Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.1% → 85.2%

Time: 8.1s

Alternatives: 20

Speedup: 3.2×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Initial Program: 56.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    code = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 85.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+53}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(230661.510616, \frac{1}{t\_1}, \frac{\mathsf{fma}\left(y, 27464.7644705 + x \cdot \left(y \cdot y\right), \left(y \cdot y\right) \cdot z\right)}{t\_1}\right), \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ i (* y (+ c (* y (+ b (* y (+ a y)))))))))
   (if (<= y -7e+53)
     (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
     (if (<= y 2.05e+61)
       (fma
        y
        (fma
         230661.510616
         (/ 1.0 t_1)
         (/ (fma y (+ 27464.7644705 (* x (* y y))) (* (* y y) z)) t_1))
        (/ t (fma (fma (fma (+ a y) y b) y c) y i)))
       (+ x (/ z y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = i + (y * (c + (y * (b + (y * (a + y))))));
	double tmp;
	if (y <= -7e+53) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 2.05e+61) {
		tmp = fma(y, fma(230661.510616, (1.0 / t_1), (fma(y, (27464.7644705 + (x * (y * y))), ((y * y) * z)) / t_1)), (t / fma(fma(fma((a + y), y, b), y, c), y, i)));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * Float64(a + y)))))))
	tmp = 0.0
	if (y <= -7e+53)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 2.05e+61)
		tmp = fma(y, fma(230661.510616, Float64(1.0 / t_1), Float64(fma(y, Float64(27464.7644705 + Float64(x * Float64(y * y))), Float64(Float64(y * y) * z)) / t_1)), Float64(t / fma(fma(fma(Float64(a + y), y, b), y, c), y, i)));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * N[(a + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+53], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 2.05e+61], N[(y * N[(230661.510616 * N[(1.0 / t$95$1), $MachinePrecision] + N[(N[(y * N[(27464.7644705 + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.00000000000000038e53

   1. Initial program 3.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 56.6%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 72.0

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

   7. Applied rewrites 72.0%

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

   if -7.00000000000000038e53 < y < 2.04999999999999986e61

   1. Initial program 93.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied rewrites 93.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{28832688827}{125000} \cdot \frac{1}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \left(\frac{y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{{y}^{2} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]
   5. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{28832688827}{125000}, \color{blue}{\frac{1}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}}, \frac{y \cdot \left(\frac{54929528941}{2000000} + x \cdot {y}^{2}\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + \frac{{y}^{2} \cdot z}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right), \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]

   6. Applied rewrites 93.7%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\mathsf{fma}\left(230661.510616, \frac{1}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}, \frac{\mathsf{fma}\left(y, 27464.7644705 + x \cdot \left(y \cdot y\right), \left(y \cdot y\right) \cdot z\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}\right)}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]

   if 2.04999999999999986e61 < y

   1. Initial program 1.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 1.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 73.6

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

   7. Applied rewrites 73.6%

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

Alternative 2: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+53}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right)}{t\_1}, \frac{t}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma (fma (fma (+ a y) y b) y c) y i)))
   (if (<= y -7e+53)
     (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
     (if (<= y 2.05e+61)
       (fma
        y
        (/ (fma (fma (fma y x z) y 27464.7644705) y 230661.510616) t_1)
        (/ t t_1))
       (+ x (/ z y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(fma(fma((a + y), y, b), y, c), y, i);
	double tmp;
	if (y <= -7e+53) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 2.05e+61) {
		tmp = fma(y, (fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616) / t_1), (t / t_1));
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(fma(fma(Float64(a + y), y, b), y, c), y, i)
	tmp = 0.0
	if (y <= -7e+53)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 2.05e+61)
		tmp = fma(y, Float64(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616) / t_1), Float64(t / t_1));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]}, If[LessEqual[y, -7e+53], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 2.05e+61], N[(y * N[(N[(N[(N[(y * x + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.00000000000000038e53

   1. Initial program 3.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 56.6%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 72.0

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

   7. Applied rewrites 72.0%

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

   if -7.00000000000000038e53 < y < 2.04999999999999986e61

   1. Initial program 93.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied rewrites 93.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right)} \]

   if 2.04999999999999986e61 < y

   1. Initial program 1.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 1.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 73.6

