49) (- (log t) y) (if (<= x 1.15e+131) (- z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -2.3e+68) {
		tmp = t_1;
	} else if (x <= 2.35e-49) {
		tmp = log(t) - y;
	} else if (x <= 1.15e+131) {
		tmp = -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 <= (-2.3d+68)) then
        tmp = t_1
    else if (x <= 2.35d-49) then
        tmp = log(t) - y
    else if (x <= 1.15d+131) then
        tmp = -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 <= -2.3e+68) {
		tmp = t_1;
	} else if (x <= 2.35e-49) {
		tmp = Math.log(t) - y;
	} else if (x <= 1.15e+131) {
		tmp = -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -2.3e+68:
		tmp = t_1
	elif x <= 2.35e-49:
		tmp = math.log(t) - y
	elif x <= 1.15e+131:
		tmp = -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 <= -2.3e+68)
		tmp = t_1;
	elseif (x <= 2.35e-49)
		tmp = Float64(log(t) - y);
	elseif (x <= 1.15e+131)
		tmp = Float64(-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 <= -2.3e+68)
		tmp = t_1;
	elseif (x <= 2.35e-49)
		tmp = log(t) - y;
	elseif (x <= 1.15e+131)
		tmp = -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, -2.3e+68], t$95$1, If[LessEqual[x, 2.35e-49], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 1.15e+131], (-z), t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3e68 or 1.14999999999999996e131 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--r- 99.7%

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

      5. fma-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+r- 99.8%

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

      8. associate-+r- 99.8%

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

      9. +-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. log-rec 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. +-commutative 99.8%

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

      14. log-rec 99.8%

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

      15. remove-double-neg 99.8%

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

      16. +-commutative 99.8%

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

      17. sub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in x around inf 75.0%

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

   if -2.3e68 < x < 2.35000000000000011e-49

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 60.7%

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

      1. remove-double-neg 60.7%

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

      2. log-rec 60.7%

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

      3. mul-1-neg 60.7%

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

      4. mul-1-neg 60.7%

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

      5. log-rec 60.7%

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

      6. remove-double-neg 60.7%

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

      7. log-pow 57.4%

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

      8. log-prod 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in x around 0 60.0%

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

   if 2.35000000000000011e-49 < x < 1.14999999999999996e131

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.8%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--r- 99.8%

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

      5. fma-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+r- 99.8%

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

      8. associate-+r- 99.8%

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

      9. +-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. log-rec 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. +-commutative 99.8%

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

      14. log-rec 99.8%

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

      15. remove-double-neg 99.8%

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

      16. +-commutative 99.8%

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

      17. sub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around inf 50.3%

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

      1. neg-mul-1 50.3%

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

   7. Simplified 50.3%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-49}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+131}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 9: 83.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+69} \lor \neg \left(x \leq 4.6 \cdot 10^{+134}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5e+69) (not (<= x 4.6e+134)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5e+69) || !(x <= 4.6e+134)) {
		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 <= (-5d+69)) .or. (.not. (x <= 4.6d+134))) 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 <= -5e+69) || !(x <= 4.6e+134)) {
		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 <= -5e+69) or not (x <= 4.6e+134):
		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 <= -5e+69) || !(x <= 4.6e+134))
		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 <= -5e+69) || ~((x <= 4.6e+134)))
		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, -5e+69], N[Not[LessEqual[x, 4.6e+134]], $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 < -5.00000000000000036e69 or 4.5999999999999996e134 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

      1. associate--l+ 99.7%

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

      2. +-commutative 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--r- 99.7%

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

      5. fma-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+r- 99.8%

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

      8. associate-+r- 99.8%

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

      9. +-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. log-rec 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. +-commutative 99.8%

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

      14. log-rec 99.8%

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

      15. remove-double-neg 99.8%

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

      16. +-commutative 99.8%

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

      17. sub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in x around inf 75.0%

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

   if -5.00000000000000036e69 < x < 4.5999999999999996e134

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 93.6%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+69} \lor \neg \left(x \leq 4.6 \cdot 10^{+134}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]

Alternative 10: 46.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-30}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-275}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-153}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+78}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e-30)
   (- z)
   (if (<= z 2.7e-275)
     (- y)
     (if (<= z 1.45e-153) (log t) (if (<= z 3.25e+78) (- y) (- z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e-30) {
		tmp = -z;
	} else if (z <= 2.7e-275) {
		tmp = -y;
	} else if (z <= 1.45e-153) {
		tmp = log(t);
	} else if (z <= 3.25e+78) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.1d-30)) then
        tmp = -z
    else if (z <= 2.7d-275) then
        tmp = -y
    else if (z <= 1.45d-153) then
        tmp = log(t)
    else if (z <= 3.25d+78) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e-30) {
		tmp = -z;
	} else if (z <= 2.7e-275) {
		tmp = -y;
	} else if (z <= 1.45e-153) {
		tmp = Math.log(t);
	} else if (z <= 3.25e+78) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e-30:
		tmp = -z
	elif z <= 2.7e-275:
		tmp = -y
	elif z <= 1.45e-153:
		tmp = math.log(t)
	elif z <= 3.25e+78:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e-30)
		tmp = Float64(-z);
	elseif (z <= 2.7e-275)
		tmp = Float64(-y);
	elseif (z <= 1.45e-153)
		tmp = log(t);
	elseif (z <= 3.25e+78)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.1e-30)
		tmp = -z;
	elseif (z <= 2.7e-275)
		tmp = -y;
	elseif (z <= 1.45e-153)
		tmp = log(t);
	elseif (z <= 3.25e+78)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.1e-30], (-z), If[LessEqual[z, 2.7e-275], (-y), If[LessEqual[z, 1.45e-153], N[Log[t], $MachinePrecision], If[LessEqual[z, 3.25e+78], (-y), (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.09999999999999992e-30 or 3.25000000000000018e78 < 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 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--r- 99.9%

