Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 55.5% → 82.1%

Time: 9.5s

Alternatives: 18

Speedup: 1.7×

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: 55.5% 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: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)\\ t_2 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1 \cdot 10^{+174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(\frac{27464.7644705}{a \cdot \left(x \cdot y\right)} + \left(\frac{230661.510616}{a \cdot \left(x \cdot \left(y \cdot y\right)\right)} + \left(\frac{t}{a \cdot \left(x \cdot \left(\left(y \cdot y\right) \cdot y\right)\right)} + \left(\frac{y}{a} + \frac{z}{a \cdot x}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right)}{t\_1}, \frac{t}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (fma (fma (fma (+ a y) y b) y c) y i))
        (t_2 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1e+174)
     t_2
     (if (<= y -3.3e+56)
       (*
        x
        (+
         (/ 27464.7644705 (* a (* x y)))
         (+
          (/ 230661.510616 (* a (* x (* y y))))
          (+ (/ t (* a (* x (* (* y y) y)))) (+ (/ y a) (/ z (* a x)))))))
       (if (<= y 7e+63)
         (fma
          y
          (/ (fma (fma (fma y x z) y 27464.7644705) y 230661.510616) t_1)
          (/ t t_1))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = fma(fma(fma((a + y), y, b), y, c), y, i);
	double t_2 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1e+174) {
		tmp = t_2;
	} else if (y <= -3.3e+56) {
		tmp = x * ((27464.7644705 / (a * (x * y))) + ((230661.510616 / (a * (x * (y * y)))) + ((t / (a * (x * ((y * y) * y)))) + ((y / a) + (z / (a * x))))));
	} else if (y <= 7e+63) {
		tmp = fma(y, (fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616) / t_1), (t / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = fma(fma(fma(Float64(a + y), y, b), y, c), y, i)
	t_2 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1e+174)
		tmp = t_2;
	elseif (y <= -3.3e+56)
		tmp = Float64(x * Float64(Float64(27464.7644705 / Float64(a * Float64(x * y))) + Float64(Float64(230661.510616 / Float64(a * Float64(x * Float64(y * y)))) + Float64(Float64(t / Float64(a * Float64(x * Float64(Float64(y * y) * y)))) + Float64(Float64(y / a) + Float64(z / Float64(a * x)))))));
	elseif (y <= 7e+63)
		tmp = fma(y, Float64(fma(fma(fma(y, x, z), y, 27464.7644705), y, 230661.510616) / t_1), Float64(t / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]}, Block[{t$95$2 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1e+174], t$95$2, If[LessEqual[y, -3.3e+56], N[(x * N[(N[(27464.7644705 / N[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 / N[(a * N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(a * N[(x * N[(N[(y * y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / a), $MachinePrecision] + N[(z / N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+63], N[(y * N[(N[(N[(N[(y * x + z), $MachinePrecision] * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000007e174 or 7.00000000000000059e63 < y

   1. Initial program 1.1%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 73.5

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

   4. Applied rewrites 73.5%

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

   if -1.00000000000000007e174 < y < -3.30000000000000002e56

   1. Initial program 4.5%

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

   3. Applied rewrites 7.0%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(\frac{\frac{54929528941}{2000000}}{a \cdot \left(x \cdot y\right)} + \color{blue}{\left(\frac{\frac{28832688827}{125000}}{a \cdot \left(x \cdot {y}^{2}\right)} + \left(\frac{t}{a \cdot \left(x \cdot {y}^{3}\right)} + \left(\frac{y}{a} + \frac{z}{a \cdot x}\right)\right)\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(\frac{\frac{54929528941}{2000000}}{a \cdot \left(x \cdot y\right)} + \left(\frac{\frac{28832688827}{125000}}{a \cdot \left(x \cdot {y}^{2}\right)} + \color{blue}{\left(\frac{t}{a \cdot \left(x \cdot {y}^{3}\right)} + \left(\frac{y}{a} + \frac{z}{a \cdot x}\right)\right)}\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \left(\frac{\frac{54929528941}{2000000}}{a \cdot \left(x \cdot y\right)} + \left(\frac{\frac{28832688827}{125000}}{a \cdot \left(x \cdot {y}^{2}\right)} + \left(\color{blue}{\frac{t}{a \cdot \left(x \cdot {y}^{3}\right)}} + \left(\frac{y}{a} + \frac{z}{a \cdot x}\right)\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(\frac{\frac{54929528941}{2000000}}{a \cdot \left(x \cdot y\right)} + \left(\frac{\frac{28832688827}{125000}}{a \cdot \left(x \cdot {y}^{2}\right)} + \left(\frac{t}{\color{blue}{a \cdot \left(x \cdot {y}^{3}\right)}} + \left(\frac{y}{a} + \frac{z}{a \cdot x}\right)\right)\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto x \cdot \left(\frac{\frac{54929528941}{2000000}}{a \cdot \left(x \cdot y\right)} + \left(\frac{\frac{28832688827}{125000}}{a \cdot \left(x \cdot {y}^{2}\right)} + \left(\frac{t}{a \cdot \color{blue}{\left(x \cdot {y}^{3}\right)}} + \left(\frac{y}{a} + \frac{z}{a \cdot x}\right)\right)\right)\right) \]

