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

Percentage Accurate: 99.9% → 99.9%

Time: 3.7s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[Log[y], $MachinePrecision] * x + (-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. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. lift-log.f64 N/A

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

   5. mul-1-neg N/A

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

   6. lower-neg.f64 99.9

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

4. Applied rewrites 99.9%

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

Alternative 2: 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]

Derivation

1. Initial program 99.9%

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

Alternative 3: 90.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\log y, x, \log t\right)\\ \mathbf{if}\;z \leq -5200000000:\\ \;\;\;\;t\_1 - z\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+50}:\\ \;\;\;\;t\_1 - y\\ \mathbf{else}:\\ \;\;\;\;\left(1 - \frac{-y}{z}\right) \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (log y) x (log t))))
   (if (<= z -5200000000.0)
     (- t_1 z)
     (if (<= z 1.4e+50) (- t_1 y) (* (- 1.0 (/ (- y) z)) (- z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(log(y), x, log(t));
	double tmp;
	if (z <= -5200000000.0) {
		tmp = t_1 - z;
	} else if (z <= 1.4e+50) {
		tmp = t_1 - y;
	} else {
		tmp = (1.0 - (-y / z)) * -z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(log(y), x, log(t))
	tmp = 0.0
	if (z <= -5200000000.0)
		tmp = Float64(t_1 - z);
	elseif (z <= 1.4e+50)
		tmp = Float64(t_1 - y);
	else
		tmp = Float64(Float64(1.0 - Float64(Float64(-y) / z)) * Float64(-z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * x + N[Log[t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5200000000.0], N[(t$95$1 - z), $MachinePrecision], If[LessEqual[z, 1.4e+50], N[(t$95$1 - y), $MachinePrecision], N[(N[(1.0 - N[((-y) / z), $MachinePrecision]), $MachinePrecision] * (-z)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2e9

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 78.6

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

   4. Applied rewrites 78.6%

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

   if -5.2e9 < z < 1.3999999999999999e50

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 96.9

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

   4. Applied rewrites 96.9%

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

   if 1.3999999999999999e50 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 81.3

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

   7. Applied rewrites 81.3%

      \[\leadsto \left(1 - \frac{-y}{z}\right) \cdot \left(-z\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 89.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x - z\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 25000:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* (log y) x) z)))
   (if (<= x -5.5e+28) t_1 (if (<= x 25000.0) (- (- (log t) y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (log(y) * x) - z;
	double tmp;
	if (x <= -5.5e+28) {
		tmp = t_1;
	} else if (x <= 25000.0) {
		tmp = (log(t) - y) - z;
	} 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) :: tmp
    t_1 = (log(y) * x) - z
    if (x <= (-5.5d+28)) then
        tmp = t_1
    else if (x <= 25000.0d0) then
        tmp = (log(t) - y) - 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 = (Math.log(y) * x) - z;
	double tmp;
	if (x <= -5.5e+28) {
		tmp = t_1;
	} else if (x <= 25000.0) {
		tmp = (Math.log(t) - y) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (math.log(y) * x) - z
	tmp = 0
	if x <= -5.5e+28:
		tmp = t_1
	elif x <= 25000.0:
		tmp = (math.log(t) - y) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(log(y) * x) - z)
	tmp = 0.0
	if (x <= -5.5e+28)
		tmp = t_1;
	elseif (x <= 25000.0)
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (log(y) * x) - z;
	tmp = 0.0;
	if (x <= -5.5e+28)
		tmp = t_1;
	elseif (x <= 25000.0)
		tmp = (log(t) - y) - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[x, -5.5e+28], t$95$1, If[LessEqual[x, 25000.0], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5000000000000003e28 or 25000 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 81.4

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

   4. Applied rewrites 81.4%

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

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \log y - z \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 81.2

