Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.4% → 95.7%

Time: 6.3s

Alternatives: 13

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t\_1}\\ t_3 := \frac{z}{t\_1}\\ t_4 := x \cdot \mathsf{fma}\left(-1, \frac{a}{x} \cdot t\_3, \frac{y}{t\_1} + \frac{t}{x} \cdot t\_3\right)\\ t_5 := \mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \mathsf{fma}\left(\frac{y}{z}, \frac{t - a}{{\left(b - y\right)}^{2}}, \frac{a}{b - y}\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+303}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-277}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-292}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+273}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (+ (* x y) (* z (- t a))) t_1))
        (t_3 (/ z t_1))
        (t_4 (* x (fma -1.0 (* (/ a x) t_3) (+ (/ y t_1) (* (/ t x) t_3)))))
        (t_5
         (-
          (fma (/ x z) (/ y (- b y)) (/ t (- b y)))
          (fma (/ y z) (/ (- t a) (pow (- b y) 2.0)) (/ a (- b y))))))
   (if (<= t_2 -2e+303)
     t_4
     (if (<= t_2 -4e-277)
       t_2
       (if (<= t_2 2e-292)
         t_5
         (if (<= t_2 5e+273) t_2 (if (<= t_2 INFINITY) t_4 t_5)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((x * y) + (z * (t - a))) / t_1;
	double t_3 = z / t_1;
	double t_4 = x * fma(-1.0, ((a / x) * t_3), ((y / t_1) + ((t / x) * t_3)));
	double t_5 = fma((x / z), (y / (b - y)), (t / (b - y))) - fma((y / z), ((t - a) / pow((b - y), 2.0)), (a / (b - y)));
	double tmp;
	if (t_2 <= -2e+303) {
		tmp = t_4;
	} else if (t_2 <= -4e-277) {
		tmp = t_2;
	} else if (t_2 <= 2e-292) {
		tmp = t_5;
	} else if (t_2 <= 5e+273) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_1)
	t_3 = Float64(z / t_1)
	t_4 = Float64(x * fma(-1.0, Float64(Float64(a / x) * t_3), Float64(Float64(y / t_1) + Float64(Float64(t / x) * t_3))))
	t_5 = Float64(fma(Float64(x / z), Float64(y / Float64(b - y)), Float64(t / Float64(b - y))) - fma(Float64(y / z), Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)), Float64(a / Float64(b - y))))
	tmp = 0.0
	if (t_2 <= -2e+303)
		tmp = t_4;
	elseif (t_2 <= -4e-277)
		tmp = t_2;
	elseif (t_2 <= 2e-292)
		tmp = t_5;
	elseif (t_2 <= 5e+273)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_4;
	else
		tmp = t_5;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(z / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(-1.0 * N[(N[(a / x), $MachinePrecision] * t$95$3), $MachinePrecision] + N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(t / x), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y / z), $MachinePrecision] * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] + N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+303], t$95$4, If[LessEqual[t$95$2, -4e-277], t$95$2, If[LessEqual[t$95$2, 2e-292], t$95$5, If[LessEqual[t$95$2, 5e+273], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$4, t$95$5]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e303 or 4.99999999999999961e273 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 32.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. div-add-rev N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 48.0%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

   8. Applied rewrites 85.7%

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

   if -2e303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999988e-277 or 2.0000000000000001e-292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.99999999999999961e273

   1. Initial program 99.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   if -3.99999999999999988e-277 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.0000000000000001e-292 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 7.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

         \[\leadsto \left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \color{blue}{\left(\frac{a}{b - y} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right)} \]

      2. +-commutative N/A

         \[\leadsto \left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right) - \left(\color{blue}{\frac{a}{b - y}} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right) \]

      3. times-frac N/A

         \[\leadsto \left(\frac{x}{z} \cdot \frac{y}{b - y} + \frac{t}{b - y}\right) - \left(\frac{\color{blue}{a}}{b - y} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \left(\color{blue}{\frac{a}{b - y}} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \left(\frac{\color{blue}{a}}{b - y} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right) \]

      6. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \left(\frac{a}{\color{blue}{b - y}} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right) \]

      7. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \left(\frac{a}{b - \color{blue}{y}} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right) \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \left(\frac{a}{b - y} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right) \]

