Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Percentage Accurate: 56.0% → 81.5%

Time: 20.1s

Alternatives: 12

Speedup: 1.9×

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 56.0% 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

real(8) function code(x, y, z, t, a, b, c, i)
    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: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+54} \lor \neg \left(y \leq 1.96 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -8.2e+54) (not (<= y 1.96e+15)))
   (+ x (/ (- z (* x a)) y))
   (/
    (+ (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)) t)
    (+ i (* y (+ c (* y (+ b (* y a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.2e+54) || !(y <= 1.96e+15)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-8.2d+54)) .or. (.not. (y <= 1.96d+15))) then
        tmp = x + ((z - (x * a)) / y)
    else
        tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705d0)) + 230661.510616d0)) + t) / (i + (y * (c + (y * (b + (y * a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.2e+54) || !(y <= 1.96e+15)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -8.2e+54) or not (y <= 1.96e+15):
		tmp = x + ((z - (x * a)) / y)
	else:
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * (b + (y * a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -8.2e+54) || !(y <= 1.96e+15))
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	else
		tmp = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -8.2e+54) || ~((y <= 1.96e+15)))
		tmp = x + ((z - (x * a)) / y);
	else
		tmp = ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / (i + (y * (c + (y * (b + (y * a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -8.2e+54], N[Not[LessEqual[y, 1.96e+15]], $MachinePrecision]], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(N[(y * N[(N[(y * N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] + 27464.7644705), $MachinePrecision]), $MachinePrecision] + 230661.510616), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.19999999999999935e54 or 1.96e15 < y

   1. Initial program 2.2%

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

   3. Taylor expanded in y around -inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. unsub-neg 70.9%

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

      3. sub-neg 70.9%

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

      4. mul-1-neg 70.9%

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

      5. mul-1-neg 70.9%

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

      6. remove-double-neg 70.9%

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

   5. Simplified 70.9%

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

   if -8.19999999999999935e54 < y < 1.96e15

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 97.0%

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot \left(b + a \cdot y\right)} + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+54} \lor \neg \left(y \leq 1.96 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.6% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))
        (t_2
         (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))))
   (if (<= (/ (+ t_2 t) t_1) INFINITY)
     (+ (/ t t_1) (/ t_2 t_1))
     (+ x (/ (- z (* x a)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * ((y * ((y * (y + a)) + b)) + c)) + i;
	double t_2 = y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616);
	double tmp;
	if (((t_2 + t) / t_1) <= ((double) INFINITY)) {
		tmp = (t / t_1) + (t_2 / t_1);
	} else {
		tmp = x + ((z - (x * a)) / y);
	}
	return tmp;
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.6%

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

   3. Taylor expanded in t around 0 91.6%

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

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

   1. Initial program 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. Add Preprocessing

   3. Taylor expanded in y around -inf 72.9%

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

      1. mul-1-neg 72.9%

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

      2. unsub-neg 72.9%

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

      3. sub-neg 72.9%

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

      4. mul-1-neg 72.9%

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

      5. mul-1-neg 72.9%

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

      6. remove-double-neg 72.9%

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

   5. Simplified 72.9%

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

4. Final simplification 84.1%

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

Alternative 3: 82.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1
         (/
          (+
           (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616))
           t)
          (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))
   (if (<= t_1 INFINITY) t_1 (+ x (/ (- z (* x a)) y)))))

C

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(Float64(x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.6%

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

   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. Add Preprocessing

   3. Taylor expanded in y around -inf 72.9%

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

      1. mul-1-neg 72.9%

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

      2. unsub-neg 72.9%

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

      3. sub-neg 72.9%

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

      4. mul-1-neg 72.9%

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

      5. mul-1-neg 72.9%

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

      6. remove-double-neg 72.9%

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

   5. Simplified 72.9%

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

4. Final simplification 84.1%

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

Alternative 4: 78.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+36} \lor \neg \left(y \leq 1.96 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -8.5e+36) (not (<= y 1.96e+15)))
   (+ x (/ (- z (* x a)) y))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y (+ b (* y a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.5e+36) || !(y <= 1.96e+15)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-8.5d+36)) .or. (.not. (y <= 1.96d+15))) then
        tmp = x + ((z - (x * a)) / y)
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.5e+36) || !(y <= 1.96e+15)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -8.5e+36) or not (y <= 1.96e+15):
		tmp = x + ((z - (x * a)) / y)
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -8.5e+36) || !(y <= 1.96e+15))
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * Float64(b + Float64(y * a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -8.5e+36) || ~((y <= 1.96e+15)))
		tmp = x + ((z - (x * a)) / y);
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * (b + (y * a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -8.5e+36], N[Not[LessEqual[y, 1.96e+15]], $MachinePrecision]], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * N[(b + N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.50000000000000014e36 or 1.96e15 < y

