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

Percentage Accurate: 76.4% → 92.5%

Time: 4.2s

Alternatives: 14

Speedup: 1.0×

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: 76.4% 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: 92.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \frac{y}{a - t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ t_3 := \left(x + y\right) - \frac{\mathsf{fma}\left(-t, y, z \cdot y\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-262}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;x + \left(-\frac{y \cdot \left(a - z\right)}{t}\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* z (/ y (- a t)))))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t))))
        (t_3 (- (+ x y) (/ (fma (- t) y (* z y)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-262)
       t_3
       (if (<= t_2 0.0)
         (+ x (- (/ (* y (- a z)) t)))
         (if (<= t_2 2e+300) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * (y / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double t_3 = (x + y) - (fma(-t, y, (z * y)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-262) {
		tmp = t_3;
	} else if (t_2 <= 0.0) {
		tmp = x + -((y * (a - z)) / t);
	} else if (t_2 <= 2e+300) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z * Float64(y / Float64(a - t))))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	t_3 = Float64(Float64(x + y) - Float64(fma(Float64(-t), y, Float64(z * y)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-262)
		tmp = t_3;
	elseif (t_2 <= 0.0)
		tmp = Float64(x + Float64(-Float64(Float64(y * Float64(a - z)) / t)));
	elseif (t_2 <= 2e+300)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $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]}, Block[{t$95$3 = N[(N[(x + y), $MachinePrecision] - N[(N[((-t) * y + N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-262], t$95$3, If[LessEqual[t$95$2, 0.0], N[(x + (-N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[t$95$2, 2e+300], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0 or 2.0000000000000001e300 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 39.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 38.6%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 59.2%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 76.3

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

   9. Applied rewrites 76.3%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2.00000000000000002e-262 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 2.0000000000000001e300

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 97.7

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

   4. Applied rewrites 97.7%

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

   if -2.00000000000000002e-262 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 6.6%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in t around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 98.1

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

   7. Applied rewrites 98.1%

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

Alternative 2: 92.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \frac{y}{a - t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{-262}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;x + \left(-\frac{y \cdot \left(a - z\right)}{t}\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* z (/ y (- a t)))))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-262)
       t_2
       (if (<= t_2 0.0)
         (+ x (- (/ (* y (- a z)) t)))
         (if (<= t_2 2e+300) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * (y / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-262) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = x + -((y * (a - z)) / t);
	} else if (t_2 <= 2e+300) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * (y / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-262) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = x + -((y * (a - z)) / t);
	} else if (t_2 <= 2e+300) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (z * (y / (a - t)))
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-262:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = x + -((y * (a - z)) / t)
	elif t_2 <= 2e+300:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z * Float64(y / Float64(a - t))))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-262)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(x + Float64(-Float64(Float64(y * Float64(a - z)) / t)));
	elseif (t_2 <= 2e+300)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (z * (y / (a - t)));
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-262)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = x + -((y * (a - z)) / t);
	elseif (t_2 <= 2e+300)
		tmp = t_2;
	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 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $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[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e-262], t$95$2, If[LessEqual[t$95$2, 0.0], N[(x + (-N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[t$95$2, 2e+300], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0 or 2.0000000000000001e300 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 39.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 38.6%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 59.2%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 76.3

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

   9. Applied rewrites 76.3%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2.00000000000000002e-262 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 2.0000000000000001e300

   1. Initial program 97.7%

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

   if -2.00000000000000002e-262 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 6.6%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 72.8

