
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
double code(double x, double y, double z, double t) {
return x + ((y - x) * (z / t));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x + ((y - x) * (z / t))
end function
public static double code(double x, double y, double z, double t) {
return x + ((y - x) * (z / t));
}
def code(x, y, z, t): return x + ((y - x) * (z / t))
function code(x, y, z, t) return Float64(x + Float64(Float64(y - x) * Float64(z / t))) end
function tmp = code(x, y, z, t) tmp = x + ((y - x) * (z / t)); end
code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(y - x\right) \cdot \frac{z}{t}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 5 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
double code(double x, double y, double z, double t) {
return x + ((y - x) * (z / t));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x + ((y - x) * (z / t))
end function
public static double code(double x, double y, double z, double t) {
return x + ((y - x) * (z / t));
}
def code(x, y, z, t): return x + ((y - x) * (z / t))
function code(x, y, z, t) return Float64(x + Float64(Float64(y - x) * Float64(z / t))) end
function tmp = code(x, y, z, t) tmp = x + ((y - x) * (z / t)); end
code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(y - x\right) \cdot \frac{z}{t}
\end{array}
(FPCore (x y z t) :precision binary64 (+ x (* (- y x) (/ z t))))
double code(double x, double y, double z, double t) {
return x + ((y - x) * (z / t));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x + ((y - x) * (z / t))
end function
public static double code(double x, double y, double z, double t) {
return x + ((y - x) * (z / t));
}
def code(x, y, z, t): return x + ((y - x) * (z / t))
function code(x, y, z, t) return Float64(x + Float64(Float64(y - x) * Float64(z / t))) end
function tmp = code(x, y, z, t) tmp = x + ((y - x) * (z / t)); end
code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(y - x\right) \cdot \frac{z}{t}
\end{array}
Initial program 98.0%
Final simplification98.0%
(FPCore (x y z t) :precision binary64 (if (or (<= x -3.7e+63) (not (<= x 2.95e+87))) (- x (* x (/ z t))) (+ x (* y (/ z t)))))
double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -3.7e+63) || !(x <= 2.95e+87)) {
tmp = x - (x * (z / t));
} else {
tmp = x + (y * (z / t));
}
return tmp;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: tmp
if ((x <= (-3.7d+63)) .or. (.not. (x <= 2.95d+87))) then
tmp = x - (x * (z / t))
else
tmp = x + (y * (z / t))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -3.7e+63) || !(x <= 2.95e+87)) {
tmp = x - (x * (z / t));
} else {
tmp = x + (y * (z / t));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (x <= -3.7e+63) or not (x <= 2.95e+87): tmp = x - (x * (z / t)) else: tmp = x + (y * (z / t)) return tmp
function code(x, y, z, t) tmp = 0.0 if ((x <= -3.7e+63) || !(x <= 2.95e+87)) tmp = Float64(x - Float64(x * Float64(z / t))); else tmp = Float64(x + Float64(y * Float64(z / t))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((x <= -3.7e+63) || ~((x <= 2.95e+87))) tmp = x - (x * (z / t)); else tmp = x + (y * (z / t)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.7e+63], N[Not[LessEqual[x, 2.95e+87]], $MachinePrecision]], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.7 \cdot 10^{+63} \lor \neg \left(x \leq 2.95 \cdot 10^{+87}\right):\\
\;\;\;\;x - x \cdot \frac{z}{t}\\
\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{z}{t}\\
\end{array}
\end{array}
if x < -3.69999999999999968e63 or 2.9499999999999998e87 < x Initial program 100.0%
Taylor expanded in y around 0 82.4%
mul-1-neg82.4%
associate-/l*94.3%
distribute-lft-neg-out94.3%
*-commutative94.3%
Simplified94.3%
distribute-rgt-neg-out94.3%
unsub-neg94.3%
*-commutative94.3%
Applied egg-rr94.3%
if -3.69999999999999968e63 < x < 2.9499999999999998e87Initial program 96.8%
Taylor expanded in y around inf 85.1%
associate-*r/86.2%
Simplified86.2%
Final simplification89.2%
(FPCore (x y z t) :precision binary64 (if (<= x -1.8e+67) (- x (* x (/ z t))) (if (<= x 5.2e+87) (+ x (* y (/ z t))) (- x (/ x (/ t z))))))
double code(double x, double y, double z, double t) {
double tmp;
if (x <= -1.8e+67) {
tmp = x - (x * (z / t));
} else if (x <= 5.2e+87) {
tmp = x + (y * (z / t));
} else {
tmp = x - (x / (t / z));
}
return tmp;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: tmp
if (x <= (-1.8d+67)) then
tmp = x - (x * (z / t))
else if (x <= 5.2d+87) then
tmp = x + (y * (z / t))
else
tmp = x - (x / (t / z))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (x <= -1.8e+67) {
tmp = x - (x * (z / t));
} else if (x <= 5.2e+87) {
tmp = x + (y * (z / t));
} else {
tmp = x - (x / (t / z));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if x <= -1.8e+67: tmp = x - (x * (z / t)) elif x <= 5.2e+87: tmp = x + (y * (z / t)) else: tmp = x - (x / (t / z)) return tmp
