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

Percentage Accurate: 99.9% → 99.9%

Time: 8.0s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[Log[y], $MachinePrecision] * x + N[(N[(N[Log[t], $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. Taylor expanded in z around inf

   \[\leadsto \color{blue}{z \cdot \left(\left(\frac{\log t}{z} + \frac{x \cdot \log y}{z}\right) - \left(1 + \frac{y}{z}\right)\right)} \]
4. Step-by-step derivation

5. Applied rewrites 78.8%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 83.9%

   \[\leadsto \mathsf{fma}\left(\frac{\mathsf{fma}\left(\log y, x, \log t\right)}{z} - 1, \color{blue}{z}, -y\right) \]
9. Step-by-step derivation

10. Applied rewrites 83.8%

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

11. Taylor expanded in x around 0

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

13. Applied rewrites 99.9%

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

Alternative 2: 79.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -500:\\ \;\;\;\;\mathsf{fma}\left(-1, z, -y\right)\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+85}:\\ \;\;\;\;\left(-z\right) + \log t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= t_1 -500.0)
     (fma -1.0 z (- y))
     (if (<= t_1 4e+85) (+ (- z) (log t)) (* (log y) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * log(y)) - y;
	double tmp;
	if (t_1 <= -500.0) {
		tmp = fma(-1.0, z, -y);
	} else if (t_1 <= 4e+85) {
		tmp = -z + log(t);
	} else {
		tmp = log(y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * log(y)) - y)
	tmp = 0.0
	if (t_1 <= -500.0)
		tmp = fma(-1.0, z, Float64(-y));
	elseif (t_1 <= 4e+85)
		tmp = Float64(Float64(-z) + log(t));
	else
		tmp = Float64(log(y) * x);
	end
	return 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, -500.0], N[(-1.0 * z + (-y)), $MachinePrecision], If[LessEqual[t$95$1, 4e+85], N[((-z) + N[Log[t], $MachinePrecision]), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -500

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(\frac{\log t}{z} + \frac{x \cdot \log y}{z}\right) - \left(1 + \frac{y}{z}\right)\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 86.7%

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

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(-1, z, -y\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 72.4%

       \[\leadsto \mathsf{fma}\left(-1, z, -y\right) \]

   if -500 < (-.f64 (*.f64 x (log.f64 y)) y) < 4.0000000000000001e85

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 93.0%

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

   if 4.0000000000000001e85 < (-.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 inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   4. Step-by-step derivation

   5. Applied rewrites 83.1%

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

Alternative 3: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -720 \lor \neg \left(z \leq 11.8\right):\\ \;\;\;\;\left(\frac{\log y \cdot x - y}{z} - 1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -720.0) (not (<= z 11.8)))
   (* (- (/ (- (* (log y) x) y) z) 1.0) z)
   (- (fma (log y) x (log t)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -720.0) || !(z <= 11.8)) {
		tmp = ((((log(y) * x) - y) / z) - 1.0) * z;
	} else {
		tmp = fma(log(y), x, log(t)) - y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -720.0) || !(z <= 11.8))
		tmp = Float64(Float64(Float64(Float64(Float64(log(y) * x) - y) / z) - 1.0) * z);
	else
		tmp = Float64(fma(log(y), x, log(t)) - y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -720.0], N[Not[LessEqual[z, 11.8]], $MachinePrecision]], N[(N[(N[(N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -720 or 11.800000000000001 < 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 z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(\frac{\log t}{z} + \frac{x \cdot \log y}{z}\right) - \left(1 + \frac{y}{z}\right)\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(\frac{x \cdot \log y - y}{z} - 1\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 98.8%