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

   4. Applied rewrites 72.8%

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

   5. Taylor expanded in t around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 98.1

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

   7. Applied rewrites 98.1%

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

Alternative 3: 91.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(\frac{t}{a - t} + 1\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y\\ \mathbf{if}\;y \leq -8 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-77}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- (+ (+ (/ t (- a t)) 1.0) (/ x y)) (/ z (- a t))) y)))
   (if (<= y -8e-163)
     t_1
     (if (<= y 1.3e-77) (- (+ 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 = ((((t / (a - t)) + 1.0) + (x / y)) - (z / (a - t))) * y;
	double tmp;
	if (y <= -8e-163) {
		tmp = t_1;
	} else if (y <= 1.3e-77) {
		tmp = (x + y) - (((z - t) * y) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((((t / (a - t)) + 1.0d0) + (x / y)) - (z / (a - t))) * y
    if (y <= (-8d-163)) then
        tmp = t_1
    else if (y <= 1.3d-77) then
        tmp = (x + y) - (((z - t) * y) / (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 = ((((t / (a - t)) + 1.0) + (x / y)) - (z / (a - t))) * y;
	double tmp;
	if (y <= -8e-163) {
		tmp = t_1;
	} else if (y <= 1.3e-77) {
		tmp = (x + y) - (((z - t) * y) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((((t / (a - t)) + 1.0) + (x / y)) - (z / (a - t))) * y
	tmp = 0
	if y <= -8e-163:
		tmp = t_1
	elif y <= 1.3e-77:
		tmp = (x + y) - (((z - t) * y) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(Float64(Float64(t / Float64(a - t)) + 1.0) + Float64(x / y)) - Float64(z / Float64(a - t))) * y)
	tmp = 0.0
	if (y <= -8e-163)
		tmp = t_1;
	elseif (y <= 1.3e-77)
		tmp = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((((t / (a - t)) + 1.0) + (x / y)) - (z / (a - t))) * y;
	tmp = 0.0;
	if (y <= -8e-163)
		tmp = t_1;
	elseif (y <= 1.3e-77)
		tmp = (x + y) - (((z - t) * y) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -8e-163], t$95$1, If[LessEqual[y, 1.3e-77], 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 y < -7.99999999999999939e-163 or 1.3000000000000001e-77 < y

   1. Initial program 68.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 89.3

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

   4. Applied rewrites 89.3%

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

   if -7.99999999999999939e-163 < y < 1.3000000000000001e-77

   1. Initial program 95.4%

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

Alternative 4: 86.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - z \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3800:\\ \;\;\;\;x - \frac{z \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (* z (/ y a)))))
   (if (<= a -4.2e-79) t_1 (if (<= a 3800.0) (- x (/ (* z y) (- a t))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (z * (y / a));
	double tmp;
	if (a <= -4.2e-79) {
		tmp = t_1;
	} else if (a <= 3800.0) {
		tmp = x - ((z * y) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (z * (y / a))
    if (a <= (-4.2d-79)) then
        tmp = t_1
    else if (a <= 3800.0d0) then
        tmp = x - ((z * y) / (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 = (x + y) - (z * (y / a));
	double tmp;
	if (a <= -4.2e-79) {
		tmp = t_1;
	} else if (a <= 3800.0) {
		tmp = x - ((z * y) / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (z * (y / a))
	tmp = 0
	if a <= -4.2e-79:
		tmp = t_1
	elif a <= 3800.0:
		tmp = x - ((z * y) / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(z * Float64(y / a)))
	tmp = 0.0
	if (a <= -4.2e-79)
		tmp = t_1;
	elseif (a <= 3800.0)
		tmp = Float64(x - Float64(Float64(z * y) / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (z * (y / a));
	tmp = 0.0;
	if (a <= -4.2e-79)
		tmp = t_1;
	elseif (a <= 3800.0)
		tmp = x - ((z * y) / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e-79], t$95$1, If[LessEqual[a, 3800.0], N[(x - N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.1999999999999999e-79 or 3800 < a

   1. Initial program 78.3%

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

   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 78.1

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

   4. Applied rewrites 78.1%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 83.4

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

   6. Applied rewrites 83.4%

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

   if -4.1999999999999999e-79 < a < 3800

   1. Initial program 74.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 69.1%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 89.3%

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

Alternative 5: 85.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+56}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+96}:\\ \;\;\;\;x - z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.2e+56)
   (+ y x)
   (if (<= a 2.5e+96) (- x (* z (/ y (- a t)))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.2e+56) {
		tmp = y + x;
	} else if (a <= 2.5e+96) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.2d+56)) then
        tmp = y + x
    else if (a <= 2.5d+96) then
        tmp = x - (z * (y / (a - t)))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.2e+56) {
		tmp = y + x;
	} else if (a <= 2.5e+96) {
		tmp = x - (z * (y / (a - t)));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.2e+56:
		tmp = y + x
	elif a <= 2.5e+96:
		tmp = x - (z * (y / (a - t)))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.2e+56)
		tmp = Float64(y + x);
	elseif (a <= 2.5e+96)
		tmp = Float64(x - Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.2e+56)
		tmp = y + x;
	elseif (a <= 2.5e+96)
		tmp = x - (z * (y / (a - t)));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.2e+56], N[(y + x), $MachinePrecision], If[LessEqual[a, 2.5e+96], N[(x - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.20000000000000022e56 or 2.5000000000000002e96 < a