      6. lower-+.f64 N/A

         \[\leadsto x \cdot \left(\frac{\frac{54929528941}{2000000}}{a \cdot \left(x \cdot y\right)} + \left(\frac{\frac{28832688827}{125000}}{a \cdot \left(x \cdot {y}^{2}\right)} + \left(\frac{t}{a \cdot \left(x \cdot {y}^{3}\right)} + \color{blue}{\left(\frac{y}{a} + \frac{z}{a \cdot x}\right)}\right)\right)\right) \]

   9. Applied rewrites 30.3%

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

   if -3.30000000000000002e56 < y < 7.00000000000000059e63

   1. Initial program 91.9%

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

   3. Applied rewrites 92.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y, x, z\right), y, 27464.7644705\right), y, 230661.510616\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}, \frac{t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 81.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(\frac{27464.7644705}{a \cdot \left(x \cdot y\right)} + \left(\frac{230661.510616}{a \cdot \left(x \cdot \left(y \cdot y\right)\right)} + \left(\frac{t}{a \cdot \left(x \cdot \left(\left(y \cdot y\right) \cdot y\right)\right)} + \left(\frac{y}{a} + \frac{z}{a \cdot x}\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1e+174)
     t_1
     (if (<= y -1.1e+56)
       (*
        x
        (+
         (/ 27464.7644705 (* a (* x y)))
         (+
          (/ 230661.510616 (* a (* x (* y y))))
          (+ (/ t (* a (* x (* (* y y) y)))) (+ (/ y a) (/ z (* a x)))))))
       (if (<= y 1.5e+55)
         (/
          (+
           (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y)
           t)
          (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1e+174) {
		tmp = t_1;
	} else if (y <= -1.1e+56) {
		tmp = x * ((27464.7644705 / (a * (x * y))) + ((230661.510616 / (a * (x * (y * y)))) + ((t / (a * (x * ((y * y) * y)))) + ((y / a) + (z / (a * x))))));
	} else if (y <= 1.5e+55) {
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -((-z - (-a * x)) / y) + x
    if (y <= (-1d+174)) then
        tmp = t_1
    else if (y <= (-1.1d+56)) then
        tmp = x * ((27464.7644705d0 / (a * (x * y))) + ((230661.510616d0 / (a * (x * (y * y)))) + ((t / (a * (x * ((y * y) * y)))) + ((y / a) + (z / (a * x))))))
    else if (y <= 1.5d+55) then
        tmp = ((((((((x * y) + z) * y) + 27464.7644705d0) * y) + 230661.510616d0) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1e+174) {
		tmp = t_1;
	} else if (y <= -1.1e+56) {
		tmp = x * ((27464.7644705 / (a * (x * y))) + ((230661.510616 / (a * (x * (y * y)))) + ((t / (a * (x * ((y * y) * y)))) + ((y / a) + (z / (a * x))))));
	} else if (y <= 1.5e+55) {
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -((-z - (-a * x)) / y) + x
	tmp = 0
	if y <= -1e+174:
		tmp = t_1
	elif y <= -1.1e+56:
		tmp = x * ((27464.7644705 / (a * (x * y))) + ((230661.510616 / (a * (x * (y * y)))) + ((t / (a * (x * ((y * y) * y)))) + ((y / a) + (z / (a * x))))))
	elif y <= 1.5e+55:
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1e+174)
		tmp = t_1;
	elseif (y <= -1.1e+56)
		tmp = Float64(x * Float64(Float64(27464.7644705 / Float64(a * Float64(x * y))) + Float64(Float64(230661.510616 / Float64(a * Float64(x * Float64(y * y)))) + Float64(Float64(t / Float64(a * Float64(x * Float64(Float64(y * y) * y)))) + Float64(Float64(y / a) + Float64(z / Float64(a * x)))))));
	elseif (y <= 1.5e+55)
		tmp = Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -((-z - (-a * x)) / y) + x;
	tmp = 0.0;
	if (y <= -1e+174)
		tmp = t_1;
	elseif (y <= -1.1e+56)
		tmp = x * ((27464.7644705 / (a * (x * y))) + ((230661.510616 / (a * (x * (y * y)))) + ((t / (a * (x * ((y * y) * y)))) + ((y / a) + (z / (a * x))))));
	elseif (y <= 1.5e+55)
		tmp = ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1e+174], t$95$1, If[LessEqual[y, -1.1e+56], N[(x * N[(N[(27464.7644705 / N[(a * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(230661.510616 / N[(a * N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(a * N[(x * N[(N[(y * y), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / a), $MachinePrecision] + N[(z / N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+55], 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], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000007e174 or 1.50000000000000008e55 < y

