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

Percentage Accurate: 99.9% → 99.9%

Time: 11.4s

Alternatives: 15

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. Add Preprocessing

5. Final simplification 99.9%

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

Alternative 2: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(t\_1 - y\right) - z\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+19} \lor \neg \left(t\_2 \leq 200000000\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\log t + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- t_1 y) z)))
   (if (or (<= t_2 -2e+19) (not (<= t_2 200000000.0))) t_2 (+ (log t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = (t_1 - y) - z;
	double tmp;
	if ((t_2 <= -2e+19) || !(t_2 <= 200000000.0)) {
		tmp = t_2;
	} else {
		tmp = log(t) + 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 = (t_1 - y) - z
    if ((t_2 <= (-2d+19)) .or. (.not. (t_2 <= 200000000.0d0))) then
        tmp = t_2
    else
        tmp = log(t) + 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 = (t_1 - y) - z;
	double tmp;
	if ((t_2 <= -2e+19) || !(t_2 <= 200000000.0)) {
		tmp = t_2;
	} else {
		tmp = Math.log(t) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = (t_1 - y) - z
	tmp = 0
	if (t_2 <= -2e+19) or not (t_2 <= 200000000.0):
		tmp = t_2
	else:
		tmp = math.log(t) + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(Float64(t_1 - y) - z)
	tmp = 0.0
	if ((t_2 <= -2e+19) || !(t_2 <= 200000000.0))
		tmp = t_2;
	else
		tmp = Float64(log(t) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = (t_1 - y) - z;
	tmp = 0.0;
	if ((t_2 <= -2e+19) || ~((t_2 <= 200000000.0)))
		tmp = t_2;
	else
		tmp = log(t) + 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[(t$95$1 - y), $MachinePrecision] - z), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e+19], N[Not[LessEqual[t$95$2, 200000000.0]], $MachinePrecision]], t$95$2, N[(N[Log[t], $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -2e19 or 2e8 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z)

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

   if -2e19 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 2e8

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate--l+ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 94.2%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \log y - y\right) - z \leq -2 \cdot 10^{+19} \lor \neg \left(\left(x \cdot \log y - y\right) - z \leq 200000000\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t + x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -500000 \lor \neg \left(t\_1 \leq 2 \cdot 10^{-18}\right):\\ \;\;\;\;t\_1 - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (or (<= t_1 -500000.0) (not (<= t_1 2e-18)))
     (- t_1 z)
     (- (log t) (+ y z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if ((t_1 <= -500000.0) || !(t_1 <= 2e-18)) {
		tmp = t_1 - z;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) - y
    if ((t_1 <= (-500000.0d0)) .or. (.not. (t_1 <= 2d-18))) then
        tmp = t_1 - z
    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 t_1 = (x * Math.log(y)) - y;
	double tmp;
	if ((t_1 <= -500000.0) || !(t_1 <= 2e-18)) {
		tmp = t_1 - z;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if (t_1 <= -500000.0) or not (t_1 <= 2e-18):
		tmp = t_1 - z
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if ((t_1 <= -500000.0) || !(t_1 <= 2e-18))
		tmp = Float64(t_1 - z);
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - y;
	tmp = 0.0;
	if ((t_1 <= -500000.0) || ~((t_1 <= 2e-18)))
		tmp = t_1 - z;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -500000.0], N[Not[LessEqual[t$95$1, 2e-18]], $MachinePrecision]], N[(t$95$1 - z), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -5e5 or 2.0000000000000001e-18 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 98.6%