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

   7. Applied rewrites 73.6%

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

Alternative 3: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+53}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+56}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right) \cdot y\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.5e+53)
   (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
   (if (<= y 4.8e+56)
     (/
      (+
       (fma
        (* (* y y) (* y y))
        x
        (* (fma (fma z y 27464.7644705) y 230661.510616) y))
       t)
      (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -5.5e+53) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 4.8e+56) {
		tmp = (fma(((y * y) * (y * y)), x, (fma(fma(z, y, 27464.7644705), y, 230661.510616) * y)) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.5e+53)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 4.8e+56)
		tmp = Float64(Float64(fma(Float64(Float64(y * y) * Float64(y * y)), x, Float64(fma(fma(z, y, 27464.7644705), y, 230661.510616) * y)) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.5e+53], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 4.8e+56], N[(N[(N[(N[(N[(y * y), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.49999999999999975e53

   1. Initial program 3.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 56.5%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 71.9

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

   7. Applied rewrites 71.9%

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

   if -5.49999999999999975e53 < y < 4.80000000000000027e56

   1. Initial program 93.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{\left(x \cdot {y}^{4} + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left({y}^{4} \cdot x + \color{blue}{y} \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left({y}^{4}, \color{blue}{x}, y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. sqr-pow N/A

         \[\leadsto \frac{\mathsf{fma}\left({y}^{\left(\frac{4}{2}\right)} \cdot {y}^{\left(\frac{4}{2}\right)}, x, y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. metadata-eval N/A

         \[\leadsto \frac{\mathsf{fma}\left({y}^{2} \cdot {y}^{\left(\frac{4}{2}\right)}, x, y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. metadata-eval N/A

         \[\leadsto \frac{\mathsf{fma}\left({y}^{2} \cdot {y}^{2}, x, y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left({y}^{2} \cdot {y}^{2}, x, y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. unpow2 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot {y}^{2}, x, y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot {y}^{2}, x, y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. unpow2 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right), x, y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right), x, y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      11. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right), x, \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right) \cdot y\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      12. lower-*.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right), x, \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right) \cdot y\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      13. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right), x, \left(y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right) + \frac{28832688827}{125000}\right) \cdot y\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      14. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right), x, \left(\left(\frac{54929528941}{2000000} + y \cdot z\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      15. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right), x, \mathsf{fma}\left(\frac{54929528941}{2000000} + y \cdot z, y, \frac{28832688827}{125000}\right) \cdot y\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      16. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right), x, \mathsf{fma}\left(y \cdot z + \frac{54929528941}{2000000}, y, \frac{28832688827}{125000}\right) \cdot y\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      17. *-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right), x, \mathsf{fma}\left(z \cdot y + \frac{54929528941}{2000000}, y, \frac{28832688827}{125000}\right) \cdot y\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      18. lower-fma.f64 93.4

          \[\leadsto \frac{\mathsf{fma}\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right) \cdot y\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 93.4%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\left(y \cdot y\right) \cdot \left(y \cdot y\right), x, \mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right) \cdot y\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 4.80000000000000027e56 < y

   1. Initial program 1.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 1.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 72.9

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

   7. Applied rewrites 72.9%

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

Alternative 4: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+53}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+56}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, 230661.510616, \left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) \cdot y\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.5e+53)
   (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
   (if (<= y 4.8e+56)
     (/
      (+ (fma y 230661.510616 (* (* (fma (fma y x z) y 27464.7644705) y) y)) t)
      (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -5.5e+53) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 4.8e+56) {
		tmp = (fma(y, 230661.510616, ((fma(fma(y, x, z), y, 27464.7644705) * y) * y)) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.5e+53)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 4.8e+56)
		tmp = Float64(Float64(fma(y, 230661.510616, Float64(Float64(fma(fma(y, x, z), y, 27464.7644705) * y) * y)) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.5e+53], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 4.8e+56], N[(N[(N[(y * 230661.510616 + N[(N[(N[(N[(y * x + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.49999999999999975e53

   1. Initial program 3.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 56.5%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 71.9