      9. lift--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \left(\frac{a}{b - y} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \left(\frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} + \color{blue}{\frac{a}{b - y}}\right) \]

      11. times-frac N/A

          \[\leadsto \mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \left(\frac{y}{z} \cdot \frac{t - a}{{\left(b - y\right)}^{2}} + \frac{\color{blue}{a}}{b - y}\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \mathsf{fma}\left(\frac{y}{z}, \color{blue}{\frac{t - a}{{\left(b - y\right)}^{2}}}, \frac{a}{b - y}\right) \]

   5. Applied rewrites 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \mathsf{fma}\left(\frac{y}{z}, \frac{t - a}{{\left(b - y\right)}^{2}}, \frac{a}{b - y}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{+303}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-1, \frac{a}{x} \cdot \frac{z}{y + z \cdot \left(b - y\right)}, \frac{y}{y + z \cdot \left(b - y\right)} + \frac{t}{x} \cdot \frac{z}{y + z \cdot \left(b - y\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-277}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{-292}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \mathsf{fma}\left(\frac{y}{z}, \frac{t - a}{{\left(b - y\right)}^{2}}, \frac{a}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+273}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-1, \frac{a}{x} \cdot \frac{z}{y + z \cdot \left(b - y\right)}, \frac{y}{y + z \cdot \left(b - y\right)} + \frac{t}{x} \cdot \frac{z}{y + z \cdot \left(b - y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, \frac{y}{b - y}, \frac{t}{b - y}\right) - \mathsf{fma}\left(\frac{y}{z}, \frac{t - a}{{\left(b - y\right)}^{2}}, \frac{a}{b - y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot \left(b - y\right)\\ t_3 := \frac{x \cdot y + z \cdot \left(t - a\right)}{t\_2}\\ t_4 := \frac{z}{t\_2}\\ t_5 := x \cdot \mathsf{fma}\left(-1, \frac{a}{x} \cdot t\_4, \frac{y}{t\_2} + \frac{t}{x} \cdot t\_4\right)\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+303}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_3 \leq -4 \cdot 10^{-277}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{-292}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x \cdot \frac{y}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{-z}, -1, t\_1\right)\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+273}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (+ y (* z (- b y))))
        (t_3 (/ (+ (* x y) (* z (- t a))) t_2))
        (t_4 (/ z t_2))
        (t_5 (* x (fma -1.0 (* (/ a x) t_4) (+ (/ y t_2) (* (/ t x) t_4))))))
   (if (<= t_3 -2e+303)
     t_5
     (if (<= t_3 -4e-277)
       t_3
       (if (<= t_3 2e-292)
         (fma
          (/ (- (* x (/ y (- b y))) (/ (* (- t a) y) (pow (- b y) 2.0))) (- z))
          -1.0
          t_1)
         (if (<= t_3 5e+273) t_3 (if (<= t_3 INFINITY) t_5 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = y + (z * (b - y));
	double t_3 = ((x * y) + (z * (t - a))) / t_2;
	double t_4 = z / t_2;
	double t_5 = x * fma(-1.0, ((a / x) * t_4), ((y / t_2) + ((t / x) * t_4)));
	double tmp;
	if (t_3 <= -2e+303) {
		tmp = t_5;
	} else if (t_3 <= -4e-277) {
		tmp = t_3;
	} else if (t_3 <= 2e-292) {
		tmp = fma((((x * (y / (b - y))) - (((t - a) * y) / pow((b - y), 2.0))) / -z), -1.0, t_1);
	} else if (t_3 <= 5e+273) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(y + Float64(z * Float64(b - y)))
	t_3 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / t_2)
	t_4 = Float64(z / t_2)
	t_5 = Float64(x * fma(-1.0, Float64(Float64(a / x) * t_4), Float64(Float64(y / t_2) + Float64(Float64(t / x) * t_4))))
	tmp = 0.0
	if (t_3 <= -2e+303)
		tmp = t_5;
	elseif (t_3 <= -4e-277)
		tmp = t_3;
	elseif (t_3 <= 2e-292)
		tmp = fma(Float64(Float64(Float64(x * Float64(y / Float64(b - y))) - Float64(Float64(Float64(t - a) * y) / (Float64(b - y) ^ 2.0))) / Float64(-z)), -1.0, t_1);
	elseif (t_3 <= 5e+273)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_5;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(z / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(x * N[(-1.0 * N[(N[(a / x), $MachinePrecision] * t$95$4), $MachinePrecision] + N[(N[(y / t$95$2), $MachinePrecision] + N[(N[(t / x), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+303], t$95$5, If[LessEqual[t$95$3, -4e-277], t$95$3, If[LessEqual[t$95$3, 2e-292], N[(N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(t - a), $MachinePrecision] * y), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-z)), $MachinePrecision] * -1.0 + t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 5e+273], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$5, t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2e303 or 4.99999999999999961e273 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 32.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