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

   if -5e5 < (-.f64 (*.f64 x (log.f64 y)) y) < 2.0000000000000001e-18

   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%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -500000 \lor \neg \left(x \cdot \log y - y \leq 2 \cdot 10^{-18}\right):\\ \;\;\;\;\left(x \cdot \log y - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{+251}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -4e+251)
     t_2
     (if (<= t_2 2e-18) (- (log t) (+ y z)) (- t_1 z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -4e+251) {
		tmp = t_2;
	} else if (t_2 <= 2e-18) {
		tmp = log(t) - (y + z);
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-4d+251)) then
        tmp = t_2
    else if (t_2 <= 2d-18) then
        tmp = log(t) - (y + z)
    else
        tmp = t_1 - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -4e+251) {
		tmp = t_2;
	} else if (t_2 <= 2e-18) {
		tmp = Math.log(t) - (y + z);
	} else {
		tmp = t_1 - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = t_1 - y
	tmp = 0
	if t_2 <= -4e+251:
		tmp = t_2
	elif t_2 <= 2e-18:
		tmp = math.log(t) - (y + z)
	else:
		tmp = t_1 - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	t_2 = Float64(t_1 - y)
	tmp = 0.0
	if (t_2 <= -4e+251)
		tmp = t_2;
	elseif (t_2 <= 2e-18)
		tmp = Float64(log(t) - Float64(y + z));
	else
		tmp = Float64(t_1 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	t_2 = t_1 - y;
	tmp = 0.0;
	if (t_2 <= -4e+251)
		tmp = t_2;
	elseif (t_2 <= 2e-18)
		tmp = log(t) - (y + z);
	else
		tmp = t_1 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+251], t$95$2, If[LessEqual[t$95$2, 2e-18], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -4.0000000000000002e251

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

   6. Taylor expanded in z around 0 97.7%

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

   if -4.0000000000000002e251 < (-.f64 (*.f64 x (log.f64 y)) y) < 2.0000000000000001e-18

   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%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 87.1%

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

   if 2.0000000000000001e-18 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 97.3%

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

   6. Taylor expanded in y around 0 97.2%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log y - y \leq -4 \cdot 10^{+251}:\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{elif}\;x \cdot \log y - y \leq 2 \cdot 10^{-18}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 6: 69.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(-y\right) - z\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-153}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-218}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 10^{-191}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- y) z)))
   (if (<= x -1.02e+133)
     t_1
     (if (<= x -6.6e-106)
       t_2
       (if (<= x -6.8e-153)
         (log t)
         (if (<= x 3e-218)
           t_2
           (if (<= x 1e-191) (log t) (if (<= x 2.05e+165) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double t_2 = -y - z;
	double tmp;
	if (x <= -1.02e+133) {
		tmp = t_1;
	} else if (x <= -6.6e-106) {
		tmp = t_2;
	} else if (x <= -6.8e-153) {
		tmp = log(t);
	} else if (x <= 3e-218) {
		tmp = t_2;
	} else if (x <= 1e-191) {
		tmp = log(t);
	} else if (x <= 2.05e+165) {
		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 = -y - z
    if (x <= (-1.02d+133)) then
        tmp = t_1
    else if (x <= (-6.6d-106)) then
        tmp = t_2
    else if (x <= (-6.8d-153)) then
        tmp = log(t)
    else if (x <= 3d-218) then
        tmp = t_2
    else if (x <= 1d-191) then
        tmp = log(t)
    else if (x <= 2.05d+165) 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 = -y - z;
	double tmp;
	if (x <= -1.02e+133) {
		tmp = t_1;
	} else if (x <= -6.6e-106) {
		tmp = t_2;
	} else if (x <= -6.8e-153) {
		tmp = Math.log(t);
	} else if (x <= 3e-218) {
		tmp = t_2;
	} else if (x <= 1e-191) {
		tmp = Math.log(t);
	} else if (x <= 2.05e+165) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	t_2 = -y - z
	tmp = 0
	if x <= -1.02e+133:
		tmp = t_1
	elif x <= -6.6e-106:
		tmp = t_2
	elif x <= -6.8e-153:
		tmp = math.log(t)
	elif x <= 3e-218:
		tmp = t_2
	elif x <= 1e-191:
		tmp = math.log(t)
	elif x <= 2.05e+165:
		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(Float64(-y) - z)
	tmp = 0.0
	if (x <= -1.02e+133)
		tmp = t_1;
	elseif (x <= -6.6e-106)
		tmp = t_2;
	elseif (x <= -6.8e-153)
		tmp = log(t);
	elseif (x <= 3e-218)
		tmp = t_2;
	elseif (x <= 1e-191)
		tmp = log(t);
	elseif (x <= 2.05e+165)
		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 = -y - z;
	tmp = 0.0;
	if (x <= -1.02e+133)
		tmp = t_1;
	elseif (x <= -6.6e-106)
		tmp = t_2;
	elseif (x <= -6.8e-153)
		tmp = log(t);
	elseif (x <= 3e-218)
		tmp = t_2;
	elseif (x <= 1e-191)
		tmp = log(t);
	elseif (x <= 2.05e+165)
		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[((-y) - z), $MachinePrecision]}, If[LessEqual[x, -1.02e+133], t$95$1, If[LessEqual[x, -6.6e-106], t$95$2, If[LessEqual[x, -6.8e-153], N[Log[t], $MachinePrecision], If[LessEqual[x, 3e-218], t$95$2, If[LessEqual[x, 1e-191], N[Log[t], $MachinePrecision], If[LessEqual[x, 2.05e+165], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.02e133 or 2.0500000000000001e165 < x

