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

Percentage Accurate: 99.9% → 99.9%

Time: 9.4s

Alternatives: 10

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * N[Log[y], $MachinePrecision] + N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] - y), $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. associate-+l- 99.9%

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

   2. associate--l- 99.9%

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

   3. +-commutative 99.9%

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

   4. associate--r+ 99.9%

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

   5. fma-neg 99.9%

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

   6. neg-sub0 99.9%

      \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

   7. associate-+l- 99.9%

      \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

   8. neg-sub0 99.9%

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

   9. +-commutative 99.9%

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

   10. unsub-neg 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 88.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+97}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+64}:\\ \;\;\;\;\left(\log t + t_1\right) - y\\ \mathbf{else}:\\ \;\;\;\;t_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= z -9.2e+97)
     (- (- (log t) z) y)
     (if (<= z 1.4e+64) (- (+ (log t) t_1) y) (- t_1 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (z <= -9.2e+97) {
		tmp = (log(t) - z) - y;
	} else if (z <= 1.4e+64) {
		tmp = (log(t) + t_1) - y;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (z <= (-9.2d+97)) then
        tmp = (log(t) - z) - y
    else if (z <= 1.4d+64) then
        tmp = (log(t) + t_1) - y
    else
        tmp = t_1 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (z <= -9.2e+97) {
		tmp = (Math.log(t) - z) - y;
	} else if (z <= 1.4e+64) {
		tmp = (Math.log(t) + t_1) - y;
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if z <= -9.2e+97:
		tmp = (math.log(t) - z) - y
	elif z <= 1.4e+64:
		tmp = (math.log(t) + t_1) - y
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -9.2e+97)
		tmp = Float64(Float64(log(t) - z) - y);
	elseif (z <= 1.4e+64)
		tmp = Float64(Float64(log(t) + t_1) - y);
	else
		tmp = Float64(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 (z <= -9.2e+97)
		tmp = (log(t) - z) - y;
	elseif (z <= 1.4e+64)
		tmp = (log(t) + t_1) - y;
	else
		tmp = t_1 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.2e+97], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], If[LessEqual[z, 1.4e+64], N[(N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision] - y), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.20000000000000022e97

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l- 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--r+ 100.0%

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

      5. fma-neg 100.0%

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

      6. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      7. associate-+l- 100.0%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      8. neg-sub0 100.0%

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

      9. +-commutative 100.0%

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

      10. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 93.6%

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

   if -9.20000000000000022e97 < z < 1.40000000000000012e64

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 94.9%

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

   if 1.40000000000000012e64 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 85.2%

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

      1. +-commutative 85.2%

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

      2. associate-+r- 85.2%

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

      3. fma-def 85.2%

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

   4. Simplified 85.2%

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

      1. fma-udef 85.2%

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

      2. associate-+r- 85.2%

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

   6. Applied egg-rr 85.2%

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

   7. Taylor expanded in x around inf 85.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+97}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+64}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]

Alternative 3: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t + x \cdot \log y\\ \mathbf{if}\;y \leq 3 \cdot 10^{+48}:\\ \;\;\;\;t_1 - z\\ \mathbf{else}:\\ \;\;\;\;t_1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (log t) (* x (log y)))))
   (if (<= y 3e+48) (- t_1 z) (- t_1 y))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) + (x * log(y));
	double tmp;
	if (y <= 3e+48) {
		tmp = t_1 - z;
	} else {
		tmp = t_1 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) + (x * log(y))
    if (y <= 3d+48) then
        tmp = t_1 - z
    else
        tmp = t_1 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(t) + (x * Math.log(y));
	double tmp;
	if (y <= 3e+48) {
		tmp = t_1 - z;
	} else {
		tmp = t_1 - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) + (x * math.log(y))
	tmp = 0
	if y <= 3e+48:
		tmp = t_1 - z
	else:
		tmp = t_1 - y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) + Float64(x * log(y)))
	tmp = 0.0
	if (y <= 3e+48)
		tmp = Float64(t_1 - z);
	else
		tmp = Float64(t_1 - 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 (y <= 3e+48)
		tmp = t_1 - z;
	else
		tmp = t_1 - 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[y, 3e+48], N[(t$95$1 - z), $MachinePrecision], N[(t$95$1 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 3e48