   1. Initial program 2.1%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 72.2

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

   4. Applied rewrites 72.2%

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

   if -1.00000000000000007e174 < y < -1.10000000000000008e56

   1. Initial program 4.5%

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

   3. Applied rewrites 7.1%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in x around inf

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

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(\frac{\frac{54929528941}{2000000}}{a \cdot \left(x \cdot y\right)} + \color{blue}{\left(\frac{\frac{28832688827}{125000}}{a \cdot \left(x \cdot {y}^{2}\right)} + \left(\frac{t}{a \cdot \left(x \cdot {y}^{3}\right)} + \left(\frac{y}{a} + \frac{z}{a \cdot x}\right)\right)\right)}\right) \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(\frac{\frac{54929528941}{2000000}}{a \cdot \left(x \cdot y\right)} + \left(\frac{\frac{28832688827}{125000}}{a \cdot \left(x \cdot {y}^{2}\right)} + \color{blue}{\left(\frac{t}{a \cdot \left(x \cdot {y}^{3}\right)} + \left(\frac{y}{a} + \frac{z}{a \cdot x}\right)\right)}\right)\right) \]

      3. lower-/.f64 N/A

         \[\leadsto x \cdot \left(\frac{\frac{54929528941}{2000000}}{a \cdot \left(x \cdot y\right)} + \left(\frac{\frac{28832688827}{125000}}{a \cdot \left(x \cdot {y}^{2}\right)} + \left(\color{blue}{\frac{t}{a \cdot \left(x \cdot {y}^{3}\right)}} + \left(\frac{y}{a} + \frac{z}{a \cdot x}\right)\right)\right)\right) \]

      4. lower-*.f64 N/A

         \[\leadsto x \cdot \left(\frac{\frac{54929528941}{2000000}}{a \cdot \left(x \cdot y\right)} + \left(\frac{\frac{28832688827}{125000}}{a \cdot \left(x \cdot {y}^{2}\right)} + \left(\frac{t}{\color{blue}{a \cdot \left(x \cdot {y}^{3}\right)}} + \left(\frac{y}{a} + \frac{z}{a \cdot x}\right)\right)\right)\right) \]

      5. lower-*.f64 N/A

         \[\leadsto x \cdot \left(\frac{\frac{54929528941}{2000000}}{a \cdot \left(x \cdot y\right)} + \left(\frac{\frac{28832688827}{125000}}{a \cdot \left(x \cdot {y}^{2}\right)} + \left(\frac{t}{a \cdot \color{blue}{\left(x \cdot {y}^{3}\right)}} + \left(\frac{y}{a} + \frac{z}{a \cdot x}\right)\right)\right)\right) \]

      6. lower-+.f64 N/A

         \[\leadsto x \cdot \left(\frac{\frac{54929528941}{2000000}}{a \cdot \left(x \cdot y\right)} + \left(\frac{\frac{28832688827}{125000}}{a \cdot \left(x \cdot {y}^{2}\right)} + \left(\frac{t}{a \cdot \left(x \cdot {y}^{3}\right)} + \color{blue}{\left(\frac{y}{a} + \frac{z}{a \cdot x}\right)}\right)\right)\right) \]

   9. Applied rewrites 30.3%

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

   if -1.10000000000000008e56 < y < 1.50000000000000008e55

   1. Initial program 92.8%

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 80.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+55}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1e+174)
     t_1
     (if (<= y -9.5e+55)
       (/ (+ z (fma 27464.7644705 (/ 1.0 y) (* x y))) a)
       (if (<= y 1.45e+55)
         (/
          (fma (fma (fma z y 27464.7644705) y 230661.510616) y t)
          (fma (fma (fma (+ a y) y b) y c) y i))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1e+174) {
		tmp = t_1;
	} else if (y <= -9.5e+55) {
		tmp = (z + fma(27464.7644705, (1.0 / y), (x * y))) / a;
	} else if (y <= 1.45e+55) {
		tmp = fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma((a + y), y, b), y, c), y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1e+174)
		tmp = t_1;
	elseif (y <= -9.5e+55)
		tmp = Float64(Float64(z + fma(27464.7644705, Float64(1.0 / y), Float64(x * y))) / a);
	elseif (y <= 1.45e+55)
		tmp = Float64(fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(fma(Float64(a + y), y, b), y, c), y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1e+174], t$95$1, If[LessEqual[y, -9.5e+55], N[(N[(z + N[(27464.7644705 * N[(1.0 / y), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.45e+55], N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(N[(N[(a + y), $MachinePrecision] * y + b), $MachinePrecision] * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000007e174 or 1.4499999999999999e55 < y

