System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2

Percentage Accurate: 61.6% → 92.4%

Time: 8.2s

Alternatives: 8

Speedup: 31.2×

• could not determine a ground truth

  1. x = 5.095755069369715e-297
  2. y = 2.9518104726398465e-58
  3. z = 5.3298947196491813e+191
  4. t = -500890.9728149878

Specification

Math

\[\begin{array}{l} \\ x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))

C

double code(double x, double y, double z, double t) {
	return x - (log(((1.0 - y) + (y * exp(z)))) / 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(((1.0d0 - y) + (y * exp(z)))) / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x - (Math.log(((1.0 - y) + (y * Math.exp(z)))) / t);
}

Python

def code(x, y, z, t):
	return x - (math.log(((1.0 - y) + (y * math.exp(z)))) / t)

Julia

function code(x, y, z, t)
	return Float64(x - Float64(log(Float64(Float64(1.0 - y) + Float64(y * exp(z)))) / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - (log(((1.0 - y) + (y * exp(z)))) / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Initial Program: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))

C

double code(double x, double y, double z, double t) {
	return x - (log(((1.0 - y) + (y * exp(z)))) / 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(((1.0d0 - y) + (y * exp(z)))) / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x - (Math.log(((1.0 - y) + (y * Math.exp(z)))) / t);
}

Python

def code(x, y, z, t):
	return x - (math.log(((1.0 - y) + (y * math.exp(z)))) / t)

Julia

function code(x, y, z, t)
	return Float64(x - Float64(log(Float64(Float64(1.0 - y) + Float64(y * exp(z)))) / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - (log(((1.0 - y) + (y * exp(z)))) / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Alternative 1: 92.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{expm1}\left(z\right) \cdot y\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+130}:\\ \;\;\;\;x - \frac{\log t\_1}{t}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+172}:\\ \;\;\;\;x - \frac{t\_1}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(\mathsf{fma}\left(z, y, 1\right)\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (expm1 z) y)))
   (if (<= y -1.95e+130)
     (- x (/ (log t_1) t))
     (if (<= y 1.06e+172) (- x (/ t_1 t)) (- x (/ (log (fma z y 1.0)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = expm1(z) * y;
	double tmp;
	if (y <= -1.95e+130) {
		tmp = x - (log(t_1) / t);
	} else if (y <= 1.06e+172) {
		tmp = x - (t_1 / t);
	} else {
		tmp = x - (log(fma(z, y, 1.0)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(expm1(z) * y)
	tmp = 0.0
	if (y <= -1.95e+130)
		tmp = Float64(x - Float64(log(t_1) / t));
	elseif (y <= 1.06e+172)
		tmp = Float64(x - Float64(t_1 / t));
	else
		tmp = Float64(x - Float64(log(fma(z, y, 1.0)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(Exp[z] - 1), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.95e+130], N[(x - N[(N[Log[t$95$1], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e+172], N[(x - N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[N[(z * y + 1.0), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9500000000000001e130

   1. Initial program 48.5%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 82.1

         \[\leadsto x - \frac{\log \left(\mathsf{expm1}\left(z\right) \cdot y\right)}{t} \]

   4. Applied rewrites 82.1%

      \[\leadsto x - \frac{\log \color{blue}{\left(\mathsf{expm1}\left(z\right) \cdot y\right)}}{t} \]

   if -1.9500000000000001e130 < y < 1.05999999999999996e172

   1. Initial program 67.5%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 93.3

         \[\leadsto x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t} \]

   4. Applied rewrites 93.3%

      \[\leadsto x - \frac{\color{blue}{\mathsf{expm1}\left(z\right) \cdot y}}{t} \]

