Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.9% → 84.6%

Time: 6.9s

Alternatives: 14

Speedup: 0.8×

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: 55.9% 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: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
           t)
          (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))))
   (if (<= t_1 INFINITY) 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 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

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 * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = x + (z / y)
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

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

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 55.9%

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

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 33.4

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

   7. Applied rewrites 33.4%

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

Alternative 2: 84.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      INFINITY)
   (*
    (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t)
    (/ 1.0 (fma (fma (fma (+ 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 ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= ((double) INFINITY)) {
		tmp = fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) * (1.0 / fma(fma(fma((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 (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(fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) * Float64(1.0 / fma(fma(fma(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[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[(N[(N[(N[(N[(x * y + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] * N[(1.0 / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]

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 55.9%

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

   3. Applied rewrites 55.8%

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

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 33.4

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

   7. Applied rewrites 33.4%

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

Alternative 3: 80.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\\ \mathbf{if}\;\frac{t\_1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \leq \infty:\\ \;\;\;\;\frac{t\_1}{\left(\left(b + y \cdot y\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (+
          (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
          t)))
   (if (<= (/ t_1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)) INFINITY)
     (/ t_1 (+ (* (+ (* (+ b (* y y)) 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 = (((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t;
	double tmp;
	if ((t_1 / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= ((double) INFINITY)) {
		tmp = t_1 / (((((b + (y * y)) * y) + c) * y) + i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

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 * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t;
	double tmp;
	if ((t_1 / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= Double.POSITIVE_INFINITY) {
		tmp = t_1 / (((((b + (y * y)) * y) + c) * y) + i);
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t
	tmp = 0
	if (t_1 / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= math.inf:
		tmp = t_1 / (((((b + (y * y)) * 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(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t)
	tmp = 0.0
	if (Float64(t_1 / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i)) <= Inf)
		tmp = Float64(t_1 / Float64(Float64(Float64(Float64(Float64(b + Float64(y * y)) * 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)
	t_1 = (((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t;
	tmp = 0.0;
	if ((t_1 / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= Inf)
		tmp = t_1 / (((((b + (y * y)) * y) + c) * y) + i);
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

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

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 55.9%

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

   2. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 52.2

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

   4. Applied rewrites 52.2%

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

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 33.4

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

   7. Applied rewrites 33.4%

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

Alternative 4: 80.8% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      INFINITY)
   (*
    (fma (fma (fma (fma x y z) y 27464.7644705) y 230661.510616) y t)
    (/ 1.0 (fma (fma (+ b (* y y)) 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 ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= ((double) INFINITY)) {
		tmp = fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) * (1.0 / fma(fma((b + (y * y)), 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 (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(fma(fma(fma(fma(x, y, z), y, 27464.7644705), y, 230661.510616), y, t) * Float64(1.0 / fma(fma(Float64(b + Float64(y * y)), 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[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[(N[(N[(N[(N[(x * y + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] * N[(1.0 / N[(N[(N[(b + N[(y * y), $MachinePrecision]), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]

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 55.9%

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

   3. Applied rewrites 55.8%

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

   4. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. pow2 N/A

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

      3. lift-*.f64 52.1

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

   6. Applied rewrites 52.1%

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

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 33.4

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

   7. Applied rewrites 33.4%

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

Alternative 5: 76.2% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      INFINITY)
   (/
    (fma (- 230661.510616 (* -27464.7644705 y)) y t)
    (fma (fma (fma (+ 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 ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= ((double) INFINITY)) {
		tmp = fma((230661.510616 - (-27464.7644705 * y)), y, t) / fma(fma(fma((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 (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(fma(Float64(230661.510616 - Float64(-27464.7644705 * y)), y, t) / fma(fma(fma(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[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[(N[(N[(230661.510616 - N[(-27464.7644705 * y), $MachinePrecision]), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(y + a), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]

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 55.9%

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

   2. Taylor expanded in y around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. metadata-eval 48.0

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

   4. Applied rewrites 48.0%

      \[\leadsto \frac{\color{blue}{\left(230661.510616 - -27464.7644705 \cdot y\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lower-fma.f64 48.0