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

      9. lift--.f64 N/A

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

      10. div-add-rev N/A

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

      11. lower-/.f64 N/A

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

   5. Applied rewrites 48.0%

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

   6. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

   8. Applied rewrites 85.7%

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

   if -2e303 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999988e-277 or 2.0000000000000001e-292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 4.99999999999999961e273

   1. Initial program 99.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   if -3.99999999999999988e-277 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2.0000000000000001e-292

   1. Initial program 17.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \frac{t}{b - y}\right) - \frac{a}{b - y}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto -1 \cdot \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} + \color{blue}{\left(\frac{t}{b - y} - \frac{a}{b - y}\right)} \]

      2. *-commutative N/A

         \[\leadsto \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} \cdot -1 + \left(\color{blue}{\frac{t}{b - y}} - \frac{a}{b - y}\right) \]

      3. div-sub N/A

         \[\leadsto \frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z} \cdot -1 + \frac{t - a}{\color{blue}{b - y}} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1 \cdot \frac{x \cdot y}{b - y} - -1 \cdot \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}, \color{blue}{-1}, \frac{t - a}{b - y}\right) \]

   5. Applied rewrites 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\left(-x \cdot \frac{y}{b - y}\right) - \left(-\frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}\right)}{z}, -1, \frac{t - a}{b - y}\right)} \]

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

   1. Initial program 0.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 79.3

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

   5. Applied rewrites 79.3%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{+303}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-1, \frac{a}{x} \cdot \frac{z}{y + z \cdot \left(b - y\right)}, \frac{y}{y + z \cdot \left(b - y\right)} + \frac{t}{x} \cdot \frac{z}{y + z \cdot \left(b - y\right)}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-277}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{-292}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x \cdot \frac{y}{b - y} - \frac{\left(t - a\right) \cdot y}{{\left(b - y\right)}^{2}}}{-z}, -1, \frac{t - a}{b - y}\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+273}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x \cdot \mathsf{fma}\left(-1, \frac{a}{x} \cdot \frac{z}{y + z \cdot \left(b - y\right)}, \frac{y}{y + z \cdot \left(b - y\right)} + \frac{t}{x} \cdot \frac{z}{y + z \cdot \left(b - y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+61} \lor \neg \left(z \leq 8 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.35e+61) (not (<= z 8e+16)))
   (/ (- t a) (- b y))
   (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.35e+61) || !(z <= 8e+16)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.35d+61)) .or. (.not. (z <= 8d+16))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.35e+61) || !(z <= 8e+16)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.35e+61) or not (z <= 8e+16):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.35e+61) || !(z <= 8e+16))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.35e+61) || ~((z <= 8e+16)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.35e+61], N[Not[LessEqual[z, 8e+16]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3499999999999999e61 or 8e16 < z

   1. Initial program 43.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 89.6

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

   5. Applied rewrites 89.6%

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

   if -2.3499999999999999e61 < z < 8e16

   1. Initial program 85.9%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+61} \lor \neg \left(z \leq 8 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+61} \lor \neg \left(z \leq 6.8 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, z, y \cdot x\right)}{\mathsf{fma}\left(b - y, z, y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.4e+61) (not (<= z 6.8e+15)))
   (/ (- t a) (- b y))
   (/ (fma t z (* y x)) (fma (- b y) z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+61) || !(z <= 6.8e+15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = fma(t, z, (y * x)) / fma((b - y), z, y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.4e+61) || !(z <= 6.8e+15))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(fma(t, z, Float64(y * x)) / fma(Float64(b - y), z, y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.4e+61], N[Not[LessEqual[z, 6.8e+15]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(t * z + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(N[(b - y), $MachinePrecision] * z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4000000000000001e61 or 6.8e15 < z

