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

Percentage Accurate: 98.1% → 98.7%

Time: 3.6s

Alternatives: 14

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 (- INFINITY)) (* z (/ y (- a t))) (+ x (* y t_1)))))

C

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

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y / (a - t));
	} else {
		tmp = x + (y * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z * (y / (a - t))
	else:
		tmp = x + (y * t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * Float64(y / Float64(a - t)));
	else
		tmp = Float64(x + Float64(y * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z * (y / (a - t));
	else
		tmp = x + (y * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -inf.0

   1. Initial program 59.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 91.1

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

   4. Applied rewrites 91.1%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 1.8

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

   7. Applied rewrites 1.8%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 11.5

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

   9. Applied rewrites 11.5%

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

   10. Taylor expanded in z around inf

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

   12. Applied rewrites 91.1%

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

   if -inf.0 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.8%

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

Alternative 2: 96.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a - t}\\ t_2 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;t\_2 \leq 1:\\ \;\;\;\;\mathsf{fma}\left(\frac{-t}{a - t}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- a t))))) (t_2 (/ (- z t) (- a t))))
   (if (<= t_2 (- INFINITY))
     (* z (/ y (- a t)))
     (if (<= t_2 -5e+16)
       t_1
       (if (<= t_2 4e-21)
         (fma y (/ (- z t) a) x)
         (if (<= t_2 1.0) (fma (/ (- t) (- a t)) y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (a - t)));
	double t_2 = (z - t) / (a - t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * (y / (a - t));
	} else if (t_2 <= -5e+16) {
		tmp = t_1;
	} else if (t_2 <= 4e-21) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (t_2 <= 1.0) {
		tmp = fma((-t / (a - t)), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(a - t))))
	t_2 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t_2 <= -5e+16)
		tmp = t_1;
	elseif (t_2 <= 4e-21)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (t_2 <= 1.0)
		tmp = fma(Float64(Float64(-t) / Float64(a - t)), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e+16], t$95$1, If[LessEqual[t$95$2, 4e-21], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 1.0], N[(N[((-t) / N[(a - t), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -inf.0

   1. Initial program 59.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 91.1

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

   4. Applied rewrites 91.1%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 1.8

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

   7. Applied rewrites 1.8%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 11.5

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

   9. Applied rewrites 11.5%

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

   10. Taylor expanded in z around inf

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

   12. Applied rewrites 91.1%

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

   if -inf.0 < (/.f64 (-.f64 z t) (-.f64 a t)) < -5e16 or 1 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 95.1%

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

   if -5e16 < (/.f64 (-.f64 z t) (-.f64 a t)) < 3.99999999999999963e-21

   1. Initial program 99.1%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 97.2

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

   4. Applied rewrites 97.2%

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

   if 3.99999999999999963e-21 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 98.5

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

   4. Applied rewrites 98.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 98.5

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

   6. Applied rewrites 98.5%

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

Alternative 3: 96.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{a - t}\\ t_2 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;t\_2 \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z (- a t))))) (t_2 (/ (- z t) (- a t))))
   (if (<= t_2 (- INFINITY))
     (* z (/ y (- a t)))
     (if (<= t_2 -5e+16)
       t_1
       (if (<= t_2 4e-19)
         (fma y (/ (- z t) a) x)
         (if (<= t_2 1.0) (+ x y) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / (a - t)));
	double t_2 = (z - t) / (a - t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * (y / (a - t));
	} else if (t_2 <= -5e+16) {
		tmp = t_1;
	} else if (t_2 <= 4e-19) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (t_2 <= 1.0) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / Float64(a - t))))
	t_2 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(y / Float64(a - t)));
	elseif (t_2 <= -5e+16)
		tmp = t_1;
	elseif (t_2 <= 4e-19)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (t_2 <= 1.0)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -5e+16], t$95$1, If[LessEqual[t$95$2, 4e-19], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 1.0], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -inf.0