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

      4. lift-+.f64 N/A

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

   6. Applied rewrites 48.0%

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

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 33.4

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

   7. Applied rewrites 33.4%

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

Alternative 6: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\\ \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{t\_1} \leq \infty:\\ \;\;\;\;\frac{t - -230661.510616 \cdot y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
   (if (<=
        (/
         (+
          (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
          t)
         t_1)
        INFINITY)
     (/ (- t (* -230661.510616 y)) 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 = ((((((y + a) * y) + b) * y) + c) * y) + i;
	double tmp;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / t_1) <= ((double) INFINITY)) {
		tmp = (t - (-230661.510616 * y)) / t_1;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((((((y + a) * y) + b) * y) + c) * y) + i;
	double tmp;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = (t - (-230661.510616 * y)) / t_1;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((((((y + a) * y) + b) * y) + c) * y) + i
	tmp = 0
	if (((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / t_1) <= math.inf:
		tmp = (t - (-230661.510616 * y)) / t_1
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + 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) / t_1) <= Inf)
		tmp = Float64(Float64(t - Float64(-230661.510616 * y)) / t_1);
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((((((y + a) * y) + b) * y) + c) * y) + i;
	tmp = 0.0;
	if ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / t_1) <= Inf)
		tmp = (t - (-230661.510616 * y)) / t_1;
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]}, 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] / t$95$1), $MachinePrecision], Infinity], N[(N[(t - N[(-230661.510616 * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]

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 55.9%

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

   2. Taylor expanded in 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. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. metadata-eval 48.0

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

   4. Applied rewrites 48.0%

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

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 33.4

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

   7. Applied rewrites 33.4%

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

Alternative 7: 73.4% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      INFINITY)
   (/
    (+ (* (- 230661.510616 (* -27464.7644705 y)) y) t)
    (+ (* (+ (* 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 ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= ((double) INFINITY)) {
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((((b * y) + c) * y) + i);
	} else {
		tmp = x + (z / y);
	}
	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 = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((((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 (((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= math.inf:
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((((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 (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(Float64(Float64(Float64(230661.510616 - Float64(-27464.7644705 * y)) * y) + t) / Float64(Float64(Float64(Float64(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 ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= Inf)
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((((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[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[(N[(N[(N[(230661.510616 - N[(-27464.7644705 * y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(b * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]

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 55.9%

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

   2. Taylor expanded in y around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. metadata-eval 48.0

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

   4. Applied rewrites 48.0%

      \[\leadsto \frac{\color{blue}{\left(230661.510616 - -27464.7644705 \cdot y\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 45.2

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

   7. Applied rewrites 45.2%

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

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 33.4

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

   7. Applied rewrites 33.4%

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

Alternative 8: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\\ t_2 := \frac{t}{t\_1}\\ t_3 := \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{t\_1}\\ \mathbf{if}\;t\_3 \leq -4 \cdot 10^{-112}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{-143}:\\ \;\;\;\;\frac{\left(230661.510616 - -27464.7644705 \cdot y\right) \cdot y + t}{c \cdot y + i}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
        (t_2 (/ t t_1))
        (t_3
         (/
          (+
           (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
           t)
          t_1)))
   (if (<= t_3 -4e-112)
     t_2
     (if (<= t_3 1e-143)
       (/ (+ (* (- 230661.510616 (* -27464.7644705 y)) y) t) (+ (* c y) i))
       (if (<= t_3 INFINITY) t_2 (+ 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 = ((((((y + a) * y) + b) * y) + c) * y) + i;
	double t_2 = t / t_1;
	double t_3 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / t_1;
	double tmp;
	if (t_3 <= -4e-112) {
		tmp = t_2;
	} else if (t_3 <= 1e-143) {
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((c * y) + i);
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = ((((((y + a) * y) + b) * y) + c) * y) + i;
	double t_2 = t / t_1;
	double t_3 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / t_1;
	double tmp;
	if (t_3 <= -4e-112) {
		tmp = t_2;
	} else if (t_3 <= 1e-143) {
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((c * y) + i);
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = ((((((y + a) * y) + b) * y) + c) * y) + i
	t_2 = t / t_1
	t_3 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / t_1
	tmp = 0
	if t_3 <= -4e-112:
		tmp = t_2
	elif t_3 <= 1e-143:
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((c * y) + i)
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = x + (z / y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i)
	t_2 = Float64(t / t_1)
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / t_1)
	tmp = 0.0
	if (t_3 <= -4e-112)
		tmp = t_2;
	elseif (t_3 <= 1e-143)
		tmp = Float64(Float64(Float64(Float64(230661.510616 - Float64(-27464.7644705 * y)) * y) + t) / Float64(Float64(c * y) + i));
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(x + Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = ((((((y + a) * y) + b) * y) + c) * y) + i;
	t_2 = t / t_1;
	t_3 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / t_1;
	tmp = 0.0;
	if (t_3 <= -4e-112)
		tmp = t_2;
	elseif (t_3 <= 1e-143)
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((c * y) + i);
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = x + (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]}, Block[{t$95$2 = N[(t / t$95$1), $MachinePrecision]}, Block[{t$95$3 = 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] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -4e-112], t$95$2, If[LessEqual[t$95$3, 1e-143], N[(N[(N[(N[(230661.510616 - N[(-27464.7644705 * y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 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)) < -3.9999999999999998e-112 or 9.9999999999999995e-144 < (/.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 55.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 41.0%