   if 1.05999999999999996e172 < y

   1. Initial program 5.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 86.7

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

   4. Applied rewrites 86.7%

      \[\leadsto x - \frac{\log \color{blue}{\left(\mathsf{fma}\left(z, y, 1\right)\right)}}{t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 91.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{expm1}\left(z\right) \cdot y\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+130}:\\ \;\;\;\;x - \frac{\log t\_1}{t}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+172}:\\ \;\;\;\;x - \frac{t\_1}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, z \cdot y, 0.5 \cdot y\right), z, y\right), z, 1\right)\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (expm1 z) y)))
   (if (<= y -1.95e+130)
     (- x (/ (log t_1) t))
     (if (<= y 1.06e+172)
       (- x (/ t_1 t))
       (-
        x
        (/
         (log
          (fma (fma (fma 0.16666666666666666 (* z y) (* 0.5 y)) z y) z 1.0))
         t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = expm1(z) * y;
	double tmp;
	if (y <= -1.95e+130) {
		tmp = x - (log(t_1) / t);
	} else if (y <= 1.06e+172) {
		tmp = x - (t_1 / t);
	} else {
		tmp = x - (log(fma(fma(fma(0.16666666666666666, (z * y), (0.5 * y)), z, y), z, 1.0)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(expm1(z) * y)
	tmp = 0.0
	if (y <= -1.95e+130)
		tmp = Float64(x - Float64(log(t_1) / t));
	elseif (y <= 1.06e+172)
		tmp = Float64(x - Float64(t_1 / t));
	else
		tmp = Float64(x - Float64(log(fma(fma(fma(0.16666666666666666, Float64(z * y), Float64(0.5 * y)), z, y), z, 1.0)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(Exp[z] - 1), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.95e+130], N[(x - N[(N[Log[t$95$1], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.06e+172], N[(x - N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[N[(N[(N[(0.16666666666666666 * N[(z * y), $MachinePrecision] + N[(0.5 * y), $MachinePrecision]), $MachinePrecision] * z + y), $MachinePrecision] * z + 1.0), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9500000000000001e130

   1. Initial program 48.5%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 82.1

         \[\leadsto x - \frac{\log \left(\mathsf{expm1}\left(z\right) \cdot y\right)}{t} \]

   4. Applied rewrites 82.1%

      \[\leadsto x - \frac{\log \color{blue}{\left(\mathsf{expm1}\left(z\right) \cdot y\right)}}{t} \]

   if -1.9500000000000001e130 < y < 1.05999999999999996e172

   1. Initial program 67.5%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 93.3

         \[\leadsto x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t} \]

   4. Applied rewrites 93.3%

      \[\leadsto x - \frac{\color{blue}{\mathsf{expm1}\left(z\right) \cdot y}}{t} \]

   if 1.05999999999999996e172 < y

   1. Initial program 5.2%

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

   2. Taylor expanded in z around 0

      \[\leadsto x - \frac{\log \color{blue}{\left(1 + z \cdot \left(y + z \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) + \frac{1}{2} \cdot y\right)\right)\right)}}{t} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x - \frac{\log \left(z \cdot \left(y + z \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) + \frac{1}{2} \cdot y\right)\right) + \color{blue}{1}\right)}{t} \]

      2. *-commutative N/A

         \[\leadsto x - \frac{\log \left(\left(y + z \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) + \frac{1}{2} \cdot y\right)\right) \cdot z + 1\right)}{t} \]

      3. lower-fma.f64 N/A

         \[\leadsto x - \frac{\log \left(\mathsf{fma}\left(y + z \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) + \frac{1}{2} \cdot y\right), \color{blue}{z}, 1\right)\right)}{t} \]

      4. +-commutative N/A

         \[\leadsto x - \frac{\log \left(\mathsf{fma}\left(z \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) + \frac{1}{2} \cdot y\right) + y, z, 1\right)\right)}{t} \]

      5. *-commutative N/A

         \[\leadsto x - \frac{\log \left(\mathsf{fma}\left(\left(\frac{1}{6} \cdot \left(y \cdot z\right) + \frac{1}{2} \cdot y\right) \cdot z + y, z, 1\right)\right)}{t} \]

      6. lower-fma.f64 N/A

         \[\leadsto x - \frac{\log \left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6} \cdot \left(y \cdot z\right) + \frac{1}{2} \cdot y, z, y\right), z, 1\right)\right)}{t} \]

      7. lower-fma.f64 N/A

         \[\leadsto x - \frac{\log \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, y \cdot z, \frac{1}{2} \cdot y\right), z, y\right), z, 1\right)\right)}{t} \]