   1. Initial program 78.8%

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

   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 82.3

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

   4. Applied rewrites 82.3%

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

   if -5.20000000000000022e56 < a < 2.5000000000000002e96

   1. Initial program 74.9%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 67.0%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 84.8%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 86.7

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

   9. Applied rewrites 86.7%

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

Alternative 6: 77.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+19}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq 3300:\\ \;\;\;\;x - \frac{z \cdot y}{-t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.25e+19)
   (+ y x)
   (if (<= a 3300.0) (- x (/ (* z y) (- t))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e+19) {
		tmp = y + x;
	} else if (a <= 3300.0) {
		tmp = x - ((z * y) / -t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.25d+19)) then
        tmp = y + x
    else if (a <= 3300.0d0) then
        tmp = x - ((z * y) / -t)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e+19) {
		tmp = y + x;
	} else if (a <= 3300.0) {
		tmp = x - ((z * y) / -t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.25e+19:
		tmp = y + x
	elif a <= 3300.0:
		tmp = x - ((z * y) / -t)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.25e+19)
		tmp = Float64(y + x);
	elseif (a <= 3300.0)
		tmp = Float64(x - Float64(Float64(z * y) / Float64(-t)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.25e+19)
		tmp = y + x;
	elseif (a <= 3300.0)
		tmp = x - ((z * y) / -t);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.25e+19], N[(y + x), $MachinePrecision], If[LessEqual[a, 3300.0], N[(x - N[(N[(z * y), $MachinePrecision] / (-t)), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.25e19 or 3300 < a

   1. Initial program 78.4%

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

   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 77.8

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

   4. Applied rewrites 77.8%

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

   if -1.25e19 < a < 3300

   1. Initial program 74.6%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 68.7%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 88.1%

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

   8. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 76.5

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

   10. Applied rewrites 76.5%

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

Alternative 7: 69.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(1 - \frac{z}{a}\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-221}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{a - t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (* (- 1.0 (/ z a)) y)
     (if (<= t_1 -2e-221)
       (+ y x)
       (if (<= t_1 0.0)
         x
         (if (<= t_1 1e+307) (+ y x) (* (/ (- z) (- a t)) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (1.0 - (z / a)) * y;
	} else if (t_1 <= -2e-221) {
		tmp = y + x;
	} else if (t_1 <= 0.0) {
		tmp = x;
	} else if (t_1 <= 1e+307) {
		tmp = y + x;
	} else {
		tmp = (-z / (a - t)) * y;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (1.0 - (z / a)) * y;
	} else if (t_1 <= -2e-221) {
		tmp = y + x;
	} else if (t_1 <= 0.0) {
		tmp = x;
	} else if (t_1 <= 1e+307) {
		tmp = y + x;
	} else {
		tmp = (-z / (a - t)) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (1.0 - (z / a)) * y
	elif t_1 <= -2e-221:
		tmp = y + x
	elif t_1 <= 0.0:
		tmp = x
	elif t_1 <= 1e+307:
		tmp = y + x
	else:
		tmp = (-z / (a - t)) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(1.0 - Float64(z / a)) * y);
	elseif (t_1 <= -2e-221)
		tmp = Float64(y + x);
	elseif (t_1 <= 0.0)
		tmp = x;
	elseif (t_1 <= 1e+307)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(Float64(-z) / Float64(a - t)) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (1.0 - (z / a)) * y;
	elseif (t_1 <= -2e-221)
		tmp = y + x;
	elseif (t_1 <= 0.0)
		tmp = x;
	elseif (t_1 <= 1e+307)
		tmp = y + x;
	else
		tmp = (-z / (a - t)) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -2e-221], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], x, If[LessEqual[t$95$1, 1e+307], N[(y + x), $MachinePrecision], N[(N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0

   1. Initial program 37.8%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift--.f64 60.7

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

   4. Applied rewrites 60.7%

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

   5. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 45.7

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

   7. Applied rewrites 45.7%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2.00000000000000003e-221 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.99999999999999986e306

