Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 77.1% → 86.7%

Time: 4.8s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return (x + y) - (((z - t) * y) / (a - 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, a)
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), intent (in) :: a
    code = (x + y) - (((z - t) * y) / (a - t))
end function

Java

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

Python

def code(x, y, z, t, a):
	return (x + y) - (((z - t) * y) / (a - t))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return (x + y) - (((z - t) * y) / (a - 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, a)
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), intent (in) :: a
    code = (x + y) - (((z - t) * y) / (a - t))
end function

Java

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

Python

def code(x, y, z, t, a):
	return (x + y) - (((z - t) * y) / (a - t))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+179}:\\ \;\;\;\;\left(-\frac{a \cdot y - z \cdot y}{t}\right) + x\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-12}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;-\left(-1 \cdot \left(y \cdot \left(\frac{1}{y} - -1 \cdot \frac{-1 \cdot \left(z \cdot \mathsf{fma}\left(-1, \frac{1 + \frac{t}{a - t}}{z}, \frac{1}{a - t}\right)\right)}{x}\right)\right)\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e+179)
   (+ (- (/ (- (* a y) (* z y)) t)) x)
   (if (<= t 6.6e-12)
     (- (+ x y) (* y (/ z (- a t))))
     (-
      (*
       (*
        -1.0
        (*
         y
         (-
          (/ 1.0 y)
          (*
           -1.0
           (/
            (*
             -1.0
             (* z (fma -1.0 (/ (+ 1.0 (/ t (- a t))) z) (/ 1.0 (- a t)))))
            x)))))
       x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+179) {
		tmp = -(((a * y) - (z * y)) / t) + x;
	} else if (t <= 6.6e-12) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = -((-1.0 * (y * ((1.0 / y) - (-1.0 * ((-1.0 * (z * fma(-1.0, ((1.0 + (t / (a - t))) / z), (1.0 / (a - t))))) / x))))) * x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e+179)
		tmp = Float64(Float64(-Float64(Float64(Float64(a * y) - Float64(z * y)) / t)) + x);
	elseif (t <= 6.6e-12)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(-Float64(Float64(-1.0 * Float64(y * Float64(Float64(1.0 / y) - Float64(-1.0 * Float64(Float64(-1.0 * Float64(z * fma(-1.0, Float64(Float64(1.0 + Float64(t / Float64(a - t))) / z), Float64(1.0 / Float64(a - t))))) / x))))) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e+179], N[((-N[(N[(N[(a * y), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[t, 6.6e-12], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(N[(-1.0 * N[(y * N[(N[(1.0 / y), $MachinePrecision] - N[(-1.0 * N[(N[(-1.0 * N[(z * N[(-1.0 * N[(N[(1.0 + N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if t < -6.2e179

