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

Percentage Accurate: 99.9% → 99.9%

Time: 2.1s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 89.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+193}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq -5000000000000:\\ \;\;\;\;\left(\log y - y\right) - z\\ \mathbf{elif}\;t\_2 \leq 10^{-7}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -1e+193)
     t_2
     (if (<= t_2 -5000000000000.0)
       (- (- (log y) y) z)
       (if (<= t_2 1e-7) (- (log t) 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 <= -1e+193) {
		tmp = t_2;
	} else if (t_2 <= -5000000000000.0) {
		tmp = (log(y) - y) - z;
	} else if (t_2 <= 1e-7) {
		tmp = log(t) - 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 <= (-1d+193)) then
        tmp = t_2
    else if (t_2 <= (-5000000000000.0d0)) then
        tmp = (log(y) - y) - z
    else if (t_2 <= 1d-7) then
        tmp = log(t) - 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 <= -1e+193) {
		tmp = t_2;
	} else if (t_2 <= -5000000000000.0) {
		tmp = (Math.log(y) - y) - z;
	} else if (t_2 <= 1e-7) {
		tmp = Math.log(t) - 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 <= -1e+193:
		tmp = t_2
	elif t_2 <= -5000000000000.0:
		tmp = (math.log(y) - y) - z
	elif t_2 <= 1e-7:
		tmp = math.log(t) - 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 <= -1e+193)
		tmp = t_2;
	elseif (t_2 <= -5000000000000.0)
		tmp = Float64(Float64(log(y) - y) - z);
	elseif (t_2 <= 1e-7)
		tmp = Float64(log(t) - 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 <= -1e+193)
		tmp = t_2;
	elseif (t_2 <= -5000000000000.0)
		tmp = (log(y) - y) - z;
	elseif (t_2 <= 1e-7)
		tmp = log(t) - 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, -1e+193], t$95$2, If[LessEqual[t$95$2, -5000000000000.0], N[(N[(N[Log[y], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[t$95$2, 1e-7], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(t$95$1 - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -1.00000000000000007e193

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 89.1%

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

   if -1.00000000000000007e193 < (-.f64 (*.f64 x (log.f64 y)) y) < -5e12

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 76.3%

      \[\leadsto \left(\log y - y\right) - z \]

   if -5e12 < (-.f64 (*.f64 x (log.f64 y)) y) < 9.9999999999999995e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 56.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 98.6%

      \[\leadsto \log t - z \]

   if 9.9999999999999995e-8 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 97.5%

      \[\leadsto x \cdot \log y - z \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq -5000000000000:\\ \;\;\;\;\left(\log y - y\right) - z\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= t_1 -1e+193)
     t_1
     (if (<= t_1 -5000000000000.0)
       (- (- (log y) y) z)
       (if (<= t_1 2e+20) (- (log t) z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if (t_1 <= -1e+193) {
		tmp = t_1;
	} else if (t_1 <= -5000000000000.0) {
		tmp = (log(y) - y) - z;
	} else if (t_1 <= 2e+20) {
		tmp = log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * log(y)) - y
    if (t_1 <= (-1d+193)) then
        tmp = t_1
    else if (t_1 <= (-5000000000000.0d0)) then
        tmp = (log(y) - y) - z
    else if (t_1 <= 2d+20) then
        tmp = log(t) - z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * Math.log(y)) - y;
	double tmp;
	if (t_1 <= -1e+193) {
		tmp = t_1;
	} else if (t_1 <= -5000000000000.0) {
		tmp = (Math.log(y) - y) - z;
	} else if (t_1 <= 2e+20) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if t_1 <= -1e+193:
		tmp = t_1
	elif t_1 <= -5000000000000.0:
		tmp = (math.log(y) - y) - z
	elif t_1 <= 2e+20:
		tmp = math.log(t) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (t_1 <= -1e+193)
		tmp = t_1;
	elseif (t_1 <= -5000000000000.0)
		tmp = Float64(Float64(log(y) - y) - z);
	elseif (t_1 <= 2e+20)
		tmp = Float64(log(t) - z);
	else
		tmp = t_1;
	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 <= -1e+193)
		tmp = t_1;
	elseif (t_1 <= -5000000000000.0)
		tmp = (log(y) - y) - z;
	elseif (t_1 <= 2e+20)
		tmp = log(t) - z;
	else
		tmp = t_1;
	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[LessEqual[t$95$1, -1e+193], t$95$1, If[LessEqual[t$95$1, -5000000000000.0], N[(N[(N[Log[y], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[t$95$1, 2e+20], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -1.00000000000000007e193 or 2e20 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 88.2%