   1. Initial program 59.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 91.1

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

   4. Applied rewrites 91.1%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 1.8

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

   7. Applied rewrites 1.8%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 11.5

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

   9. Applied rewrites 11.5%

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

   10. Taylor expanded in z around inf

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

   12. Applied rewrites 91.1%

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

   if -inf.0 < (/.f64 (-.f64 z t) (-.f64 a t)) < -5e16 or 1 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 95.1%

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

   if -5e16 < (/.f64 (-.f64 z t) (-.f64 a t)) < 3.9999999999999999e-19

   1. Initial program 99.1%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 97.2

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

   4. Applied rewrites 97.2%

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

   if 3.9999999999999999e-19 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 97.0%

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

Alternative 4: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{y}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+197}:\\ \;\;\;\;z \cdot t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (/ y (- a t))))
   (if (<= t_1 -5e+197)
     (* z t_2)
     (if (<= t_1 4e-19)
       (fma y (/ (- z t) a) x)
       (if (<= t_1 2.5e+15) (+ x y) (* (- z t) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = y / (a - t);
	double tmp;
	if (t_1 <= -5e+197) {
		tmp = z * t_2;
	} else if (t_1 <= 4e-19) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (t_1 <= 2.5e+15) {
		tmp = x + y;
	} else {
		tmp = (z - t) * t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(y / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -5e+197)
		tmp = Float64(z * t_2);
	elseif (t_1 <= 4e-19)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (t_1 <= 2.5e+15)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(z - t) * t_2);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+197], N[(z * t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 4e-19], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2.5e+15], N[(x + y), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000009e197

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 1.8

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

   7. Applied rewrites 1.8%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 6.9

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

   9. Applied rewrites 6.9%

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

   10. Taylor expanded in z around inf

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

   12. Applied rewrites 85.0%

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

   if -5.00000000000000009e197 < (/.f64 (-.f64 z t) (-.f64 a t)) < 3.9999999999999999e-19

   1. Initial program 99.2%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 89.7

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

   4. Applied rewrites 89.7%

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

   if 3.9999999999999999e-19 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.5e15

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 94.8%

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

   if 2.5e15 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 95.0%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 62.5

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

   4. Applied rewrites 62.5%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 65.9

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

   6. Applied rewrites 65.9%

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

Alternative 5: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-19}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* z (/ y (- a t)))))
   (if (<= t_1 -5e+197)
     t_2
     (if (<= t_1 4e-19)
       (fma y (/ (- z t) a) x)
       (if (<= t_1 2.5e+15) (+ x y) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = z * (y / (a - t));
	double tmp;
	if (t_1 <= -5e+197) {
		tmp = t_2;
	} else if (t_1 <= 4e-19) {
		tmp = fma(y, ((z - t) / a), x);
	} else if (t_1 <= 2.5e+15) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(z * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -5e+197)
		tmp = t_2;
	elseif (t_1 <= 4e-19)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	elseif (t_1 <= 2.5e+15)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+197], t$95$2, If[LessEqual[t$95$1, 4e-19], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2.5e+15], N[(x + y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000009e197 or 2.5e15 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 92.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 68.1

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

   4. Applied rewrites 68.1%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 5.0

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

   7. Applied rewrites 5.0%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 7.6

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

   9. Applied rewrites 7.6%

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

   10. Taylor expanded in z around inf

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

   12. Applied rewrites 70.6%

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

   if -5.00000000000000009e197 < (/.f64 (-.f64 z t) (-.f64 a t)) < 3.9999999999999999e-19

   1. Initial program 99.2%

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

   2. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift--.f64 89.7

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

   4. Applied rewrites 89.7%

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

   if 3.9999999999999999e-19 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.5e15

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 94.8%

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

Alternative 6: 83.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* z (/ y (- a t)))))
   (if (<= t_1 -5e+197)
     t_2
     (if (<= t_1 4e-21) (fma y (/ z a) x) (if (<= t_1 2.5e+15) (+ x y) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = z * (y / (a - t));
	double tmp;
	if (t_1 <= -5e+197) {
		tmp = t_2;
	} else if (t_1 <= 4e-21) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 2.5e+15) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(z * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -5e+197)
		tmp = t_2;
	elseif (t_1 <= 4e-21)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 2.5e+15)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+197], t$95$2, If[LessEqual[t$95$1, 4e-21], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2.5e+15], N[(x + y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000009e197 or 2.5e15 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 92.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 68.1