      8. *-commutative N/A

         \[\leadsto x - \frac{\log \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, z \cdot y, \frac{1}{2} \cdot y\right), z, y\right), z, 1\right)\right)}{t} \]

      9. lower-*.f64 N/A

         \[\leadsto x - \frac{\log \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{1}{6}, z \cdot y, \frac{1}{2} \cdot y\right), z, y\right), z, 1\right)\right)}{t} \]

      10. lower-*.f64 87.0

          \[\leadsto x - \frac{\log \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, z \cdot y, 0.5 \cdot y\right), z, y\right), z, 1\right)\right)}{t} \]

   4. Applied rewrites 87.0%

      \[\leadsto x - \frac{\log \color{blue}{\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(0.16666666666666666, z \cdot y, 0.5 \cdot y\right), z, y\right), z, 1\right)\right)}}{t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 91.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log \left(\left(1 - y\right) + y \cdot e^{z}\right)\\ \mathbf{if}\;t\_1 \leq 10^{-8}:\\ \;\;\;\;x - \left(-\frac{\mathsf{fma}\left(\left(\mathsf{expm1}\left(z\right) \cdot \mathsf{expm1}\left(z\right)\right) \cdot y, 0.5, -\mathsf{expm1}\left(z\right)\right)}{t}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t\_1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (log (+ (- 1.0 y) (* y (exp z))))))
   (if (<= t_1 1e-8)
     (-
      x
      (* (- (/ (fma (* (* (expm1 z) (expm1 z)) y) 0.5 (- (expm1 z))) t)) y))
     (- x (/ t_1 t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(((1.0 - y) + (y * exp(z))));
	double tmp;
	if (t_1 <= 1e-8) {
		tmp = x - (-(fma(((expm1(z) * expm1(z)) * y), 0.5, -expm1(z)) / t) * y);
	} else {
		tmp = x - (t_1 / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = log(Float64(Float64(1.0 - y) + Float64(y * exp(z))))
	tmp = 0.0
	if (t_1 <= 1e-8)
		tmp = Float64(x - Float64(Float64(-Float64(fma(Float64(Float64(expm1(z) * expm1(z)) * y), 0.5, Float64(-expm1(z))) / t)) * y));
	else
		tmp = Float64(x - Float64(t_1 / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$1, 1e-8], N[(x - N[((-N[(N[(N[(N[(N[(Exp[z] - 1), $MachinePrecision] * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] * 0.5 + (-N[(Exp[z] - 1), $MachinePrecision])), $MachinePrecision] / t), $MachinePrecision]) * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < 1e-8

   1. Initial program 56.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto x - \color{blue}{y \cdot \left(\left(\frac{-1}{2} \cdot \frac{y \cdot {\left(e^{z} - 1\right)}^{2}}{t} + \frac{e^{z}}{t}\right) - \frac{1}{t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x - \left(\left(\frac{-1}{2} \cdot \frac{y \cdot {\left(e^{z} - 1\right)}^{2}}{t} + \frac{e^{z}}{t}\right) - \frac{1}{t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto x - \left(\left(\frac{-1}{2} \cdot \frac{y \cdot {\left(e^{z} - 1\right)}^{2}}{t} + \frac{e^{z}}{t}\right) - \frac{1}{t}\right) \cdot \color{blue}{y} \]

   4. Applied rewrites 92.0%

      \[\leadsto x - \color{blue}{\mathsf{fma}\left(-0.5, \frac{\left(\mathsf{expm1}\left(z\right) \cdot \mathsf{expm1}\left(z\right)\right) \cdot y}{t}, \frac{\mathsf{expm1}\left(z\right)}{t}\right) \cdot y} \]

   5. Taylor expanded in t around -inf

      \[\leadsto x - \left(-1 \cdot \frac{-1 \cdot \left(e^{z} - 1\right) + \frac{1}{2} \cdot \left(y \cdot {\left(e^{z} - 1\right)}^{2}\right)}{t}\right) \cdot y \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1 \cdot \left(e^{z} - 1\right) + \frac{1}{2} \cdot \left(y \cdot {\left(e^{z} - 1\right)}^{2}\right)}{t}\right)\right) \cdot y \]