   1. Initial program 3.0%

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

   3. Taylor expanded in y around -inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. sub-neg 68.7%

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

      4. mul-1-neg 68.7%

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

      5. mul-1-neg 68.7%

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

      6. remove-double-neg 68.7%

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

   5. Simplified 68.7%

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

   if -8.50000000000000014e36 < y < 1.96e15

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 94.1%

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

   4. Taylor expanded in y around 0 94.1%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot \left(b + a \cdot y\right)} + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+36} \lor \neg \left(y \leq 1.96 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot \left(b + y \cdot a\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+35} \lor \neg \left(y \leq 1.7 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.4e+35) (not (<= y 1.7e+15)))
   (+ x (/ (- z (* x a)) y))
   (/
    (+ t (* y (+ 230661.510616 (* y (+ 27464.7644705 (* y z))))))
    (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.4e+35) || !(y <= 1.7e+15)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-5.4d+35)) .or. (.not. (y <= 1.7d+15))) then
        tmp = x + ((z - (x * a)) / y)
    else
        tmp = (t + (y * (230661.510616d0 + (y * (27464.7644705d0 + (y * z)))))) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.4e+35) || !(y <= 1.7e+15)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -5.4e+35) or not (y <= 1.7e+15):
		tmp = x + ((z - (x * a)) / y)
	else:
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -5.4e+35) || !(y <= 1.7e+15))
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	else
		tmp = Float64(Float64(t + Float64(y * Float64(230661.510616 + Float64(y * Float64(27464.7644705 + Float64(y * z)))))) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -5.4e+35) || ~((y <= 1.7e+15)))
		tmp = x + ((z - (x * a)) / y);
	else
		tmp = (t + (y * (230661.510616 + (y * (27464.7644705 + (y * z)))))) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -5.4e+35], N[Not[LessEqual[y, 1.7e+15]], $MachinePrecision]], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * N[(230661.510616 + N[(y * N[(27464.7644705 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.40000000000000005e35 or 1.7e15 < y

   1. Initial program 3.0%

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

   3. Taylor expanded in y around -inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. sub-neg 68.7%

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

      4. mul-1-neg 68.7%

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

      5. mul-1-neg 68.7%

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

      6. remove-double-neg 68.7%

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

   5. Simplified 68.7%

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

   if -5.40000000000000005e35 < y < 1.7e15

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 94.1%

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

   4. Taylor expanded in y around 0 88.7%

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

      1. *-commutative 88.7%

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

   6. Simplified 88.7%

      \[\leadsto \frac{\left(y \cdot \left(27464.7644705 + y \cdot z\right) + 230661.510616\right) \cdot y + t}{\left(\color{blue}{y \cdot b} + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+35} \lor \neg \left(y \leq 1.7 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + y \cdot z\right)\right)}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+36} \lor \neg \left(y \leq 1.96 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -8.8e+36) (not (<= y 1.96e+15)))
   (+ x (/ (- z (* x a)) y))
   (/ (+ t (* y 230661.510616)) (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.8e+36) || !(y <= 1.96e+15)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-8.8d+36)) .or. (.not. (y <= 1.96d+15))) then
        tmp = x + ((z - (x * a)) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -8.8e+36) || !(y <= 1.96e+15)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -8.8e+36) or not (y <= 1.96e+15):
		tmp = x + ((z - (x * a)) / y)
	else:
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -8.8e+36) || !(y <= 1.96e+15))
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(Float64(y * Float64(Float64(y * Float64(Float64(y * Float64(y + a)) + b)) + c)) + i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -8.8e+36) || ~((y <= 1.96e+15)))
		tmp = x + ((z - (x * a)) / y);
	else
		tmp = (t + (y * 230661.510616)) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -8.8e+36], N[Not[LessEqual[y, 1.96e+15]], $MachinePrecision]], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(N[(y * N[(N[(y * N[(N[(y * N[(y + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]), $MachinePrecision] + i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.80000000000000002e36 or 1.96e15 < y