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 97.9%

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

   if 3e48 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 83.4%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{+48}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t + x \cdot \log y\right) - y\\ \end{array} \]

Alternative 4: 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 5: 54.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ t_2 := x \cdot \log y\\ \mathbf{if}\;x \leq -8 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-272}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+29}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 1.54 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)) (t_2 (* x (log y))))
   (if (<= x -8e+142)
     t_2
     (if (<= x -1e-272)
       (- y)
       (if (<= x 2.7e-48)
         t_1
         (if (<= x 1.25e+29) (- y) (if (<= x 1.54e+85) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double t_2 = x * log(y);
	double tmp;
	if (x <= -8e+142) {
		tmp = t_2;
	} else if (x <= -1e-272) {
		tmp = -y;
	} else if (x <= 2.7e-48) {
		tmp = t_1;
	} else if (x <= 1.25e+29) {
		tmp = -y;
	} else if (x <= 1.54e+85) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = log(t) - z
    t_2 = x * log(y)
    if (x <= (-8d+142)) then
        tmp = t_2
    else if (x <= (-1d-272)) then
        tmp = -y
    else if (x <= 2.7d-48) then
        tmp = t_1
    else if (x <= 1.25d+29) then
        tmp = -y
    else if (x <= 1.54d+85) then
        tmp = t_1
    else
        tmp = t_2
    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) - z;
	double t_2 = x * Math.log(y);
	double tmp;
	if (x <= -8e+142) {
		tmp = t_2;
	} else if (x <= -1e-272) {
		tmp = -y;
	} else if (x <= 2.7e-48) {
		tmp = t_1;
	} else if (x <= 1.25e+29) {
		tmp = -y;
	} else if (x <= 1.54e+85) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - z
	t_2 = x * math.log(y)
	tmp = 0
	if x <= -8e+142:
		tmp = t_2
	elif x <= -1e-272:
		tmp = -y
	elif x <= 2.7e-48:
		tmp = t_1
	elif x <= 1.25e+29:
		tmp = -y
	elif x <= 1.54e+85:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - z)
	t_2 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -8e+142)
		tmp = t_2;
	elseif (x <= -1e-272)
		tmp = Float64(-y);
	elseif (x <= 2.7e-48)
		tmp = t_1;
	elseif (x <= 1.25e+29)
		tmp = Float64(-y);
	elseif (x <= 1.54e+85)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - z;
	t_2 = x * log(y);
	tmp = 0.0;
	if (x <= -8e+142)
		tmp = t_2;
	elseif (x <= -1e-272)
		tmp = -y;
	elseif (x <= 2.7e-48)
		tmp = t_1;
	elseif (x <= 1.25e+29)
		tmp = -y;
	elseif (x <= 1.54e+85)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+142], t$95$2, If[LessEqual[x, -1e-272], (-y), If[LessEqual[x, 2.7e-48], t$95$1, If[LessEqual[x, 1.25e+29], (-y), If[LessEqual[x, 1.54e+85], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.00000000000000041e142 or 1.5400000000000001e85 < 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. +-commutative 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-+r- 99.7%

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

      4. associate--l- 99.7%

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

      5. fma-def 99.7%

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

      6. associate--l- 99.7%

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

      7. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around inf 71.1%

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

   if -8.00000000000000041e142 < x < -9.9999999999999993e-273 or 2.70000000000000011e-48 < x < 1.25e29

   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. +-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+r- 100.0%

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

      4. associate--l- 100.0%

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

      5. fma-def 100.0%

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

      6. associate--l- 100.0%

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

      7. +-commutative 100.0%

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

   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 54.7%

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

      1. neg-mul-1 54.7%

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

   7. Simplified 54.7%

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

   if -9.9999999999999993e-273 < x < 2.70000000000000011e-48 or 1.25e29 < x < 1.5400000000000001e85

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. associate-+r- 73.7%

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

      3. fma-def 73.7%

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

   4. Simplified 73.7%

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

   5. Taylor expanded in x around 0 67.9%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-272}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-48}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+29}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 1.54 \cdot 10^{+85}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]