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

   7. Applied rewrites 71.9%

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

   if -5.49999999999999975e53 < y < 4.80000000000000027e56

   1. Initial program 93.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. lift-+.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      3. lift-*.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y} + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      4. lift-+.f64 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right)} \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(\color{blue}{\left(x \cdot y + z\right) \cdot y} + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      6. lift-*.f64 N/A

         \[\leadsto \frac{\left(\left(\left(\color{blue}{x \cdot y} + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      7. lift-+.f64 N/A

         \[\leadsto \frac{\left(\left(\color{blue}{\left(x \cdot y + z\right)} \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      8. *-commutative N/A

         \[\leadsto \frac{\left(\left(\color{blue}{y \cdot \left(x \cdot y + z\right)} + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      9. +-commutative N/A

         \[\leadsto \frac{\left(\left(y \cdot \color{blue}{\left(z + x \cdot y\right)} + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      10. +-commutative N/A

          \[\leadsto \frac{\left(\color{blue}{\left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)} \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      11. *-commutative N/A

          \[\leadsto \frac{\left(\color{blue}{y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)} + \frac{28832688827}{125000}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      12. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      13. *-commutative N/A

          \[\leadsto \frac{\color{blue}{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      14. distribute-rgt-in N/A

          \[\leadsto \frac{\color{blue}{\left(\frac{28832688827}{125000} \cdot y + \left(y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right) \cdot y\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      15. *-commutative N/A

          \[\leadsto \frac{\left(\color{blue}{y \cdot \frac{28832688827}{125000}} + \left(y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right) \cdot y\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      16. lower-fma.f64 N/A

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, \frac{28832688827}{125000}, \left(y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right) \cdot y\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied rewrites 93.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, 230661.510616, \left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right) \cdot y\right) \cdot y\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 4.80000000000000027e56 < y

   1. Initial program 1.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 1.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 72.9

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

   7. Applied rewrites 72.9%

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

Alternative 5: 84.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+53}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+56}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -5.5e+53)
   (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
   (if (<= y 4.8e+56)
     (/
      (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
      (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -5.5e+53) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 4.8e+56) {
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = x + (z / 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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-5.5d+53)) then
        tmp = -((z * ((a / y) - 1.0d0)) / y) + x
    else if (y <= 4.8d+56) then
        tmp = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
    else
        tmp = x + (z / 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 c, double i) {
	double tmp;
	if (y <= -5.5e+53) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 4.8e+56) {
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -5.5e+53:
		tmp = -((z * ((a / y) - 1.0)) / y) + x
	elif y <= 4.8e+56:
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -5.5e+53)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 4.8e+56)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -5.5e+53)
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	elseif (y <= 4.8e+56)
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -5.5e+53], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 4.8e+56], N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.49999999999999975e53

   1. Initial program 3.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 56.5%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 71.9

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

   7. Applied rewrites 71.9%

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

   if -5.49999999999999975e53 < y < 4.80000000000000027e56

   1. Initial program 93.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 4.80000000000000027e56 < y

   1. Initial program 1.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 1.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 72.9

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

   7. Applied rewrites 72.9%

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

Alternative 6: 81.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+53}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+56}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.8e+53)
   (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
   (if (<= y 2.8e+56)
     (/
      (fma (fma (fma (fma y x z) y 27464.7644705) y 230661.510616) y t)
      (fma (fma (fma y y b) y c) y i))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.8e+53) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 2.8e+56) {
		tmp = fma(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(y, y, b), y, c), y, i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.8e+53)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 2.8e+56)
		tmp = Float64(fma(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(y, y, b), y, c), y, i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.8e+53], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 2.8e+56], N[(N[(N[(N[(N[(y * x + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(y * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8e53

   1. Initial program 3.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 56.5%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 71.9

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

   7. Applied rewrites 71.9%

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

   if -4.8e53 < y < 2.80000000000000008e56

   1. Initial program 93.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 87.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   if 2.80000000000000008e56 < y

   1. Initial program 1.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 1.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 72.8

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

   7. Applied rewrites 72.8%

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

Alternative 7: 81.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+45}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+46}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.7e+45)
   (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
   (if (<= y 4e+46)
     (/
      (fma (fma (fma z y 27464.7644705) y 230661.510616) y t)
      (fma (fma (fma (+ a y) y b) y c) y i))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.7e+45) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 4e+46) {
		tmp = fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma((a + y), y, b), y, c), y, i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.7e+45)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 4e+46)
		tmp = Float64(fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(Float64(a + y), y, b), y, c), y, i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.7e+45], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 4e+46], N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.70000000000000002e45

   1. Initial program 3.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 55.7%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 70.6

