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

Percentage Accurate: 77.0% → 89.4%

Time: 4.5s

Alternatives: 13

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (x + y) - (((z - t) * y) / (a - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (x + y) - (((z - t) * y) / (a - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(-1, a, z\right)}{t}, x\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+168}:\\ \;\;\;\;\left(y + x\right) - \left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (fma -1.0 a z) t) x)))
   (if (<= t -7.5e+174)
     t_1
     (if (<= t 7e+168) (- (+ y x) (* (- z t) (/ y (- a t)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (fma(-1.0, a, z) / t), x);
	double tmp;
	if (t <= -7.5e+174) {
		tmp = t_1;
	} else if (t <= 7e+168) {
		tmp = (y + x) - ((z - t) * (y / (a - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(fma(-1.0, a, z) / t), x)
	tmp = 0.0
	if (t <= -7.5e+174)
		tmp = t_1;
	elseif (t <= 7e+168)
		tmp = Float64(Float64(y + x) - Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(-1.0 * a + z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -7.5e+174], t$95$1, If[LessEqual[t, 7e+168], N[(N[(y + x), $MachinePrecision] - N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5000000000000004e174 or 7.0000000000000004e168 < t

   1. Initial program 49.4%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. +-commutative N/A

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

      3. lower-+.f64 49.4

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 62.4

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

   3. Applied rewrites 62.4%

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

   4. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 41.3

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

   6. Applied rewrites 41.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 42.3

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

   8. Applied rewrites 42.3%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 92.3%

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

   if -7.5000000000000004e174 < t < 7.0000000000000004e168

   1. Initial program 84.7%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. +-commutative N/A

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

      3. lower-+.f64 84.7

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 88.6

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

   3. Applied rewrites 88.6%

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

Alternative 2: 86.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(-1, a, z\right)}{t}, x\right)\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+144}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (fma -1.0 a z) t) x)))
   (if (<= t -7.4e+174)
     t_1
     (if (<= t 4.5e+144) (- (+ x y) (/ (* (- z t) y) (- a t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (fma(-1.0, a, z) / t), x);
	double tmp;
	if (t <= -7.4e+174) {
		tmp = t_1;
	} else if (t <= 4.5e+144) {
		tmp = (x + y) - (((z - t) * y) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(fma(-1.0, a, z) / t), x)
	tmp = 0.0
	if (t <= -7.4e+174)
		tmp = t_1;
	elseif (t <= 4.5e+144)
		tmp = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(-1.0 * a + z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -7.4e+174], t$95$1, If[LessEqual[t, 4.5e+144], N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.4000000000000004e174 or 4.49999999999999967e144 < t