   1. Initial program 2.1%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 72.2

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

   4. Applied rewrites 72.2%

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

   if -1.00000000000000007e174 < y < -9.49999999999999989e55

   1. Initial program 4.6%

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

   3. Applied rewrites 7.2%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 26.3%

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

   7. Taylor expanded in x around inf

      \[\leadsto \frac{z + \mathsf{fma}\left(\frac{54929528941}{2000000}, \frac{1}{y}, x \cdot y\right)}{a} \]
   8. Step-by-step derivation

      1. lower-*.f64 26.0

         \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   9. Applied rewrites 26.0%

      \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   if -9.49999999999999989e55 < y < 1.4499999999999999e55

   1. Initial program 92.8%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 87.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 76.8% accurate, 0.5× speedup

Math

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

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

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 = -((-z - (-a * x)) / y) + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double 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 = -((-z - (-a * x)) / y) + x;
	}
	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 = -((-z - (-a * x)) / y) + x
	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(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x);
	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 = -((-z - (-a * x)) / y) + x;
	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[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $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 89.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 70.1

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

   4. Applied rewrites 70.1%

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

Alternative 5: 73.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(b, y, c\right), y, i\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1e+174)
     t_1
     (if (<= y -5.5e+55)
       (/ (+ z (fma 27464.7644705 (/ 1.0 y) (* x y))) a)
       (if (<= y 3.5e+53)
         (/
          (fma (fma (fma z y 27464.7644705) y 230661.510616) y t)
          (fma (fma b y c) y i))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1e+174) {
		tmp = t_1;
	} else if (y <= -5.5e+55) {
		tmp = (z + fma(27464.7644705, (1.0 / y), (x * y))) / a;
	} else if (y <= 3.5e+53) {
		tmp = fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(b, y, c), y, i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1e+174)
		tmp = t_1;
	elseif (y <= -5.5e+55)
		tmp = Float64(Float64(z + fma(27464.7644705, Float64(1.0 / y), Float64(x * y))) / a);
	elseif (y <= 3.5e+53)
		tmp = Float64(fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(fma(b, y, c), y, i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1e+174], t$95$1, If[LessEqual[y, -5.5e+55], N[(N[(z + N[(27464.7644705 * N[(1.0 / y), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 3.5e+53], N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(b * y + c), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000007e174 or 3.50000000000000019e53 < y

   1. Initial program 2.1%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 72.1

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

   4. Applied rewrites 72.1%

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

   if -1.00000000000000007e174 < y < -5.5000000000000004e55

   1. Initial program 4.6%

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

   3. Applied rewrites 7.2%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 26.3%

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

   7. Taylor expanded in x around inf

      \[\leadsto \frac{z + \mathsf{fma}\left(\frac{54929528941}{2000000}, \frac{1}{y}, x \cdot y\right)}{a} \]
   8. Step-by-step derivation

      1. lower-*.f64 26.1

         \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   9. Applied rewrites 26.1%

      \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   if -5.5000000000000004e55 < y < 3.50000000000000019e53

   1. Initial program 93.0%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 87.5%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 82.1%

      \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(b, y, c\right), y, i\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 71.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-7}:\\ \;\;\;\;\frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{\mathsf{fma}\left(230661.510616, y, t\right)}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1e+174)
     t_1
     (if (<= y -7.6e-7)
       (/ (+ z (fma 27464.7644705 (/ 1.0 y) (* x y))) a)
       (if (<= y 9.5e+54)
         (/
          (fma 230661.510616 y t)
          (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1e+174) {
		tmp = t_1;
	} else if (y <= -7.6e-7) {
		tmp = (z + fma(27464.7644705, (1.0 / y), (x * y))) / a;
	} else if (y <= 9.5e+54) {
		tmp = fma(230661.510616, y, t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1e+174)
		tmp = t_1;
	elseif (y <= -7.6e-7)
		tmp = Float64(Float64(z + fma(27464.7644705, Float64(1.0 / y), Float64(x * y))) / a);
	elseif (y <= 9.5e+54)
		tmp = Float64(fma(230661.510616, y, t) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(y + a) * y) + b) * y) + c) * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1e+174], t$95$1, If[LessEqual[y, -7.6e-7], N[(N[(z + N[(27464.7644705 * N[(1.0 / y), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 9.5e+54], N[(N[(230661.510616 * y + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000007e174 or 9.4999999999999999e54 < y

   1. Initial program 2.1%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 72.2

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

   4. Applied rewrites 72.2%

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

   if -1.00000000000000007e174 < y < -7.60000000000000029e-7

   1. Initial program 21.9%

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

   3. Applied rewrites 25.3%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 26.5%

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

   7. Taylor expanded in x around inf

      \[\leadsto \frac{z + \mathsf{fma}\left(\frac{54929528941}{2000000}, \frac{1}{y}, x \cdot y\right)}{a} \]
   8. Step-by-step derivation

      1. lower-*.f64 24.6

         \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   9. Applied rewrites 24.6%