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

   7. Applied rewrites 81.2%

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

   if -5.5000000000000003e28 < x < 25000

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-log.f64 98.1

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

   4. Applied rewrites 98.1%

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

Alternative 5: 89.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x - y\\ \mathbf{if}\;x \leq -8.6 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+29}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* (log y) x) y)))
   (if (<= x -8.6e+21) t_1 (if (<= x 3.7e+29) (- (- (log t) y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (log(y) * x) - y;
	double tmp;
	if (x <= -8.6e+21) {
		tmp = t_1;
	} else if (x <= 3.7e+29) {
		tmp = (log(t) - y) - z;
	} 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) :: tmp
    t_1 = (log(y) * x) - y
    if (x <= (-8.6d+21)) then
        tmp = t_1
    else if (x <= 3.7d+29) then
        tmp = (log(t) - y) - 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 = (Math.log(y) * x) - y;
	double tmp;
	if (x <= -8.6e+21) {
		tmp = t_1;
	} else if (x <= 3.7e+29) {
		tmp = (Math.log(t) - y) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (math.log(y) * x) - y
	tmp = 0
	if x <= -8.6e+21:
		tmp = t_1
	elif x <= 3.7e+29:
		tmp = (math.log(t) - y) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(log(y) * x) - y)
	tmp = 0.0
	if (x <= -8.6e+21)
		tmp = t_1;
	elseif (x <= 3.7e+29)
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (log(y) * x) - y;
	tmp = 0.0;
	if (x <= -8.6e+21)
		tmp = t_1;
	elseif (x <= 3.7e+29)
		tmp = (log(t) - y) - z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[x, -8.6e+21], t$95$1, If[LessEqual[x, 3.7e+29], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.6e21 or 3.69999999999999974e29 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 80.0

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

   4. Applied rewrites 80.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto x \cdot \log y - y \]
   6. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 80.0

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

   7. Applied rewrites 80.0%

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

   if -8.6e21 < x < 3.69999999999999974e29

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-log.f64 97.4

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

   4. Applied rewrites 97.4%

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

Alternative 6: 82.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+33}:\\ \;\;\;\;\left(\log t - y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -1.15e+29) t_1 (if (<= x 1.05e+33) (- (- (log t) y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -1.15e+29) {
		tmp = t_1;
	} else if (x <= 1.05e+33) {
		tmp = (log(t) - y) - z;
	} 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) :: tmp
    t_1 = log(y) * x
    if (x <= (-1.15d+29)) then
        tmp = t_1
    else if (x <= 1.05d+33) then
        tmp = (log(t) - y) - 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 = Math.log(y) * x;
	double tmp;
	if (x <= -1.15e+29) {
		tmp = t_1;
	} else if (x <= 1.05e+33) {
		tmp = (Math.log(t) - y) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	tmp = 0
	if x <= -1.15e+29:
		tmp = t_1
	elif x <= 1.05e+33:
		tmp = (math.log(t) - y) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -1.15e+29)
		tmp = t_1;
	elseif (x <= 1.05e+33)
		tmp = Float64(Float64(log(t) - y) - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	tmp = 0.0;
	if (x <= -1.15e+29)
		tmp = t_1;
	elseif (x <= 1.05e+33)
		tmp = (log(t) - y) - z;
	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]}, If[LessEqual[x, -1.15e+29], t$95$1, If[LessEqual[x, 1.05e+33], N[(N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision] - z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1500000000000001e29 or 1.05e33 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 63.0

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

   4. Applied rewrites 63.0%

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

   if -1.1500000000000001e29 < x < 1.05e33

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

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

      1. associate--r+ N/A

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

      2. lower--.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-log.f64 97.1

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

   4. Applied rewrites 97.1%

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

Alternative 7: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y - y\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+222}:\\ \;\;\;\;-y\\ \mathbf{elif}\;t\_1 \leq -10000000000000:\\ \;\;\;\;\left(1 - \frac{-y}{z}\right) \cdot \left(-z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+27}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (log y)) y)))
   (if (<= t_1 -4e+222)
     (- y)
     (if (<= t_1 -10000000000000.0)
       (* (- 1.0 (/ (- y) z)) (- z))
       (if (<= t_1 5e+27) (- (log t) z) (* (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 <= -4e+222) {
		tmp = -y;
	} else if (t_1 <= -10000000000000.0) {
		tmp = (1.0 - (-y / z)) * -z;
	} else if (t_1 <= 5e+27) {
		tmp = log(t) - z;
	} else {
		tmp = log(y) * x;
	}
	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) :: tmp
    t_1 = (x * log(y)) - y
    if (t_1 <= (-4d+222)) then
        tmp = -y
    else if (t_1 <= (-10000000000000.0d0)) then
        tmp = (1.0d0 - (-y / z)) * -z
    else if (t_1 <= 5d+27) then
        tmp = log(t) - z
    else
        tmp = log(y) * x
    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 <= -4e+222) {
		tmp = -y;
	} else if (t_1 <= -10000000000000.0) {
		tmp = (1.0 - (-y / z)) * -z;
	} else if (t_1 <= 5e+27) {
		tmp = Math.log(t) - z;
	} else {
		tmp = Math.log(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * math.log(y)) - y
	tmp = 0
	if t_1 <= -4e+222:
		tmp = -y
	elif t_1 <= -10000000000000.0:
		tmp = (1.0 - (-y / z)) * -z
	elif t_1 <= 5e+27:
		tmp = math.log(t) - z
	else:
		tmp = math.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 <= -4e+222)
		tmp = Float64(-y);
	elseif (t_1 <= -10000000000000.0)
		tmp = Float64(Float64(1.0 - Float64(Float64(-y) / z)) * Float64(-z));
	elseif (t_1 <= 5e+27)
		tmp = Float64(log(t) - z);
	else
		tmp = Float64(log(y) * x);
	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 <= -4e+222)
		tmp = -y;
	elseif (t_1 <= -10000000000000.0)
		tmp = (1.0 - (-y / z)) * -z;
	elseif (t_1 <= 5e+27)
		tmp = log(t) - z;
	else
		tmp = log(y) * x;
	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, -4e+222], (-y), If[LessEqual[t$95$1, -10000000000000.0], N[(N[(1.0 - N[((-y) / z), $MachinePrecision]), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[t$95$1, 5e+27], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (*.f64 x (log.f64 y)) y) < -4.0000000000000002e222