   1. Initial program 50.9%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. +-commutative N/A

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

      3. lower-+.f64 50.9

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 63.6

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

   3. Applied rewrites 63.6%

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

   4. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 42.2

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

   6. Applied rewrites 42.2%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 43.3

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

   8. Applied rewrites 43.3%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 91.4%

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

   if -7.4000000000000004e174 < t < 4.49999999999999967e144

   1. Initial program 85.2%

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

Alternative 3: 60.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot \frac{z}{a}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+153}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+219}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y) (/ z a))))
   (if (<= z -8.6e+257)
     t_1
     (if (<= z 3e+153) (+ y x) (if (<= z 1.4e+219) (* (/ z t) y) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y * (z / a);
	double tmp;
	if (z <= -8.6e+257) {
		tmp = t_1;
	} else if (z <= 3e+153) {
		tmp = y + x;
	} else if (z <= 1.4e+219) {
		tmp = (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 = -y * (z / a)
    if (z <= (-8.6d+257)) then
        tmp = t_1
    else if (z <= 3d+153) then
        tmp = y + x
    else if (z <= 1.4d+219) then
        tmp = (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 = -y * (z / a);
	double tmp;
	if (z <= -8.6e+257) {
		tmp = t_1;
	} else if (z <= 3e+153) {
		tmp = y + x;
	} else if (z <= 1.4e+219) {
		tmp = (z / t) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y * (z / a)
	tmp = 0
	if z <= -8.6e+257:
		tmp = t_1
	elif z <= 3e+153:
		tmp = y + x
	elif z <= 1.4e+219:
		tmp = (z / t) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) * Float64(z / a))
	tmp = 0.0
	if (z <= -8.6e+257)
		tmp = t_1;
	elseif (z <= 3e+153)
		tmp = Float64(y + x);
	elseif (z <= 1.4e+219)
		tmp = Float64(Float64(z / t) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y * (z / a);
	tmp = 0.0;
	if (z <= -8.6e+257)
		tmp = t_1;
	elseif (z <= 3e+153)
		tmp = y + x;
	elseif (z <= 1.4e+219)
		tmp = (z / t) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.6e+257], t$95$1, If[LessEqual[z, 3e+153], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.4e+219], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5999999999999996e257 or 1.40000000000000008e219 < z

   1. Initial program 77.7%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lift--.f64 50.8

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

   4. Applied rewrites 50.8%

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

   5. Taylor expanded in t around 0

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

   7. Applied rewrites 31.0%

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

      1. lift-/.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lift-neg.f64 N/A

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

      9. lower-/.f64 34.5

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

   9. Applied rewrites 34.5%

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

   if -8.5999999999999996e257 < z < 3.00000000000000019e153

   1. Initial program 76.8%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 65.2

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

   4. Applied rewrites 65.2%

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

   if 3.00000000000000019e153 < z < 1.40000000000000008e219

   1. Initial program 79.3%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lift--.f64 43.9

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

   4. Applied rewrites 43.9%

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

   5. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift-/.f64 33.5

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

   7. Applied rewrites 33.5%

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

Alternative 4: 79.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(-1, a, z\right)}{t}, x\right)\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+22}:\\ \;\;\;\;\left(y + x\right) - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ (fma -1.0 a z) t) x)))
   (if (<= t -7.4e+174)
     t_1
     (if (<= t 7.8e+22) (- (+ y x) (* z (/ y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (fma(-1.0, a, z) / t), x);
	double tmp;
	if (t <= -7.4e+174) {
		tmp = t_1;
	} else if (t <= 7.8e+22) {
		tmp = (y + x) - (z * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(fma(-1.0, a, z) / t), x)
	tmp = 0.0
	if (t <= -7.4e+174)
		tmp = t_1;
	elseif (t <= 7.8e+22)
		tmp = Float64(Float64(y + x) - Float64(z * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(-1.0 * a + z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -7.4e+174], t$95$1, If[LessEqual[t, 7.8e+22], N[(N[(y + x), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.4000000000000004e174 or 7.80000000000000042e22 < t