   1. Initial program 77.1%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 57.5

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

   4. Applied rewrites 57.5%

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

   if -6.2e179 < t < 6.6000000000000001e-12

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 81.7

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

   4. Applied rewrites 81.7%

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

   if 6.6000000000000001e-12 < t

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 79.7

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

   7. Applied rewrites 79.7%

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

   8. Taylor expanded in z around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 83.3

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

   10. Applied rewrites 83.3%

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

Alternative 2: 85.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+179}:\\ \;\;\;\;\left(-\frac{a \cdot y - z \cdot y}{t}\right) + x\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-12}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;-\left(-1 \cdot \left(y \cdot \left(\frac{1}{y} - -1 \cdot \frac{1 + -1 \cdot \frac{z - t}{a - t}}{x}\right)\right)\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e+179)
   (+ (- (/ (- (* a y) (* z y)) t)) x)
   (if (<= t 6.6e-12)
     (- (+ x y) (* y (/ z (- a t))))
     (-
      (*
       (*
        -1.0
        (*
         y
         (- (/ 1.0 y) (* -1.0 (/ (+ 1.0 (* -1.0 (/ (- z t) (- a t)))) x)))))
       x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+179) {
		tmp = -(((a * y) - (z * y)) / t) + x;
	} else if (t <= 6.6e-12) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = -((-1.0 * (y * ((1.0 / y) - (-1.0 * ((1.0 + (-1.0 * ((z - t) / (a - t)))) / x))))) * 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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.2d+179)) then
        tmp = -(((a * y) - (z * y)) / t) + x
    else if (t <= 6.6d-12) then
        tmp = (x + y) - (y * (z / (a - t)))
    else
        tmp = -(((-1.0d0) * (y * ((1.0d0 / y) - ((-1.0d0) * ((1.0d0 + ((-1.0d0) * ((z - t) / (a - t)))) / x))))) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+179) {
		tmp = -(((a * y) - (z * y)) / t) + x;
	} else if (t <= 6.6e-12) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = -((-1.0 * (y * ((1.0 / y) - (-1.0 * ((1.0 + (-1.0 * ((z - t) / (a - t)))) / x))))) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.2e+179:
		tmp = -(((a * y) - (z * y)) / t) + x
	elif t <= 6.6e-12:
		tmp = (x + y) - (y * (z / (a - t)))
	else:
		tmp = -((-1.0 * (y * ((1.0 / y) - (-1.0 * ((1.0 + (-1.0 * ((z - t) / (a - t)))) / x))))) * x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e+179)
		tmp = Float64(Float64(-Float64(Float64(Float64(a * y) - Float64(z * y)) / t)) + x);
	elseif (t <= 6.6e-12)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(-Float64(Float64(-1.0 * Float64(y * Float64(Float64(1.0 / y) - Float64(-1.0 * Float64(Float64(1.0 + Float64(-1.0 * Float64(Float64(z - t) / Float64(a - t)))) / x))))) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.2e+179)
		tmp = -(((a * y) - (z * y)) / t) + x;
	elseif (t <= 6.6e-12)
		tmp = (x + y) - (y * (z / (a - t)));
	else
		tmp = -((-1.0 * (y * ((1.0 / y) - (-1.0 * ((1.0 + (-1.0 * ((z - t) / (a - t)))) / x))))) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e+179], N[((-N[(N[(N[(a * y), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[t, 6.6e-12], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(N[(-1.0 * N[(y * N[(N[(1.0 / y), $MachinePrecision] - N[(-1.0 * N[(N[(1.0 + N[(-1.0 * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if t < -6.2e179

   1. Initial program 77.1%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 57.5

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

   4. Applied rewrites 57.5%

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

   if -6.2e179 < t < 6.6000000000000001e-12

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 81.7

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

   4. Applied rewrites 81.7%

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

   if 6.6000000000000001e-12 < t

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 79.7

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

   7. Applied rewrites 79.7%

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

Alternative 3: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+179}:\\ \;\;\;\;\left(-\frac{a \cdot y - z \cdot y}{t}\right) + x\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+228}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;-\left(-1 \cdot \left(y \cdot \left(\frac{1}{y} - -1 \cdot \frac{z - a}{t \cdot x}\right)\right)\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e+179)
   (+ (- (/ (- (* a y) (* z y)) t)) x)
   (if (<= t 5.8e+228)
     (- (+ x y) (* y (/ z (- a t))))
     (- (* (* -1.0 (* y (- (/ 1.0 y) (* -1.0 (/ (- z a) (* t x)))))) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+179) {
		tmp = -(((a * y) - (z * y)) / t) + x;
	} else if (t <= 5.8e+228) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = -((-1.0 * (y * ((1.0 / y) - (-1.0 * ((z - a) / (t * x)))))) * 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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.2d+179)) then
        tmp = -(((a * y) - (z * y)) / t) + x
    else if (t <= 5.8d+228) then
        tmp = (x + y) - (y * (z / (a - t)))
    else
        tmp = -(((-1.0d0) * (y * ((1.0d0 / y) - ((-1.0d0) * ((z - a) / (t * x)))))) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+179) {
		tmp = -(((a * y) - (z * y)) / t) + x;
	} else if (t <= 5.8e+228) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = -((-1.0 * (y * ((1.0 / y) - (-1.0 * ((z - a) / (t * x)))))) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.2e+179:
		tmp = -(((a * y) - (z * y)) / t) + x
	elif t <= 5.8e+228:
		tmp = (x + y) - (y * (z / (a - t)))
	else:
		tmp = -((-1.0 * (y * ((1.0 / y) - (-1.0 * ((z - a) / (t * x)))))) * x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e+179)
		tmp = Float64(Float64(-Float64(Float64(Float64(a * y) - Float64(z * y)) / t)) + x);
	elseif (t <= 5.8e+228)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(-Float64(Float64(-1.0 * Float64(y * Float64(Float64(1.0 / y) - Float64(-1.0 * Float64(Float64(z - a) / Float64(t * x)))))) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.2e+179)
		tmp = -(((a * y) - (z * y)) / t) + x;
	elseif (t <= 5.8e+228)
		tmp = (x + y) - (y * (z / (a - t)));
	else
		tmp = -((-1.0 * (y * ((1.0 / y) - (-1.0 * ((z - a) / (t * x)))))) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e+179], N[((-N[(N[(N[(a * y), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[t, 5.8e+228], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(N[(-1.0 * N[(y * N[(N[(1.0 / y), $MachinePrecision] - N[(-1.0 * N[(N[(z - a), $MachinePrecision] / N[(t * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if t < -6.2e179