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

   4. Applied rewrites 68.1%

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

   5. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 5.0

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

   7. Applied rewrites 5.0%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 7.6

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

   9. Applied rewrites 7.6%

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

   10. Taylor expanded in z around inf

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

   12. Applied rewrites 70.6%

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

   if -5.00000000000000009e197 < (/.f64 (-.f64 z t) (-.f64 a t)) < 3.99999999999999963e-21

   1. Initial program 99.2%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 79.8

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

   4. Applied rewrites 79.8%

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

   if 3.99999999999999963e-21 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.5e15

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 94.7%

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

Alternative 7: 82.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{-21}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2.5 \cdot 10^{+15}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* y (/ z (- a t)))))
   (if (<= t_1 -5e+197)
     t_2
     (if (<= t_1 4e-21) (fma y (/ z a) x) (if (<= t_1 2.5e+15) (+ x y) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = y * (z / (a - t));
	double tmp;
	if (t_1 <= -5e+197) {
		tmp = t_2;
	} else if (t_1 <= 4e-21) {
		tmp = fma(y, (z / a), x);
	} else if (t_1 <= 2.5e+15) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -5e+197)
		tmp = t_2;
	elseif (t_1 <= 4e-21)
		tmp = fma(y, Float64(z / a), x);
	elseif (t_1 <= 2.5e+15)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+197], t$95$2, If[LessEqual[t$95$1, 4e-21], N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2.5e+15], N[(x + y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000009e197 or 2.5e15 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 92.5%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 67.6

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

   4. Applied rewrites 67.6%

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

   if -5.00000000000000009e197 < (/.f64 (-.f64 z t) (-.f64 a t)) < 3.99999999999999963e-21

   1. Initial program 99.2%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 79.8

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

   4. Applied rewrites 79.8%

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

   if 3.99999999999999963e-21 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.5e15

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 94.7%

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

Alternative 8: 80.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{z}{a}, x\right)\\ t_2 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+224}:\\ \;\;\;\;\frac{\left(-y\right) \cdot z}{t}\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+21}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ z a) x)) (t_2 (/ (- z t) (- a t))))
   (if (<= t_2 -2e+224)
     (/ (* (- y) z) t)
     (if (<= t_2 4e-21) t_1 (if (<= t_2 5e+21) (+ x y) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (z / a), x);
	double t_2 = (z - t) / (a - t);
	double tmp;
	if (t_2 <= -2e+224) {
		tmp = (-y * z) / t;
	} else if (t_2 <= 4e-21) {
		tmp = t_1;
	} else if (t_2 <= 5e+21) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(z / a), x)
	t_2 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_2 <= -2e+224)
		tmp = Float64(Float64(Float64(-y) * z) / t);
	elseif (t_2 <= 4e-21)
		tmp = t_1;
	elseif (t_2 <= 5e+21)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+224], N[(N[((-y) * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$2, 4e-21], t$95$1, If[LessEqual[t$95$2, 5e+21], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -1.99999999999999994e224

   1. Initial program 81.9%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 73.2

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

   4. Applied rewrites 73.2%

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

   5. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 51.0

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

   7. Applied rewrites 51.0%

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

   if -1.99999999999999994e224 < (/.f64 (-.f64 z t) (-.f64 a t)) < 3.99999999999999963e-21 or 5e21 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 74.8