   1. Initial program 56.9%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. +-commutative N/A

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

      3. lower-+.f64 56.9

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 68.1

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

   3. Applied rewrites 68.1%

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

   4. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 46.0

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

   6. Applied rewrites 46.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 47.5

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

   8. Applied rewrites 47.5%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 87.2%

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

   if -7.4000000000000004e174 < t < 7.80000000000000042e22

   1. Initial program 87.3%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. +-commutative N/A

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

      3. lower-+.f64 87.3

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 90.4

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

   3. Applied rewrites 90.4%

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

   4. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 74.0

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

   6. Applied rewrites 74.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 75.8

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

   8. Applied rewrites 75.8%

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

Alternative 5: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-245}:\\ \;\;\;\;\left(y + x\right) - z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+135}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.5e-245)
   (- (+ y x) (* z (/ y a)))
   (if (<= t 2.3e+135) (- (+ x y) (/ (* z y) a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.5e-245) {
		tmp = (y + x) - (z * (y / a));
	} else if (t <= 2.3e+135) {
		tmp = (x + y) - ((z * y) / a);
	} else {
		tmp = 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 <= (-9.5d-245)) then
        tmp = (y + x) - (z * (y / a))
    else if (t <= 2.3d+135) then
        tmp = (x + y) - ((z * y) / a)
    else
        tmp = 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 <= -9.5e-245) {
		tmp = (y + x) - (z * (y / a));
	} else if (t <= 2.3e+135) {
		tmp = (x + y) - ((z * y) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.5e-245:
		tmp = (y + x) - (z * (y / a))
	elif t <= 2.3e+135:
		tmp = (x + y) - ((z * y) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.5e-245)
		tmp = Float64(Float64(y + x) - Float64(z * Float64(y / a)));
	elseif (t <= 2.3e+135)
		tmp = Float64(Float64(x + y) - Float64(Float64(z * y) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.5e-245)
		tmp = (y + x) - (z * (y / a));
	elseif (t <= 2.3e+135)
		tmp = (x + y) - ((z * y) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.5e-245], N[(N[(y + x), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+135], N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if t < -9.5000000000000002e-245

   1. Initial program 74.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. +-commutative N/A

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

      3. lower-+.f64 74.8

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 81.8

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

   3. Applied rewrites 81.8%

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

   4. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 61.1

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

   6. Applied rewrites 61.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 63.0

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

   8. Applied rewrites 63.0%

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

   if -9.5000000000000002e-245 < t < 2.3000000000000001e135

   1. Initial program 87.5%

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

   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. *-commutative N/A

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

      3. lower-*.f64 75.7

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

   4. Applied rewrites 75.7%

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

   if 2.3000000000000001e135 < t

   1. Initial program 52.6%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 67.4%

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

Alternative 6: 64.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+94}:\\ \;\;\;\;y - z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+151}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+94)
   (- y (* z (/ y (- a t))))
   (if (<= z 1.85e+151) (+ y x) (* (- y) (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+94) {
		tmp = y - (z * (y / (a - t)));
	} else if (z <= 1.85e+151) {
		tmp = y + x;
	} else {
		tmp = -y * (z / (a - t));
	}
	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 (z <= (-8.5d+94)) then
        tmp = y - (z * (y / (a - t)))
    else if (z <= 1.85d+151) then
        tmp = y + x
    else
        tmp = -y * (z / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+94) {
		tmp = y - (z * (y / (a - t)));
	} else if (z <= 1.85e+151) {
		tmp = y + x;
	} else {
		tmp = -y * (z / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+94:
		tmp = y - (z * (y / (a - t)))
	elif z <= 1.85e+151:
		tmp = y + x
	else:
		tmp = -y * (z / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+94)
		tmp = Float64(y - Float64(z * Float64(y / Float64(a - t))));
	elseif (z <= 1.85e+151)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(-y) * Float64(z / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.5e+94)
		tmp = y - (z * (y / (a - t)));
	elseif (z <= 1.85e+151)
		tmp = y + x;
	else
		tmp = -y * (z / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+94], N[(y - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+151], N[(y + x), $MachinePrecision], N[((-y) * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.50000000000000054e94

   1. Initial program 79.4%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower--.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 55.8

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

   4. Applied rewrites 55.8%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 55.1%

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

   if -8.50000000000000054e94 < z < 1.8499999999999999e151

   1. Initial program 76.2%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 68.2

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

   4. Applied rewrites 68.2%

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

   if 1.8499999999999999e151 < z

   1. Initial program 78.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lift--.f64 47.4

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

   4. Applied rewrites 47.4%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-neg.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-lft-neg-out N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lift-neg.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 56.1