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

   7. Applied rewrites 70.6%

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

   if -4.70000000000000002e45 < y < 4e46

   1. Initial program 95.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)}} \]

      2. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right) + t}{\color{blue}{i} + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \frac{\left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right)\right) \cdot y + t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      4. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right), y, t\right)}{\color{blue}{i} + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      5. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(y \cdot \left(\frac{54929528941}{2000000} + y \cdot z\right) + \frac{28832688827}{125000}, y, t\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      6. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\left(\frac{54929528941}{2000000} + y \cdot z\right) \cdot y + \frac{28832688827}{125000}, y, t\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      7. lower-fma.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\frac{54929528941}{2000000} + y \cdot z, y, \frac{28832688827}{125000}\right), y, t\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      8. +-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(y \cdot z + \frac{54929528941}{2000000}, y, \frac{28832688827}{125000}\right), y, t\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      9. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot y + \frac{54929528941}{2000000}, y, \frac{28832688827}{125000}\right), y, t\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      10. lower-fma.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, \frac{54929528941}{2000000}\right), y, \frac{28832688827}{125000}\right), y, t\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} \]

      11. +-commutative N/A

          \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, \frac{54929528941}{2000000}\right), y, \frac{28832688827}{125000}\right), y, t\right)}{y \cdot \left(c + y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) + \color{blue}{i}} \]

   4. Applied rewrites 89.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}} \]

   if 4e46 < y

   1. Initial program 2.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 2.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 70.6

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

   7. Applied rewrites 70.6%

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

Alternative 8: 76.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+52}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+32}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -4.5e+52)
   (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
   (if (<= y 1.12e+32)
     (/
      (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
      (fma c y i))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -4.5e+52) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 1.12e+32) {
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / fma(c, y, i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -4.5e+52)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 1.12e+32)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / fma(c, y, i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -4.5e+52], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 1.12e+32], N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5e52

   1. Initial program 3.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 56.4%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 71.6

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

   7. Applied rewrites 71.6%

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

   if -4.5e52 < y < 1.12000000000000007e32

   1. Initial program 95.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{i + c \cdot y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{c \cdot y + \color{blue}{i}} \]

      2. lower-fma.f64 78.3

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, \color{blue}{y}, i\right)} \]

   4. Applied rewrites 78.3%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(c, y, i\right)}} \]

   if 1.12000000000000007e32 < y

   1. Initial program 4.9%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 4.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 68.0

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

   7. Applied rewrites 68.0%

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

Alternative 9: 76.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;\frac{230661.510616 \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.2e+43)
   (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
   (if (<= y 2.7e+44)
     (/ (+ (* 230661.510616 y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.2e+43) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 2.7e+44) {
		tmp = ((230661.510616 * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = x + (z / 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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (y <= (-3.2d+43)) then
        tmp = -((z * ((a / y) - 1.0d0)) / y) + x
    else if (y <= 2.7d+44) then
        tmp = ((230661.510616d0 * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
    else
        tmp = x + (z / 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 c, double i) {
	double tmp;
	if (y <= -3.2e+43) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 2.7e+44) {
		tmp = ((230661.510616 * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if y <= -3.2e+43:
		tmp = -((z * ((a / y) - 1.0)) / y) + x
	elif y <= 2.7e+44:
		tmp = ((230661.510616 * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.2e+43)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 2.7e+44)
		tmp = Float64(Float64(Float64(230661.510616 * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (y <= -3.2e+43)
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	elseif (y <= 2.7e+44)
		tmp = ((230661.510616 * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.2e+43], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 2.7e+44], N[(N[(N[(230661.510616 * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.20000000000000014e43

   1. Initial program 4.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 55.2%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 70.1

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

   7. Applied rewrites 70.1%

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

   if -3.20000000000000014e43 < y < 2.7e44

   1. Initial program 95.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000}} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   3. Step-by-step derivation

   4. Applied rewrites 81.4%

      \[\leadsto \frac{\color{blue}{230661.510616} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 2.7e44 < y

   1. Initial program 3.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 2.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 70.1

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

   7. Applied rewrites 70.1%

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

Alternative 10: 74.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.2e+43)
   (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
   (if (<= y 2.7e+44)
     (/ (fma 230661.510616 y t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.2e+43) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 2.7e+44) {
		tmp = fma(230661.510616, y, t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.2e+43)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 2.7e+44)
		tmp = Float64(fma(230661.510616, y, t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.2e+43], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 2.7e+44], N[(N[(230661.510616 * y + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.20000000000000014e43