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

   4. Applied rewrites 74.8%

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

   if 3.99999999999999963e-21 < (/.f64 (-.f64 z t) (-.f64 a t)) < 5e21

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 94.1%

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

Alternative 9: 70.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{\left(-y\right) \cdot z}{t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 10^{+143}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (/ (* (- y) z) t)))
   (if (<= t_1 -5e+197)
     t_2
     (if (<= t_1 2e-91) x (if (<= t_1 1e+143) (+ x y) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (-y * z) / t;
	double tmp;
	if (t_1 <= -5e+197) {
		tmp = t_2;
	} else if (t_1 <= 2e-91) {
		tmp = x;
	} else if (t_1 <= 1e+143) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	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 = (z - t) / (a - t)
    t_2 = (-y * z) / t
    if (t_1 <= (-5d+197)) then
        tmp = t_2
    else if (t_1 <= 2d-91) then
        tmp = x
    else if (t_1 <= 1d+143) then
        tmp = x + y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (-y * z) / t;
	double tmp;
	if (t_1 <= -5e+197) {
		tmp = t_2;
	} else if (t_1 <= 2e-91) {
		tmp = x;
	} else if (t_1 <= 1e+143) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	t_2 = (-y * z) / t
	tmp = 0
	if t_1 <= -5e+197:
		tmp = t_2
	elif t_1 <= 2e-91:
		tmp = x
	elif t_1 <= 1e+143:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(Float64(-y) * z) / t)
	tmp = 0.0
	if (t_1 <= -5e+197)
		tmp = t_2;
	elseif (t_1 <= 2e-91)
		tmp = x;
	elseif (t_1 <= 1e+143)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	t_2 = (-y * z) / t;
	tmp = 0.0;
	if (t_1 <= -5e+197)
		tmp = t_2;
	elseif (t_1 <= 2e-91)
		tmp = x;
	elseif (t_1 <= 1e+143)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-y) * z), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+197], t$95$2, If[LessEqual[t$95$1, 2e-91], x, If[LessEqual[t$95$1, 1e+143], N[(x + y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.00000000000000009e197 or 1e143 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 73.8

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

   4. Applied rewrites 73.8%

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

   5. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 49.1

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

   7. Applied rewrites 49.1%

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

   if -5.00000000000000009e197 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.00000000000000004e-91

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 62.5%

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

   if 2.00000000000000004e-91 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1e143

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 82.5%

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

Alternative 10: 70.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+164}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+23}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))))
   (if (<= t_1 -5e+164)
     (/ (* y z) a)
     (if (<= t_1 2e-91) x (if (<= t_1 5e+23) (+ x y) (* y (/ z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e+164) {
		tmp = (y * z) / a;
	} else if (t_1 <= 2e-91) {
		tmp = x;
	} else if (t_1 <= 5e+23) {
		tmp = x + y;
	} else {
		tmp = y * (z / 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) :: t_1
    real(8) :: tmp
    t_1 = (z - t) / (a - t)
    if (t_1 <= (-5d+164)) then
        tmp = (y * z) / a
    else if (t_1 <= 2d-91) then
        tmp = x
    else if (t_1 <= 5d+23) then
        tmp = x + y
    else
        tmp = y * (z / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e+164) {
		tmp = (y * z) / a;
	} else if (t_1 <= 2e-91) {
		tmp = x;
	} else if (t_1 <= 5e+23) {
		tmp = x + y;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -5e+164:
		tmp = (y * z) / a
	elif t_1 <= 2e-91:
		tmp = x
	elif t_1 <= 5e+23:
		tmp = x + y
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -5e+164)
		tmp = Float64(Float64(y * z) / a);
	elseif (t_1 <= 2e-91)
		tmp = x;
	elseif (t_1 <= 5e+23)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -5e+164)
		tmp = (y * z) / a;
	elseif (t_1 <= 2e-91)
		tmp = x;
	elseif (t_1 <= 5e+23)
		tmp = x + y;
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+164], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$1, 2e-91], x, If[LessEqual[t$95$1, 5e+23], N[(x + y), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4.9999999999999995e164

   1. Initial program 87.9%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 82.5

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

   4. Applied rewrites 82.5%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 53.6

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

   7. Applied rewrites 53.6%

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

   if -4.9999999999999995e164 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.00000000000000004e-91

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 63.9%

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

   if 2.00000000000000004e-91 < (/.f64 (-.f64 z t) (-.f64 a t)) < 4.9999999999999999e23

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 89.1%

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

   if 4.9999999999999999e23 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 65.8