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y\right) \]

      2. lower-neg.f64 60.3

         \[\leadsto -y \]

   4. Applied rewrites 60.3%

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

   if -4.0000000000000002e222 < (-.f64 (*.f64 x (log.f64 y)) y) < -1e13

   1. Initial program 99.9%

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

   2. Taylor expanded in z around -inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. distribute-rgt-neg-in N/A

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

      4. mul-1-neg N/A

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

      5. lower-*.f64 N/A

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

   4. Applied rewrites 80.1%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 63.4

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

   7. Applied rewrites 63.4%

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

   if -1e13 < (-.f64 (*.f64 x (log.f64 y)) y) < 4.99999999999999979e27

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 97.2

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

   4. Applied rewrites 97.2%

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

   5. Taylor expanded in x around 0

      \[\leadsto \log t - z \]
   6. Step-by-step derivation

      1. lift-log.f64 93.4

         \[\leadsto \log t - z \]

   7. Applied rewrites 93.4%

      \[\leadsto \log t - z \]

   if 4.99999999999999979e27 < (-.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. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 77.7

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

   4. Applied rewrites 77.7%

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

Alternative 8: 61.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot x\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;\log t - y\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+16}:\\ \;\;\;\;\log t - z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) x)))
   (if (<= x -5.5e+28)
     t_1
     (if (<= x -1.15e-127)
       (- (log t) y)
       (if (<= x 1.25e+16) (- (log t) z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * x;
	double tmp;
	if (x <= -5.5e+28) {
		tmp = t_1;
	} else if (x <= -1.15e-127) {
		tmp = log(t) - y;
	} else if (x <= 1.25e+16) {
		tmp = log(t) - z;
	} 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) :: tmp
    t_1 = log(y) * x
    if (x <= (-5.5d+28)) then
        tmp = t_1
    else if (x <= (-1.15d-127)) then
        tmp = log(t) - y
    else if (x <= 1.25d+16) 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 = Math.log(y) * x;
	double tmp;
	if (x <= -5.5e+28) {
		tmp = t_1;
	} else if (x <= -1.15e-127) {
		tmp = Math.log(t) - y;
	} else if (x <= 1.25e+16) {
		tmp = Math.log(t) - z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * x
	tmp = 0
	if x <= -5.5e+28:
		tmp = t_1
	elif x <= -1.15e-127:
		tmp = math.log(t) - y
	elif x <= 1.25e+16:
		tmp = math.log(t) - z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * x)
	tmp = 0.0
	if (x <= -5.5e+28)
		tmp = t_1;
	elseif (x <= -1.15e-127)
		tmp = Float64(log(t) - y);
	elseif (x <= 1.25e+16)
		tmp = Float64(log(t) - z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * x;
	tmp = 0.0;
	if (x <= -5.5e+28)
		tmp = t_1;
	elseif (x <= -1.15e-127)
		tmp = log(t) - y;
	elseif (x <= 1.25e+16)
		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[Log[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -5.5e+28], t$95$1, If[LessEqual[x, -1.15e-127], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], If[LessEqual[x, 1.25e+16], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5000000000000003e28 or 1.25e16 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-log.f64 61.9

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

   4. Applied rewrites 61.9%

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

   if -5.5000000000000003e28 < x < -1.15000000000000009e-127

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 63.9

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

   4. Applied rewrites 63.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \log t - y \]
   6. Step-by-step derivation

      1. lift-log.f64 58.4

         \[\leadsto \log t - y \]

   7. Applied rewrites 58.4%

      \[\leadsto \log t - y \]

   if -1.15000000000000009e-127 < x < 1.25e16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 62.8

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

   4. Applied rewrites 62.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto \log t - z \]
   6. Step-by-step derivation

      1. lift-log.f64 61.7

         \[\leadsto \log t - z \]

