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

Percentage Accurate: 76.9% → 93.6%

Time: 4.7s

Alternatives: 11

Speedup: 0.8×

Specification

Math

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

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: 76.9% accurate, 1.0× speedup

Math

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

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: 93.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.9%

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

2. Taylor expanded in y around 0

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lower-+.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lower-/.f64 N/A

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

   8. lower--.f64 93.6%

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

4. Applied rewrites 93.6%

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

Alternative 2: 91.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - a}{t} \cdot y + x\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+205}:\\ \;\;\;\;x - \left(\frac{y}{a - t} \cdot \left(z - t\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ (* (/ (- z a) t) y) x)))
  (if (<= t -3.6e+159)
    t_1
    (if (<= t 4.8e+205) (- x (- (* (/ y (- a t)) (- z t)) y)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (((z - a) / t) * y) + x;
	double tmp;
	if (t <= -3.6e+159) {
		tmp = t_1;
	} else if (t <= 4.8e+205) {
		tmp = x - (((y / (a - t)) * (z - t)) - y);
	} 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 = (((z - a) / t) * y) + x
    if (t <= (-3.6d+159)) then
        tmp = t_1
    else if (t <= 4.8d+205) then
        tmp = x - (((y / (a - t)) * (z - t)) - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (((z - a) / t) * y) + x;
	double tmp;
	if (t <= -3.6e+159) {
		tmp = t_1;
	} else if (t <= 4.8e+205) {
		tmp = x - (((y / (a - t)) * (z - t)) - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (((z - a) / t) * y) + x
	tmp = 0
	if t <= -3.6e+159:
		tmp = t_1
	elif t <= 4.8e+205:
		tmp = x - (((y / (a - t)) * (z - t)) - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(Float64(z - a) / t) * y) + x)
	tmp = 0.0
	if (t <= -3.6e+159)
		tmp = t_1;
	elseif (t <= 4.8e+205)
		tmp = Float64(x - Float64(Float64(Float64(y / Float64(a - t)) * Float64(z - t)) - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (((z - a) / t) * y) + x;
	tmp = 0.0;
	if (t <= -3.6e+159)
		tmp = t_1;
	elseif (t <= 4.8e+205)
		tmp = x - (((y / (a - t)) * (z - t)) - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -3.6e+159], t$95$1, If[LessEqual[t, 4.8e+205], N[(x - N[(N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6000000000000004e159 or 4.7999999999999997e205 < t

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 59.3%

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

   7. Applied rewrites 59.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 59.3%

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 59.3%

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

      7. lift-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lift-/.f64 N/A

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

      10. distribute-neg-frac N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 59.3%

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

   9. Applied rewrites 59.3%

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

   if -3.6000000000000004e159 < t < 4.7999999999999997e205

   1. Initial program 76.9%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. associate--l+ N/A

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

      4. add-flip N/A

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

      5. sub-negate-rev N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 79.7%

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/l* N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 87.8%

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

   3. Applied rewrites 87.8%

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

Alternative 3: 90.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - a}{t} \cdot y + x\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 10^{+118}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{z}{a - t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ (* (/ (- z a) t) y) x)))
  (if (<= t -1.65e+140)
    t_1
    (if (<= t 1e+118) (+ x (* y (- 1.0 (/ z (- a t))))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (((z - a) / t) * y) + x;
	double tmp;
	if (t <= -1.65e+140) {
		tmp = t_1;
	} else if (t <= 1e+118) {
		tmp = x + (y * (1.0 - (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 = (((z - a) / t) * y) + x
    if (t <= (-1.65d+140)) then
        tmp = t_1
    else if (t <= 1d+118) then
        tmp = x + (y * (1.0d0 - (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 = (((z - a) / t) * y) + x;
	double tmp;
	if (t <= -1.65e+140) {
		tmp = t_1;
	} else if (t <= 1e+118) {
		tmp = x + (y * (1.0 - (z / (a - t))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (((z - a) / t) * y) + x
	tmp = 0
	if t <= -1.65e+140:
		tmp = t_1
	elif t <= 1e+118:
		tmp = x + (y * (1.0 - (z / (a - t))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(Float64(z - a) / t) * y) + x)
	tmp = 0.0
	if (t <= -1.65e+140)
		tmp = t_1;
	elseif (t <= 1e+118)
		tmp = Float64(x + Float64(y * Float64(1.0 - 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 = (((z - a) / t) * y) + x;
	tmp = 0.0;
	if (t <= -1.65e+140)
		tmp = t_1;
	elseif (t <= 1e+118)
		tmp = x + (y * (1.0 - (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[(z - a), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -1.65e+140], t$95$1, If[LessEqual[t, 1e+118], N[(x + N[(y * N[(1.0 - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6500000000000001e140 or 9.9999999999999997e117 < t