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

   6. Applied rewrites 56.1%

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

Alternative 7: 64.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot \frac{z}{a - t}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+151}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y) (/ z (- a t)))))
   (if (<= z -1.45e+172) t_1 (if (<= z 1.85e+151) (+ y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y * (z / (a - t));
	double tmp;
	if (z <= -1.45e+172) {
		tmp = t_1;
	} else if (z <= 1.85e+151) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -y * (z / (a - t))
    if (z <= (-1.45d+172)) then
        tmp = t_1
    else if (z <= 1.85d+151) then
        tmp = y + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -y * (z / (a - t));
	double tmp;
	if (z <= -1.45e+172) {
		tmp = t_1;
	} else if (z <= 1.85e+151) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y * (z / (a - t))
	tmp = 0
	if z <= -1.45e+172:
		tmp = t_1
	elif z <= 1.85e+151:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (z <= -1.45e+172)
		tmp = t_1;
	elseif (z <= 1.85e+151)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y * (z / (a - t));
	tmp = 0.0;
	if (z <= -1.45e+172)
		tmp = t_1;
	elseif (z <= 1.85e+151)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+172], t$95$1, If[LessEqual[z, 1.85e+151], N[(y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e172 or 1.8499999999999999e151 < z

   1. Initial program 79.1%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lift--.f64 48.2

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

   4. Applied rewrites 48.2%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-neg.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-lft-neg-out N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lift-neg.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lift--.f64 56.3

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

   6. Applied rewrites 56.3%

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

   if -1.45e172 < z < 1.8499999999999999e151

   1. Initial program 76.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 67.2

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

   4. Applied rewrites 67.2%

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

Alternative 8: 63.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+172}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+117}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+172)
   (- x (* z (/ y a)))
   (if (<= z 2.8e+117) (+ y x) (- x (/ (* z y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+172) {
		tmp = x - (z * (y / a));
	} else if (z <= 2.8e+117) {
		tmp = y + x;
	} else {
		tmp = x - ((z * y) / a);
	}
	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 (z <= (-7d+172)) then
        tmp = x - (z * (y / a))
    else if (z <= 2.8d+117) then
        tmp = y + x
    else
        tmp = x - ((z * y) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+172) {
		tmp = x - (z * (y / a));
	} else if (z <= 2.8e+117) {
		tmp = y + x;
	} else {
		tmp = x - ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+172:
		tmp = x - (z * (y / a))
	elif z <= 2.8e+117:
		tmp = y + x
	else:
		tmp = x - ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+172)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	elseif (z <= 2.8e+117)
		tmp = Float64(y + x);
	else
		tmp = Float64(x - Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7e+172)
		tmp = x - (z * (y / a));
	elseif (z <= 2.8e+117)
		tmp = y + x;
	else
		tmp = x - ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+172], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+117], N[(y + x), $MachinePrecision], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999955e172