      \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   if -7.60000000000000029e-7 < y < 9.4999999999999999e54

   1. Initial program 95.9%

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

   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. +-commutative N/A

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

      2. lower-fma.f64 83.3

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

   4. Applied rewrites 83.3%

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

Alternative 7: 67.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{\left(\left(y \cdot y\right) \cdot z\right) \cdot y + t}{\left(b \cdot y + c\right) \cdot y + i}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;\frac{\left(27464.7644705 \cdot y + 230661.510616\right) \cdot y + t}{c \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1e+174)
     t_1
     (if (<= y -5.5e+55)
       (/ (+ z (fma 27464.7644705 (/ 1.0 y) (* x y))) a)
       (if (<= y -2.1e-97)
         (/ (+ (* (* (* y y) z) y) t) (+ (* (+ (* b y) c) y) i))
         (if (<= y 1.05e+54)
           (/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (+ (* c y) i))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1e+174) {
		tmp = t_1;
	} else if (y <= -5.5e+55) {
		tmp = (z + fma(27464.7644705, (1.0 / y), (x * y))) / a;
	} else if (y <= -2.1e-97) {
		tmp = ((((y * y) * z) * y) + t) / ((((b * y) + c) * y) + i);
	} else if (y <= 1.05e+54) {
		tmp = ((((27464.7644705 * y) + 230661.510616) * y) + t) / ((c * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1e+174)
		tmp = t_1;
	elseif (y <= -5.5e+55)
		tmp = Float64(Float64(z + fma(27464.7644705, Float64(1.0 / y), Float64(x * y))) / a);
	elseif (y <= -2.1e-97)
		tmp = Float64(Float64(Float64(Float64(Float64(y * y) * z) * y) + t) / Float64(Float64(Float64(Float64(b * y) + c) * y) + i));
	elseif (y <= 1.05e+54)
		tmp = Float64(Float64(Float64(Float64(Float64(27464.7644705 * y) + 230661.510616) * y) + t) / Float64(Float64(c * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1e+174], t$95$1, If[LessEqual[y, -5.5e+55], N[(N[(z + N[(27464.7644705 * N[(1.0 / y), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -2.1e-97], N[(N[(N[(N[(N[(y * y), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(b * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+54], N[(N[(N[(N[(N[(27464.7644705 * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.00000000000000007e174 or 1.04999999999999993e54 < y

   1. Initial program 2.1%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 72.1

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

   4. Applied rewrites 72.1%

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

   if -1.00000000000000007e174 < y < -5.5000000000000004e55

   1. Initial program 4.6%

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

   3. Applied rewrites 7.2%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 26.3%

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

   7. Taylor expanded in x around inf

      \[\leadsto \frac{z + \mathsf{fma}\left(\frac{54929528941}{2000000}, \frac{1}{y}, x \cdot y\right)}{a} \]
   8. Step-by-step derivation

      1. lower-*.f64 26.1

         \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   9. Applied rewrites 26.1%

      \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   if -5.5000000000000004e55 < y < -2.1000000000000001e-97

   1. Initial program 83.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 54.8

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

   4. Applied rewrites 54.8%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 46.5%

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

   if -2.1000000000000001e-97 < y < 1.04999999999999993e54

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf

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

      1. unpow3 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 64.8

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

   4. Applied rewrites 64.8%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 61.8%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 79.1%

       \[\leadsto \frac{\left(27464.7644705 \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{c} \cdot y + i} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 67.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, y, 27464.7644705\right), y, 230661.510616\right), y, t\right)}{\mathsf{fma}\left(b \cdot y, y, i\right)}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;\frac{\left(27464.7644705 \cdot y + 230661.510616\right) \cdot y + t}{c \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1e+174)
     t_1
     (if (<= y -4.2e-7)
       (/ (+ z (fma 27464.7644705 (/ 1.0 y) (* x y))) a)
       (if (<= y -5.5e-47)
         (/
          (fma (fma (fma z y 27464.7644705) y 230661.510616) y t)
          (fma (* b y) y i))
         (if (<= y 1.05e+54)
           (/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (+ (* c y) i))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1e+174) {
		tmp = t_1;
	} else if (y <= -4.2e-7) {
		tmp = (z + fma(27464.7644705, (1.0 / y), (x * y))) / a;
	} else if (y <= -5.5e-47) {
		tmp = fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma((b * y), y, i);
	} else if (y <= 1.05e+54) {
		tmp = ((((27464.7644705 * y) + 230661.510616) * y) + t) / ((c * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1e+174)
		tmp = t_1;
	elseif (y <= -4.2e-7)
		tmp = Float64(Float64(z + fma(27464.7644705, Float64(1.0 / y), Float64(x * y))) / a);
	elseif (y <= -5.5e-47)
		tmp = Float64(fma(fma(fma(z, y, 27464.7644705), y, 230661.510616), y, t) / fma(Float64(b * y), y, i));
	elseif (y <= 1.05e+54)
		tmp = Float64(Float64(Float64(Float64(Float64(27464.7644705 * y) + 230661.510616) * y) + t) / Float64(Float64(c * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1e+174], t$95$1, If[LessEqual[y, -4.2e-7], N[(N[(z + N[(27464.7644705 * N[(1.0 / y), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -5.5e-47], N[(N[(N[(N[(z * y + 27464.7644705), $MachinePrecision] * y + 230661.510616), $MachinePrecision] * y + t), $MachinePrecision] / N[(N[(b * y), $MachinePrecision] * y + i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+54], N[(N[(N[(N[(N[(27464.7644705 * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.00000000000000007e174 or 1.04999999999999993e54 < y