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

   4. Applied rewrites 65.8%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 41.1

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

   7. Applied rewrites 41.1%

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

Alternative 11: 70.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{y \cdot z}{a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 10^{+245}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- z t) (- a t))) (t_2 (/ (* y z) a)))
   (if (<= t_1 -5e+164)
     t_2
     (if (<= t_1 2e-91) x (if (<= t_1 1e+245) (+ x y) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (y * z) / a;
	double tmp;
	if (t_1 <= -5e+164) {
		tmp = t_2;
	} else if (t_1 <= 2e-91) {
		tmp = x;
	} else if (t_1 <= 1e+245) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	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 = (z - t) / (a - t)
    t_2 = (y * z) / a
    if (t_1 <= (-5d+164)) then
        tmp = t_2
    else if (t_1 <= 2d-91) then
        tmp = x
    else if (t_1 <= 1d+245) then
        tmp = x + y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (y * z) / a;
	double tmp;
	if (t_1 <= -5e+164) {
		tmp = t_2;
	} else if (t_1 <= 2e-91) {
		tmp = x;
	} else if (t_1 <= 1e+245) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	t_2 = (y * z) / a
	tmp = 0
	if t_1 <= -5e+164:
		tmp = t_2
	elif t_1 <= 2e-91:
		tmp = x
	elif t_1 <= 1e+245:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(y * z) / a)
	tmp = 0.0
	if (t_1 <= -5e+164)
		tmp = t_2;
	elseif (t_1 <= 2e-91)
		tmp = x;
	elseif (t_1 <= 1e+245)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	t_2 = (y * z) / a;
	tmp = 0.0;
	if (t_1 <= -5e+164)
		tmp = t_2;
	elseif (t_1 <= 2e-91)
		tmp = x;
	elseif (t_1 <= 1e+245)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+164], t$95$2, If[LessEqual[t$95$1, 2e-91], x, If[LessEqual[t$95$1, 1e+245], N[(x + y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4.9999999999999995e164 or 1.00000000000000004e245 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 84.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 84.6

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

   4. Applied rewrites 84.6%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 56.0

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

   7. Applied rewrites 56.0%

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

   if -4.9999999999999995e164 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2.00000000000000004e-91

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 63.9%

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

   if 2.00000000000000004e-91 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.00000000000000004e245

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 78.0%

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

Alternative 12: 66.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 7.5 \cdot 10^{-90}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (- z t) (- a t)) 7.5e-90) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) / (a - t)) <= 7.5e-90) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((z - t) / (a - t)) <= 7.5d-90) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) / (a - t)) <= 7.5e-90) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) / (a - t)) <= 7.5e-90:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(z - t) / Float64(a - t)) <= 7.5e-90)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z - t) / (a - t)) <= 7.5e-90)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], 7.5e-90], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 7.4999999999999999e-90

   1. Initial program 97.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 56.8%

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

   if 7.4999999999999999e-90 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.6%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 74.1%

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

Alternative 13: 54.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+154}:\\ \;\;\;\;y\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+219}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= t_1 -4e+154) y (if (<= t_1 4e+219) x y))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t_1 <= -4e+154) {
		tmp = y;
	} else if (t_1 <= 4e+219) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (t_1 <= (-4d+154)) then
        tmp = y
    else if (t_1 <= 4d+219) 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 t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (t_1 <= -4e+154) {
		tmp = y;
	} else if (t_1 <= 4e+219) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if t_1 <= -4e+154:
		tmp = y
	elif t_1 <= 4e+219:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -4e+154)
		tmp = y;
	elseif (t_1 <= 4e+219)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (t_1 <= -4e+154)
		tmp = y;
	elseif (t_1 <= 4e+219)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+154], y, If[LessEqual[t$95$1, 4e+219], x, y]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) < -4.00000000000000015e154 or 3.99999999999999986e219 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 63.3

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

   4. Applied rewrites 63.3%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 26.2%

      \[\leadsto y \]

   if -4.00000000000000015e154 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))) < 3.99999999999999986e219

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 63.9%

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

Alternative 14: 50.6% accurate, 15.3× 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 98.1%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 50.6%

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

Reproduce

herbie shell --seed 2025119 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64
  (+ x (* y (/ (- z t) (- a t)))))