   1. Initial program 77.1%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 57.5

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

   4. Applied rewrites 57.5%

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

   if -6.2e179 < t < 5.80000000000000003e228

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 81.7

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

   4. Applied rewrites 81.7%

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

   if 5.80000000000000003e228 < t

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 79.7

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

   7. Applied rewrites 79.7%

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

   8. Taylor expanded in t around -inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 56.5

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

   10. Applied rewrites 56.5%

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

Alternative 4: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+179}:\\ \;\;\;\;\left(-\frac{a \cdot y - z \cdot y}{t}\right) + x\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+247}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;-\left(-1 \cdot \left(y \cdot \mathsf{fma}\left(-1, \frac{\frac{a - z}{x}}{t}, \frac{1}{y}\right)\right)\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e+179)
   (+ (- (/ (- (* a y) (* z y)) t)) x)
   (if (<= t 1.1e+247)
     (- (+ x y) (* y (/ z (- a t))))
     (- (* (* -1.0 (* y (fma -1.0 (/ (/ (- a z) x) t) (/ 1.0 y)))) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+179) {
		tmp = -(((a * y) - (z * y)) / t) + x;
	} else if (t <= 1.1e+247) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = -((-1.0 * (y * fma(-1.0, (((a - z) / x) / t), (1.0 / y)))) * x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e+179)
		tmp = Float64(Float64(-Float64(Float64(Float64(a * y) - Float64(z * y)) / t)) + x);
	elseif (t <= 1.1e+247)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = Float64(-Float64(Float64(-1.0 * Float64(y * fma(-1.0, Float64(Float64(Float64(a - z) / x) / t), Float64(1.0 / y)))) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e+179], N[((-N[(N[(N[(a * y), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[t, 1.1e+247], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(N[(-1.0 * N[(y * N[(-1.0 * N[(N[(N[(a - z), $MachinePrecision] / x), $MachinePrecision] / t), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if t < -6.2e179

   1. Initial program 77.1%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 57.5

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

   4. Applied rewrites 57.5%

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

   if -6.2e179 < t < 1.10000000000000006e247

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 81.7

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

   4. Applied rewrites 81.7%

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

   if 1.10000000000000006e247 < t

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in y around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 79.7

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

   7. Applied rewrites 79.7%

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

   8. Taylor expanded in t around -inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. sub-div N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lift-/.f64 53.8