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in x around inf 75.5%

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

   if -1.02e133 < x < -6.60000000000000031e-106 or -6.7999999999999997e-153 < x < 2.9999999999999998e-218 or 1e-191 < x < 2.0500000000000001e165

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 86.3%

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

   6. Taylor expanded in x around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. distribute-neg-in 73.8%

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

      3. sub-neg 73.8%

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

   8. Simplified 73.8%

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

   if -6.60000000000000031e-106 < x < -6.7999999999999997e-153 or 2.9999999999999998e-218 < x < 1e-191

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. associate--l+ 100.0%

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

      3. fma-def 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 84.7%

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

      1. mul-1-neg 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in y around 0 78.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-106}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-153}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-218}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;x \leq 10^{-191}:\\ \;\;\;\;\log t\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+165}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - y\\ t_2 := \left(-y\right) - z\\ t_3 := x \cdot \log y\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-69}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-269}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0035:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) y)) (t_2 (- (- y) z)) (t_3 (* x (log y))))
   (if (<= z -1.55e+31)
     t_2
     (if (<= z -4.8e-69)
       t_3
       (if (<= z -3.2e-231)
         t_1
         (if (<= z -2.6e-269)
           t_3
           (if (<= z 1e-15) t_1 (if (<= z 0.0035) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - y;
	double t_2 = -y - z;
	double t_3 = x * log(y);
	double tmp;
	if (z <= -1.55e+31) {
		tmp = t_2;
	} else if (z <= -4.8e-69) {
		tmp = t_3;
	} else if (z <= -3.2e-231) {
		tmp = t_1;
	} else if (z <= -2.6e-269) {
		tmp = t_3;
	} else if (z <= 1e-15) {
		tmp = t_1;
	} else if (z <= 0.0035) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = log(t) - y
    t_2 = -y - z
    t_3 = x * log(y)
    if (z <= (-1.55d+31)) then
        tmp = t_2
    else if (z <= (-4.8d-69)) then
        tmp = t_3
    else if (z <= (-3.2d-231)) then
        tmp = t_1
    else if (z <= (-2.6d-269)) then
        tmp = t_3
    else if (z <= 1d-15) then
        tmp = t_1
    else if (z <= 0.0035d0) then
        tmp = t_3
    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) - y;
	double t_2 = -y - z;
	double t_3 = x * Math.log(y);
	double tmp;
	if (z <= -1.55e+31) {
		tmp = t_2;
	} else if (z <= -4.8e-69) {
		tmp = t_3;
	} else if (z <= -3.2e-231) {
		tmp = t_1;
	} else if (z <= -2.6e-269) {
		tmp = t_3;
	} else if (z <= 1e-15) {
		tmp = t_1;
	} else if (z <= 0.0035) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - y
	t_2 = -y - z
	t_3 = x * math.log(y)
	tmp = 0
	if z <= -1.55e+31:
		tmp = t_2
	elif z <= -4.8e-69:
		tmp = t_3
	elif z <= -3.2e-231:
		tmp = t_1
	elif z <= -2.6e-269:
		tmp = t_3
	elif z <= 1e-15:
		tmp = t_1
	elif z <= 0.0035:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - y)
	t_2 = Float64(Float64(-y) - z)
	t_3 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -1.55e+31)
		tmp = t_2;
	elseif (z <= -4.8e-69)
		tmp = t_3;
	elseif (z <= -3.2e-231)
		tmp = t_1;
	elseif (z <= -2.6e-269)
		tmp = t_3;
	elseif (z <= 1e-15)
		tmp = t_1;
	elseif (z <= 0.0035)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - y;
	t_2 = -y - z;
	t_3 = x * log(y);
	tmp = 0.0;
	if (z <= -1.55e+31)
		tmp = t_2;
	elseif (z <= -4.8e-69)
		tmp = t_3;
	elseif (z <= -3.2e-231)
		tmp = t_1;
	elseif (z <= -2.6e-269)
		tmp = t_3;
	elseif (z <= 1e-15)
		tmp = t_1;
	elseif (z <= 0.0035)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision]}, Block[{t$95$2 = N[((-y) - z), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+31], t$95$2, If[LessEqual[z, -4.8e-69], t$95$3, If[LessEqual[z, -3.2e-231], t$95$1, If[LessEqual[z, -2.6e-269], t$95$3, If[LessEqual[z, 1e-15], t$95$1, If[LessEqual[z, 0.0035], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5500000000000001e31 or 0.00350000000000000007 < z