   7. Applied rewrites 61.7%

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

Alternative 9: 60.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5200000000:\\ \;\;\;\;\log t - z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+67}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5200000000.0) (- (log t) z) (if (<= z 7e+67) (- (log t) y) (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5200000000.0) {
		tmp = log(t) - z;
	} else if (z <= 7e+67) {
		tmp = log(t) - y;
	} else {
		tmp = -z;
	}
	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 (z <= (-5200000000.0d0)) then
        tmp = log(t) - z
    else if (z <= 7d+67) then
        tmp = log(t) - y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5200000000.0) {
		tmp = Math.log(t) - z;
	} else if (z <= 7e+67) {
		tmp = Math.log(t) - y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5200000000.0:
		tmp = math.log(t) - z
	elif z <= 7e+67:
		tmp = math.log(t) - y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5200000000.0)
		tmp = Float64(log(t) - z);
	elseif (z <= 7e+67)
		tmp = Float64(log(t) - y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5200000000.0)
		tmp = log(t) - z;
	elseif (z <= 7e+67)
		tmp = log(t) - y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5200000000.0], N[(N[Log[t], $MachinePrecision] - z), $MachinePrecision], If[LessEqual[z, 7e+67], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2e9

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 78.6

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

   4. Applied rewrites 78.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \log t - z \]
   6. Step-by-step derivation

      1. lift-log.f64 58.3

         \[\leadsto \log t - z \]

   7. Applied rewrites 58.3%

      \[\leadsto \log t - z \]

   if -5.2e9 < z < 7e67

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \log t - y \]
   6. Step-by-step derivation

      1. lift-log.f64 59.1

         \[\leadsto \log t - y \]

   7. Applied rewrites 59.1%

      \[\leadsto \log t - y \]

   if 7e67 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. lower-neg.f64 66.1

         \[\leadsto -z \]

   4. Applied rewrites 66.1%

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

Alternative 10: 60.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5200000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+67}:\\ \;\;\;\;\log t - y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5200000000.0) (- z) (if (<= z 7e+67) (- (log t) y) (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5200000000.0) {
		tmp = -z;
	} else if (z <= 7e+67) {
		tmp = log(t) - y;
	} else {
		tmp = -z;
	}
	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 (z <= (-5200000000.0d0)) then
        tmp = -z
    else if (z <= 7d+67) then
        tmp = log(t) - y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5200000000.0) {
		tmp = -z;
	} else if (z <= 7e+67) {
		tmp = Math.log(t) - y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5200000000.0:
		tmp = -z
	elif z <= 7e+67:
		tmp = math.log(t) - y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5200000000.0)
		tmp = Float64(-z);
	elseif (z <= 7e+67)
		tmp = Float64(log(t) - y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5200000000.0)
		tmp = -z;
	elseif (z <= 7e+67)
		tmp = log(t) - y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5200000000.0], (-z), If[LessEqual[z, 7e+67], N[(N[Log[t], $MachinePrecision] - y), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e9 or 7e67 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. lower-neg.f64 61.7

         \[\leadsto -z \]

   4. Applied rewrites 61.7%

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

   if -5.2e9 < z < 7e67

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-log.f64 N/A

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

      6. lift-log.f64 96.0

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

   4. Applied rewrites 96.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \log t - y \]
   6. Step-by-step derivation

      1. lift-log.f64 59.1

         \[\leadsto \log t - y \]

   7. Applied rewrites 59.1%

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

Alternative 11: 48.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5200000000:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+67}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5200000000.0) (- z) (if (<= z 7e+67) (- y) (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5200000000.0) {
		tmp = -z;
	} else if (z <= 7e+67) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	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 (z <= (-5200000000.0d0)) then
        tmp = -z
    else if (z <= 7d+67) then
        tmp = -y
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5200000000.0) {
		tmp = -z;
	} else if (z <= 7e+67) {
		tmp = -y;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5200000000.0:
		tmp = -z
	elif z <= 7e+67:
		tmp = -y
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5200000000.0)
		tmp = Float64(-z);
	elseif (z <= 7e+67)
		tmp = Float64(-y);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5200000000.0)
		tmp = -z;
	elseif (z <= 7e+67)
		tmp = -y;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5200000000.0], (-z), If[LessEqual[z, 7e+67], (-y), (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e9 or 7e67 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z\right) \]

      2. lower-neg.f64 61.7

         \[\leadsto -z \]

   4. Applied rewrites 61.7%

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

   if -5.2e9 < z < 7e67

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(y\right) \]

      2. lower-neg.f64 37.2

         \[\leadsto -y \]

   4. Applied rewrites 37.2%

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

Alternative 12: 29.5% accurate, 11.9× 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. Taylor expanded in y around inf

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(y\right) \]

   2. lower-neg.f64 29.5

      \[\leadsto -y \]

4. Applied rewrites 29.5%

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

Reproduce

herbie shell --seed 2025112 
(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)))