Average Error: 13.4 → 0.2
Time: 31.3s
Precision: binary64
\[\left(\left(\left(x = 0 \lor 0.5884142 \leq x \land x \leq 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \leq y \land y \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq y \land y \leq 1.751224 \cdot 10^{+308}\right)\right) \land \left(-1.776707 \cdot 10^{+308} \leq z \land z \leq -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \leq z \land z \leq 1.725154 \cdot 10^{+308}\right)\right) \land \left(-1.796658 \cdot 10^{+308} \leq a \land a \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq a \land a \leq 1.751224 \cdot 10^{+308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right) \]
↓
\[\begin{array}{l} t_0 := 1 - \tan y \cdot \tan z\\ x + \left(t_0 \cdot \sin a - \left(\tan y + \tan z\right) \cdot \cos a\right) \cdot \frac{-1}{\cos a \cdot t_0} \end{array} \]
(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))
↓
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (- 1.0 (* (tan y) (tan z)))))
   (+
    x
    (*
     (- (* t_0 (sin a)) (* (+ (tan y) (tan z)) (cos a)))
     (/ -1.0 (* (cos a) t_0))))))
double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}
↓
double code(double x, double y, double z, double a) {
	double t_0 = 1.0 - (tan(y) * tan(z));
	return x + (((t_0 * sin(a)) - ((tan(y) + tan(z)) * cos(a))) * (-1.0 / (cos(a) * t_0)));
}

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function
↓
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: t_0
    t_0 = 1.0d0 - (tan(y) * tan(z))
    code = x + (((t_0 * sin(a)) - ((tan(y) + tan(z)) * cos(a))) * ((-1.0d0) / (cos(a) * t_0)))
end function

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}
↓
public static double code(double x, double y, double z, double a) {
	double t_0 = 1.0 - (Math.tan(y) * Math.tan(z));
	return x + (((t_0 * Math.sin(a)) - ((Math.tan(y) + Math.tan(z)) * Math.cos(a))) * (-1.0 / (Math.cos(a) * t_0)));
}

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))
↓
def code(x, y, z, a):
	t_0 = 1.0 - (math.tan(y) * math.tan(z))
	return x + (((t_0 * math.sin(a)) - ((math.tan(y) + math.tan(z)) * math.cos(a))) * (-1.0 / (math.cos(a) * t_0)))

function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end
↓
function code(x, y, z, a)
	t_0 = Float64(1.0 - Float64(tan(y) * tan(z)))
	return Float64(x + Float64(Float64(Float64(t_0 * sin(a)) - Float64(Float64(tan(y) + tan(z)) * cos(a))) * Float64(-1.0 / Float64(cos(a) * t_0))))
end

function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end
↓
function tmp = code(x, y, z, a)
	t_0 = 1.0 - (tan(y) * tan(z));
	tmp = x + (((t_0 * sin(a)) - ((tan(y) + tan(z)) * cos(a))) * (-1.0 / (cos(a) * t_0)));
end

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, a_] := Block[{t$95$0 = N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x + N[(N[(N[(t$95$0 * N[Sin[a], $MachinePrecision]), $MachinePrecision] - N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] * N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[(N[Cos[a], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\begin{array}{l}
t_0 := 1 - \tan y \cdot \tan z\\
x + \left(t_0 \cdot \sin a - \left(\tan y + \tan z\right) \cdot \cos a\right) \cdot \frac{-1}{\cos a \cdot t_0}
\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.4

    \[x + \left(\tan \left(y + z\right) - \tan a\right) \]

  2. Applied egg-rr0.2

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

  3. Applied egg-rr0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2022206 
(FPCore (x y z a)
  :name "tan-example"
  :precision binary64
  :pre (and (and (and (or (== x 0.0) (and (<= 0.5884142 x) (<= x 505.5909))) (or (and (<= -1.796658e+308 y) (<= y -9.425585e-310)) (and (<= 1.284938e-309 y) (<= y 1.751224e+308)))) (or (and (<= -1.776707e+308 z) (<= z -8.599796e-310)) (and (<= 3.293145e-311 z) (<= z 1.725154e+308)))) (or (and (<= -1.796658e+308 a) (<= a -9.425585e-310)) (and (<= 1.284938e-309 a) (<= a 1.751224e+308))))
  (+ x (- (tan (+ y z)) (tan a))))