   1. Initial program 43.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 89.6

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

   5. Applied rewrites 89.6%

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

   if -1.4000000000000001e61 < z < 6.8e15

   1. Initial program 85.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 70.6

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

   5. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, z, y \cdot x\right)}{\mathsf{fma}\left(b - y, z, y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+61} \lor \neg \left(z \leq 6.8 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, z, y \cdot x\right)}{\mathsf{fma}\left(b - y, z, y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z - 1}\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- x) (- z 1.0))))
   (if (<= y -9.2e+58)
     t_1
     (if (<= y -6.5e-74)
       (/ t (- b y))
       (if (<= y 5.5e+43) (/ (- t a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -x / (z - 1.0);
	double tmp;
	if (y <= -9.2e+58) {
		tmp = t_1;
	} else if (y <= -6.5e-74) {
		tmp = t / (b - y);
	} else if (y <= 5.5e+43) {
		tmp = (t - a) / b;
	} 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, b)
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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -x / (z - 1.0d0)
    if (y <= (-9.2d+58)) then
        tmp = t_1
    else if (y <= (-6.5d-74)) then
        tmp = t / (b - y)
    else if (y <= 5.5d+43) then
        tmp = (t - a) / b
    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 b) {
	double t_1 = -x / (z - 1.0);
	double tmp;
	if (y <= -9.2e+58) {
		tmp = t_1;
	} else if (y <= -6.5e-74) {
		tmp = t / (b - y);
	} else if (y <= 5.5e+43) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -x / (z - 1.0)
	tmp = 0
	if y <= -9.2e+58:
		tmp = t_1
	elif y <= -6.5e-74:
		tmp = t / (b - y)
	elif y <= 5.5e+43:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-x) / Float64(z - 1.0))
	tmp = 0.0
	if (y <= -9.2e+58)
		tmp = t_1;
	elseif (y <= -6.5e-74)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 5.5e+43)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -x / (z - 1.0);
	tmp = 0.0;
	if (y <= -9.2e+58)
		tmp = t_1;
	elseif (y <= -6.5e-74)
		tmp = t / (b - y);
	elseif (y <= 5.5e+43)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-x) / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+58], t$95$1, If[LessEqual[y, -6.5e-74], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+43], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.2000000000000001e58 or 5.49999999999999989e43 < y

   1. Initial program 50.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

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

      1. associate-*r/ N/A

         \[\leadsto \frac{-1 \cdot x}{\color{blue}{z - 1}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot x}{\color{blue}{z - 1}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(x\right)}{\color{blue}{z} - 1} \]

      4. lower-neg.f64 N/A

         \[\leadsto \frac{-x}{\color{blue}{z} - 1} \]

      5. lower--.f64 59.4

         \[\leadsto \frac{-x}{z - \color{blue}{1}} \]

   5. Applied rewrites 59.4%

      \[\leadsto \color{blue}{\frac{-x}{z - 1}} \]

   if -9.2000000000000001e58 < y < -6.5000000000000002e-74

   1. Initial program 70.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 49.2

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

   5. Applied rewrites 49.2%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{t}{\color{blue}{b - y}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t}{b - \color{blue}{y}} \]

      2. lift--.f64 51.6

         \[\leadsto \frac{t}{b - y} \]

   8. Applied rewrites 51.6%

      \[\leadsto \frac{t}{\color{blue}{b - y}} \]

   if -6.5000000000000002e-74 < y < 5.49999999999999989e43

   1. Initial program 81.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t - a}{\color{blue}{b}} \]

      2. lift--.f64 58.3

         \[\leadsto \frac{t - a}{b} \]

   5. Applied rewrites 58.3%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 72.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-22} \lor \neg \left(z \leq 0.00048\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - a}{y}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.6e-22) (not (<= z 0.00048)))
   (/ (- t a) (- b y))
   (fma (/ (- t a) y) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.6e-22) || !(z <= 0.00048)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = fma(((t - a) / y), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.6e-22) || !(z <= 0.00048))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = fma(Float64(Float64(t - a) / y), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.6e-22], N[Not[LessEqual[z, 0.00048]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.60000000000000046e-22 or 4.80000000000000012e-4 < z