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

   6. Taylor expanded in x around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. distribute-neg-in 85.8%

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

      3. sub-neg 85.8%

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

   8. Simplified 85.8%

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

   if -1.5500000000000001e31 < z < -4.8000000000000002e-69 or -3.20000000000000008e-231 < z < -2.6e-269 or 1.0000000000000001e-15 < z < 0.00350000000000000007

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 84.4%

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

   6. Taylor expanded in x around inf 68.1%

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

   if -4.8000000000000002e-69 < z < -3.20000000000000008e-231 or -2.6e-269 < z < 1.0000000000000001e-15

   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. Add Preprocessing

   5. Taylor expanded in y around inf 72.7%

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

      1. mul-1-neg 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in y around 0 72.7%

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

      1. mul-1-neg 72.7%

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

      2. sub-neg 72.7%

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

   10. Simplified 72.7%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+31}:\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-231}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-269}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;z \leq 10^{-15}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;z \leq 0.0035:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;y \leq 1.4 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-22}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 410000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= y 1.4e-278)
     t_1
     (if (<= y 1.02e-22)
       (- (log t) z)
       (if (<= y 410000000.0) t_1 (- (- y) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (y <= 1.4e-278) {
		tmp = t_1;
	} else if (y <= 1.02e-22) {
		tmp = log(t) - z;
	} else if (y <= 410000000.0) {
		tmp = t_1;
	} else {
		tmp = -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) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (y <= 1.4d-278) then
        tmp = t_1
    else if (y <= 1.02d-22) then
        tmp = log(t) - z
    else if (y <= 410000000.0d0) then
        tmp = t_1
    else
        tmp = -y - 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 (y <= 1.4e-278) {
		tmp = t_1;
	} else if (y <= 1.02e-22) {
		tmp = Math.log(t) - z;
	} else if (y <= 410000000.0) {
		tmp = t_1;
	} else {
		tmp = -y - z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if y <= 1.4e-278:
		tmp = t_1
	elif y <= 1.02e-22:
		tmp = math.log(t) - z
	elif y <= 410000000.0:
		tmp = t_1
	else:
		tmp = -y - z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (y <= 1.4e-278)
		tmp = t_1;
	elseif (y <= 1.02e-22)
		tmp = Float64(log(t) - z);
	elseif (y <= 410000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(-y) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (y <= 1.4e-278)
		tmp = t_1;
	elseif (y <= 1.02e-22)
		tmp = log(t) - z;
	elseif (y <= 410000000.0)
		tmp = t_1;
	else
		tmp = -y - 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[y, 1.4e-278], t$95$1, If[LessEqual[y, 1.02e-22], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], If[LessEqual[y, 410000000.0], t$95$1, N[((-y) - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.40000000000000004e-278 or 1.02000000000000002e-22 < y < 4.1e8