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

   if -1.00000000000000007e193 < (-.f64 (*.f64 x (log.f64 y)) y) < -5e12

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 76.3%

      \[\leadsto \left(\log y - y\right) - z \]

   if -5e12 < (-.f64 (*.f64 x (log.f64 y)) y) < 2e20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 58.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 97.2%

      \[\leadsto \log t - z \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ t_2 := t\_1 - z\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 4000:\\ \;\;\;\;t\_1 + \log t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)) (t_2 (- t_1 z)))
   (if (<= t_2 -2e+24) t_2 (if (<= t_2 4000.0) (+ t_1 (log t)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double t_2 = t_1 - z;
	double tmp;
	if (t_2 <= -2e+24) {
		tmp = t_2;
	} else if (t_2 <= 4000.0) {
		tmp = t_1 + log(t);
	} 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 = (x * log(y)) - y
    t_2 = t_1 - z
    if (t_2 <= (-2d+24)) then
        tmp = t_2
    else if (t_2 <= 4000.0d0) then
        tmp = t_1 + log(t)
    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 = (x * Math.log(y)) - y;
	double t_2 = t_1 - z;
	double tmp;
	if (t_2 <= -2e+24) {
		tmp = t_2;
	} else if (t_2 <= 4000.0) {
		tmp = t_1 + Math.log(t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	t_2 = t_1 - z
	tmp = 0
	if t_2 <= -2e+24:
		tmp = t_2
	elif t_2 <= 4000.0:
		tmp = t_1 + math.log(t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	t_2 = Float64(t_1 - z)
	tmp = 0.0
	if (t_2 <= -2e+24)
		tmp = t_2;
	elseif (t_2 <= 4000.0)
		tmp = Float64(t_1 + log(t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * log(y)) - y;
	t_2 = t_1 - z;
	tmp = 0.0;
	if (t_2 <= -2e+24)
		tmp = t_2;
	elseif (t_2 <= 4000.0)
		tmp = t_1 + log(t);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(t$95$1 - z), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+24], t$95$2, If[LessEqual[t$95$2, 4000.0], N[(t$95$1 + N[Log[t], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -2e24 or 4e3 < (-.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. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.9%

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

   if -2e24 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 4e3

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.3%

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

Alternative 5: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := \left(t\_1 - y\right) - z\\ \mathbf{if}\;t\_2 \leq -5000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 4000:\\ \;\;\;\;t\_1 + \log t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- (- t_1 y) z)))
   (if (<= t_2 -5000000000000.0)
     t_2
     (if (<= t_2 4000.0) (+ t_1 (log t)) t_2))))

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 <= -5000000000000.0) {
		tmp = t_2;
	} else if (t_2 <= 4000.0) {
		tmp = t_1 + log(t);
	} 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 = x * log(y)
    t_2 = (t_1 - y) - z
    if (t_2 <= (-5000000000000.0d0)) then
        tmp = t_2
    else if (t_2 <= 4000.0d0) then
        tmp = t_1 + log(t)
    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 = x * Math.log(y);
	double t_2 = (t_1 - y) - z;
	double tmp;
	if (t_2 <= -5000000000000.0) {
		tmp = t_2;
	} else if (t_2 <= 4000.0) {
		tmp = t_1 + Math.log(t);
	} else {
		tmp = t_2;
	}
	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 <= -5000000000000.0:
		tmp = t_2
	elif t_2 <= 4000.0:
		tmp = t_1 + math.log(t)
	else:
		tmp = t_2
	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 <= -5000000000000.0)
		tmp = t_2;
	elseif (t_2 <= 4000.0)
		tmp = Float64(t_1 + log(t));
	else
		tmp = t_2;
	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 <= -5000000000000.0)
		tmp = t_2;
	elseif (t_2 <= 4000.0)
		tmp = t_1 + log(t);
	else
		tmp = t_2;
	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[LessEqual[t$95$2, -5000000000000.0], t$95$2, If[LessEqual[t$95$2, 4000.0], N[(t$95$1 + N[Log[t], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -5e12 or 4e3 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z)