   1. Initial program 4.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 55.2%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 70.1

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

   7. Applied rewrites 70.1%

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

   if -3.20000000000000014e43 < y < 2.7e44

   1. Initial program 95.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t + \frac{28832688827}{125000} \cdot y}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\frac{28832688827}{125000} \cdot y + \color{blue}{t}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

      2. lower-fma.f64 81.4

         \[\leadsto \frac{\mathsf{fma}\left(230661.510616, \color{blue}{y}, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   4. Applied rewrites 81.4%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(230661.510616, y, t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   if 2.7e44 < y

   1. Initial program 3.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 2.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 70.1

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

   7. Applied rewrites 70.1%

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

Alternative 11: 73.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+45}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{\left(\left(y \cdot z\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -1.15e+45)
   (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
   (if (<= y 3.5e+31)
     (/ (+ (* (+ (* (* y z) y) 230661.510616) y) t) (fma c y i))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -1.15e+45) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 3.5e+31) {
		tmp = (((((y * z) * y) + 230661.510616) * y) + t) / fma(c, y, i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -1.15e+45)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 3.5e+31)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(y * z) * y) + 230661.510616) * y) + t) / fma(c, y, i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -1.15e+45], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 3.5e+31], N[(N[(N[(N[(N[(N[(y * z), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000006e45

   1. Initial program 3.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 55.6%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 70.6

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

   7. Applied rewrites 70.6%

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

   if -1.15000000000000006e45 < y < 3.5e31

   1. Initial program 96.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{i + c \cdot y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{c \cdot y + \color{blue}{i}} \]

      2. lower-fma.f64 79.0

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, \color{blue}{y}, i\right)} \]

   4. Applied rewrites 79.0%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(c, y, i\right)}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \frac{\left(\color{blue}{\left(y \cdot z\right)} \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 76.0

         \[\leadsto \frac{\left(\left(y \cdot \color{blue}{z}\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]

   7. Applied rewrites 76.0%

      \[\leadsto \frac{\left(\color{blue}{\left(y \cdot z\right)} \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]

   if 3.5e31 < y

   1. Initial program 5.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 4.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 67.8

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

   7. Applied rewrites 67.8%

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

Alternative 12: 71.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+43}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-94}:\\ \;\;\;\;\frac{\left(27464.7644705 \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{\left(\left(y \cdot y\right) \cdot z\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.6e+43)
   (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
   (if (<= y 7.2e-94)
     (/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (fma c y i))
     (if (<= y 3.5e+31)
       (/ (+ (* (* (* y y) z) y) t) (fma c y i))
       (+ x (/ z y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.6e+43) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 7.2e-94) {
		tmp = ((((27464.7644705 * y) + 230661.510616) * y) + t) / fma(c, y, i);
	} else if (y <= 3.5e+31) {
		tmp = ((((y * y) * z) * y) + t) / fma(c, y, i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.6e+43)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 7.2e-94)
		tmp = Float64(Float64(Float64(Float64(Float64(27464.7644705 * y) + 230661.510616) * y) + t) / fma(c, y, i));
	elseif (y <= 3.5e+31)
		tmp = Float64(Float64(Float64(Float64(Float64(y * y) * z) * y) + t) / fma(c, y, i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.6e+43], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 7.2e-94], N[(N[(N[(N[(N[(27464.7644705 * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+31], N[(N[(N[(N[(N[(y * y), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.6000000000000001e43

   1. Initial program 4.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 55.2%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 70.1

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

   7. Applied rewrites 70.1%

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

   if -3.6000000000000001e43 < y < 7.2e-94

   1. Initial program 97.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{i + c \cdot y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{c \cdot y + \color{blue}{i}} \]

      2. lower-fma.f64 84.1

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, \color{blue}{y}, i\right)} \]

   4. Applied rewrites 84.1%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(c, y, i\right)}} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{\left(\color{blue}{\frac{54929528941}{2000000}} \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 80.1%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705} \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]

   if 7.2e-94 < y < 3.5e31

   1. Initial program 92.6%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{i + c \cdot y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{c \cdot y + \color{blue}{i}} \]

      2. lower-fma.f64 56.5

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, \color{blue}{y}, i\right)} \]