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 59.3%

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

   7. Applied rewrites 59.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 59.3%

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 59.3%

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

      7. lift-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lift-/.f64 N/A

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

      10. distribute-neg-frac N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 59.3%

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

   9. Applied rewrites 59.3%

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

   if -1.6500000000000001e140 < t < 9.9999999999999997e117

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 81.9%

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

Alternative 4: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -0.235:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+47}:\\ \;\;\;\;\left(x + y\right) - \frac{z}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{z - a}{t} \cdot y + x\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= t -0.235)
  (+ x (* y (/ z t)))
  (if (<= t 6e+47)
    (- (+ x y) (* (/ z a) y))
    (+ (* (/ (- z a) t) y) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -0.235) {
		tmp = x + (y * (z / t));
	} else if (t <= 6e+47) {
		tmp = (x + y) - ((z / a) * y);
	} else {
		tmp = (((z - a) / t) * y) + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 <= (-0.235d0)) then
        tmp = x + (y * (z / t))
    else if (t <= 6d+47) then
        tmp = (x + y) - ((z / a) * y)
    else
        tmp = (((z - a) / t) * y) + 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 <= -0.235) {
		tmp = x + (y * (z / t));
	} else if (t <= 6e+47) {
		tmp = (x + y) - ((z / a) * y);
	} else {
		tmp = (((z - a) / t) * y) + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -0.235:
		tmp = x + (y * (z / t))
	elif t <= 6e+47:
		tmp = (x + y) - ((z / a) * y)
	else:
		tmp = (((z - a) / t) * y) + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -0.235)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 6e+47)
		tmp = Float64(Float64(x + y) - Float64(Float64(z / a) * y));
	else
		tmp = Float64(Float64(Float64(Float64(z - a) / t) * y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -0.235)
		tmp = x + (y * (z / t));
	elseif (t <= 6e+47)
		tmp = (x + y) - ((z / a) * y);
	else
		tmp = (((z - a) / t) * y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -0.235], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+47], N[(N[(x + y), $MachinePrecision] - N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.23499999999999999

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 80.5%

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

   10. Applied rewrites 80.5%

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

   11. Taylor expanded in a around 0

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

       1. lower-/.f64 60.7%

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

   13. Applied rewrites 60.7%

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

   if -0.23499999999999999 < t < 6.0000000000000003e47

   1. Initial program 76.9%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 65.0%

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

   4. Applied rewrites 65.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 67.0%

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

   6. Applied rewrites 67.0%

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

   if 6.0000000000000003e47 < t

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 59.3%

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

   7. Applied rewrites 59.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 59.3%

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 59.3%

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

      7. lift-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lift-/.f64 N/A

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

      10. distribute-neg-frac N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 59.3%

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

   9. Applied rewrites 59.3%

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

Alternative 5: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{z - a}{t} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -4.4e-118)
  (+ x y)
  (if (<= a 1.1e+18) (+ (* (/ (- z a) t) y) x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.4e-118) {
		tmp = x + y;
	} else if (a <= 1.1e+18) {
		tmp = (((z - a) / t) * y) + x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 (a <= (-4.4d-118)) then
        tmp = x + y
    else if (a <= 1.1d+18) then
        tmp = (((z - a) / t) * y) + x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.4e-118) {
		tmp = x + y;
	} else if (a <= 1.1e+18) {
		tmp = (((z - a) / t) * y) + x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.4e-118:
		tmp = x + y
	elif a <= 1.1e+18:
		tmp = (((z - a) / t) * y) + x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.4e-118)
		tmp = Float64(x + y);
	elseif (a <= 1.1e+18)
		tmp = Float64(Float64(Float64(Float64(z - a) / t) * y) + x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.4e-118)
		tmp = x + y;
	elseif (a <= 1.1e+18)
		tmp = (((z - a) / t) * y) + x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.4e-118], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.1e+18], N[(N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.3999999999999997e-118 or 1.1e18 < a

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 80.5%

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

   10. Applied rewrites 80.5%

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

   11. Taylor expanded in a around inf

       \[\leadsto x + \color{blue}{y} \]
   12. Step-by-step derivation

       1. lower-+.f64 60.1%

          \[\leadsto x + y \]

   13. Applied rewrites 60.1%

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

   if -4.3999999999999997e-118 < a < 1.1e18

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 59.3%

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

   7. Applied rewrites 59.3%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 59.3%

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 59.3%

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

      7. lift-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lift-/.f64 N/A

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

      10. distribute-neg-frac N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 59.3%