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

   if -3.9999999999999998e-112 < (/.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)) < 9.9999999999999995e-144

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. metadata-eval 48.0

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

   4. Applied rewrites 48.0%

      \[\leadsto \frac{\color{blue}{\left(230661.510616 - -27464.7644705 \cdot y\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 41.7

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

   7. Applied rewrites 41.7%

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

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 33.4

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

   7. Applied rewrites 33.4%

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

Alternative 9: 70.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(b + y \cdot y, y, c\right), y, i\right)}\\ t_2 := \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-143}:\\ \;\;\;\;\frac{\left(230661.510616 - -27464.7644705 \cdot y\right) \cdot y + t}{c \cdot y + i}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (* t (/ 1.0 (fma (fma (+ b (* y y)) y c) y i))))
        (t_2
         (/
          (+
           (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
           t)
          (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))))
   (if (<= t_2 -1e+29)
     t_1
     (if (<= t_2 1e-143)
       (/ (+ (* (- 230661.510616 (* -27464.7644705 y)) y) t) (+ (* c y) i))
       (if (<= t_2 INFINITY) 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 = t * (1.0 / fma(fma((b + (y * y)), y, c), y, i));
	double t_2 = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	double tmp;
	if (t_2 <= -1e+29) {
		tmp = t_1;
	} else if (t_2 <= 1e-143) {
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((c * y) + i);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x + (z / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(t * Float64(1.0 / fma(fma(Float64(b + Float64(y * y)), y, c), y, i)))
	t_2 = 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))
	tmp = 0.0
	if (t_2 <= -1e+29)
		tmp = t_1;
	elseif (t_2 <= 1e-143)
		tmp = Float64(Float64(Float64(Float64(230661.510616 - Float64(-27464.7644705 * y)) * y) + t) / Float64(Float64(c * y) + i));
	elseif (t_2 <= Inf)
		tmp = 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[(t * N[(1.0 / N[(N[(N[(b + N[(y * y), $MachinePrecision]), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, If[LessEqual[t$95$2, -1e+29], t$95$1, If[LessEqual[t$95$2, 1e-143], N[(N[(N[(N[(230661.510616 - N[(-27464.7644705 * y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 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)) < -9.99999999999999914e28 or 9.9999999999999995e-144 < (/.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 55.9%

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

   3. Applied rewrites 55.8%

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

   4. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. pow2 N/A

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

      3. lift-*.f64 52.1

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

   6. Applied rewrites 52.1%

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

   7. Taylor expanded in y around 0

      \[\leadsto \color{blue}{t} \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(b + y \cdot y, y, c\right), y, i\right)} \]
   8. Step-by-step derivation

   9. Applied rewrites 39.5%

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

   if -9.99999999999999914e28 < (/.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)) < 9.9999999999999995e-144

   1. Initial program 55.9%

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

   2. Taylor expanded in y around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. metadata-eval 48.0

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

   4. Applied rewrites 48.0%

      \[\leadsto \frac{\color{blue}{\left(230661.510616 - -27464.7644705 \cdot y\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 41.7

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

   7. Applied rewrites 41.7%

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

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 33.4

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

   7. Applied rewrites 33.4%

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

Alternative 10: 69.6% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      INFINITY)
   (/ (+ (* (- 230661.510616 (* -27464.7644705 y)) y) t) (+ (* 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 ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= ((double) INFINITY)) {
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((c * y) + i);
	} else {
		tmp = x + (z / y);
	}
	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 = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((c * y) + i);
	} else {
		tmp = x + (z / y);
	}
	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 = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((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 (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(Float64(Float64(Float64(230661.510616 - Float64(-27464.7644705 * y)) * y) + t) / Float64(Float64(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 ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= Inf)
		tmp = (((230661.510616 - (-27464.7644705 * y)) * y) + t) / ((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[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[(N[(N[(N[(230661.510616 - N[(-27464.7644705 * y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]

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 55.9%

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

   2. Taylor expanded in y around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. lower--.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. metadata-eval 48.0

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

   4. Applied rewrites 48.0%

      \[\leadsto \frac{\color{blue}{\left(230661.510616 - -27464.7644705 \cdot y\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 41.7