Alternative 6: 71.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{+69} \lor \neg \left(y \leq 8.5 \cdot 10^{+88}\right) \land y \leq 1.85 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y 1.05e+69) (and (not (<= y 8.5e+88)) (<= y 1.85e+112)))
   (- (* x (log y)) z)
   (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= 1.05e+69) || (!(y <= 8.5e+88) && (y <= 1.85e+112))) {
		tmp = (x * log(y)) - z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= 1.05d+69) .or. (.not. (y <= 8.5d+88)) .and. (y <= 1.85d+112)) then
        tmp = (x * log(y)) - z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= 1.05e+69) || (!(y <= 8.5e+88) && (y <= 1.85e+112))) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= 1.05e+69) or (not (y <= 8.5e+88) and (y <= 1.85e+112)):
		tmp = (x * math.log(y)) - z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= 1.05e+69) || (!(y <= 8.5e+88) && (y <= 1.85e+112)))
		tmp = Float64(Float64(x * log(y)) - z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= 1.05e+69) || (~((y <= 8.5e+88)) && (y <= 1.85e+112)))
		tmp = (x * log(y)) - z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, 1.05e+69], And[N[Not[LessEqual[y, 8.5e+88]], $MachinePrecision], LessEqual[y, 1.85e+112]]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 1.05000000000000008e69 or 8.5000000000000005e88 < y < 1.85000000000000002e112

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-+r- 94.1%

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

      3. fma-def 94.1%

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

   4. Simplified 94.1%

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

      1. fma-udef 94.1%

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

      2. associate-+r- 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in x around inf 79.5%

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

   if 1.05000000000000008e69 < y < 8.5000000000000005e88 or 1.85000000000000002e112 < y

   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. +-commutative 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. associate--l- 99.9%

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

      5. fma-def 99.9%

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

      6. associate--l- 99.9%

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

      7. +-commutative 99.9%

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

   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 69.9%

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

      1. neg-mul-1 69.9%

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

   7. Simplified 69.9%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{+69} \lor \neg \left(y \leq 8.5 \cdot 10^{+88}\right) \land y \leq 1.85 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 7: 48.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 6.2 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-89}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6200000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+50}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= y 6.2e-162)
     t_1
     (if (<= y 3.5e-89)
       (- z)
       (if (<= y 6200000000.0) t_1 (if (<= y 3e+50) (- z) (- y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (y <= 6.2e-162) {
		tmp = t_1;
	} else if (y <= 3.5e-89) {
		tmp = -z;
	} else if (y <= 6200000000.0) {
		tmp = t_1;
	} else if (y <= 3e+50) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (y <= 6.2d-162) then
        tmp = t_1
    else if (y <= 3.5d-89) then
        tmp = -z
    else if (y <= 6200000000.0d0) then
        tmp = t_1
    else if (y <= 3d+50) 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 t_1 = x * Math.log(y);
	double tmp;
	if (y <= 6.2e-162) {
		tmp = t_1;
	} else if (y <= 3.5e-89) {
		tmp = -z;
	} else if (y <= 6200000000.0) {
		tmp = t_1;
	} else if (y <= 3e+50) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if y <= 6.2e-162:
		tmp = t_1
	elif y <= 3.5e-89:
		tmp = -z
	elif y <= 6200000000.0:
		tmp = t_1
	elif y <= 3e+50:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 6.2e-162)
		tmp = t_1;
	elseif (y <= 3.5e-89)
		tmp = Float64(-z);
	elseif (y <= 6200000000.0)
		tmp = t_1;
	elseif (y <= 3e+50)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (y <= 6.2e-162)
		tmp = t_1;
	elseif (y <= 3.5e-89)
		tmp = -z;
	elseif (y <= 6200000000.0)
		tmp = t_1;
	elseif (y <= 3e+50)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 6.2e-162], t$95$1, If[LessEqual[y, 3.5e-89], (-z), If[LessEqual[y, 6200000000.0], t$95$1, If[LessEqual[y, 3e+50], (-z), (-y)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.1999999999999997e-162 or 3.4999999999999997e-89 < y < 6.2e9

   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. +-commutative 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. associate--l- 99.8%