   1. Initial program 2.1%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 72.1

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

   4. Applied rewrites 72.1%

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

   if -1.00000000000000007e174 < y < -4.2e-7

   1. Initial program 22.1%

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

   3. Applied rewrites 25.5%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in x around inf

      \[\leadsto \frac{z + \mathsf{fma}\left(\frac{54929528941}{2000000}, \frac{1}{y}, x \cdot y\right)}{a} \]
   8. Step-by-step derivation

      1. lower-*.f64 24.6

         \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   9. Applied rewrites 24.6%

      \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   if -4.2e-7 < y < -5.5000000000000002e-47

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. +-commutative N/A

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

   4. Applied rewrites 79.4%

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

   5. Taylor expanded in b around inf

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

      1. lower-*.f64 43.2

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

   7. Applied rewrites 43.2%

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

   if -5.5000000000000002e-47 < y < 1.04999999999999993e54

   1. Initial program 95.8%

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

   2. Taylor expanded in y around inf

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

      1. unpow3 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 63.3

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

   4. Applied rewrites 63.3%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 59.8%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 77.7%

       \[\leadsto \frac{\left(27464.7644705 \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{c} \cdot y + i} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 67.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;\frac{\left(27464.7644705 \cdot y + 230661.510616\right) \cdot y + t}{c \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1e+174)
     t_1
     (if (<= y -6.5e-34)
       (/ (+ z (fma 27464.7644705 (/ 1.0 y) (* x y))) a)
       (if (<= y 1.05e+54)
         (/ (+ (* (+ (* 27464.7644705 y) 230661.510616) y) t) (+ (* c y) i))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1e+174) {
		tmp = t_1;
	} else if (y <= -6.5e-34) {
		tmp = (z + fma(27464.7644705, (1.0 / y), (x * y))) / a;
	} else if (y <= 1.05e+54) {
		tmp = ((((27464.7644705 * y) + 230661.510616) * y) + t) / ((c * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1e+174)
		tmp = t_1;
	elseif (y <= -6.5e-34)
		tmp = Float64(Float64(z + fma(27464.7644705, Float64(1.0 / y), Float64(x * y))) / a);
	elseif (y <= 1.05e+54)
		tmp = Float64(Float64(Float64(Float64(Float64(27464.7644705 * y) + 230661.510616) * y) + t) / Float64(Float64(c * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1e+174], t$95$1, If[LessEqual[y, -6.5e-34], N[(N[(z + N[(27464.7644705 * N[(1.0 / y), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.05e+54], N[(N[(N[(N[(N[(27464.7644705 * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000007e174 or 1.04999999999999993e54 < y

   1. Initial program 2.1%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 72.1

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

   4. Applied rewrites 72.1%

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

   if -1.00000000000000007e174 < y < -6.49999999999999985e-34

   1. Initial program 33.0%

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

   3. Applied rewrites 35.9%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 25.4%

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

   7. Taylor expanded in x around inf

      \[\leadsto \frac{z + \mathsf{fma}\left(\frac{54929528941}{2000000}, \frac{1}{y}, x \cdot y\right)}{a} \]
   8. Step-by-step derivation

      1. lower-*.f64 22.5

         \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   9. Applied rewrites 22.5%

      \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   if -6.49999999999999985e-34 < y < 1.04999999999999993e54

   1. Initial program 95.9%

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

   2. Taylor expanded in y around inf

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

      1. unpow3 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 62.6

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

   4. Applied rewrites 62.6%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 58.9%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 76.8%