      2. lower-neg.f64 N/A

         \[\leadsto x - \left(-\frac{-1 \cdot \left(e^{z} - 1\right) + \frac{1}{2} \cdot \left(y \cdot {\left(e^{z} - 1\right)}^{2}\right)}{t}\right) \cdot y \]

      3. lower-/.f64 N/A

         \[\leadsto x - \left(-\frac{-1 \cdot \left(e^{z} - 1\right) + \frac{1}{2} \cdot \left(y \cdot {\left(e^{z} - 1\right)}^{2}\right)}{t}\right) \cdot y \]

   7. Applied rewrites 92.0%

      \[\leadsto x - \left(-\frac{\mathsf{fma}\left(\left(\mathsf{expm1}\left(z\right) \cdot \mathsf{expm1}\left(z\right)\right) \cdot y, 0.5, -\mathsf{expm1}\left(z\right)\right)}{t}\right) \cdot y \]

   if 1e-8 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z))))

   1. Initial program 95.6%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 89.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\log \left(\left(1 - y\right) + y \cdot e^{z}\right) \leq 200:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x - \log \left(1 - y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (log (+ (- 1.0 y) (* y (exp z)))) 200.0)
   (- x (/ (* (expm1 z) y) t))
   (/ (- (* t x) (log (- 1.0 y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (log(((1.0 - y) + (y * exp(z)))) <= 200.0) {
		tmp = x - ((expm1(z) * y) / t);
	} else {
		tmp = ((t * x) - log((1.0 - y))) / t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (Math.log(((1.0 - y) + (y * Math.exp(z)))) <= 200.0) {
		tmp = x - ((Math.expm1(z) * y) / t);
	} else {
		tmp = ((t * x) - Math.log((1.0 - y))) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if math.log(((1.0 - y) + (y * math.exp(z)))) <= 200.0:
		tmp = x - ((math.expm1(z) * y) / t)
	else:
		tmp = ((t * x) - math.log((1.0 - y))) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (log(Float64(Float64(1.0 - y) + Float64(y * exp(z)))) <= 200.0)
		tmp = Float64(x - Float64(Float64(expm1(z) * y) / t));
	else
		tmp = Float64(Float64(Float64(t * x) - log(Float64(1.0 - y))) / t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 200.0], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * x), $MachinePrecision] - N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z)))) < 200

   1. Initial program 58.5%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 90.3

         \[\leadsto x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t} \]

   4. Applied rewrites 90.3%

      \[\leadsto x - \frac{\color{blue}{\mathsf{expm1}\left(z\right) \cdot y}}{t} \]

   if 200 < (log.f64 (+.f64 (-.f64 #s(literal 1 binary64) y) (*.f64 y (exp.f64 z))))

   1. Initial program 94.6%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. lower--.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-exp.f64 81.1

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

   4. Applied rewrites 81.1%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 77.1%

      \[\leadsto \frac{t \cdot x - \log \left(1 - y\right)}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 86.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.06 \cdot 10^{+172}:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(\mathsf{fma}\left(z, y, 1\right)\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.06e+172)
   (- x (/ (* (expm1 z) y) t))
   (- x (/ (log (fma z y 1.0)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.06e+172) {
		tmp = x - ((expm1(z) * y) / t);
	} else {
		tmp = x - (log(fma(z, y, 1.0)) / t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.06e+172)
		tmp = Float64(x - Float64(Float64(expm1(z) * y) / t));
	else
		tmp = Float64(x - Float64(log(fma(z, y, 1.0)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.06e+172], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[N[(z * y + 1.0), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.05999999999999996e172

   1. Initial program 64.7%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 86.7

         \[\leadsto x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t} \]