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

   9. Applied rewrites 59.3%

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

Alternative 6: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-118}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;x + \left(z - a\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -3e-118)
  (+ x y)
  (if (<= a 1.1e+18) (+ x (* (- z a) (/ y t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e-118) {
		tmp = x + y;
	} else if (a <= 1.1e+18) {
		tmp = x + ((z - a) * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 (a <= (-3d-118)) then
        tmp = x + y
    else if (a <= 1.1d+18) then
        tmp = x + ((z - a) * (y / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3e-118) {
		tmp = x + y;
	} else if (a <= 1.1e+18) {
		tmp = x + ((z - a) * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3e-118:
		tmp = x + y
	elif a <= 1.1e+18:
		tmp = x + ((z - a) * (y / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3e-118)
		tmp = Float64(x + y);
	elseif (a <= 1.1e+18)
		tmp = Float64(x + Float64(Float64(z - a) * Float64(y / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3e-118)
		tmp = x + y;
	elseif (a <= 1.1e+18)
		tmp = x + ((z - a) * (y / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3e-118], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.1e+18], N[(x + N[(N[(z - a), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.0000000000000002e-118 or 1.1e18 < a

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 80.5%

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

   10. Applied rewrites 80.5%

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

   11. Taylor expanded in a around inf

       \[\leadsto x + \color{blue}{y} \]
   12. Step-by-step derivation

       1. lower-+.f64 60.1%

          \[\leadsto x + y \]

   13. Applied rewrites 60.1%

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

   if -3.0000000000000002e-118 < a < 1.1e18

   1. Initial program 76.9%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 56.6%

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

   4. Applied rewrites 56.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. div-flip N/A

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

      5. lower-unsound-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-unsound-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. distribute-rgt-out-- N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 56.9%

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

   6. Applied rewrites 56.9%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-flip-rev N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 60.3%

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

   8. Applied rewrites 60.3%

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

Alternative 7: 74.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -1.34 \cdot 10^{-117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -1.34e-117)
  (+ x y)
  (if (<= a 1.1e+18) (+ x (* y (/ z t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.34e-117) {
		tmp = x + y;
	} else if (a <= 1.1e+18) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 (a <= (-1.34d-117)) then
        tmp = x + y
    else if (a <= 1.1d+18) then
        tmp = x + (y * (z / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.34e-117) {
		tmp = x + y;
	} else if (a <= 1.1e+18) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.34e-117:
		tmp = x + y
	elif a <= 1.1e+18:
		tmp = x + (y * (z / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.34e-117)
		tmp = Float64(x + y);
	elseif (a <= 1.1e+18)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.34e-117)
		tmp = x + y;
	elseif (a <= 1.1e+18)
		tmp = x + (y * (z / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.34e-117], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.1e+18], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3400000000000001e-117 or 1.1e18 < a

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 80.5%

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

   10. Applied rewrites 80.5%

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

   11. Taylor expanded in a around inf

       \[\leadsto x + \color{blue}{y} \]
   12. Step-by-step derivation

       1. lower-+.f64 60.1%

          \[\leadsto x + y \]

   13. Applied rewrites 60.1%

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

   if -1.3400000000000001e-117 < a < 1.1e18

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 80.5%

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

   10. Applied rewrites 80.5%

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

   11. Taylor expanded in a around 0

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

       1. lower-/.f64 60.7%

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

   13. Applied rewrites 60.7%

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

Alternative 8: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{-117}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -2.15e-117)
  (+ x y)
  (if (<= a 1.1e+18) (+ x (* z (/ y t))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.15e-117) {
		tmp = x + y;
	} else if (a <= 1.1e+18) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 (a <= (-2.15d-117)) then
        tmp = x + y
    else if (a <= 1.1d+18) then
        tmp = x + (z * (y / t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.15e-117) {
		tmp = x + y;
	} else if (a <= 1.1e+18) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.15e-117:
		tmp = x + y
	elif a <= 1.1e+18:
		tmp = x + (z * (y / t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.15e-117)
		tmp = Float64(x + y);
	elseif (a <= 1.1e+18)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.15e-117)
		tmp = x + y;
	elseif (a <= 1.1e+18)
		tmp = x + (z * (y / t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.15e-117], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.1e+18], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.15e-117 or 1.1e18 < a

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 80.5%

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

   10. Applied rewrites 80.5%

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

   11. Taylor expanded in a around inf

       \[\leadsto x + \color{blue}{y} \]
   12. Step-by-step derivation

       1. lower-+.f64 60.1%

          \[\leadsto x + y \]