   1. Initial program 97.8%

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

   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 79.3

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

   4. Applied rewrites 79.3%

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

   if -2.00000000000000003e-221 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 11.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 47.4%

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

   if 9.99999999999999986e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 97.8%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 81.1

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

   4. Applied rewrites 81.1%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 18.4

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

   7. Applied rewrites 18.4%

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

Alternative 8: 69.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(1 - \frac{z}{a}\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-221}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{z - a}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (* (- 1.0 (/ z a)) y)
     (if (<= t_1 -2e-221)
       (+ y x)
       (if (<= t_1 0.0) x (if (<= t_1 1e+307) (+ y x) (* (/ (- z a) t) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (1.0 - (z / a)) * y;
	} else if (t_1 <= -2e-221) {
		tmp = y + x;
	} else if (t_1 <= 0.0) {
		tmp = x;
	} else if (t_1 <= 1e+307) {
		tmp = y + x;
	} else {
		tmp = ((z - a) / t) * y;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (1.0 - (z / a)) * y;
	} else if (t_1 <= -2e-221) {
		tmp = y + x;
	} else if (t_1 <= 0.0) {
		tmp = x;
	} else if (t_1 <= 1e+307) {
		tmp = y + x;
	} else {
		tmp = ((z - a) / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (1.0 - (z / a)) * y
	elif t_1 <= -2e-221:
		tmp = y + x
	elif t_1 <= 0.0:
		tmp = x
	elif t_1 <= 1e+307:
		tmp = y + x
	else:
		tmp = ((z - a) / t) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(1.0 - Float64(z / a)) * y);
	elseif (t_1 <= -2e-221)
		tmp = Float64(y + x);
	elseif (t_1 <= 0.0)
		tmp = x;
	elseif (t_1 <= 1e+307)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(Float64(z - a) / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (1.0 - (z / a)) * y;
	elseif (t_1 <= -2e-221)
		tmp = y + x;
	elseif (t_1 <= 0.0)
		tmp = x;
	elseif (t_1 <= 1e+307)
		tmp = y + x;
	else
		tmp = ((z - a) / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -2e-221], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], x, If[LessEqual[t$95$1, 1e+307], N[(y + x), $MachinePrecision], N[(N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision] * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0

   1. Initial program 37.8%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift--.f64 60.7

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

   4. Applied rewrites 60.7%

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

   5. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 45.7

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

   7. Applied rewrites 45.7%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2.00000000000000003e-221 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.99999999999999986e306

   1. Initial program 97.8%

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

   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 79.3

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

   4. Applied rewrites 79.3%

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

   if -2.00000000000000003e-221 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 11.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 47.4%

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

   if 9.99999999999999986e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 97.8%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift--.f64 38.2

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

   4. Applied rewrites 38.2%

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

   5. Taylor expanded in t around -inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 12.2

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

   7. Applied rewrites 12.2%

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

Alternative 9: 67.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(1 - \frac{z}{a}\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-221}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - a\right) \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (* (- 1.0 (/ z a)) y)
     (if (<= t_1 -2e-221)
       (+ y x)
       (if (<= t_1 0.0) x (if (<= t_1 1e+307) (+ y x) (/ (* (- z a) y) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (1.0 - (z / a)) * y;
	} else if (t_1 <= -2e-221) {
		tmp = y + x;
	} else if (t_1 <= 0.0) {
		tmp = x;
	} else if (t_1 <= 1e+307) {
		tmp = y + x;
	} else {
		tmp = ((z - a) * y) / t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (1.0 - (z / a)) * y;
	} else if (t_1 <= -2e-221) {
		tmp = y + x;
	} else if (t_1 <= 0.0) {
		tmp = x;
	} else if (t_1 <= 1e+307) {
		tmp = y + x;
	} else {
		tmp = ((z - a) * y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (1.0 - (z / a)) * y
	elif t_1 <= -2e-221:
		tmp = y + x
	elif t_1 <= 0.0:
		tmp = x
	elif t_1 <= 1e+307:
		tmp = y + x
	else:
		tmp = ((z - a) * y) / t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(1.0 - Float64(z / a)) * y);
	elseif (t_1 <= -2e-221)
		tmp = Float64(y + x);
	elseif (t_1 <= 0.0)
		tmp = x;
	elseif (t_1 <= 1e+307)
		tmp = Float64(y + x);
	else
		tmp = Float64(Float64(Float64(z - a) * y) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (1.0 - (z / a)) * y;
	elseif (t_1 <= -2e-221)
		tmp = y + x;
	elseif (t_1 <= 0.0)
		tmp = x;
	elseif (t_1 <= 1e+307)
		tmp = y + x;
	else
		tmp = ((z - a) * y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -2e-221], N[(y + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], x, If[LessEqual[t$95$1, 1e+307], N[(y + x), $MachinePrecision], N[(N[(N[(z - a), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -inf.0

