
(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))
double code(double x, double y, double z, double a) {
return x + (tan((y + z)) - tan(a));
}
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
public static double code(double x, double y, double z, double a) {
return x + (Math.tan((y + z)) - Math.tan(a));
}
def code(x, y, z, a): return x + (math.tan((y + z)) - math.tan(a))
function code(x, y, z, a) return Float64(x + Float64(tan(Float64(y + z)) - tan(a))) end
function tmp = code(x, y, z, a) tmp = x + (tan((y + z)) - tan(a)); end
code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(\tan \left(y + z\right) - \tan a\right)
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 9 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))
double code(double x, double y, double z, double a) {
return x + (tan((y + z)) - tan(a));
}
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
public static double code(double x, double y, double z, double a) {
return x + (Math.tan((y + z)) - Math.tan(a));
}
def code(x, y, z, a): return x + (math.tan((y + z)) - math.tan(a))
function code(x, y, z, a) return Float64(x + Float64(tan(Float64(y + z)) - tan(a))) end
function tmp = code(x, y, z, a) tmp = x + (tan((y + z)) - tan(a)); end
code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(\tan \left(y + z\right) - \tan a\right)
\end{array}
(FPCore (x y z a) :precision binary64 (+ x (- (* (+ (tan y) (tan z)) (/ 1.0 (- 1.0 (* (tan y) (tan z))))) (tan a))))
double code(double x, double y, double z, double a) {
return x + (((tan(y) + tan(z)) * (1.0 / (1.0 - (tan(y) * tan(z))))) - tan(a));
}
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) + tan(z)) * (1.0d0 / (1.0d0 - (tan(y) * tan(z))))) - tan(a))
end function
public static double code(double x, double y, double z, double a) {
return x + (((Math.tan(y) + Math.tan(z)) * (1.0 / (1.0 - (Math.tan(y) * Math.tan(z))))) - Math.tan(a));
}
def code(x, y, z, a): return x + (((math.tan(y) + math.tan(z)) * (1.0 / (1.0 - (math.tan(y) * math.tan(z))))) - math.tan(a))
function code(x, y, z, a) return Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) * Float64(1.0 / Float64(1.0 - Float64(tan(y) * tan(z))))) - tan(a))) end
function tmp = code(x, y, z, a) tmp = x + (((tan(y) + tan(z)) * (1.0 / (1.0 - (tan(y) * tan(z))))) - tan(a)); end
code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z} - \tan a\right)
\end{array}
(FPCore (x y z a) :precision binary64 (+ x (- (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) (tan a))))
double code(double x, double y, double z, double a) {
return x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - tan(a));
}
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) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) - tan(a))
end function
public static double code(double x, double y, double z, double a) {
return x + (((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))) - Math.tan(a));
}
def code(x, y, z, a): return x + (((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) - math.tan(a))
function code(x, y, z, a) return Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))) - tan(a))) end
function tmp = code(x, y, z, a) tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - tan(a)); end
code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right)
\end{array}
(FPCore (x y z a)
:precision binary64
(let* ((t_0 (+ (tan y) (tan z))))
(if (<= a -0.0048)
(+ x (- (* (sin (+ y z)) (/ 1.0 (cos (+ y z)))) (tan a)))