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

   if -720 < z < 11.800000000000001

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 99.3%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -720 \lor \neg \left(z \leq 11.8\right):\\ \;\;\;\;\left(\frac{\log y \cdot x - y}{z} - 1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \log t\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ t_2 := \left(\frac{t\_1 - y}{z} - 1\right) \cdot z\\ \mathbf{if}\;x \leq -3 \cdot 10^{+167}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -20500000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-7}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+211}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)) (t_2 (* (- (/ (- t_1 y) z) 1.0) z)))
   (if (<= x -3e+167)
     t_1
     (if (<= x -20500000.0)
       t_2
       (if (<= x 5.8e-7) (- (- (log t) z) y) (if (<= x 9.5e+211) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double t_2 = (((t_1 - y) / z) - 1.0) * z;
	double tmp;
	if (x <= -3e+167) {
		tmp = t_1;
	} else if (x <= -20500000.0) {
		tmp = t_2;
	} else if (x <= 5.8e-7) {
		tmp = (log(t) - z) - y;
	} else if (x <= 9.5e+211) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = log(y) * x
    t_2 = (((t_1 - y) / z) - 1.0d0) * z
    if (x <= (-3d+167)) then
        tmp = t_1
    else if (x <= (-20500000.0d0)) then
        tmp = t_2
    else if (x <= 5.8d-7) then
        tmp = (log(t) - z) - y
    else if (x <= 9.5d+211) 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 = Math.log(y) * x;
	double t_2 = (((t_1 - y) / z) - 1.0) * z;
	double tmp;
	if (x <= -3e+167) {
		tmp = t_1;
	} else if (x <= -20500000.0) {
		tmp = t_2;
	} else if (x <= 5.8e-7) {
		tmp = (Math.log(t) - z) - y;
	} else if (x <= 9.5e+211) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	t_2 = (((t_1 - y) / z) - 1.0) * z
	tmp = 0
	if x <= -3e+167:
		tmp = t_1
	elif x <= -20500000.0:
		tmp = t_2
	elif x <= 5.8e-7:
		tmp = (math.log(t) - z) - y
	elif x <= 9.5e+211:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	t_2 = Float64(Float64(Float64(Float64(t_1 - y) / z) - 1.0) * z)
	tmp = 0.0
	if (x <= -3e+167)
		tmp = t_1;
	elseif (x <= -20500000.0)
		tmp = t_2;
	elseif (x <= 5.8e-7)
		tmp = Float64(Float64(log(t) - z) - y);
	elseif (x <= 9.5e+211)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	t_2 = (((t_1 - y) / z) - 1.0) * z;
	tmp = 0.0;
	if (x <= -3e+167)
		tmp = t_1;
	elseif (x <= -20500000.0)
		tmp = t_2;
	elseif (x <= 5.8e-7)
		tmp = (log(t) - z) - y;
	elseif (x <= 9.5e+211)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(t$95$1 - y), $MachinePrecision] / z), $MachinePrecision] - 1.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[x, -3e+167], t$95$1, If[LessEqual[x, -20500000.0], t$95$2, If[LessEqual[x, 5.8e-7], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 9.5e+211], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.00000000000000012e167 or 9.4999999999999997e211 < 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 inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   4. Step-by-step derivation

   5. Applied rewrites 85.7%

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

   if -3.00000000000000012e167 < x < -2.05e7 or 5.7999999999999995e-7 < x < 9.4999999999999997e211

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(\frac{\log t}{z} + \frac{x \cdot \log y}{z}\right) - \left(1 + \frac{y}{z}\right)\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 82.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(\frac{x \cdot \log y - y}{z} - 1\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 81.5%

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

   if -2.05e7 < x < 5.7999999999999995e-7

   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

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

   5. Applied rewrites 99.2%

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

Alternative 5: 67.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ t_2 := \mathsf{fma}\left(-1, z, -y\right)\\ \mathbf{if}\;x \leq -4.4 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-285}:\\ \;\;\;\;\left(-y\right) + \log t\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+161}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)) (t_2 (fma -1.0 z (- y))))
   (if (<= x -4.4e+164)
     t_1
     (if (<= x -2.8e-100)
       t_2
       (if (<= x -7.5e-285) (+ (- y) (log t)) (if (<= x 9.5e+161) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double t_2 = fma(-1.0, z, -y);
	double tmp;
	if (x <= -4.4e+164) {
		tmp = t_1;
	} else if (x <= -2.8e-100) {
		tmp = t_2;
	} else if (x <= -7.5e-285) {
		tmp = -y + log(t);
	} else if (x <= 9.5e+161) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	t_2 = fma(-1.0, z, Float64(-y))
	tmp = 0.0
	if (x <= -4.4e+164)
		tmp = t_1;
	elseif (x <= -2.8e-100)
		tmp = t_2;
	elseif (x <= -7.5e-285)
		tmp = Float64(Float64(-y) + log(t));
	elseif (x <= 9.5e+161)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 * z + (-y)), $MachinePrecision]}, If[LessEqual[x, -4.4e+164], t$95$1, If[LessEqual[x, -2.8e-100], t$95$2, If[LessEqual[x, -7.5e-285], N[((-y) + N[Log[t], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.5e+161], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.40000000000000011e164 or 9.50000000000000061e161 < 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 inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   4. Step-by-step derivation

   5. Applied rewrites 85.0%

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

   if -4.40000000000000011e164 < x < -2.79999999999999995e-100 or -7.4999999999999999e-285 < x < 9.50000000000000061e161

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(\frac{\log t}{z} + \frac{x \cdot \log y}{z}\right) - \left(1 + \frac{y}{z}\right)\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 92.1%