   1. Initial program 80.5%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. +-commutative N/A

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

      3. lower-+.f64 80.5

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 92.6

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

   3. Applied rewrites 92.6%

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

   4. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 53.1

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

   6. Applied rewrites 53.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 60.1

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

   8. Applied rewrites 60.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 54.4%

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

   if -6.99999999999999955e172 < z < 2.79999999999999997e117

   1. Initial program 76.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 67.9

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

   4. Applied rewrites 67.9%

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

   if 2.79999999999999997e117 < z

   1. Initial program 77.9%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. +-commutative N/A

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

      3. lower-+.f64 77.9

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 91.5

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

   3. Applied rewrites 91.5%

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

   4. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 52.7

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

   6. Applied rewrites 52.7%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 49.3%

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

Alternative 9: 64.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+117}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* z (/ y a)))))
   (if (<= z -7e+172) t_1 (if (<= z 2.8e+117) (+ y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * (y / a));
	double tmp;
	if (z <= -7e+172) {
		tmp = t_1;
	} else if (z <= 2.8e+117) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (z * (y / a))
    if (z <= (-7d+172)) then
        tmp = t_1
    else if (z <= 2.8d+117) then
        tmp = y + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * (y / a));
	double tmp;
	if (z <= -7e+172) {
		tmp = t_1;
	} else if (z <= 2.8e+117) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z * (y / a))
	tmp = 0
	if z <= -7e+172:
		tmp = t_1
	elif z <= 2.8e+117:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z * Float64(y / a)))
	tmp = 0.0
	if (z <= -7e+172)
		tmp = t_1;
	elseif (z <= 2.8e+117)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (z * (y / a));
	tmp = 0.0;
	if (z <= -7e+172)
		tmp = t_1;
	elseif (z <= 2.8e+117)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+172], t$95$1, If[LessEqual[z, 2.8e+117], N[(y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.99999999999999955e172 or 2.79999999999999997e117 < z

   1. Initial program 79.0%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. +-commutative N/A

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

      3. lower-+.f64 79.0

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. associate-/l* N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 91.9

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

   3. Applied rewrites 91.9%

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

   4. Taylor expanded in t around 0

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 52.9

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

   6. Applied rewrites 52.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift-/.f64 60.1

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

   8. Applied rewrites 60.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 54.1%

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

   if -6.99999999999999955e172 < z < 2.79999999999999997e117

   1. Initial program 76.3%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 67.9

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

   4. Applied rewrites 67.9%

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

Alternative 10: 60.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3 \cdot 10^{+153}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 3e+153) (+ y x) (* (/ z t) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 3e+153) {
		tmp = y + x;
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 (z <= 3d+153) then
        tmp = y + x
    else
        tmp = (z / t) * 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 (z <= 3e+153) {
		tmp = y + x;
	} else {
		tmp = (z / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 3e+153:
		tmp = y + x
	else:
		tmp = (z / t) * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 3e+153)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(z / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 3e+153)
		tmp = y + x;
	else
		tmp = (z / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 3e+153], N[(y + x), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.00000000000000019e153

   1. Initial program 76.9%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 63.7

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

   4. Applied rewrites 63.7%

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

   if 3.00000000000000019e153 < z

   1. Initial program 78.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lift--.f64 47.3

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

   4. Applied rewrites 47.3%

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

   5. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift-/.f64 38.2

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

   7. Applied rewrites 38.2%

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

Alternative 11: 53.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+185}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.1e+185) y (if (<= y 7.5e+84) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.1e+185) {
		tmp = y;
	} else if (y <= 7.5e+84) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5.1d+185)) then
        tmp = y
    else if (y <= 7.5d+84) then
        tmp = x
    else
        tmp = 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 <= -5.1e+185) {
		tmp = y;
	} else if (y <= 7.5e+84) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.1e+185:
		tmp = y
	elif y <= 7.5e+84:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.1e+185)
		tmp = y;
	elseif (y <= 7.5e+84)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.1e+185)
		tmp = y;
	elseif (y <= 7.5e+84)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.1e+185], y, If[LessEqual[y, 7.5e+84], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -5.09999999999999996e185 or 7.5000000000000001e84 < y

   1. Initial program 56.6%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower--.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 61.2

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

   4. Applied rewrites 61.2%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 30.9%

      \[\leadsto y \]

   if -5.09999999999999996e185 < y < 7.5000000000000001e84

   1. Initial program 85.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 63.1%

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

Alternative 12: 62.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 8.5 \cdot 10^{+182}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 8.5e+182) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 8.5e+182) {
		tmp = y + x;
	} else {
		tmp = 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 <= 8.5d+182) then
        tmp = y + x
    else
        tmp = 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 <= 8.5e+182) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 8.5e+182:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 8.5e+182)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 8.5e+182)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 8.5e+182], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < 8.5e182

   1. Initial program 80.2%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 61.5

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

   4. Applied rewrites 61.5%

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

   if 8.5e182 < t

   1. Initial program 47.8%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 69.4%

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

Alternative 13: 50.7% accurate, 29.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.0%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 50.7%

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

Developer Target 1: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (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 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2025093 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

  (- (+ x y) (/ (* (- z t) y) (- a t))))