   1. Initial program 37.8%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift--.f64 60.7

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

   4. Applied rewrites 60.7%

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

   5. Taylor expanded in t around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 45.7

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

   7. Applied rewrites 45.7%

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

   if -inf.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -2.00000000000000003e-221 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 9.99999999999999986e306

   1. Initial program 97.8%

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

   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 79.3

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

   4. Applied rewrites 79.3%

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

   if -2.00000000000000003e-221 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 11.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 47.4%

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

   if 9.99999999999999986e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 97.8%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift--.f64 38.2

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

   4. Applied rewrites 38.2%

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

   5. Taylor expanded in t around -inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 13.0

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

   7. Applied rewrites 13.0%

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

Alternative 10: 63.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-80}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-225}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-198}:\\ \;\;\;\;\frac{\left(z - a\right) \cdot y}{t}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e-80)
   (+ y x)
   (if (<= a -5e-225)
     x
     (if (<= a 1.52e-198)
       (/ (* (- z a) y) t)
       (if (<= a 2.25e-10) x (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-80) {
		tmp = y + x;
	} else if (a <= -5e-225) {
		tmp = x;
	} else if (a <= 1.52e-198) {
		tmp = ((z - a) * y) / t;
	} else if (a <= 2.25e-10) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.2d-80)) then
        tmp = y + x
    else if (a <= (-5d-225)) then
        tmp = x
    else if (a <= 1.52d-198) then
        tmp = ((z - a) * y) / t
    else if (a <= 2.25d-10) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-80) {
		tmp = y + x;
	} else if (a <= -5e-225) {
		tmp = x;
	} else if (a <= 1.52e-198) {
		tmp = ((z - a) * y) / t;
	} else if (a <= 2.25e-10) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e-80:
		tmp = y + x
	elif a <= -5e-225:
		tmp = x
	elif a <= 1.52e-198:
		tmp = ((z - a) * y) / t
	elif a <= 2.25e-10:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e-80)
		tmp = Float64(y + x);
	elseif (a <= -5e-225)
		tmp = x;
	elseif (a <= 1.52e-198)
		tmp = Float64(Float64(Float64(z - a) * y) / t);
	elseif (a <= 2.25e-10)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e-80)
		tmp = y + x;
	elseif (a <= -5e-225)
		tmp = x;
	elseif (a <= 1.52e-198)
		tmp = ((z - a) * y) / t;
	elseif (a <= 2.25e-10)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e-80], N[(y + x), $MachinePrecision], If[LessEqual[a, -5e-225], x, If[LessEqual[a, 1.52e-198], N[(N[(N[(z - a), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 2.25e-10], x, N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.1999999999999999e-80 or 2.25e-10 < a

   1. Initial program 78.4%

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

   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 74.5

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

   4. Applied rewrites 74.5%

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

   if -3.1999999999999999e-80 < a < -5.0000000000000001e-225 or 1.5199999999999999e-198 < a < 2.25e-10