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

   10. Applied rewrites 53.8%

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

Alternative 5: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{a \cdot y - z \cdot y}{t}\right) + x\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{+214}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (* a y) (* z y)) t)) x)))
   (if (<= t -6.2e+179)
     t_1
     (if (<= t 1.36e+214) (- (+ x y) (* y (/ z (- a t)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -(((a * y) - (z * y)) / t) + x;
	double tmp;
	if (t <= -6.2e+179) {
		tmp = t_1;
	} else if (t <= 1.36e+214) {
		tmp = (x + y) - (y * (z / (a - t)));
	} 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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -(((a * y) - (z * y)) / t) + x
    if (t <= (-6.2d+179)) then
        tmp = t_1
    else if (t <= 1.36d+214) then
        tmp = (x + y) - (y * (z / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -(((a * y) - (z * y)) / t) + x;
	double tmp;
	if (t <= -6.2e+179) {
		tmp = t_1;
	} else if (t <= 1.36e+214) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -(((a * y) - (z * y)) / t) + x
	tmp = 0
	if t <= -6.2e+179:
		tmp = t_1
	elif t <= 1.36e+214:
		tmp = (x + y) - (y * (z / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-Float64(Float64(Float64(a * y) - Float64(z * y)) / t)) + x)
	tmp = 0.0
	if (t <= -6.2e+179)
		tmp = t_1;
	elseif (t <= 1.36e+214)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -(((a * y) - (z * y)) / t) + x;
	tmp = 0.0;
	if (t <= -6.2e+179)
		tmp = t_1;
	elseif (t <= 1.36e+214)
		tmp = (x + y) - (y * (z / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-N[(N[(N[(a * y), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[t, -6.2e+179], t$95$1, If[LessEqual[t, 1.36e+214], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2e179 or 1.35999999999999997e214 < t

   1. Initial program 77.1%

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

   2. Taylor expanded in t around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{a \cdot y - y \cdot z}{t}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{a \cdot y - y \cdot z}{t} + \color{blue}{x} \]

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 57.5

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

   4. Applied rewrites 57.5%

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

   if -6.2e179 < t < 1.35999999999999997e214

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 81.7

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

   4. Applied rewrites 81.7%

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

Alternative 6: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := --1 \cdot x\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+247}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* -1.0 x))))
   (if (<= t -6.2e+179)
     t_1
     (if (<= t 5.2e+247) (- (+ x y) (* y (/ z (- a t)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -(-1.0 * x);
	double tmp;
	if (t <= -6.2e+179) {
		tmp = t_1;
	} else if (t <= 5.2e+247) {
		tmp = (x + y) - (y * (z / (a - t)));
	} 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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -((-1.0d0) * x)
    if (t <= (-6.2d+179)) then
        tmp = t_1
    else if (t <= 5.2d+247) then
        tmp = (x + y) - (y * (z / (a - t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -(-1.0 * x);
	double tmp;
	if (t <= -6.2e+179) {
		tmp = t_1;
	} else if (t <= 5.2e+247) {
		tmp = (x + y) - (y * (z / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -(-1.0 * x)
	tmp = 0
	if t <= -6.2e+179:
		tmp = t_1
	elif t <= 5.2e+247:
		tmp = (x + y) - (y * (z / (a - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-Float64(-1.0 * x))
	tmp = 0.0
	if (t <= -6.2e+179)
		tmp = t_1;
	elseif (t <= 5.2e+247)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -(-1.0 * x);
	tmp = 0.0;
	if (t <= -6.2e+179)
		tmp = t_1;
	elseif (t <= 5.2e+247)
		tmp = (x + y) - (y * (z / (a - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = (-N[(-1.0 * x), $MachinePrecision])}, If[LessEqual[t, -6.2e+179], t$95$1, If[LessEqual[t, 5.2e+247], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2e179 or 5.19999999999999981e247 < t

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto --1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.0%

      \[\leadsto --1 \cdot x \]