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

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(-1, z, -y\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 73.9%

       \[\leadsto \mathsf{fma}\left(-1, z, -y\right) \]

   if -2.79999999999999995e-100 < x < -7.4999999999999999e-285

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 92.4%

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

Alternative 6: 83.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+164} \lor \neg \left(x \leq 9.5 \cdot 10^{+161}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.4e+164) (not (<= x 9.5e+161)))
   (* (log y) x)
   (- (- (log t) z) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.4e+164) || !(x <= 9.5e+161)) {
		tmp = log(y) * x;
	} else {
		tmp = (log(t) - z) - y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.4d+164)) .or. (.not. (x <= 9.5d+161))) then
        tmp = log(y) * x
    else
        tmp = (log(t) - z) - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.4e+164) || !(x <= 9.5e+161)) {
		tmp = Math.log(y) * x;
	} else {
		tmp = (Math.log(t) - z) - y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.4e+164) or not (x <= 9.5e+161):
		tmp = math.log(y) * x
	else:
		tmp = (math.log(t) - z) - y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.4e+164) || !(x <= 9.5e+161))
		tmp = Float64(log(y) * x);
	else
		tmp = Float64(Float64(log(t) - z) - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.4e+164) || ~((x <= 9.5e+161)))
		tmp = log(y) * x;
	else
		tmp = (log(t) - z) - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.4e+164], N[Not[LessEqual[x, 9.5e+161]], $MachinePrecision]], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision], N[(N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision] - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.40000000000000011e164 or 9.50000000000000061e161 < 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 inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   4. Step-by-step derivation

   5. Applied rewrites 85.0%

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

   if -4.40000000000000011e164 < x < 9.50000000000000061e161

   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

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

   5. Applied rewrites 86.7%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+164} \lor \neg \left(x \leq 9.5 \cdot 10^{+161}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(\log t - z\right) - y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+164} \lor \neg \left(x \leq 9.5 \cdot 10^{+161}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, z, -y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.4e+164) (not (<= x 9.5e+161)))
   (* (log y) x)
   (fma -1.0 z (- y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.4e+164) || !(x <= 9.5e+161)) {
		tmp = log(y) * x;
	} else {
		tmp = fma(-1.0, z, -y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.4e+164) || !(x <= 9.5e+161))
		tmp = Float64(log(y) * x);
	else
		tmp = fma(-1.0, z, Float64(-y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.4e+164], N[Not[LessEqual[x, 9.5e+161]], $MachinePrecision]], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision], N[(-1.0 * z + (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.40000000000000011e164 or 9.50000000000000061e161 < 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 inf

      \[\leadsto \color{blue}{x \cdot \log y} \]
   4. Step-by-step derivation

   5. Applied rewrites 85.0%

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

   if -4.40000000000000011e164 < x < 9.50000000000000061e161

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(\frac{\log t}{z} + \frac{x \cdot \log y}{z}\right) - \left(1 + \frac{y}{z}\right)\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 86.2%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 93.2%

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

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(-1, z, -y\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 71.9%

       \[\leadsto \mathsf{fma}\left(-1, z, -y\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+164} \lor \neg \left(x \leq 9.5 \cdot 10^{+161}\right):\\ \;\;\;\;\log y \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, z, -y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 46.3% accurate, 23.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.32 \cdot 10^{+109}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= y 1.32e+109) (- z) (- y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.32e+109) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 1.32d+109) 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 <= 1.32e+109) {
		tmp = -z;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.32e+109:
		tmp = -z
	else:
		tmp = -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.32e+109)
		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 <= 1.32e+109)
		tmp = -z;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.32e+109], (-z), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 1.32000000000000008e109

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 40.5%

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

   if 1.32000000000000008e109 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 66.9%

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

Alternative 9: 57.0% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-1, z, -y\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma -1.0 z (- y)))

C

double code(double x, double y, double z, double t) {
	return fma(-1.0, z, -y);
}

Julia

function code(x, y, z, t)
	return fma(-1.0, z, Float64(-y))
end

Wolfram

code[x_, y_, z_, t_] := N[(-1.0 * z + (-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 z around inf

   \[\leadsto \color{blue}{z \cdot \left(\left(\frac{\log t}{z} + \frac{x \cdot \log y}{z}\right) - \left(1 + \frac{y}{z}\right)\right)} \]
4. Step-by-step derivation

5. Applied rewrites 78.8%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 83.9%

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

9. Taylor expanded in z around inf

   \[\leadsto \mathsf{fma}\left(-1, z, -y\right) \]
10. Step-by-step derivation

11. Applied rewrites 56.7%

    \[\leadsto \mathsf{fma}\left(-1, z, -y\right) \]
12. Add Preprocessing

Alternative 10: 29.3% accurate, 71.7× 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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. Add Preprocessing

3. Taylor expanded in y around inf

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

5. Applied rewrites 28.1%

   \[\leadsto \color{blue}{-y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025019 
(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)))