   4. Applied rewrites 56.5%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(c, y, i\right)}} \]

   5. Taylor expanded in z around inf

      \[\leadsto \frac{\color{blue}{\left({y}^{2} \cdot z\right)} \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{\left({y}^{2} \cdot \color{blue}{z}\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]

      2. unpow2 N/A

         \[\leadsto \frac{\left(\left(y \cdot y\right) \cdot z\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]

      3. lower-*.f64 38.9

         \[\leadsto \frac{\left(\left(y \cdot y\right) \cdot z\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]

   7. Applied rewrites 38.9%

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

   if 3.5e31 < y

   1. Initial program 5.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 4.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 67.8

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

   7. Applied rewrites 67.8%

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

Alternative 13: 70.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+43}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 0.0048:\\ \;\;\;\;\frac{\left(27464.7644705 \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.6e+43)
   (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
   (if (<= y 0.0048)
     (/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (fma c y i))
     (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.6e+43) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 0.0048) {
		tmp = ((((27464.7644705 * y) + 230661.510616) * y) + t) / fma(c, y, i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.6e+43)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 0.0048)
		tmp = Float64(Float64(Float64(Float64(Float64(27464.7644705 * y) + 230661.510616) * y) + t) / fma(c, y, i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.6e+43], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 0.0048], N[(N[(N[(N[(N[(27464.7644705 * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6000000000000001e43

   1. Initial program 4.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 55.2%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 70.1

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

   7. Applied rewrites 70.1%

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

   if -3.6000000000000001e43 < y < 0.00479999999999999958

   1. Initial program 97.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{i + c \cdot y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{c \cdot y + \color{blue}{i}} \]

      2. lower-fma.f64 81.2

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, \color{blue}{y}, i\right)} \]

   4. Applied rewrites 81.2%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(c, y, i\right)}} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{\left(\color{blue}{\frac{54929528941}{2000000}} \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 75.0%

      \[\leadsto \frac{\left(\color{blue}{27464.7644705} \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]

   if 0.00479999999999999958 < y

   1. Initial program 11.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 9.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 62.1

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

   7. Applied rewrites 62.1%

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

Alternative 14: 70.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;\left(-\frac{z \cdot \left(\frac{a}{y} - 1\right)}{y}\right) + x\\ \mathbf{elif}\;y \leq 0.0048:\\ \;\;\;\;\frac{230661.510616 \cdot y + t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= y -3.2e+43)
   (+ (- (/ (* z (- (/ a y) 1.0)) y)) x)
   (if (<= y 0.0048) (/ (+ (* 230661.510616 y) t) (fma c y i)) (+ x (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (y <= -3.2e+43) {
		tmp = -((z * ((a / y) - 1.0)) / y) + x;
	} else if (y <= 0.0048) {
		tmp = ((230661.510616 * y) + t) / fma(c, y, i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (y <= -3.2e+43)
		tmp = Float64(Float64(-Float64(Float64(z * Float64(Float64(a / y) - 1.0)) / y)) + x);
	elseif (y <= 0.0048)
		tmp = Float64(Float64(Float64(230661.510616 * y) + t) / fma(c, y, i));
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[y, -3.2e+43], N[((-N[(N[(z * N[(N[(a / y), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision], If[LessEqual[y, 0.0048], N[(N[(N[(230661.510616 * y), $MachinePrecision] + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.20000000000000014e43

   1. Initial program 4.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around -inf

      \[\leadsto \color{blue}{x + -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

      2. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\left(-1 \cdot z + -1 \cdot \frac{\frac{54929528941}{2000000} - \left(-1 \cdot \left(a \cdot \left(-1 \cdot z - -1 \cdot \left(a \cdot x\right)\right)\right) + b \cdot x\right)}{y}\right) - -1 \cdot \left(a \cdot x\right)}{y} + \color{blue}{x} \]

   4. Applied rewrites 55.2%

      \[\leadsto \color{blue}{\left(-\frac{\left(\left(-\frac{27464.7644705 - \mathsf{fma}\left(-a, \left(-z\right) - \left(-a\right) \cdot x, b \cdot x\right)}{y}\right) + \left(-z\right)\right) - \left(-a\right) \cdot x}{y}\right) + x} \]

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 70.1

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

   7. Applied rewrites 70.1%

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

   if -3.20000000000000014e43 < y < 0.00479999999999999958

   1. Initial program 97.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{i + c \cdot y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{c \cdot y + \color{blue}{i}} \]