function code(x, y, z, t) tmp = 0.0 if (x <= -1.8e+67) tmp = Float64(x - Float64(x * Float64(z / t))); elseif (x <= 5.2e+87) tmp = Float64(x + Float64(y * Float64(z / t))); else tmp = Float64(x - Float64(x / Float64(t / z))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (x <= -1.8e+67) tmp = x - (x * (z / t)); elseif (x <= 5.2e+87) tmp = x + (y * (z / t)); else tmp = x - (x / (t / z)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[x, -1.8e+67], N[(x - N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e+87], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.8 \cdot 10^{+67}:\\
\;\;\;\;x - x \cdot \frac{z}{t}\\
\mathbf{elif}\;x \leq 5.2 \cdot 10^{+87}:\\
\;\;\;\;x + y \cdot \frac{z}{t}\\
\mathbf{else}:\\
\;\;\;\;x - \frac{x}{\frac{t}{z}}\\
\end{array}
\end{array}
if x < -1.7999999999999999e67Initial program 100.0%
Taylor expanded in y around 0 82.0%
mul-1-neg82.0%
associate-/l*92.6%
distribute-lft-neg-out92.6%
*-commutative92.6%
Simplified92.6%
distribute-rgt-neg-out92.6%
unsub-neg92.6%
*-commutative92.6%
Applied egg-rr92.6%
if -1.7999999999999999e67 < x < 5.19999999999999997e87Initial program 96.8%
Taylor expanded in y around inf 85.1%
associate-*r/86.2%
Simplified86.2%
if 5.19999999999999997e87 < x Initial program 100.0%
Taylor expanded in y around 0 82.8%
mul-1-neg82.8%
associate-/l*96.0%
distribute-lft-neg-out96.0%
*-commutative96.0%
Simplified96.0%
distribute-rgt-neg-out96.0%
unsub-neg96.0%
*-commutative96.0%
Applied egg-rr96.0%
clear-num96.0%
un-div-inv96.0%
Applied egg-rr96.0%
Final simplification89.2%
(FPCore (x y z t) :precision binary64 (+ x (* y (/ z t))))
double code(double x, double y, double z, double t) {
return x + (y * (z / t));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x + (y * (z / t))
end function
public static double code(double x, double y, double z, double t) {
return x + (y * (z / t));
}
def code(x, y, z, t): return x + (y * (z / t))
function code(x, y, z, t) return Float64(x + Float64(y * Float64(z / t))) end
function tmp = code(x, y, z, t) tmp = x + (y * (z / t)); end
code[x_, y_, z_, t_] := N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + y \cdot \frac{z}{t}
\end{array}
Initial program 98.0%
Taylor expanded in y around inf 77.1%
associate-*r/78.5%
Simplified78.5%
Final simplification78.5%
(FPCore (x y z t) :precision binary64 x)
double code(double x, double y, double z, double t) {
return x;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x
end function
public static double code(double x, double y, double z, double t) {
return x;
}
def code(x, y, z, t): return x
function code(x, y, z, t) return x end
function tmp = code(x, y, z, t) tmp = x; end
code[x_, y_, z_, t_] := x
\begin{array}{l}
\\
x
\end{array}
Initial program 98.0%
Taylor expanded in y around inf 77.1%
associate-*r/78.5%
Simplified78.5%
Taylor expanded in x around inf 38.5%
Final simplification38.5%
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (* (- y x) (/ z t))) (t_2 (+ x (/ (- y x) (/ t z)))))
(if (< t_1 -1013646692435.8867)
t_2
(if (< t_1 0.0) (+ x (/ (* (- y x) z) t)) t_2))))
double code(double x, double y, double z, double t) {
double t_1 = (y - x) * (z / t);
double t_2 = x + ((y - x) / (t / z));
double tmp;
if (t_1 < -1013646692435.8867) {
tmp = t_2;
} else if (t_1 < 0.0) {
tmp = x + (((y - x) * z) / t);
} else {
tmp = t_2;
}
return tmp;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: t_1
real(8) :: t_2
real(8) :: tmp
t_1 = (y - x) * (z / t)
t_2 = x + ((y - x) / (t / z))
if (t_1 < (-1013646692435.8867d0)) then
tmp = t_2
else if (t_1 < 0.0d0) then
tmp = x + (((y - x) * z) / t)
else
tmp = t_2
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double t_1 = (y - x) * (z / t);
double t_2 = x + ((y - x) / (t / z));
double tmp;
if (t_1 < -1013646692435.8867) {
tmp = t_2;
} else if (t_1 < 0.0) {
tmp = x + (((y - x) * z) / t);
} else {
tmp = t_2;
}
return tmp;
}
def code(x, y, z, t): t_1 = (y - x) * (z / t) t_2 = x + ((y - x) / (t / z)) tmp = 0 if t_1 < -1013646692435.8867: tmp = t_2 elif t_1 < 0.0: tmp = x + (((y - x) * z) / t) else: tmp = t_2 return tmp
function code(x, y, z, t) t_1 = Float64(Float64(y - x) * Float64(z / t)) t_2 = Float64(x + Float64(Float64(y - x) / Float64(t / z))) tmp = 0.0 if (t_1 < -1013646692435.8867) tmp = t_2; elseif (t_1 < 0.0) tmp = Float64(x + Float64(Float64(Float64(y - x) * z) / t)); else tmp = t_2; end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = (y - x) * (z / t); t_2 = x + ((y - x) / (t / z)); tmp = 0.0; if (t_1 < -1013646692435.8867) tmp = t_2; elseif (t_1 < 0.0) tmp = x + (((y - x) * z) / t); else tmp = t_2; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$1, -1013646692435.8867], t$95$2, If[Less[t$95$1, 0.0], N[(x + N[(N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \left(y - x\right) \cdot \frac{z}{t}\\
t_2 := x + \frac{y - x}{\frac{t}{z}}\\
\mathbf{if}\;t\_1 < -1013646692435.8867:\\
\;\;\;\;t\_2\\
\mathbf{elif}\;t\_1 < 0:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\
\mathbf{else}:\\
\;\;\;\;t\_2\\
\end{array}
\end{array}
herbie shell --seed 2024055
(FPCore (x y z t)
:name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
:precision binary64
:alt
(if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))
(+ x (* (- y x) (/ z t))))