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.6%

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

   if -5e12 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 4e3

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 97.4%

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

Alternative 6: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \log y - y\right) - z\\ \mathbf{if}\;t\_1 \leq -5000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0.002:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- (* x (log y)) y) z)))
   (if (<= t_1 -5000000000000.0) t_1 (if (<= t_1 0.002) (- (log t) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * log(y)) - y) - z;
	double tmp;
	if (t_1 <= -5000000000000.0) {
		tmp = t_1;
	} else if (t_1 <= 0.002) {
		tmp = log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * log(y)) - y) - z
    if (t_1 <= (-5000000000000.0d0)) then
        tmp = t_1
    else if (t_1 <= 0.002d0) then
        tmp = log(t) - z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x * Math.log(y)) - y) - z;
	double tmp;
	if (t_1 <= -5000000000000.0) {
		tmp = t_1;
	} else if (t_1 <= 0.002) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x * math.log(y)) - y) - z
	tmp = 0
	if t_1 <= -5000000000000.0:
		tmp = t_1
	elif t_1 <= 0.002:
		tmp = math.log(t) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * log(y)) - y) - z)
	tmp = 0.0
	if (t_1 <= -5000000000000.0)
		tmp = t_1;
	elseif (t_1 <= 0.002)
		tmp = Float64(log(t) - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x * log(y)) - y) - z;
	tmp = 0.0;
	if (t_1 <= -5000000000000.0)
		tmp = t_1;
	elseif (t_1 <= 0.002)
		tmp = log(t) - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[t$95$1, -5000000000000.0], t$95$1, If[LessEqual[t$95$1, 0.002], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < -5e12 or 2e-3 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z)

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.3%

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

   if -5e12 < (-.f64 (-.f64 (*.f64 x (log.f64 y)) y) z) < 2e-3

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 4.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 96.9%

      \[\leadsto \log t - z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 80.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ t_2 := t\_1 - y\\ \mathbf{if}\;t\_2 \leq -5000000000000:\\ \;\;\;\;\left(\log y - y\right) - z\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+20}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))) (t_2 (- t_1 y)))
   (if (<= t_2 -5000000000000.0)
     (- (- (log y) y) z)
     (if (<= t_2 2e+20) (- (log t) z) 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;
	double tmp;
	if (t_2 <= -5000000000000.0) {
		tmp = (log(y) - y) - z;
	} else if (t_2 <= 2e+20) {
		tmp = log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * log(y)
    t_2 = t_1 - y
    if (t_2 <= (-5000000000000.0d0)) then
        tmp = (log(y) - y) - z
    else if (t_2 <= 2d+20) then
        tmp = log(t) - z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double t_2 = t_1 - y;
	double tmp;
	if (t_2 <= -5000000000000.0) {
		tmp = (Math.log(y) - y) - z;
	} else if (t_2 <= 2e+20) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1;
	}
	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 <= -5000000000000.0:
		tmp = (math.log(y) - y) - z
	elif t_2 <= 2e+20:
		tmp = math.log(t) - z
	else:
		tmp = t_1
	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 <= -5000000000000.0)
		tmp = Float64(Float64(log(y) - y) - z);
	elseif (t_2 <= 2e+20)
		tmp = Float64(log(t) - z);
	else
		tmp = 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;
	tmp = 0.0;
	if (t_2 <= -5000000000000.0)
		tmp = (log(y) - y) - z;
	elseif (t_2 <= 2e+20)
		tmp = log(t) - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - y), $MachinePrecision]}, If[LessEqual[t$95$2, -5000000000000.0], N[(N[(N[Log[y], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[t$95$2, 2e+20], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -5e12