   if -6.2e179 < t < 5.19999999999999981e247

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 81.7

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

   4. Applied rewrites 81.7%

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

Alternative 7: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := --1 \cdot x\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10500000000000:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+247}:\\ \;\;\;\;\left(x + y\right) - y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* -1.0 x))))
   (if (<= t -7.6e+108)
     t_1
     (if (<= t 10500000000000.0)
       (- (+ x y) (* y (/ z a)))
       (if (<= t 5.2e+247) (- (+ x y) (* y (- 1.0 (/ z t)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -(-1.0 * x);
	double tmp;
	if (t <= -7.6e+108) {
		tmp = t_1;
	} else if (t <= 10500000000000.0) {
		tmp = (x + y) - (y * (z / a));
	} else if (t <= 5.2e+247) {
		tmp = (x + y) - (y * (1.0 - (z / t)));
	} 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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -((-1.0d0) * x)
    if (t <= (-7.6d+108)) then
        tmp = t_1
    else if (t <= 10500000000000.0d0) then
        tmp = (x + y) - (y * (z / a))
    else if (t <= 5.2d+247) then
        tmp = (x + y) - (y * (1.0d0 - (z / t)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -(-1.0 * x);
	double tmp;
	if (t <= -7.6e+108) {
		tmp = t_1;
	} else if (t <= 10500000000000.0) {
		tmp = (x + y) - (y * (z / a));
	} else if (t <= 5.2e+247) {
		tmp = (x + y) - (y * (1.0 - (z / t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -(-1.0 * x)
	tmp = 0
	if t <= -7.6e+108:
		tmp = t_1
	elif t <= 10500000000000.0:
		tmp = (x + y) - (y * (z / a))
	elif t <= 5.2e+247:
		tmp = (x + y) - (y * (1.0 - (z / t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-Float64(-1.0 * x))
	tmp = 0.0
	if (t <= -7.6e+108)
		tmp = t_1;
	elseif (t <= 10500000000000.0)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	elseif (t <= 5.2e+247)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(1.0 - Float64(z / t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -(-1.0 * x);
	tmp = 0.0;
	if (t <= -7.6e+108)
		tmp = t_1;
	elseif (t <= 10500000000000.0)
		tmp = (x + y) - (y * (z / a));
	elseif (t <= 5.2e+247)
		tmp = (x + y) - (y * (1.0 - (z / t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = (-N[(-1.0 * x), $MachinePrecision])}, If[LessEqual[t, -7.6e+108], t$95$1, If[LessEqual[t, 10500000000000.0], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e+247], N[(N[(x + y), $MachinePrecision] - N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.60000000000000015e108 or 5.19999999999999981e247 < t

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto --1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.0%

      \[\leadsto --1 \cdot x \]

   if -7.60000000000000015e108 < t < 1.05e13

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 81.7

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

   4. Applied rewrites 81.7%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 67.2%

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

   if 1.05e13 < t < 5.19999999999999981e247

   1. Initial program 77.1%

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

   2. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 50.0

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

   4. Applied rewrites 50.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 52.0

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

   7. Applied rewrites 52.0%

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

Alternative 8: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := --1 \cdot x\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 115:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+247}:\\ \;\;\;\;\left(x + y\right) - \left(-\frac{y \cdot z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* -1.0 x))))
   (if (<= t -7.6e+108)
     t_1
     (if (<= t 115.0)
       (- (+ x y) (* y (/ z a)))
       (if (<= t 2.55e+247) (- (+ x y) (- (/ (* y z) t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -(-1.0 * x);
	double tmp;
	if (t <= -7.6e+108) {
		tmp = t_1;
	} else if (t <= 115.0) {
		tmp = (x + y) - (y * (z / a));
	} else if (t <= 2.55e+247) {
		tmp = (x + y) - -((y * z) / t);
	} 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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -((-1.0d0) * x)
    if (t <= (-7.6d+108)) then
        tmp = t_1
    else if (t <= 115.0d0) then
        tmp = (x + y) - (y * (z / a))
    else if (t <= 2.55d+247) then
        tmp = (x + y) - -((y * z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -(-1.0 * x);
	double tmp;
	if (t <= -7.6e+108) {
		tmp = t_1;
	} else if (t <= 115.0) {
		tmp = (x + y) - (y * (z / a));
	} else if (t <= 2.55e+247) {
		tmp = (x + y) - -((y * z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -(-1.0 * x)
	tmp = 0
	if t <= -7.6e+108:
		tmp = t_1
	elif t <= 115.0:
		tmp = (x + y) - (y * (z / a))
	elif t <= 2.55e+247:
		tmp = (x + y) - -((y * z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-Float64(-1.0 * x))
	tmp = 0.0
	if (t <= -7.6e+108)
		tmp = t_1;
	elseif (t <= 115.0)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	elseif (t <= 2.55e+247)
		tmp = Float64(Float64(x + y) - Float64(-Float64(Float64(y * z) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -(-1.0 * x);
	tmp = 0.0;
	if (t <= -7.6e+108)
		tmp = t_1;
	elseif (t <= 115.0)
		tmp = (x + y) - (y * (z / a));
	elseif (t <= 2.55e+247)
		tmp = (x + y) - -((y * z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = (-N[(-1.0 * x), $MachinePrecision])}, If[LessEqual[t, -7.6e+108], t$95$1, If[LessEqual[t, 115.0], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e+247], N[(N[(x + y), $MachinePrecision] - (-N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.60000000000000015e108 or 2.55000000000000001e247 < t