(if (<= a 1.2e-27)
(+ x (- (* t_0 (/ 1.0 (- 1.0 (* (tan y) (tan z))))) a))
(+ x (- t_0 (tan a)))))))
double code(double x, double y, double z, double a) {
double t_0 = tan(y) + tan(z);
double tmp;
if (a <= -0.0048) {
tmp = x + ((sin((y + z)) * (1.0 / cos((y + z)))) - tan(a));
} else if (a <= 1.2e-27) {
tmp = x + ((t_0 * (1.0 / (1.0 - (tan(y) * tan(z))))) - a);
} else {
tmp = x + (t_0 - tan(a));
}
return tmp;
}
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
real(8) :: tmp
t_0 = tan(y) + tan(z)
if (a <= (-0.0048d0)) then
tmp = x + ((sin((y + z)) * (1.0d0 / cos((y + z)))) - tan(a))
else if (a <= 1.2d-27) then
tmp = x + ((t_0 * (1.0d0 / (1.0d0 - (tan(y) * tan(z))))) - a)
else
tmp = x + (t_0 - tan(a))
end if
code = tmp
end function
public static double code(double x, double y, double z, double a) {
double t_0 = Math.tan(y) + Math.tan(z);
double tmp;
if (a <= -0.0048) {
tmp = x + ((Math.sin((y + z)) * (1.0 / Math.cos((y + z)))) - Math.tan(a));
} else if (a <= 1.2e-27) {
tmp = x + ((t_0 * (1.0 / (1.0 - (Math.tan(y) * Math.tan(z))))) - a);
} else {
tmp = x + (t_0 - Math.tan(a));
}
return tmp;
}
def code(x, y, z, a): t_0 = math.tan(y) + math.tan(z) tmp = 0 if a <= -0.0048: tmp = x + ((math.sin((y + z)) * (1.0 / math.cos((y + z)))) - math.tan(a)) elif a <= 1.2e-27: tmp = x + ((t_0 * (1.0 / (1.0 - (math.tan(y) * math.tan(z))))) - a) else: tmp = x + (t_0 - math.tan(a)) return tmp
function code(x, y, z, a) t_0 = Float64(tan(y) + tan(z)) tmp = 0.0 if (a <= -0.0048) tmp = Float64(x + Float64(Float64(sin(Float64(y + z)) * Float64(1.0 / cos(Float64(y + z)))) - tan(a))); elseif (a <= 1.2e-27) tmp = Float64(x + Float64(Float64(t_0 * Float64(1.0 / Float64(1.0 - Float64(tan(y) * tan(z))))) - a)); else tmp = Float64(x + Float64(t_0 - tan(a))); end return tmp end
function tmp_2 = code(x, y, z, a) t_0 = tan(y) + tan(z); tmp = 0.0; if (a <= -0.0048) tmp = x + ((sin((y + z)) * (1.0 / cos((y + z)))) - tan(a)); elseif (a <= 1.2e-27) tmp = x + ((t_0 * (1.0 / (1.0 - (tan(y) * tan(z))))) - a); else tmp = x + (t_0 - tan(a)); end tmp_2 = tmp; end
code[x_, y_, z_, a_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0048], N[(x + N[(N[(N[Sin[N[(y + z), $MachinePrecision]], $MachinePrecision] * N[(1.0 / N[Cos[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-27], N[(x + N[(N[(t$95$0 * N[(1.0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$0 - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \tan y + \tan z\\
\mathbf{if}\;a \leq -0.0048:\\
\;\;\;\;x + \left(\sin \left(y + z\right) \cdot \frac{1}{\cos \left(y + z\right)} - \tan a\right)\\
\mathbf{elif}\;a \leq 1.2 \cdot 10^{-27}:\\
\;\;\;\;x + \left(t_0 \cdot \frac{1}{1 - \tan y \cdot \tan z} - a\right)\\
\mathbf{else}:\\
\;\;\;\;x + \left(t_0 - \tan a\right)\\
\end{array}
\end{array}
(FPCore (x y z a)
:precision binary64
(let* ((t_0 (+ (tan y) (tan z))))
(if (<= a -0.0048)
(+ x (- (* (sin (+ y z)) (/ 1.0 (cos (+ y z)))) (tan a)))
(if (<= a 1.2e-27)
(+ x (- (/ t_0 (- 1.0 (* (tan y) (tan z)))) a))
(+ x (- t_0 (tan a)))))))
double code(double x, double y, double z, double a) {
double t_0 = tan(y) + tan(z);
double tmp;
if (a <= -0.0048) {
tmp = x + ((sin((y + z)) * (1.0 / cos((y + z)))) - tan(a));
} else if (a <= 1.2e-27) {
tmp = x + ((t_0 / (1.0 - (tan(y) * tan(z)))) - a);
} else {
tmp = x + (t_0 - tan(a));
}
return tmp;
}
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
real(8) :: tmp
t_0 = tan(y) + tan(z)
if (a <= (-0.0048d0)) then