   1. Initial program 3.0%

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

   3. Taylor expanded in y around -inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. sub-neg 68.7%

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

      4. mul-1-neg 68.7%

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

      5. mul-1-neg 68.7%

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

      6. remove-double-neg 68.7%

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

   5. Simplified 68.7%

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

   if -8.80000000000000002e36 < y < 1.96e15

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 85.4%

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

      1. *-commutative 85.4%

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

   5. Simplified 85.4%

      \[\leadsto \frac{\color{blue}{y \cdot 230661.510616} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+36} \lor \neg \left(y \leq 1.96 \cdot 10^{+15}\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+34} \lor \neg \left(y \leq 7000000000000\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.7e+34) (not (<= y 7000000000000.0)))
   (+ x (/ (- z (* x a)) y))
   (/ (+ t (* y 230661.510616)) (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.7e+34) || !(y <= 7000000000000.0)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.7d+34)) .or. (.not. (y <= 7000000000000.0d0))) then
        tmp = x + ((z - (x * a)) / y)
    else
        tmp = (t + (y * 230661.510616d0)) / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.7e+34) || !(y <= 7000000000000.0)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.7e+34) or not (y <= 7000000000000.0):
		tmp = x + ((z - (x * a)) / y)
	else:
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.7e+34) || !(y <= 7000000000000.0))
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	else
		tmp = Float64(Float64(t + Float64(y * 230661.510616)) / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.7e+34) || ~((y <= 7000000000000.0)))
		tmp = x + ((z - (x * a)) / y);
	else
		tmp = (t + (y * 230661.510616)) / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.7e+34], N[Not[LessEqual[y, 7000000000000.0]], $MachinePrecision]], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(t + N[(y * 230661.510616), $MachinePrecision]), $MachinePrecision] / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e34 or 7e12 < y

   1. Initial program 3.0%

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

   3. Taylor expanded in y around -inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. sub-neg 68.7%

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

      4. mul-1-neg 68.7%

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

      5. mul-1-neg 68.7%

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

      6. remove-double-neg 68.7%

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

   5. Simplified 68.7%

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

   if -1.7e34 < y < 7e12

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 92.0%

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

      1. *-commutative 88.7%

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

   5. Simplified 92.0%

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

   6. Taylor expanded in y around 0 81.8%

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

      1. *-commutative 85.4%

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

   8. Simplified 81.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+34} \lor \neg \left(y \leq 7000000000000\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t + y \cdot 230661.510616}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+34} \lor \neg \left(y \leq 270000000000\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.5e+34) (not (<= y 270000000000.0)))
   (+ x (/ (- z (* x a)) y))
   (/ t (+ i (* y (+ c (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.5e+34) || !(y <= 270000000000.0)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-4.5d+34)) .or. (.not. (y <= 270000000000.0d0))) then
        tmp = x + ((z - (x * a)) / y)
    else
        tmp = t / (i + (y * (c + (y * b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.5e+34) || !(y <= 270000000000.0)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = t / (i + (y * (c + (y * b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4.5e+34) or not (y <= 270000000000.0):
		tmp = x + ((z - (x * a)) / y)
	else:
		tmp = t / (i + (y * (c + (y * b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4.5e+34) || !(y <= 270000000000.0))
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	else
		tmp = Float64(t / Float64(i + Float64(y * Float64(c + Float64(y * b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4.5e+34) || ~((y <= 270000000000.0)))
		tmp = x + ((z - (x * a)) / y);
	else
		tmp = t / (i + (y * (c + (y * b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4.5e+34], N[Not[LessEqual[y, 270000000000.0]], $MachinePrecision]], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * N[(c + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e34 or 2.7e11 < y

   1. Initial program 3.0%

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

   3. Taylor expanded in y around -inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. unsub-neg 68.7%

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

      3. sub-neg 68.7%

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

      4. mul-1-neg 68.7%

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

      5. mul-1-neg 68.7%

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

      6. remove-double-neg 68.7%

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

   5. Simplified 68.7%

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

   if -4.5e34 < y < 2.7e11

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf 76.3%

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

   4. Taylor expanded in b around inf 73.6%

      \[\leadsto \frac{t}{i + y \cdot \left(c + y \cdot \color{blue}{b}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+34} \lor \neg \left(y \leq 270000000000\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot \left(c + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+37} \lor \neg \left(y \leq 9500000000000\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -1.55e+37) (not (<= y 9500000000000.0)))
   (+ x (/ (- z (* x a)) y))
   (/ t (+ i (* y c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.55e+37) || !(y <= 9500000000000.0)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = t / (i + (y * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-1.55d+37)) .or. (.not. (y <= 9500000000000.0d0))) then
        tmp = x + ((z - (x * a)) / y)
    else
        tmp = t / (i + (y * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -1.55e+37) || !(y <= 9500000000000.0)) {
		tmp = x + ((z - (x * a)) / y);
	} else {
		tmp = t / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -1.55e+37) or not (y <= 9500000000000.0):
		tmp = x + ((z - (x * a)) / y)
	else:
		tmp = t / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -1.55e+37) || !(y <= 9500000000000.0))
		tmp = Float64(x + Float64(Float64(z - Float64(x * a)) / y));
	else
		tmp = Float64(t / Float64(i + Float64(y * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -1.55e+37) || ~((y <= 9500000000000.0)))
		tmp = x + ((z - (x * a)) / y);
	else
		tmp = t / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -1.55e+37], N[Not[LessEqual[y, 9500000000000.0]], $MachinePrecision]], N[(x + N[(N[(z - N[(x * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5500000000000001e37 or 9.5e12 < y