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

   7. Applied rewrites 41.7%

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

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 33.4

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

   7. Applied rewrites 33.4%

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

Alternative 11: 59.4% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<=
      (/
       (+
        (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
        t)
       (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
      INFINITY)
   (/ (+ t (* 230661.510616 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 ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= ((double) INFINITY)) {
		tmp = (t + (230661.510616 * y)) / i;
	} else {
		tmp = x + (z / y);
	}
	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 + (230661.510616 * y)) / i;
	} else {
		tmp = x + (z / y);
	}
	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 + (230661.510616 * y)) / i
	else:
		tmp = x + (z / y)
	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(Float64(t + Float64(230661.510616 * 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 ((((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)) <= Inf)
		tmp = (t + (230661.510616 * y)) / i;
	else
		tmp = x + (z / y);
	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[(N[(t + N[(230661.510616 * y), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]

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 55.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{y \cdot \left(\frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]
   3. Step-by-step derivation

      1. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}}, \frac{t}{i}\right) \]

      2. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{28832688827}{125000} \cdot \frac{1}{i} - \color{blue}{\frac{c \cdot t}{{i}^{2}}}, \frac{t}{i}\right) \]

      3. mult-flip-rev N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \frac{\color{blue}{c \cdot t}}{{i}^{2}}, \frac{t}{i}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - \frac{\color{blue}{c \cdot t}}{{i}^{2}}, \frac{t}{i}\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - c \cdot \color{blue}{\frac{t}{{i}^{2}}}, \frac{t}{i}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - c \cdot \color{blue}{\frac{t}{{i}^{2}}}, \frac{t}{i}\right) \]

      7. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - c \cdot \frac{t}{\color{blue}{{i}^{2}}}, \frac{t}{i}\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - c \cdot \frac{t}{i \cdot \color{blue}{i}}, \frac{t}{i}\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{\frac{28832688827}{125000}}{i} - c \cdot \frac{t}{i \cdot \color{blue}{i}}, \frac{t}{i}\right) \]

      10. lower-/.f64 27.3

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

   4. Applied rewrites 27.3%

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

   5. Taylor expanded in i around inf

      \[\leadsto \frac{t + \frac{28832688827}{125000} \cdot y}{\color{blue}{i}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t + \frac{28832688827}{125000} \cdot y}{i} \]

      2. lower-+.f64 N/A

         \[\leadsto \frac{t + \frac{28832688827}{125000} \cdot y}{i} \]

      3. lower-*.f64 31.9

         \[\leadsto \frac{t + 230661.510616 \cdot y}{i} \]

   7. Applied rewrites 31.9%

      \[\leadsto \frac{t + 230661.510616 \cdot y}{\color{blue}{i}} \]

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 33.4

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

   7. Applied rewrites 33.4%

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

Alternative 12: 56.4% accurate, 0.8× speedup

Math

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

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 (/ z y))))

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 + (z / y);
	}
	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 + (z / y);
	}
	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 + (z / y)
	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 = 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 ((((((((((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 + (z / y);
	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], N[(x + N[(z / y), $MachinePrecision]), $MachinePrecision]]

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 55.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 29.0

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

   4. Applied rewrites 29.0%

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

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in a around 0

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

      1. lower-+.f64 N/A

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

      2. lower-/.f64 33.4

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

   7. Applied rewrites 33.4%

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

Alternative 13: 35.1% accurate, 0.9× speedup

Math

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

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)
   (/ z y)))

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 = z / y;
	}
	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 = z / y;
	}
	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 = z / y
	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 = Float64(z / y);
	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 = z / y;
	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], N[(z / y), $MachinePrecision]]

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 55.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 29.0

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

   4. Applied rewrites 29.0%

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

   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 55.9%

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

   2. Taylor expanded in y around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-*.f64 31.8

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

   4. Applied rewrites 31.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 10.8

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

   7. Applied rewrites 10.8%

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

Alternative 14: 10.8% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \frac{z}{y} \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, 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 = z / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(z / y), $MachinePrecision]

Derivation

1. Initial program 55.9%

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

2. Taylor expanded in y around -inf

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

   1. lower-+.f64 N/A

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

   2. mul-1-neg N/A

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

   3. lower-neg.f64 N/A

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

   4. lower-/.f64 N/A

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

   5. lower--.f64 N/A

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

   6. mul-1-neg N/A

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

   7. lower-neg.f64 N/A

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

   8. mul-1-neg N/A

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

   9. lower-neg.f64 N/A

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

   10. lower-*.f64 31.8

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

4. Applied rewrites 31.8%

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

5. Taylor expanded in x around 0

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

   1. lower-/.f64 10.8

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

7. Applied rewrites 10.8%

   \[\leadsto \frac{z}{\color{blue}{y}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025136 
(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)))