       \[\leadsto \frac{\left(27464.7644705 \cdot y + 230661.510616\right) \cdot y + t}{\color{blue}{c} \cdot y + i} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 66.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;\frac{230661.510616 \cdot y + t}{c \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1e+174)
     t_1
     (if (<= y -6.5e-34)
       (/ (+ z (fma 27464.7644705 (/ 1.0 y) (* x y))) a)
       (if (<= y 1.05e+54) (/ (+ (* 230661.510616 y) t) (+ (* c y) i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1e+174) {
		tmp = t_1;
	} else if (y <= -6.5e-34) {
		tmp = (z + fma(27464.7644705, (1.0 / y), (x * y))) / a;
	} else if (y <= 1.05e+54) {
		tmp = ((230661.510616 * y) + t) / ((c * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1e+174)
		tmp = t_1;
	elseif (y <= -6.5e-34)
		tmp = Float64(Float64(z + fma(27464.7644705, Float64(1.0 / y), Float64(x * y))) / a);
	elseif (y <= 1.05e+54)
		tmp = Float64(Float64(Float64(230661.510616 * y) + t) / Float64(Float64(c * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1e+174], t$95$1, If[LessEqual[y, -6.5e-34], N[(N[(z + N[(27464.7644705 * N[(1.0 / y), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.05e+54], N[(N[(N[(230661.510616 * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000007e174 or 1.04999999999999993e54 < y

   1. Initial program 2.1%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 72.1

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

   4. Applied rewrites 72.1%

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

   if -1.00000000000000007e174 < y < -6.49999999999999985e-34

   1. Initial program 33.0%

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

   3. Applied rewrites 35.9%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 25.4%

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

   7. Taylor expanded in x around inf

      \[\leadsto \frac{z + \mathsf{fma}\left(\frac{54929528941}{2000000}, \frac{1}{y}, x \cdot y\right)}{a} \]
   8. Step-by-step derivation

      1. lower-*.f64 22.5

         \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   9. Applied rewrites 22.5%

      \[\leadsto \frac{z + \mathsf{fma}\left(27464.7644705, \frac{1}{y}, x \cdot y\right)}{a} \]

   if -6.49999999999999985e-34 < y < 1.04999999999999993e54

   1. Initial program 95.9%

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

   2. Taylor expanded in y around inf

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

      1. unpow3 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 62.6

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

   4. Applied rewrites 62.6%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 58.9%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 76.8%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 76.5%

       \[\leadsto \frac{\color{blue}{230661.510616} \cdot y + t}{c \cdot y + i} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 66.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-z\right) - \left(-a\right) \cdot x}{y}\right) + x\\ \mathbf{if}\;y \leq -1 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-34}:\\ \;\;\;\;y \cdot \left(\frac{x}{a} + \frac{z}{a \cdot y}\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+54}:\\ \;\;\;\;\frac{230661.510616 \cdot y + t}{c \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (- (/ (- (- z) (* (- a) x)) y)) x)))
   (if (<= y -1e+174)
     t_1
     (if (<= y -6.5e-34)
       (* y (+ (/ x a) (/ z (* a y))))
       (if (<= y 1.05e+54) (/ (+ (* 230661.510616 y) t) (+ (* c y) i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1e+174) {
		tmp = t_1;
	} else if (y <= -6.5e-34) {
		tmp = y * ((x / a) + (z / (a * y)));
	} else if (y <= 1.05e+54) {
		tmp = ((230661.510616 * y) + t) / ((c * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -((-z - (-a * x)) / y) + x
    if (y <= (-1d+174)) then
        tmp = t_1
    else if (y <= (-6.5d-34)) then
        tmp = y * ((x / a) + (z / (a * y)))
    else if (y <= 1.05d+54) then
        tmp = ((230661.510616d0 * y) + t) / ((c * y) + i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = -((-z - (-a * x)) / y) + x;
	double tmp;
	if (y <= -1e+174) {
		tmp = t_1;
	} else if (y <= -6.5e-34) {
		tmp = y * ((x / a) + (z / (a * y)));
	} else if (y <= 1.05e+54) {
		tmp = ((230661.510616 * y) + t) / ((c * y) + i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = -((-z - (-a * x)) / y) + x
	tmp = 0
	if y <= -1e+174:
		tmp = t_1
	elif y <= -6.5e-34:
		tmp = y * ((x / a) + (z / (a * y)))
	elif y <= 1.05e+54:
		tmp = ((230661.510616 * y) + t) / ((c * y) + i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-z) - Float64(Float64(-a) * x)) / y)) + x)
	tmp = 0.0
	if (y <= -1e+174)
		tmp = t_1;
	elseif (y <= -6.5e-34)
		tmp = Float64(y * Float64(Float64(x / a) + Float64(z / Float64(a * y))));
	elseif (y <= 1.05e+54)
		tmp = Float64(Float64(Float64(230661.510616 * y) + t) / Float64(Float64(c * y) + i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = -((-z - (-a * x)) / y) + x;
	tmp = 0.0;
	if (y <= -1e+174)
		tmp = t_1;
	elseif (y <= -6.5e-34)
		tmp = y * ((x / a) + (z / (a * y)));
	elseif (y <= 1.05e+54)
		tmp = ((230661.510616 * y) + t) / ((c * y) + i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $MachinePrecision]}, If[LessEqual[y, -1e+174], t$95$1, If[LessEqual[y, -6.5e-34], N[(y * N[(N[(x / a), $MachinePrecision] + N[(z / N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+54], N[(N[(N[(230661.510616 * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000007e174 or 1.04999999999999993e54 < y