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 67.6%

      \[\leadsto \left(\log y - y\right) - z \]

   if -5e12 < (-.f64 (*.f64 x (log.f64 y)) y) < 2e20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 58.1%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 97.2%

      \[\leadsto \log t - z \]

   if 2e20 < (-.f64 (*.f64 x (log.f64 y)) y)

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 86.3%

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

Alternative 8: 60.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+38}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= x -1.2e+20) t_1 (if (<= x 9.2e+38) (- (log t) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (x <= -1.2e+20) {
		tmp = t_1;
	} else if (x <= 9.2e+38) {
		tmp = log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if (x <= (-1.2d+20)) then
        tmp = t_1
    else if (x <= 9.2d+38) then
        tmp = log(t) - z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (x <= -1.2e+20) {
		tmp = t_1;
	} else if (x <= 9.2e+38) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if x <= -1.2e+20:
		tmp = t_1
	elif x <= 9.2e+38:
		tmp = math.log(t) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (x <= -1.2e+20)
		tmp = t_1;
	elseif (x <= 9.2e+38)
		tmp = Float64(log(t) - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if (x <= -1.2e+20)
		tmp = t_1;
	elseif (x <= 9.2e+38)
		tmp = log(t) - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.2e+20], t$95$1, If[LessEqual[x, 9.2e+38], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e20 or 9.2000000000000005e38 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 68.2%

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

   if -1.2e20 < x < 9.2000000000000005e38

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 78.5%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 67.1%

      \[\leadsto \log t - z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 60.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log t - z\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+20}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (log t) z)))
   (if (<= z -6.2e+97) t_1 (if (<= z 1.15e+20) (- (log t) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(t) - z;
	double tmp;
	if (z <= -6.2e+97) {
		tmp = t_1;
	} else if (z <= 1.15e+20) {
		tmp = log(t) - y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = log(t) - z
    if (z <= (-6.2d+97)) then
        tmp = t_1
    else if (z <= 1.15d+20) then
        tmp = log(t) - y
    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 = Math.log(t) - z;
	double tmp;
	if (z <= -6.2e+97) {
		tmp = t_1;
	} else if (z <= 1.15e+20) {
		tmp = Math.log(t) - y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(t) - z
	tmp = 0
	if z <= -6.2e+97:
		tmp = t_1
	elif z <= 1.15e+20:
		tmp = math.log(t) - y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(t) - z)
	tmp = 0.0
	if (z <= -6.2e+97)
		tmp = t_1;
	elseif (z <= 1.15e+20)
		tmp = Float64(log(t) - y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(t) - z;
	tmp = 0.0;
	if (z <= -6.2e+97)
		tmp = t_1;
	elseif (z <= 1.15e+20)
		tmp = log(t) - y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[z, -6.2e+97], t$95$1, If[LessEqual[z, 1.15e+20], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999962e97 or 1.15e20 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 70.0%

      \[\leadsto \log t - z \]

   if -6.19999999999999962e97 < z < 1.15e20

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 80.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 80.3%

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

   9. Taylor expanded in x around 0

      \[\leadsto x \cdot \log y - y \]

   11. Applied rewrites 52.1%

       \[\leadsto \log t - y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 42.1% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 88.9%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 59.0%

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

9. Taylor expanded in x around 0

   \[\leadsto x \cdot \log y - y \]

11. Applied rewrites 36.2%

    \[\leadsto \log t - y \]
12. Add Preprocessing

Alternative 11: 14.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \log t \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[Log[t], $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 88.9%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 63.9%

   \[\leadsto x \cdot \log y - z \]

9. Taylor expanded in x around inf

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

11. Applied rewrites 12.8%

    \[\leadsto \color{blue}{\log t} \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024313 
(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)))