      2. lower-fma.f64 81.2

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, \color{blue}{y}, i\right)} \]

   4. Applied rewrites 81.2%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(c, y, i\right)}} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000}} \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 74.9%

      \[\leadsto \frac{\color{blue}{230661.510616} \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]

   if 0.00479999999999999958 < y

   1. Initial program 11.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 9.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 62.1

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

   7. Applied rewrites 62.1%

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

Alternative 15: 70.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.0048:\\ \;\;\;\;\frac{230661.510616 \cdot y + t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -3.2e+43)
     t_1
     (if (<= y 0.0048) (/ (+ (* 230661.510616 y) t) (fma c y i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -3.2e+43) {
		tmp = t_1;
	} else if (y <= 0.0048) {
		tmp = ((230661.510616 * y) + t) / fma(c, y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -3.2e+43)
		tmp = t_1;
	elseif (y <= 0.0048)
		tmp = Float64(Float64(Float64(230661.510616 * y) + t) / fma(c, y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+43], t$95$1, If[LessEqual[y, 0.0048], N[(N[(N[(230661.510616 * y), $MachinePrecision] + t), $MachinePrecision] / N[(c * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000014e43 or 0.00479999999999999958 < y

   1. Initial program 8.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 6.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 66.0

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

   7. Applied rewrites 66.0%

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

   if -3.20000000000000014e43 < y < 0.00479999999999999958

   1. Initial program 97.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{i + c \cdot y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{c \cdot y + \color{blue}{i}} \]

      2. lower-fma.f64 81.2

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, \color{blue}{y}, i\right)} \]

   4. Applied rewrites 81.2%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(c, y, i\right)}} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{\frac{28832688827}{125000}} \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 74.9%

      \[\leadsto \frac{\color{blue}{230661.510616} \cdot y + t}{\mathsf{fma}\left(c, y, i\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 64.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{-163}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{i}\right)\\ \mathbf{elif}\;y \leq 0.0048:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -3.2e+43)
     t_1
     (if (<= y -2.45e-163)
       (fma y (/ 230661.510616 i) (/ t i))
       (if (<= y 0.0048) (/ t (fma c y i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -3.2e+43) {
		tmp = t_1;
	} else if (y <= -2.45e-163) {
		tmp = fma(y, (230661.510616 / i), (t / i));
	} else if (y <= 0.0048) {
		tmp = t / fma(c, y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -3.2e+43)
		tmp = t_1;
	elseif (y <= -2.45e-163)
		tmp = fma(y, Float64(230661.510616 / i), Float64(t / i));
	elseif (y <= 0.0048)
		tmp = Float64(t / fma(c, y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+43], t$95$1, If[LessEqual[y, -2.45e-163], N[(y * N[(230661.510616 / i), $MachinePrecision] + N[(t / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0048], N[(t / N[(c * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.20000000000000014e43 or 0.00479999999999999958 < y

   1. Initial program 8.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 6.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 66.0

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

   7. Applied rewrites 66.0%

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

   if -3.20000000000000014e43 < y < -2.4500000000000001e-163

   1. Initial program 92.4%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   3. Applied rewrites 93.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right)} \]

   4. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{\frac{28832688827}{125000}}{i}}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]
   5. Step-by-step derivation

      1. lift-/.f64 46.8

         \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{\color{blue}{i}}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]

   6. Applied rewrites 46.8%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{230661.510616}{i}}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right) \]

   7. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i}, \frac{t}{\color{blue}{i}}\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 35.5%

      \[\leadsto \mathsf{fma}\left(y, \frac{230661.510616}{i}, \frac{t}{\color{blue}{i}}\right) \]

   if -2.4500000000000001e-163 < y < 0.00479999999999999958

   1. Initial program 99.7%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{i + c \cdot y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{c \cdot y + \color{blue}{i}} \]

      2. lower-fma.f64 88.6

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, \color{blue}{y}, i\right)} \]

   4. Applied rewrites 88.6%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(c, y, i\right)}} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t}}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 73.1%