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

      5. fma-def 99.8%

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

      6. associate--l- 99.8%

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

      7. +-commutative 99.8%

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

   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 50.6%

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

   if 6.1999999999999997e-162 < y < 3.4999999999999997e-89 or 6.2e9 < y < 2.9999999999999998e50

   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. +-commutative 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-+r- 100.0%

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

      4. associate--l- 100.0%

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

      5. fma-def 100.0%

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

      6. associate--l- 100.0%

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

      7. +-commutative 100.0%

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

   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 58.8%

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

      1. mul-1-neg 58.8%

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

   7. Simplified 58.8%

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

   if 2.9999999999999998e50 < y

   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. +-commutative 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. associate--l- 99.9%

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

      5. fma-def 99.9%

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

      6. associate--l- 99.9%

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

      7. +-commutative 99.9%

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

   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 64.7%

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

      1. neg-mul-1 64.7%

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

   7. Simplified 64.7%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-89}:\\ \;\;\;\;-z\\ \mathbf{elif}\;y \leq 6200000000:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+50}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 8: 89.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+64} \lor \neg \left(x \leq 1.45 \cdot 10^{+29}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.2e+64) (not (<= x 1.45e+29)))
   (- (* x (log y)) z)
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.2e+64) || !(x <= 1.45e+29)) {
		tmp = (x * log(y)) - z;
	} 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 <= (-2.2d+64)) .or. (.not. (x <= 1.45d+29))) then
        tmp = (x * log(y)) - z
    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 <= -2.2e+64) || !(x <= 1.45e+29)) {
		tmp = (x * Math.log(y)) - z;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.2e+64) or not (x <= 1.45e+29):
		tmp = (x * math.log(y)) - z
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.2e+64) || !(x <= 1.45e+29))
		tmp = Float64(Float64(x * log(y)) - z);
	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 <= -2.2e+64) || ~((x <= 1.45e+29)))
		tmp = (x * log(y)) - z;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.2e+64], N[Not[LessEqual[x, 1.45e+29]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.20000000000000002e64 or 1.45e29 < 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 84.1%

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

      1. +-commutative 84.1%

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

      2. associate-+r- 84.1%

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

      3. fma-def 84.1%

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

   4. Simplified 84.1%

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

      1. fma-udef 84.1%

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

      2. associate-+r- 84.1%

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

   6. Applied egg-rr 84.1%

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

   7. Taylor expanded in x around inf 84.1%

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

   if -2.20000000000000002e64 < x < 1.45e29

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. associate--l- 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--r+ 100.0%

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

      5. fma-neg 100.0%

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

      6. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(z - \log t\right)}\right) - y \]

      7. associate-+l- 100.0%

         \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - z\right) + \log t}\right) - y \]

      8. neg-sub0 100.0%

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

      9. +-commutative 100.0%

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

      10. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 97.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+64} \lor \neg \left(x \leq 1.45 \cdot 10^{+29}\right):\\ \;\;\;\;x \cdot \log y - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]

Alternative 9: 48.9% accurate, 51.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{+49}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 4.2e+49) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.2e+49) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 4.2d+49) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.2e+49) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 4.2e+49:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 4.2e+49)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 4.2e+49)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 4.2e+49], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 4.20000000000000022e49

   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. +-commutative 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. associate--l- 99.8%

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

      5. fma-def 99.8%

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

      6. associate--l- 99.8%

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

      7. +-commutative 99.8%

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

   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 37.7%

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

      1. mul-1-neg 37.7%

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

   7. Simplified 37.7%

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

   if 4.20000000000000022e49 < y

   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. +-commutative 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. associate--l- 99.9%

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

      5. fma-def 99.9%

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

      6. associate--l- 99.9%

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

      7. +-commutative 99.9%

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

   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 64.7%

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

      1. neg-mul-1 64.7%

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

   7. Simplified 64.7%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{+49}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 10: 29.7% 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. +-commutative 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+r- 99.9%

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

   4. associate--l- 99.9%

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

   5. fma-def 99.9%

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

   6. associate--l- 99.9%

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

   7. +-commutative 99.9%

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

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 31.3%

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

   1. neg-mul-1 31.3%

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

7. Simplified 31.3%

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

8. Final simplification 31.3%

   \[\leadsto -y \]

Reproduce

herbie shell --seed 2023293 
(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)))