   1. Initial program 2.1%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 72.1

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

   4. Applied rewrites 72.1%

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

   if -1.00000000000000007e174 < y < -6.49999999999999985e-34

   1. Initial program 33.0%

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

   3. Applied rewrites 35.9%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 25.4%

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

   7. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 20.5

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

   9. Applied rewrites 20.5%

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

   if -6.49999999999999985e-34 < y < 1.04999999999999993e54

   1. Initial program 95.9%

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

   2. Taylor expanded in y around inf

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

      1. unpow3 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 62.6

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

   4. Applied rewrites 62.6%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 58.9%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 76.8%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 76.5%

       \[\leadsto \frac{\color{blue}{230661.510616} \cdot y + t}{c \cdot y + i} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 66.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(230661.510616 * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $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 89.5%

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

   2. Taylor expanded in y around inf

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

      1. unpow3 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 56.4

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 51.4%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 66.5%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 66.0%

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

   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 0.0%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 70.1

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

   4. Applied rewrites 70.1%

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

Alternative 13: 62.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[N[(N[(N[(N[(N[(N[(N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision] + 27464.7644705), $MachinePrecision] * y), $MachinePrecision] + 230661.510616), $MachinePrecision] * y), $MachinePrecision] + t), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(y + a), $MachinePrecision] * y), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] + c), $MachinePrecision] * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], Infinity], N[(t / N[(N[(c * y), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision], N[((-N[(N[((-z) - N[((-a) * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]) + x), $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 89.5%

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

   2. Taylor expanded in y around inf

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

      1. unpow3 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 56.4

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 51.4%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 66.5%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 57.2%

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

   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 0.0%

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

   2. Taylor expanded in y around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-*r* N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. lower-neg.f64 70.1

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

   4. Applied rewrites 70.1%

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

Alternative 14: 58.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.5%

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

   2. Taylor expanded in y around inf

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

      1. unpow3 N/A

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

      2. unpow2 N/A

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

      3. lower-*.f64 N/A

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

      4. unpow2 N/A

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

      5. lower-*.f64 56.4

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

   4. Applied rewrites 56.4%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 51.4%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 66.5%

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

   11. Taylor expanded in y around 0

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

   13. Applied rewrites 57.2%

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

   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 0.0%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 60.6%

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

Alternative 15: 53.9% accurate, 0.8× speedup

Math

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

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))

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;
	}
	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;
	}
	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
	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 = x;
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.5%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 5.7%

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

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{y \cdot \left(\frac{28832688827}{125000} \cdot \frac{1}{i} - \frac{c \cdot t}{{i}^{2}}\right) + \frac{t}{i}} \]
   6. 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. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. unpow2 N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 40.7

         \[\leadsto \mathsf{fma}\left(y, 230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{i \cdot i}, \frac{t}{i}\right) \]

   7. Applied rewrites 40.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 230661.510616 \cdot \frac{1}{i} - \frac{c \cdot t}{i \cdot i}, \frac{t}{i}\right)} \]

   8. Taylor expanded in i around inf

      \[\leadsto \frac{t + \frac{28832688827}{125000} \cdot y}{\color{blue}{i}} \]
   9. 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 49.9

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

   10. Applied rewrites 49.9%

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

   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 0.0%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 60.6%

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

Alternative 16: 50.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.5%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 44.6

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

   4. Applied rewrites 44.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 60.6%

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

Alternative 17: 26.7% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+132}:\\ \;\;\;\;\frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a -2.1e+132) (/ z a) x))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -2.1e+132) {
		tmp = z / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= (-2.1d+132)) then
        tmp = z / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -2.1e+132) {
		tmp = z / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -2.1e+132:
		tmp = z / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -2.1e+132)
		tmp = Float64(z / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -2.1e+132)
		tmp = z / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -2.1e+132], N[(z / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -2.09999999999999993e132

   1. Initial program 54.2%

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

   3. Applied rewrites 54.9%

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

   4. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{a}} \]
   5. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{z + \left(\frac{54929528941}{2000000} \cdot \frac{1}{y} + \left(\frac{28832688827}{125000} \cdot \frac{1}{{y}^{2}} + \left(x \cdot y + \frac{t}{{y}^{3}}\right)\right)\right)}{\color{blue}{a}} \]

   6. Applied rewrites 31.9%

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

   7. Taylor expanded in z around inf

      \[\leadsto \frac{z}{a} \]
   8. Step-by-step derivation

   9. Applied rewrites 14.9%

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

   if -2.09999999999999993e132 < a

   1. Initial program 55.7%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 28.6%

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

Alternative 18: 26.6% accurate, 46.9× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 55.5%

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

2. Taylor expanded in y around inf

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

4. Applied rewrites 26.6%

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

Reproduce

herbie shell --seed 2025119 
(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)))