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 88.9%

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

   6. Taylor expanded in x around inf 79.9%

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

   if 1.40000000000000004e-278 < y < 1.02000000000000002e-22

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 68.6%

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

   6. Taylor expanded in y around 0 68.6%

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

   if 4.1e8 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

   6. Taylor expanded in x around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. distribute-neg-in 81.4%

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

      3. sub-neg 81.4%

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

   8. Simplified 81.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.4 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-22}:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;y \leq 410000000:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+133} \lor \neg \left(x \leq 1.9 \cdot 10^{+165}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.4e+133) (not (<= x 1.9e+165)))
   (* x (log y))
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.4e+133) || !(x <= 1.9e+165)) {
		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 <= (-1.4d+133)) .or. (.not. (x <= 1.9d+165))) 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 <= -1.4e+133) || !(x <= 1.9e+165)) {
		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 <= -1.4e+133) or not (x <= 1.9e+165):
		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 <= -1.4e+133) || !(x <= 1.9e+165))
		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 <= -1.4e+133) || ~((x <= 1.9e+165)))
		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, -1.4e+133], N[Not[LessEqual[x, 1.9e+165]], $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 < -1.40000000000000008e133 or 1.89999999999999995e165 < x

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in x around inf 75.5%

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

   if -1.40000000000000008e133 < x < 1.89999999999999995e165

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 87.3%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+133} \lor \neg \left(x \leq 1.9 \cdot 10^{+165}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+105} \lor \neg \left(x \leq 3 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.5e+105) (not (<= x 3e+80)))
   (- (* x (log y)) y)
   (- (log t) (+ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.5e+105) || !(x <= 3e+80)) {
		tmp = (x * log(y)) - y;
	} else {
		tmp = log(t) - (y + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.5d+105)) .or. (.not. (x <= 3d+80))) then
        tmp = (x * log(y)) - y
    else
        tmp = log(t) - (y + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.5e+105) || !(x <= 3e+80)) {
		tmp = (x * Math.log(y)) - y;
	} else {
		tmp = Math.log(t) - (y + z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.5e+105) or not (x <= 3e+80):
		tmp = (x * math.log(y)) - y
	else:
		tmp = math.log(t) - (y + z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.5e+105) || !(x <= 3e+80))
		tmp = Float64(Float64(x * log(y)) - y);
	else
		tmp = Float64(log(t) - Float64(y + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.5e+105) || ~((x <= 3e+80)))
		tmp = (x * log(y)) - y;
	else
		tmp = log(t) - (y + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.5e+105], N[Not[LessEqual[x, 3e+80]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision], N[(N[Log[t], $MachinePrecision] - N[(y + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5000000000000001e105 or 2.99999999999999987e80 < x

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around 0 80.1%

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

   if -4.5000000000000001e105 < x < 2.99999999999999987e80

   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%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 92.4%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+105} \lor \neg \left(x \leq 3 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \log y - y\\ \mathbf{else}:\\ \;\;\;\;\log t - \left(y + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{-280} \lor \neg \left(z \leq 2.8 \cdot 10^{-124}\right):\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z 7e-280) (not (<= z 2.8e-124))) (- (- y) z) (log t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= 7e-280) || !(z <= 2.8e-124)) {
		tmp = -y - z;
	} else {
		tmp = log(t);
	}
	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 <= 7d-280) .or. (.not. (z <= 2.8d-124))) then
        tmp = -y - z
    else
        tmp = log(t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= 7e-280) || !(z <= 2.8e-124)) {
		tmp = -y - z;
	} else {
		tmp = Math.log(t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= 7e-280) or not (z <= 2.8e-124):
		tmp = -y - z
	else:
		tmp = math.log(t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= 7e-280) || !(z <= 2.8e-124))
		tmp = Float64(Float64(-y) - z);
	else
		tmp = log(t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= 7e-280) || ~((z <= 2.8e-124)))
		tmp = -y - z;
	else
		tmp = log(t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, 7e-280], N[Not[LessEqual[z, 2.8e-124]], $MachinePrecision]], N[((-y) - z), $MachinePrecision], N[Log[t], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.0000000000000002e-280 or 2.79999999999999998e-124 < z

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 89.1%

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

   6. Taylor expanded in x around 0 63.6%

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

      1. mul-1-neg 63.6%

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

      2. distribute-neg-in 63.6%

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

      3. sub-neg 63.6%

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

   8. Simplified 63.6%

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

   if 7.0000000000000002e-280 < z < 2.79999999999999998e-124

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. associate--l+ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 64.0%