   4. Applied rewrites 86.7%

      \[\leadsto x - \frac{\color{blue}{\mathsf{expm1}\left(z\right) \cdot y}}{t} \]

   if 1.05999999999999996e172 < y

   1. Initial program 5.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 86.7

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

   4. Applied rewrites 86.7%

      \[\leadsto x - \frac{\log \color{blue}{\left(\mathsf{fma}\left(z, y, 1\right)\right)}}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 86.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{+172}:\\ \;\;\;\;x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(z \cdot y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.1e+172) (- x (/ (* (expm1 z) y) t)) (- x (/ (log (* z y)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.1e+172) {
		tmp = x - ((expm1(z) * y) / t);
	} else {
		tmp = x - (log((z * y)) / t);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.1e+172) {
		tmp = x - ((Math.expm1(z) * y) / t);
	} else {
		tmp = x - (Math.log((z * y)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.1e+172:
		tmp = x - ((math.expm1(z) * y) / t)
	else:
		tmp = x - (math.log((z * y)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.1e+172)
		tmp = Float64(x - Float64(Float64(expm1(z) * y) / t));
	else
		tmp = Float64(x - Float64(log(Float64(z * y)) / t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.1e+172], N[(x - N[(N[(N[(Exp[z] - 1), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[N[(z * y), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.1000000000000001e172

   1. Initial program 64.7%

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

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 86.7

         \[\leadsto x - \frac{\mathsf{expm1}\left(z\right) \cdot y}{t} \]

   4. Applied rewrites 86.7%

      \[\leadsto x - \frac{\color{blue}{\mathsf{expm1}\left(z\right) \cdot y}}{t} \]

   if 1.1000000000000001e172 < y

   1. Initial program 5.2%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-expm1.f64 73.6

         \[\leadsto x - \frac{\log \left(\mathsf{expm1}\left(z\right) \cdot y\right)}{t} \]

   4. Applied rewrites 73.6%

      \[\leadsto x - \frac{\log \color{blue}{\left(\mathsf{expm1}\left(z\right) \cdot y\right)}}{t} \]

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 74.5%

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

Alternative 7: 81.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{z} \leq 0:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (exp z) 0.0) x (- x (* (/ z t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (exp(z) <= 0.0) {
		tmp = x;
	} else {
		tmp = x - ((z / t) * 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 (exp(z) <= 0.0d0) then
        tmp = x
    else
        tmp = x - ((z / t) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (Math.exp(z) <= 0.0) {
		tmp = x;
	} else {
		tmp = x - ((z / t) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if math.exp(z) <= 0.0:
		tmp = x
	else:
		tmp = x - ((z / t) * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (exp(z) <= 0.0)
		tmp = x;
	else
		tmp = Float64(x - Float64(Float64(z / t) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (exp(z) <= 0.0)
		tmp = x;
	else
		tmp = x - ((z / t) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[Exp[z], $MachinePrecision], 0.0], x, N[(x - N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (exp.f64 z) < 0.0

   1. Initial program 81.8%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 63.8%

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

   if 0.0 < (exp.f64 z)

   1. Initial program 53.0%

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

   2. Taylor expanded in y around 0

      \[\leadsto x - \color{blue}{y \cdot \left(\left(\frac{-1}{2} \cdot \frac{y \cdot {\left(e^{z} - 1\right)}^{2}}{t} + \frac{e^{z}}{t}\right) - \frac{1}{t}\right)} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x - \left(\left(\frac{-1}{2} \cdot \frac{y \cdot {\left(e^{z} - 1\right)}^{2}}{t} + \frac{e^{z}}{t}\right) - \frac{1}{t}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto x - \left(\left(\frac{-1}{2} \cdot \frac{y \cdot {\left(e^{z} - 1\right)}^{2}}{t} + \frac{e^{z}}{t}\right) - \frac{1}{t}\right) \cdot \color{blue}{y} \]

   4. Applied rewrites 88.2%

      \[\leadsto x - \color{blue}{\mathsf{fma}\left(-0.5, \frac{\left(\mathsf{expm1}\left(z\right) \cdot \mathsf{expm1}\left(z\right)\right) \cdot y}{t}, \frac{\mathsf{expm1}\left(z\right)}{t}\right) \cdot y} \]

   5. Taylor expanded in z around 0

      \[\leadsto x - \frac{z}{t} \cdot y \]
   6. Step-by-step derivation

      1. lower-/.f64 89.6

         \[\leadsto x - \frac{z}{t} \cdot y \]

   7. Applied rewrites 89.6%

      \[\leadsto x - \frac{z}{t} \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 71.3% accurate, 31.2× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 61.6%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 71.3%

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

Reproduce

herbie shell --seed 2025119 
(FPCore (x y z t)
  :name "System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2"
  :precision binary64
  (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))