tmp = x + ((sin((y + z)) * (1.0d0 / cos((y + z)))) - tan(a))
else if (a <= 1.2d-27) then
tmp = x + ((t_0 / (1.0d0 - (tan(y) * tan(z)))) - a)
else
tmp = x + (t_0 - tan(a))
end if
code = tmp
end function
public static double code(double x, double y, double z, double a) {
double t_0 = Math.tan(y) + Math.tan(z);
double tmp;
if (a <= -0.0048) {
tmp = x + ((Math.sin((y + z)) * (1.0 / Math.cos((y + z)))) - Math.tan(a));
} else if (a <= 1.2e-27) {
tmp = x + ((t_0 / (1.0 - (Math.tan(y) * Math.tan(z)))) - a);
} else {
tmp = x + (t_0 - Math.tan(a));
}
return tmp;
}
def code(x, y, z, a): t_0 = math.tan(y) + math.tan(z) tmp = 0 if a <= -0.0048: tmp = x + ((math.sin((y + z)) * (1.0 / math.cos((y + z)))) - math.tan(a)) elif a <= 1.2e-27: tmp = x + ((t_0 / (1.0 - (math.tan(y) * math.tan(z)))) - a) else: tmp = x + (t_0 - math.tan(a)) return tmp
function code(x, y, z, a) t_0 = Float64(tan(y) + tan(z)) tmp = 0.0 if (a <= -0.0048) tmp = Float64(x + Float64(Float64(sin(Float64(y + z)) * Float64(1.0 / cos(Float64(y + z)))) - tan(a))); elseif (a <= 1.2e-27) tmp = Float64(x + Float64(Float64(t_0 / Float64(1.0 - Float64(tan(y) * tan(z)))) - a)); else tmp = Float64(x + Float64(t_0 - tan(a))); end return tmp end
function tmp_2 = code(x, y, z, a) t_0 = tan(y) + tan(z); tmp = 0.0; if (a <= -0.0048) tmp = x + ((sin((y + z)) * (1.0 / cos((y + z)))) - tan(a)); elseif (a <= 1.2e-27) tmp = x + ((t_0 / (1.0 - (tan(y) * tan(z)))) - a); else tmp = x + (t_0 - tan(a)); end tmp_2 = tmp; end
code[x_, y_, z_, a_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.0048], N[(x + N[(N[(N[Sin[N[(y + z), $MachinePrecision]], $MachinePrecision] * N[(1.0 / N[Cos[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.2e-27], N[(x + N[(N[(t$95$0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$0 - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \tan y + \tan z\\
\mathbf{if}\;a \leq -0.0048:\\
\;\;\;\;x + \left(\sin \left(y + z\right) \cdot \frac{1}{\cos \left(y + z\right)} - \tan a\right)\\
\mathbf{elif}\;a \leq 1.2 \cdot 10^{-27}:\\
\;\;\;\;x + \left(\frac{t_0}{1 - \tan y \cdot \tan z} - a\right)\\
\mathbf{else}:\\
\;\;\;\;x + \left(t_0 - \tan a\right)\\
\end{array}
\end{array}
(FPCore (x y z a) :precision binary64 (+ x (- (+ (tan y) (tan z)) (tan a))))
double code(double x, double y, double z, double a) {
return x + ((tan(y) + tan(z)) - tan(a));
}
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) + tan(z)) - tan(a))
end function
public static double code(double x, double y, double z, double a) {
return x + ((Math.tan(y) + Math.tan(z)) - Math.tan(a));
}
def code(x, y, z, a): return x + ((math.tan(y) + math.tan(z)) - math.tan(a))
function code(x, y, z, a) return Float64(x + Float64(Float64(tan(y) + tan(z)) - tan(a))) end
function tmp = code(x, y, z, a) tmp = x + ((tan(y) + tan(z)) - tan(a)); end
code[x_, y_, z_, a_] := N[(x + N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(\left(\tan y + \tan z\right) - \tan a\right)
\end{array}
(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))
double code(double x, double y, double z, double a) {
return x + (tan((y + z)) - tan(a));
}
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
public static double code(double x, double y, double z, double a) {
return x + (Math.tan((y + z)) - Math.tan(a));
}
def code(x, y, z, a): return x + (math.tan((y + z)) - math.tan(a))
function code(x, y, z, a) return Float64(x + Float64(tan(Float64(y + z)) - tan(a))) end