   13. Applied rewrites 60.1%

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

   if -2.15e-117 < a < 1.1e18

   1. Initial program 76.9%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 56.6%

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

   4. Applied rewrites 56.6%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.3%

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

   7. Applied rewrites 59.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 60.9%

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

   9. Applied rewrites 60.9%

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

Alternative 9: 60.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+134}:\\ \;\;\;\;\frac{z - a}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= y -3.2e+134) (* (/ (- z a) t) y) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.2e+134) {
		tmp = ((z - a) / t) * y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 <= (-3.2d+134)) then
        tmp = ((z - a) / t) * y
    else
        tmp = x + y
    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 <= -3.2e+134) {
		tmp = ((z - a) / t) * y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.2e+134:
		tmp = ((z - a) / t) * y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.2e+134)
		tmp = Float64(Float64(Float64(z - a) / t) * y);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.2e+134)
		tmp = ((z - a) / t) * y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.2e+134], N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2000000000000001e134

   1. Initial program 76.9%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 56.6%

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

   4. Applied rewrites 56.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. div-flip N/A

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

      5. lower-unsound-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-unsound-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. distribute-rgt-out-- N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 56.9%

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

   6. Applied rewrites 56.9%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 21.6%

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

   9. Applied rewrites 21.6%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. div-flip-rev N/A

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

       5. lift-/.f64 N/A

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

       6. *-commutative N/A

          \[\leadsto \frac{1}{\frac{t}{z - a}} \cdot y \]

       7. lower-*.f64 N/A

          \[\leadsto \frac{1}{\frac{t}{z - a}} \cdot y \]

       8. lift-/.f64 N/A

          \[\leadsto \frac{1}{\frac{t}{z - a}} \cdot y \]

       9. div-flip-rev N/A

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

       10. lower-/.f64 24.2%

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

   11. Applied rewrites 24.2%

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

   if -3.2000000000000001e134 < y

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 80.5%

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

   10. Applied rewrites 80.5%

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

   11. Taylor expanded in a around inf

       \[\leadsto x + \color{blue}{y} \]
   12. Step-by-step derivation

       1. lower-+.f64 60.1%

          \[\leadsto x + y \]

   13. Applied rewrites 60.1%

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

Alternative 10: 59.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+134}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= y -3.2e+134) (* (/ y t) (- z a)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.2e+134) {
		tmp = (y / t) * (z - a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 <= (-3.2d+134)) then
        tmp = (y / t) * (z - a)
    else
        tmp = x + y
    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 <= -3.2e+134) {
		tmp = (y / t) * (z - a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.2e+134:
		tmp = (y / t) * (z - a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.2e+134)
		tmp = Float64(Float64(y / t) * Float64(z - a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.2e+134)
		tmp = (y / t) * (z - a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.2e+134], N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2000000000000001e134

   1. Initial program 76.9%

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

   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. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-*.f64 56.6%

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

   4. Applied rewrites 56.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. div-flip N/A

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

      5. lower-unsound-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-unsound-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lift-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. distribute-rgt-out-- N/A

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

      14. lower-*.f64 N/A

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

      15. lower--.f64 56.9%

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

   6. Applied rewrites 56.9%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 21.6%

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

   9. Applied rewrites 21.6%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l/ N/A

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

       4. lift-/.f64 N/A

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

       5. lower-*.f64 23.9%

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

   11. Applied rewrites 23.9%

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

   if -3.2000000000000001e134 < y

   1. Initial program 76.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 93.6%

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

   4. Applied rewrites 93.6%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 81.9%

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

   8. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 80.5%

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

   10. Applied rewrites 80.5%

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

   11. Taylor expanded in a around inf

       \[\leadsto x + \color{blue}{y} \]
   12. Step-by-step derivation

       1. lower-+.f64 60.1%

          \[\leadsto x + y \]

   13. Applied rewrites 60.1%

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

Alternative 11: 59.6% accurate, 7.3× speedup

Math

\[x + y \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 76.9%

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

2. Taylor expanded in y around 0

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

   1. lower-+.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lower-+.f64 N/A

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

   5. lower-/.f64 N/A

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

   6. lower--.f64 N/A

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

   7. lower-/.f64 N/A

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

   8. lower--.f64 93.6%

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

4. Applied rewrites 93.6%

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

5. Taylor expanded in t around 0

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

7. Applied rewrites 81.9%

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

8. Taylor expanded in t around inf

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

   1. lower-*.f64 N/A

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

   2. lower--.f64 N/A

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

   3. lower-/.f64 80.5%

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

10. Applied rewrites 80.5%

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

11. Taylor expanded in a around inf

    \[\leadsto x + \color{blue}{y} \]
12. Step-by-step derivation

    1. lower-+.f64 60.1%

       \[\leadsto x + y \]

13. Applied rewrites 60.1%

    \[\leadsto x + \color{blue}{y} \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2025258 
(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))))