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

Alternative 17: 63.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.0048:\\ \;\;\;\;\frac{t}{\mathsf{fma}\left(c, y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -1.16e+42) t_1 (if (<= y 0.0048) (/ t (fma c y i)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -1.16e+42) {
		tmp = t_1;
	} else if (y <= 0.0048) {
		tmp = t / fma(c, y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -1.16e+42)
		tmp = t_1;
	elseif (y <= 0.0048)
		tmp = Float64(t / fma(c, y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.16e+42], t$95$1, If[LessEqual[y, 0.0048], N[(t / N[(c * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15999999999999995e42 or 0.00479999999999999958 < y

   1. Initial program 8.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 6.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 65.9

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

   7. Applied rewrites 65.9%

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

   if -1.15999999999999995e42 < y < 0.00479999999999999958

   1. Initial program 97.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{\color{blue}{i + c \cdot y}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{54929528941}{2000000}\right) \cdot y + \frac{28832688827}{125000}\right) \cdot y + t}{c \cdot y + \color{blue}{i}} \]

      2. lower-fma.f64 81.2

         \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\mathsf{fma}\left(c, \color{blue}{y}, i\right)} \]

   4. Applied rewrites 81.2%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{\mathsf{fma}\left(c, y, i\right)}} \]

   5. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{t}}{\mathsf{fma}\left(c, y, i\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 63.0%

      \[\leadsto \frac{\color{blue}{t}}{\mathsf{fma}\left(c, y, i\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 56.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z}{y}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.00135:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ x (/ z y))))
   (if (<= y -3.2e+43) t_1 (if (<= y 0.00135) (/ t i) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -3.2e+43) {
		tmp = t_1;
	} else if (y <= 0.00135) {
		tmp = t / i;
	} 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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z / y)
    if (y <= (-3.2d+43)) then
        tmp = t_1
    else if (y <= 0.00135d0) then
        tmp = t / i
    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 c, double i) {
	double t_1 = x + (z / y);
	double tmp;
	if (y <= -3.2e+43) {
		tmp = t_1;
	} else if (y <= 0.00135) {
		tmp = t / i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = x + (z / y)
	tmp = 0
	if y <= -3.2e+43:
		tmp = t_1
	elif y <= 0.00135:
		tmp = t / i
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(x + Float64(z / y))
	tmp = 0.0
	if (y <= -3.2e+43)
		tmp = t_1;
	elseif (y <= 0.00135)
		tmp = Float64(t / i);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = x + (z / y);
	tmp = 0.0;
	if (y <= -3.2e+43)
		tmp = t_1;
	elseif (y <= 0.00135)
		tmp = t / i;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+43], t$95$1, If[LessEqual[y, 0.00135], N[(t / i), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000014e43 or 0.0013500000000000001 < y

   1. Initial program 8.2%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in a around 0

      \[\leadsto \color{blue}{\frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]
   3. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + y \cdot \left(\frac{28832688827}{125000} + y \cdot \left(\frac{54929528941}{2000000} + y \cdot \left(z + x \cdot y\right)\right)\right)}{\color{blue}{i + y \cdot \left(c + y \cdot \left(b + {y}^{2}\right)\right)}} \]

   4. Applied rewrites 6.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, y, b\right), y, c\right), y, i\right)}} \]

   5. Taylor expanded in y around inf

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 65.9

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

   7. Applied rewrites 65.9%

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

   if -3.20000000000000014e43 < y < 0.0013500000000000001

   1. Initial program 97.5%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 49.1

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

   4. Applied rewrites 49.1%

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

Alternative 19: 48.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \leq \infty:\\ \;\;\;\;\frac{t}{i}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      INFINITY)
   (/ t i)
   x))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= ((double) INFINITY)) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= Double.POSITIVE_INFINITY) {
		tmp = t / i;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= math.inf:
		tmp = t / i
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i)) <= Inf)
		tmp = Float64(t / i);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= Inf)
		tmp = t / i;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(t / i), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i)) < +inf.0

   1. Initial program 90.1%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 43.1

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

   4. Applied rewrites 43.1%

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

   if +inf.0 < (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x y) z) y) #s(literal 54929528941/2000000 binary64)) y) #s(literal 28832688827/125000 binary64)) y) t) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 y a) y) b) y) c) y) i))

   1. Initial program 0.0%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 57.6%

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

Alternative 20: 25.2% accurate, 46.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	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, c, i)
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), intent (in) :: c
    real(8), intent (in) :: i
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.1%

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

2. Taylor expanded in y around inf

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

4. Applied rewrites 25.2%

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

Reproduce

herbie shell --seed 2025112 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))