   1. Initial program 75.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.9%

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

   if -5.0000000000000001e-225 < a < 1.5199999999999999e-198

   1. Initial program 71.3%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift--.f64 36.5

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

   4. Applied rewrites 36.5%

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

   5. Taylor expanded in t around -inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 43.3

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

   7. Applied rewrites 43.3%

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

Alternative 11: 63.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{-80}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-225}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-198}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.2e-80)
   (+ y x)
   (if (<= a -4.8e-225)
     x
     (if (<= a 1.52e-198) (/ (* y z) t) (if (<= a 2.25e-10) x (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-80) {
		tmp = y + x;
	} else if (a <= -4.8e-225) {
		tmp = x;
	} else if (a <= 1.52e-198) {
		tmp = (y * z) / t;
	} else if (a <= 2.25e-10) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.2d-80)) then
        tmp = y + x
    else if (a <= (-4.8d-225)) then
        tmp = x
    else if (a <= 1.52d-198) then
        tmp = (y * z) / t
    else if (a <= 2.25d-10) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.2e-80) {
		tmp = y + x;
	} else if (a <= -4.8e-225) {
		tmp = x;
	} else if (a <= 1.52e-198) {
		tmp = (y * z) / t;
	} else if (a <= 2.25e-10) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.2e-80:
		tmp = y + x
	elif a <= -4.8e-225:
		tmp = x
	elif a <= 1.52e-198:
		tmp = (y * z) / t
	elif a <= 2.25e-10:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.2e-80)
		tmp = Float64(y + x);
	elseif (a <= -4.8e-225)
		tmp = x;
	elseif (a <= 1.52e-198)
		tmp = Float64(Float64(y * z) / t);
	elseif (a <= 2.25e-10)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.2e-80)
		tmp = y + x;
	elseif (a <= -4.8e-225)
		tmp = x;
	elseif (a <= 1.52e-198)
		tmp = (y * z) / t;
	elseif (a <= 2.25e-10)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.2e-80], N[(y + x), $MachinePrecision], If[LessEqual[a, -4.8e-225], x, If[LessEqual[a, 1.52e-198], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 2.25e-10], x, N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.1999999999999999e-80 or 2.25e-10 < a

   1. Initial program 78.4%

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

   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 74.5

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

   4. Applied rewrites 74.5%

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

   if -3.1999999999999999e-80 < a < -4.79999999999999992e-225 or 1.5199999999999999e-198 < a < 2.25e-10

   1. Initial program 75.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.9%

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

   if -4.79999999999999992e-225 < a < 1.5199999999999999e-198

   1. Initial program 71.3%

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

   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 45.1

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

   4. Applied rewrites 45.1%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 41.3

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

   7. Applied rewrites 41.3%

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

Alternative 12: 62.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+185}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+43}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -8.5e+185) x (if (<= t 8.8e+43) (+ y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -8.5e+185) {
		tmp = x;
	} else if (t <= 8.8e+43) {
		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+185)) then
        tmp = x
    else if (t <= 8.8d+43) 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+185) {
		tmp = x;
	} else if (t <= 8.8e+43) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -8.5e+185:
		tmp = x
	elif t <= 8.8e+43:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -8.5e+185)
		tmp = x;
	elseif (t <= 8.8e+43)
		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+185)
		tmp = x;
	elseif (t <= 8.8e+43)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -8.5e+185], x, If[LessEqual[t, 8.8e+43], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -8.50000000000000013e185 or 8.80000000000000002e43 < t

   1. Initial program 55.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 64.3%

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

   if -8.50000000000000013e185 < t < 8.80000000000000002e43

   1. Initial program 86.4%

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

   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 62.7

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

   4. Applied rewrites 62.7%

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

Alternative 13: 53.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-91}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.5e-127) x (if (<= x 1.7e-91) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.5e-127) {
		tmp = x;
	} else if (x <= 1.7e-91) {
		tmp = y;
	} 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 (x <= (-4.5d-127)) then
        tmp = x
    else if (x <= 1.7d-91) then
        tmp = y
    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 (x <= -4.5e-127) {
		tmp = x;
	} else if (x <= 1.7e-91) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.5e-127:
		tmp = x
	elif x <= 1.7e-91:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.5e-127)
		tmp = x;
	elseif (x <= 1.7e-91)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.5e-127)
		tmp = x;
	elseif (x <= 1.7e-91)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.5e-127], x, If[LessEqual[x, 1.7e-91], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4999999999999999e-127 or 1.70000000000000013e-91 < x

   1. Initial program 80.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 64.2%

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

   if -4.4999999999999999e-127 < x < 1.70000000000000013e-91

   1. Initial program 68.4%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift--.f64 60.7

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

   4. Applied rewrites 60.7%

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

   5. Taylor expanded in a around inf

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

   7. Applied rewrites 31.3%

      \[\leadsto y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 50.9% accurate, 17.9× 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 76.4%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 50.9%

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

Reproduce

herbie shell --seed 2025120 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64
  (- (+ x y) (/ (* (- z t) y) (- a t))))