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

      1. mul-1-neg 64.0%

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

   7. Simplified 64.0%

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

   8. Taylor expanded in y around 0 42.0%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{-280} \lor \neg \left(z \leq 2.8 \cdot 10^{-124}\right):\\ \;\;\;\;\left(-y\right) - z\\ \mathbf{else}:\\ \;\;\;\;\log t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.5% accurate, 29.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+79}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 2.2e+79) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.2e+79) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 2.2d+79) then
        tmp = -z
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.2e+79) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.2e+79:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.2e+79)
		tmp = Float64(-z);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.2e+79)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.2e+79], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 2.1999999999999999e79

   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%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 76.5%

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

   6. Taylor expanded in z around inf 36.3%

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

      1. neg-mul-1 36.3%

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

   8. Simplified 36.3%

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

   if 2.1999999999999999e79 < y

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

   6. Taylor expanded in y around inf 69.4%

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

      1. mul-1-neg 69.4%

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

   8. Simplified 69.4%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{+79}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.0% accurate, 52.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 85.7%

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

6. Taylor expanded in x around 0 59.1%

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

   1. mul-1-neg 59.1%

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

   2. distribute-neg-in 59.1%

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

   3. sub-neg 59.1%

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

8. Simplified 59.1%

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

9. Final simplification 59.1%

   \[\leadsto \left(-y\right) - z \]
10. Add Preprocessing

Alternative 14: 30.3% accurate, 104.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 85.7%

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

6. Taylor expanded in y around inf 31.3%

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

   1. mul-1-neg 31.3%

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

8. Simplified 31.3%

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

9. Final simplification 31.3%

   \[\leadsto -y \]
10. Add Preprocessing

Alternative 15: 2.2% accurate, 209.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l- 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in z around inf 85.7%

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

   1. associate--l- 85.7%

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

   2. sub-neg 85.7%

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

   3. distribute-neg-in 85.7%

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

   4. add-sqr-sqrt 0.0%

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

   5. sqrt-unprod 49.6%

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

   6. sqr-neg 49.6%

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

   7. sqrt-unprod 55.1%

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

   8. add-sqr-sqrt 55.1%

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

   9. sub-neg 55.1%

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

   10. flip-+ 19.7%

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

   11. unpow2 19.7%

       \[\leadsto \frac{\color{blue}{{\left(x \cdot \log y\right)}^{2}} - \left(y - z\right) \cdot \left(y - z\right)}{x \cdot \log y - \left(y - z\right)} \]

   12. unpow2 19.7%

       \[\leadsto \frac{{\left(x \cdot \log y\right)}^{2} - \color{blue}{{\left(y - z\right)}^{2}}}{x \cdot \log y - \left(y - z\right)} \]

   13. add-sqr-sqrt 11.0%

       \[\leadsto \color{blue}{\sqrt{\frac{{\left(x \cdot \log y\right)}^{2} - {\left(y - z\right)}^{2}}{x \cdot \log y - \left(y - z\right)}} \cdot \sqrt{\frac{{\left(x \cdot \log y\right)}^{2} - {\left(y - z\right)}^{2}}{x \cdot \log y - \left(y - z\right)}}} \]

   14. pow2 11.0%

       \[\leadsto \color{blue}{{\left(\sqrt{\frac{{\left(x \cdot \log y\right)}^{2} - {\left(y - z\right)}^{2}}{x \cdot \log y - \left(y - z\right)}}\right)}^{2}} \]

7. Applied egg-rr 30.1%

   \[\leadsto \color{blue}{{\left(\sqrt{\mathsf{fma}\left(x, \log y, y - z\right)}\right)}^{2}} \]
8. Step-by-step derivation

   1. unpow2 30.1%

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

   2. add-sqr-sqrt 55.1%

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

   3. fma-udef 55.1%

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

   4. add-sqr-sqrt 21.1%

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

   5. associate-*r* 21.1%

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

   6. fma-def 21.1%

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

9. Applied egg-rr 21.1%

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

10. Taylor expanded in y around inf 2.2%

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

11. Final simplification 2.2%

    \[\leadsto y \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024036 
(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)))