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

      5. fma-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+r- 100.0%

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

      8. associate-+r- 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

      11. log-rec 100.0%

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

      12. distribute-neg-in 100.0%

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

      13. +-commutative 100.0%

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

      14. log-rec 100.0%

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

      15. remove-double-neg 100.0%

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

      16. +-commutative 100.0%

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

      17. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 63.0%

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

      1. neg-mul-1 63.0%

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

   7. Simplified 63.0%

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

   if -1.09999999999999992e-30 < z < 2.69999999999999993e-275 or 1.45000000000000001e-153 < z < 3.25000000000000018e78

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--r- 99.8%

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

      5. fma-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+r- 99.8%

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

      8. associate-+r- 99.8%

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

      9. +-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. log-rec 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. +-commutative 99.8%

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

      14. log-rec 99.8%

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

      15. remove-double-neg 99.8%

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

      16. +-commutative 99.8%

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

      17. sub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 40.7%

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

      1. neg-mul-1 40.7%

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

   7. Simplified 40.7%

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

   if 2.69999999999999993e-275 < z < 1.45000000000000001e-153

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.8%

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

      1. remove-double-neg 99.8%

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

      2. log-rec 99.8%

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

      3. mul-1-neg 99.8%

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

      4. mul-1-neg 99.8%

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

      5. log-rec 99.8%

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

      6. remove-double-neg 99.8%

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

      7. log-pow 49.9%

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

      8. log-prod 49.9%

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

   4. Simplified 49.9%

      \[\leadsto \color{blue}{\log \left(t \cdot {y}^{x}\right) - y} \]
   5. Step-by-step derivation

      1. add-log-exp 49.7%

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

      2. diff-log 49.8%

         \[\leadsto \color{blue}{\log \left(\frac{t \cdot {y}^{x}}{e^{y}}\right)} \]

   6. Applied egg-rr 49.8%

      \[\leadsto \color{blue}{\log \left(\frac{t \cdot {y}^{x}}{e^{y}}\right)} \]

   7. Taylor expanded in x around 0 48.9%

      \[\leadsto \color{blue}{\log \left(\frac{t}{e^{y}}\right)} \]

   8. Taylor expanded in y around 0 44.9%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-30}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-275}:\\ \;\;\;\;-y\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-153}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+78}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 11: 47.4% accurate, 34.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-30} \lor \neg \left(z \leq 9.5 \cdot 10^{+78}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.1e-30) (not (<= z 9.5e+78))) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1e-30) || !(z <= 9.5e+78)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.1d-30)) .or. (.not. (z <= 9.5d+78))) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.1e-30) || !(z <= 9.5e+78)) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.1e-30) or not (z <= 9.5e+78):
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.1e-30) || !(z <= 9.5e+78))
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.1e-30) || ~((z <= 9.5e+78)))
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.1e-30], N[Not[LessEqual[z, 9.5e+78]], $MachinePrecision]], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if z < -1.09999999999999992e-30 or 9.5000000000000006e78 < 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 99.9%

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

      1. associate--l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--r- 99.9%

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

      5. fma-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. associate-+r- 100.0%

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

      8. associate-+r- 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

      11. log-rec 100.0%

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

      12. distribute-neg-in 100.0%

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

      13. +-commutative 100.0%

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

      14. log-rec 100.0%

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

      15. remove-double-neg 100.0%

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

      16. +-commutative 100.0%

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

      17. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 63.0%

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

      1. neg-mul-1 63.0%

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

   7. Simplified 63.0%

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

   if -1.09999999999999992e-30 < z < 9.5000000000000006e78

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--r- 99.8%

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

      5. fma-neg 99.8%

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

      6. +-commutative 99.8%

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

      7. associate-+r- 99.8%

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

      8. associate-+r- 99.8%

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

      9. +-commutative 99.8%

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

      10. sub-neg 99.8%

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

      11. log-rec 99.8%

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

      12. distribute-neg-in 99.8%

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

      13. +-commutative 99.8%

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

      14. log-rec 99.8%

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

      15. remove-double-neg 99.8%

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

      16. +-commutative 99.8%

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

      17. sub-neg 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 37.5%

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

      1. neg-mul-1 37.5%

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

   7. Simplified 37.5%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-30} \lor \neg \left(z \leq 9.5 \cdot 10^{+78}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 12: 29.8% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around 0 99.9%

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

   1. associate--l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. +-commutative 99.9%

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

   4. associate--r- 99.9%

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

   5. fma-neg 99.9%

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

   6. +-commutative 99.9%

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

   7. associate-+r- 99.9%

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

   8. associate-+r- 99.9%

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

   9. +-commutative 99.9%

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

   10. sub-neg 99.9%

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

   11. log-rec 99.9%

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

   12. distribute-neg-in 99.9%

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

   13. +-commutative 99.9%

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

   14. log-rec 99.9%

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

   15. remove-double-neg 99.9%

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

   16. +-commutative 99.9%

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

   17. sub-neg 99.9%

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

4. Simplified 99.9%

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

5. Taylor expanded in y around inf 26.8%

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

   1. neg-mul-1 26.8%

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

7. Simplified 26.8%

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

8. Final simplification 26.8%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023308 
(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)))