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto --1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.0%

      \[\leadsto --1 \cdot x \]

   if -7.60000000000000015e108 < t < 115

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 81.7

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

   4. Applied rewrites 81.7%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 67.2%

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

   if 115 < t < 2.55000000000000001e247

   1. Initial program 77.1%

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

   2. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. lift-*.f64 50.0

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

   4. Applied rewrites 50.0%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 58.0

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

   7. Applied rewrites 58.0%

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

Alternative 9: 72.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := --1 \cdot x\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-6}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* -1.0 x))))
   (if (<= t -7.6e+108) t_1 (if (<= t 1.2e-6) (- (+ x y) (* y (/ z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -(-1.0 * x);
	double tmp;
	if (t <= -7.6e+108) {
		tmp = t_1;
	} else if (t <= 1.2e-6) {
		tmp = (x + y) - (y * (z / a));
	} 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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -((-1.0d0) * x)
    if (t <= (-7.6d+108)) then
        tmp = t_1
    else if (t <= 1.2d-6) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -(-1.0 * x);
	double tmp;
	if (t <= -7.6e+108) {
		tmp = t_1;
	} else if (t <= 1.2e-6) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -(-1.0 * x)
	tmp = 0
	if t <= -7.6e+108:
		tmp = t_1
	elif t <= 1.2e-6:
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-Float64(-1.0 * x))
	tmp = 0.0
	if (t <= -7.6e+108)
		tmp = t_1;
	elseif (t <= 1.2e-6)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -(-1.0 * x);
	tmp = 0.0;
	if (t <= -7.6e+108)
		tmp = t_1;
	elseif (t <= 1.2e-6)
		tmp = (x + y) - (y * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = (-N[(-1.0 * x), $MachinePrecision])}, If[LessEqual[t, -7.6e+108], t$95$1, If[LessEqual[t, 1.2e-6], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.60000000000000015e108 or 1.1999999999999999e-6 < t

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto --1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.0%

      \[\leadsto --1 \cdot x \]

   if -7.60000000000000015e108 < t < 1.1999999999999999e-6

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 81.7

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

   4. Applied rewrites 81.7%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 67.2%

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

Alternative 10: 63.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-58}:\\ \;\;\;\;--1 \cdot x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-112}:\\ \;\;\;\;y - \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;-\left(\left(-\frac{y}{x}\right) - 1\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.7e-58)
   (- (* -1.0 x))
   (if (<= x 1.6e-112)
     (- y (/ (* y z) (- a t)))
     (- (* (- (- (/ y x)) 1.0) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.7e-58) {
		tmp = -(-1.0 * x);
	} else if (x <= 1.6e-112) {
		tmp = y - ((y * z) / (a - t));
	} else {
		tmp = -((-(y / x) - 1.0) * 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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.7d-58)) then
        tmp = -((-1.0d0) * x)
    else if (x <= 1.6d-112) then
        tmp = y - ((y * z) / (a - t))
    else
        tmp = -((-(y / x) - 1.0d0) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.7e-58) {
		tmp = -(-1.0 * x);
	} else if (x <= 1.6e-112) {
		tmp = y - ((y * z) / (a - t));
	} else {
		tmp = -((-(y / x) - 1.0) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.7e-58:
		tmp = -(-1.0 * x)
	elif x <= 1.6e-112:
		tmp = y - ((y * z) / (a - t))
	else:
		tmp = -((-(y / x) - 1.0) * x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.7e-58)
		tmp = Float64(-Float64(-1.0 * x));
	elseif (x <= 1.6e-112)
		tmp = Float64(y - Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(-Float64(Float64(Float64(-Float64(y / x)) - 1.0) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.7e-58)
		tmp = -(-1.0 * x);
	elseif (x <= 1.6e-112)
		tmp = y - ((y * z) / (a - t));
	else
		tmp = -((-(y / x) - 1.0) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.7e-58], (-N[(-1.0 * x), $MachinePrecision]), If[LessEqual[x, 1.6e-112], N[(y - N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(N[((-N[(y / x), $MachinePrecision]) - 1.0), $MachinePrecision] * x), $MachinePrecision])]]