   1. Initial program 3.0%

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

   3. Taylor expanded in y around -inf 69.2%

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

      1. mul-1-neg 69.2%

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

      2. unsub-neg 69.2%

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

      3. sub-neg 69.2%

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

      4. mul-1-neg 69.2%

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

      5. mul-1-neg 69.2%

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

      6. remove-double-neg 69.2%

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

   5. Simplified 69.2%

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

   if -1.5500000000000001e37 < y < 9.5e12

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf 75.8%

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

   4. Taylor expanded in y around 0 65.4%

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

      1. *-commutative 65.4%

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

   6. Simplified 65.4%

      \[\leadsto \frac{t}{i + \color{blue}{y \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+37} \lor \neg \left(y \leq 9500000000000\right):\\ \;\;\;\;x + \frac{z - x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15} \lor \neg \left(y \leq 6 \cdot 10^{+14}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -4.2e+15) (not (<= y 6e+14))) x (/ t (+ i (* y c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.2e+15) || !(y <= 6e+14)) {
		tmp = x;
	} else {
		tmp = t / (i + (y * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-4.2d+15)) .or. (.not. (y <= 6d+14))) then
        tmp = x
    else
        tmp = t / (i + (y * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -4.2e+15) || !(y <= 6e+14)) {
		tmp = x;
	} else {
		tmp = t / (i + (y * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -4.2e+15) or not (y <= 6e+14):
		tmp = x
	else:
		tmp = t / (i + (y * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -4.2e+15) || !(y <= 6e+14))
		tmp = x;
	else
		tmp = Float64(t / Float64(i + Float64(y * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -4.2e+15) || ~((y <= 6e+14)))
		tmp = x;
	else
		tmp = t / (i + (y * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -4.2e+15], N[Not[LessEqual[y, 6e+14]], $MachinePrecision]], x, N[(t / N[(i + N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e15 or 6e14 < y

   1. Initial program 6.2%

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

   3. Taylor expanded in y around inf 59.8%

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

   if -4.2e15 < y < 6e14

   1. Initial program 99.0%

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

   3. Taylor expanded in t around inf 78.5%

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

   4. Taylor expanded in y around 0 67.7%

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

      1. *-commutative 67.7%

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

   6. Simplified 67.7%

      \[\leadsto \frac{t}{i + \color{blue}{y \cdot c}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15} \lor \neg \left(y \leq 6 \cdot 10^{+14}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i + y \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-20} \lor \neg \left(y \leq 740000000000\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -9.8e-20) (not (<= y 740000000000.0))) x (/ t i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9.8e-20) || !(y <= 740000000000.0)) {
		tmp = x;
	} else {
		tmp = t / i;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((y <= (-9.8d-20)) .or. (.not. (y <= 740000000000.0d0))) then
        tmp = x
    else
        tmp = t / i
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -9.8e-20) || !(y <= 740000000000.0)) {
		tmp = x;
	} else {
		tmp = t / i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (y <= -9.8e-20) or not (y <= 740000000000.0):
		tmp = x
	else:
		tmp = t / i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((y <= -9.8e-20) || !(y <= 740000000000.0))
		tmp = x;
	else
		tmp = Float64(t / i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((y <= -9.8e-20) || ~((y <= 740000000000.0)))
		tmp = x;
	else
		tmp = t / i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[y, -9.8e-20], N[Not[LessEqual[y, 740000000000.0]], $MachinePrecision]], x, N[(t / i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.8000000000000003e-20 or 7.4e11 < y

   1. Initial program 9.9%

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

   3. Taylor expanded in y around inf 57.2%

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

   if -9.8000000000000003e-20 < y < 7.4e11

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 58.5%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-20} \lor \neg \left(y \leq 740000000000\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{i}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 26.0% accurate, 33.0× 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

real(8) function code(x, y, z, t, a, b, c, i)
    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 54.8%

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

3. Taylor expanded in y around inf 30.2%

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

Reproduce

herbie shell --seed 2024096 
(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)))