   1. Initial program 47.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 85.9

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

   5. Applied rewrites 85.9%

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

   if -7.60000000000000046e-22 < z < 4.80000000000000012e-4

   1. Initial program 86.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. div-add-rev N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 50.2

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\frac{t - a}{y}, z, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 64.1%

      \[\leadsto \mathsf{fma}\left(\frac{t - a}{y}, z, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-22} \lor \neg \left(z \leq 0.00048\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - a}{y}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 46.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+43}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.5e+59)
   x
   (if (<= y -6.5e-74)
     (/ t (- b y))
     (if (<= y 6e+43) (/ (- t a) b) (fma x z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.5e+59) {
		tmp = x;
	} else if (y <= -6.5e-74) {
		tmp = t / (b - y);
	} else if (y <= 6e+43) {
		tmp = (t - a) / b;
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.5e+59)
		tmp = x;
	elseif (y <= -6.5e-74)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= 6e+43)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.5e+59], x, If[LessEqual[y, -6.5e-74], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+43], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], N[(x * z + x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.4999999999999996e59

   1. Initial program 56.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 43.3%

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

   if -7.4999999999999996e59 < y < -6.5000000000000002e-74

   1. Initial program 70.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 49.2

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

   5. Applied rewrites 49.2%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{t}{\color{blue}{b - y}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t}{b - \color{blue}{y}} \]

      2. lift--.f64 51.6

         \[\leadsto \frac{t}{b - y} \]

   8. Applied rewrites 51.6%

      \[\leadsto \frac{t}{\color{blue}{b - y}} \]

   if -6.5000000000000002e-74 < y < 6.00000000000000033e43

   1. Initial program 81.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t - a}{\color{blue}{b}} \]

      2. lift--.f64 58.3

         \[\leadsto \frac{t - a}{b} \]

   5. Applied rewrites 58.3%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]

   if 6.00000000000000033e43 < y

   1. Initial program 46.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. div-add-rev N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 37.3

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

   5. Applied rewrites 37.3%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(x, z, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 55.4%

      \[\leadsto \mathsf{fma}\left(x, z, x\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 68.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-22} \lor \neg \left(z \leq 4.4 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{y}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.4e-22) (not (<= z 4.4e-7)))
   (/ (- t a) (- b y))
   (fma (/ t y) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.4e-22) || !(z <= 4.4e-7)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = fma((t / y), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.4e-22) || !(z <= 4.4e-7))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = fma(Float64(t / y), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.4e-22], N[Not[LessEqual[z, 4.4e-7]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(t / y), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000002e-22 or 4.4000000000000002e-7 < z

   1. Initial program 47.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 85.9

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

   5. Applied rewrites 85.9%

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

   if -2.40000000000000002e-22 < z < 4.4000000000000002e-7

   1. Initial program 86.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. div-add-rev N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 50.2

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

   5. Applied rewrites 50.2%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(\frac{t}{y}, z, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 58.2%

      \[\leadsto \mathsf{fma}\left(\frac{t}{y}, z, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-22} \lor \neg \left(z \leq 4.4 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{y}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-56} \lor \neg \left(z \leq 2.9 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z - 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.55e-56) (not (<= z 2.9e+15)))
   (/ (- t a) (- b y))
   (/ (- x) (- z 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.55e-56) || !(z <= 2.9e+15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = -x / (z - 1.0);
	}
	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, b)
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), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.55d-56)) .or. (.not. (z <= 2.9d+15))) then
        tmp = (t - a) / (b - y)
    else
        tmp = -x / (z - 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.55e-56) || !(z <= 2.9e+15)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = -x / (z - 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.55e-56) or not (z <= 2.9e+15):
		tmp = (t - a) / (b - y)
	else:
		tmp = -x / (z - 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.55e-56) || !(z <= 2.9e+15))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(-x) / Float64(z - 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.55e-56) || ~((z <= 2.9e+15)))
		tmp = (t - a) / (b - y);
	else
		tmp = -x / (z - 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.55e-56], N[Not[LessEqual[z, 2.9e+15]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999994e-56 or 2.9e15 < z