Derivation

1. Split input into 3 regimes

2. if x < -1.69999999999999987e-58

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto --1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.0%

      \[\leadsto --1 \cdot x \]

   if -1.69999999999999987e-58 < x < 1.59999999999999997e-112

   1. Initial program 77.1%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 36.8%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 37.2

         \[\leadsto y - \frac{y \cdot \color{blue}{z}}{a - t} \]

   7. Applied rewrites 37.2%

      \[\leadsto y - \frac{\color{blue}{y \cdot z}}{a - t} \]

   if 1.59999999999999997e-112 < x

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 57.2

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

   7. Applied rewrites 57.2%

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

Alternative 11: 60.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - y \cdot \frac{z}{a}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+53}:\\ \;\;\;\;--1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* y (/ z a)))))
   (if (<= y -6.5e+40) t_1 (if (<= y 2.4e+53) (- (* -1.0 x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (y * (z / a));
	double tmp;
	if (y <= -6.5e+40) {
		tmp = t_1;
	} else if (y <= 2.4e+53) {
		tmp = -(-1.0 * x);
	} 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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (y * (z / a))
    if (y <= (-6.5d+40)) then
        tmp = t_1
    else if (y <= 2.4d+53) then
        tmp = -((-1.0d0) * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (y * (z / a));
	double tmp;
	if (y <= -6.5e+40) {
		tmp = t_1;
	} else if (y <= 2.4e+53) {
		tmp = -(-1.0 * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (y * (z / a))
	tmp = 0
	if y <= -6.5e+40:
		tmp = t_1
	elif y <= 2.4e+53:
		tmp = -(-1.0 * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(y * Float64(z / a)))
	tmp = 0.0
	if (y <= -6.5e+40)
		tmp = t_1;
	elseif (y <= 2.4e+53)
		tmp = Float64(-Float64(-1.0 * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (y * (z / a));
	tmp = 0.0;
	if (y <= -6.5e+40)
		tmp = t_1;
	elseif (y <= 2.4e+53)
		tmp = -(-1.0 * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+40], t$95$1, If[LessEqual[y, 2.4e+53], (-N[(-1.0 * x), $MachinePrecision]), t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000001e40 or 2.4e53 < y

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 81.7

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

   4. Applied rewrites 81.7%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 67.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y} - y \cdot \frac{z}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 31.3%

       \[\leadsto \color{blue}{y} - y \cdot \frac{z}{a} \]

   if -6.5000000000000001e40 < y < 2.4e53

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto --1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.0%

      \[\leadsto --1 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 59.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+126}:\\ \;\;\;\;y - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;-\left(\left(-\frac{y}{x}\right) - 1\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.2e+126) (- y (* y (/ z a))) (- (* (- (- (/ y x)) 1.0) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.2e+126) {
		tmp = y - (y * (z / a));
	} else {
		tmp = -((-(y / x) - 1.0) * 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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5.2d+126)) then
        tmp = y - (y * (z / a))
    else
        tmp = -((-(y / x) - 1.0d0) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.2e+126) {
		tmp = y - (y * (z / a));
	} else {
		tmp = -((-(y / x) - 1.0) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.2e+126:
		tmp = y - (y * (z / a))
	else:
		tmp = -((-(y / x) - 1.0) * x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.2e+126)
		tmp = Float64(y - Float64(y * Float64(z / a)));
	else
		tmp = Float64(-Float64(Float64(Float64(-Float64(y / x)) - 1.0) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.2e+126)
		tmp = y - (y * (z / a));
	else
		tmp = -((-(y / x) - 1.0) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.2e+126], N[(y - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(N[((-N[(y / x), $MachinePrecision]) - 1.0), $MachinePrecision] * x), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999999e126