function tmp = code(x, y, z, a) tmp = x + (tan((y + z)) - tan(a)); end
code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(\tan \left(y + z\right) - \tan a\right)
\end{array}
(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (/ 1.0 (+ (* a -0.3333333333333333) (/ 1.0 a))))))
double code(double x, double y, double z, double a) {
return x + (tan((y + z)) - (1.0 / ((a * -0.3333333333333333) + (1.0 / a))));
}
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)) - (1.0d0 / ((a * (-0.3333333333333333d0)) + (1.0d0 / a))))
end function
public static double code(double x, double y, double z, double a) {
return x + (Math.tan((y + z)) - (1.0 / ((a * -0.3333333333333333) + (1.0 / a))));
}
def code(x, y, z, a): return x + (math.tan((y + z)) - (1.0 / ((a * -0.3333333333333333) + (1.0 / a))))
function code(x, y, z, a) return Float64(x + Float64(tan(Float64(y + z)) - Float64(1.0 / Float64(Float64(a * -0.3333333333333333) + Float64(1.0 / a))))) end
function tmp = code(x, y, z, a) tmp = x + (tan((y + z)) - (1.0 / ((a * -0.3333333333333333) + (1.0 / a)))); end
code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[(1.0 / N[(N[(a * -0.3333333333333333), $MachinePrecision] + N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(\tan \left(y + z\right) - \frac{1}{a \cdot -0.3333333333333333 + \frac{1}{a}}\right)
\end{array}
(FPCore (x y z a) :precision binary64 (if (<= a -0.0045) x (if (<= a 1.6) (+ x (- (tan (+ y z)) a)) (+ x -1.0))))
double code(double x, double y, double z, double a) {
double tmp;
if (a <= -0.0045) {
tmp = x;
} else if (a <= 1.6) {
tmp = x + (tan((y + z)) - a);
} else {
tmp = x + -1.0;
}
return tmp;
}
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) :: tmp
if (a <= (-0.0045d0)) then
tmp = x
else if (a <= 1.6d0) then
tmp = x + (tan((y + z)) - a)
else
tmp = x + (-1.0d0)
end if
code = tmp
end function
public static double code(double x, double y, double z, double a) {
double tmp;
if (a <= -0.0045) {
tmp = x;
} else if (a <= 1.6) {
tmp = x + (Math.tan((y + z)) - a);
} else {
tmp = x + -1.0;
}
return tmp;
}
def code(x, y, z, a): tmp = 0 if a <= -0.0045: tmp = x elif a <= 1.6: tmp = x + (math.tan((y + z)) - a) else: tmp = x + -1.0 return tmp
function code(x, y, z, a) tmp = 0.0 if (a <= -0.0045) tmp = x; elseif (a <= 1.6) tmp = Float64(x + Float64(tan(Float64(y + z)) - a)); else tmp = Float64(x + -1.0); end return tmp end
function tmp_2 = code(x, y, z, a) tmp = 0.0; if (a <= -0.0045) tmp = x; elseif (a <= 1.6) tmp = x + (tan((y + z)) - a); else tmp = x + -1.0; end tmp_2 = tmp; end
code[x_, y_, z_, a_] := If[LessEqual[a, -0.0045], x, If[LessEqual[a, 1.6], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + -1.0), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;a \leq -0.0045:\\
\;\;\;\;x\\
\mathbf{elif}\;a \leq 1.6:\\
\;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\
\mathbf{else}:\\
\;\;\;\;x + -1\\
\end{array}
\end{array}
(FPCore (x y z a) :precision binary64 x)
double code(double x, double y, double z, double a) {
return x;
}
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
end function
public static double code(double x, double y, double z, double a) {
return x;
}
def code(x, y, z, a): return x
function code(x, y, z, a) return x end
function tmp = code(x, y, z, a) tmp = x; end
code[x_, y_, z_, a_] := x
\begin{array}{l}
\\
x
\end{array}
herbie shell --seed 2023350
(FPCore (x y z a)
:name "tan-example (used to crash)"
: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))))