   1. Initial program 47.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 85.2

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

   5. Applied rewrites 85.2%

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

   if -1.54999999999999994e-56 < z < 2.9e15

   1. Initial program 86.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf

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

      1. associate-*r/ N/A

         \[\leadsto \frac{-1 \cdot x}{\color{blue}{z - 1}} \]

      2. lower-/.f64 N/A

         \[\leadsto \frac{-1 \cdot x}{\color{blue}{z - 1}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{\mathsf{neg}\left(x\right)}{\color{blue}{z} - 1} \]

      4. lower-neg.f64 N/A

         \[\leadsto \frac{-x}{\color{blue}{z} - 1} \]

      5. lower--.f64 52.9

         \[\leadsto \frac{-x}{z - \color{blue}{1}} \]

   5. Applied rewrites 52.9%

      \[\leadsto \color{blue}{\frac{-x}{z - 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-56} \lor \neg \left(z \leq 2.9 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z - 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-51} \lor \neg \left(z \leq 850000000\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3e-51) (not (<= z 850000000.0))) (/ t (- b y)) (fma x z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e-51) || !(z <= 850000000.0)) {
		tmp = t / (b - y);
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3e-51) || !(z <= 850000000.0))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3e-51], N[Not[LessEqual[z, 850000000.0]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000002e-51 or 8.5e8 < z

   1. Initial program 47.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 33.0

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

   5. Applied rewrites 33.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{t}{\color{blue}{b - y}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t}{b - \color{blue}{y}} \]

      2. lift--.f64 49.8

         \[\leadsto \frac{t}{b - y} \]

   8. Applied rewrites 49.8%

      \[\leadsto \frac{t}{\color{blue}{b - y}} \]

   if -3.00000000000000002e-51 < z < 8.5e8

   1. Initial program 86.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. div-add-rev N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 49.8

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

   5. Applied rewrites 49.8%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(x, z, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 52.5%

      \[\leadsto \mathsf{fma}\left(x, z, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-51} \lor \neg \left(z \leq 850000000\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-51} \lor \neg \left(z \leq 120000000000\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3e-51) (not (<= z 120000000000.0))) (/ t b) (fma x z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3e-51) || !(z <= 120000000000.0)) {
		tmp = t / b;
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3e-51) || !(z <= 120000000000.0))
		tmp = Float64(t / b);
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3e-51], N[Not[LessEqual[z, 120000000000.0]], $MachinePrecision]], N[(t / b), $MachinePrecision], N[(x * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000002e-51 or 1.2e11 < z

   1. Initial program 47.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 32.4

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

   5. Applied rewrites 32.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{t}{\color{blue}{b}} \]
   7. Step-by-step derivation

      1. lower-/.f64 31.4

         \[\leadsto \frac{t}{b} \]

   8. Applied rewrites 31.4%

      \[\leadsto \frac{t}{\color{blue}{b}} \]

   if -3.00000000000000002e-51 < z < 1.2e11

   1. Initial program 86.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. div-add-rev N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 49.5

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

   5. Applied rewrites 49.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(x, z, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 52.1%

      \[\leadsto \mathsf{fma}\left(x, z, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-51} \lor \neg \left(z \leq 120000000000\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 25.4% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, z, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 67.0%

   \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. lower-fma.f64 N/A

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

   4. div-add-rev N/A

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

   5. sub-div N/A

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

   6. lower-/.f64 N/A

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

   7. lower--.f64 N/A

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

   8. lower-+.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 N/A

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

   11. lift--.f64 28.8

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

5. Applied rewrites 28.8%

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

6. Taylor expanded in y around inf

   \[\leadsto \mathsf{fma}\left(x, z, x\right) \]
7. Step-by-step derivation

8. Applied rewrites 28.7%

   \[\leadsto \mathsf{fma}\left(x, z, x\right) \]
9. Add Preprocessing

Alternative 13: 25.2% accurate, 39.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	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, b)
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), intent (in) :: b
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.0%

   \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

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

5. Applied rewrites 28.0%

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

Developer Target 1: 73.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025064 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z)))))

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