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 81.7

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

   4. Applied rewrites 81.7%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 67.2%

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

   8. Taylor expanded in x around 0

      \[\leadsto \color{blue}{y} - y \cdot \frac{z}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 31.3%

       \[\leadsto \color{blue}{y} - y \cdot \frac{z}{a} \]

   if -5.1999999999999999e126 < y

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 57.2

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

   7. Applied rewrites 57.2%

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

Alternative 13: 53.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := --1 \cdot x\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-182}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* -1.0 x))))
   (if (<= x -6.2e-218) t_1 (if (<= x 1.1e-182) (/ (* y z) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -(-1.0 * x);
	double tmp;
	if (x <= -6.2e-218) {
		tmp = t_1;
	} else if (x <= 1.1e-182) {
		tmp = (y * z) / t;
	} 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, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -((-1.0d0) * x)
    if (x <= (-6.2d-218)) then
        tmp = t_1
    else if (x <= 1.1d-182) then
        tmp = (y * z) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -(-1.0 * x);
	double tmp;
	if (x <= -6.2e-218) {
		tmp = t_1;
	} else if (x <= 1.1e-182) {
		tmp = (y * z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -(-1.0 * x)
	tmp = 0
	if x <= -6.2e-218:
		tmp = t_1
	elif x <= 1.1e-182:
		tmp = (y * z) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-Float64(-1.0 * x))
	tmp = 0.0
	if (x <= -6.2e-218)
		tmp = t_1;
	elseif (x <= 1.1e-182)
		tmp = Float64(Float64(y * z) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -(-1.0 * x);
	tmp = 0.0;
	if (x <= -6.2e-218)
		tmp = t_1;
	elseif (x <= 1.1e-182)
		tmp = (y * z) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = (-N[(-1.0 * x), $MachinePrecision])}, If[LessEqual[x, -6.2e-218], t$95$1, If[LessEqual[x, 1.1e-182], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.19999999999999994e-218 or 1.1e-182 < x

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto --1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.0%

      \[\leadsto --1 \cdot x \]

   if -6.19999999999999994e-218 < x < 1.1e-182

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lift--.f64 26.7

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

   4. Applied rewrites 26.7%

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

   5. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 11.0

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

   7. Applied rewrites 11.0%

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

   8. Taylor expanded in t around inf

      \[\leadsto \frac{y \cdot z}{\color{blue}{t}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lift-*.f64 18.8

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

   10. Applied rewrites 18.8%

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

Alternative 14: 51.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+121}:\\ \;\;\;\;\frac{\left(-y\right) \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;--1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.5e+121) (/ (* (- y) z) a) (- (* -1.0 x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.5e+121) {
		tmp = (-y * z) / a;
	} else {
		tmp = -(-1.0 * 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, a)
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), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5.5d+121)) then
        tmp = (-y * z) / a
    else
        tmp = -((-1.0d0) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.5e+121) {
		tmp = (-y * z) / a;
	} else {
		tmp = -(-1.0 * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.5e+121:
		tmp = (-y * z) / a
	else:
		tmp = -(-1.0 * x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.5e+121)
		tmp = Float64(Float64(Float64(-y) * z) / a);
	else
		tmp = Float64(-Float64(-1.0 * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.5e+121)
		tmp = (-y * z) / a;
	else
		tmp = -(-1.0 * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.5e+121], N[(N[((-y) * z), $MachinePrecision] / a), $MachinePrecision], (-N[(-1.0 * x), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if y < -5.4999999999999998e121

   1. Initial program 77.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lift--.f64 26.7

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

   4. Applied rewrites 26.7%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 15.1%

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

   if -5.4999999999999998e121 < y

   1. Initial program 77.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto --1 \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 51.0%

      \[\leadsto --1 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 51.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ --1 \cdot x \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return -(-1.0 * 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, a)
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), intent (in) :: a
    code = -((-1.0d0) * x)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -(-1.0 * x);
}

Python

def code(x, y, z, t, a):
	return -(-1.0 * x)

Julia

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

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -(-1.0 * x);
end

Wolfram

code[x_, y_, z_, t_, a_] := (-N[(-1.0 * x), $MachinePrecision])

Derivation

1. Initial program 77.1%

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

2. Taylor expanded in x around -inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 N/A

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

   3. *-commutative N/A

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

   4. lower-*.f64 N/A

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

4. Applied rewrites 79.8%

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

5. Taylor expanded in x around inf

   \[\leadsto --1 \cdot x \]
6. Step-by-step derivation

7. Applied rewrites 51.0%

   \[\leadsto --1 \cdot x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025139 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64
  (- (+ x y) (/ (* (- z t) y) (- a t))))