
(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 6 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) (/ t z))))
double code(double x, double y, double z, double t) {
return x + ((y - x) / (t / z));
}
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) / (t / z))
end function
public static double code(double x, double y, double z, double t) {
return x + ((y - x) / (t / z));
}
def code(x, y, z, t): return x + ((y - x) / (t / z))
function code(x, y, z, t) return Float64(x + Float64(Float64(y - x) / Float64(t / z))) end
function tmp = code(x, y, z, t) tmp = x + ((y - x) / (t / z)); end
code[x_, y_, z_, t_] := N[(x + N[(N[(y - x), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \frac{y - x}{\frac{t}{z}}
\end{array}
Initial program 98.1%
clear-num98.0%
un-div-inv98.1%
Applied egg-rr98.1%
Final simplification98.1%
(FPCore (x y z t) :precision binary64 (if (or (<= (/ z t) -8e+23) (not (<= (/ z t) 0.001))) (* (/ z t) (- y x)) (+ x (* y (/ z t)))))
double code(double x, double y, double z, double t) {
double tmp;
if (((z / t) <= -8e+23) || !((z / t) <= 0.001)) {
tmp = (z / t) * (y - x);
} 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 (((z / t) <= (-8d+23)) .or. (.not. ((z / t) <= 0.001d0))) then
tmp = (z / t) * (y - x)
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 (((z / t) <= -8e+23) || !((z / t) <= 0.001)) {
tmp = (z / t) * (y - x);
} else {
tmp = x + (y * (z / t));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if ((z / t) <= -8e+23) or not ((z / t) <= 0.001): tmp = (z / t) * (y - x) else: tmp = x + (y * (z / t)) return tmp
function code(x, y, z, t) tmp = 0.0 if ((Float64(z / t) <= -8e+23) || !(Float64(z / t) <= 0.001)) tmp = Float64(Float64(z / t) * Float64(y - x)); 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 (((z / t) <= -8e+23) || ~(((z / t) <= 0.001))) tmp = (z / t) * (y - x); else tmp = x + (y * (z / t)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z / t), $MachinePrecision], -8e+23], N[Not[LessEqual[N[(z / t), $MachinePrecision], 0.001]], $MachinePrecision]], N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} \leq -8 \cdot 10^{+23} \lor \neg \left(\frac{z}{t} \leq 0.001\right):\\
\;\;\;\;\frac{z}{t} \cdot \left(y - x\right)\\
\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{z}{t}\\
\end{array}
\end{array}
if (/.f64 z t) < -7.9999999999999993e23 or 1e-3 < (/.f64 z t) Initial program 98.2%
Taylor expanded in x around 0 73.5%
Taylor expanded in z around inf 86.0%
mul-1-neg86.0%
distribute-frac-neg86.0%
distribute-rgt-in75.7%
distribute-frac-neg75.7%
mul-1-neg75.7%
associate-*l*75.7%
associate-*l/73.0%
associate-*l/73.8%
neg-mul-173.8%
neg-sub073.8%
associate-*r/76.2%
associate-+l-76.2%
associate-*r/73.8%
associate-*l/73.0%
cancel-sign-sub-inv73.0%
associate-*l/75.7%
mul-1-neg75.7%
distribute-rgt-in86.0%
+-commutative86.0%
Simplified97.8%
if -7.9999999999999993e23 < (/.f64 z t) < 1e-3Initial program 97.9%
Taylor expanded in y around inf 96.1%
associate-*r/96.8%
Simplified96.8%
Final simplification97.3%
(FPCore (x y z t) :precision binary64 (if (or (<= x -3.8e+82) (not (<= x 8.8e+51))) (- x (* x (/ z t))) (+ x (* y (/ z t)))))
double code(double x, double y, double z, double t) {
double tmp;
if ((x <= -3.8e+82) || !(x <= 8.8e+51)) {
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 <= (-3.8d+82)) .or. (.not. (x <= 8.8d+51))) 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 <= -3.8e+82) || !(x <= 8.8e+51)) {
tmp = x - (x * (z / t));
} else {
tmp = x + (y * (z / t));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (x <= -3.8e+82) or not (x <= 8.8e+51): tmp = x - (x * (z / t)) else: tmp = x + (y * (z / t)) return tmp
function code(x, y, z, t) tmp = 0.0 if ((x <= -3.8e+82) || !(x <= 8.8e+51)) 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 <= -3.8e+82) || ~((x <= 8.8e+51))) 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, -3.8e+82], N[Not[LessEqual[x, 8.8e+51]], $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 -3.8 \cdot 10^{+82} \lor \neg \left(x \leq 8.8 \cdot 10^{+51}\right):\\
\;\;\;\;x - x \cdot \frac{z}{t}\\
\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{z}{t}\\
\end{array}
\end{array}
if x < -3.80000000000000033e82 or 8.79999999999999967e51 < x Initial program 100.0%
Taylor expanded in x around inf 91.5%
mul-1-neg91.5%
unsub-neg91.5%
distribute-lft-out--91.5%
*-rgt-identity91.5%
Simplified91.5%
if -3.80000000000000033e82 < x < 8.79999999999999967e51Initial program 96.8%
Taylor expanded in y around inf 81.5%
associate-*r/85.5%
Simplified85.5%
Final simplification87.9%
(FPCore (x y z t) :precision binary64 (+ x (* (/ z t) (- y x))))
double code(double x, double y, double z, double t) {
return x + ((z / t) * (y - 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 + ((z / t) * (y - x))
end function
public static double code(double x, double y, double z, double t) {
return x + ((z / t) * (y - x));
}
def code(x, y, z, t): return x + ((z / t) * (y - x))
function code(x, y, z, t) return Float64(x + Float64(Float64(z / t) * Float64(y - x))) end
function tmp = code(x, y, z, t) tmp = x + ((z / t) * (y - x)); end
code[x_, y_, z_, t_] := N[(x + N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \frac{z}{t} \cdot \left(y - x\right)
\end{array}
Initial program 98.1%
Final simplification98.1%
(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 98.1%
Taylor expanded in y around inf 73.9%
associate-*r/77.5%
Simplified77.5%
Final simplification77.5%
(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 98.1%
Taylor expanded in z around 0 39.3%
Final simplification39.3%
(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 2023271
(FPCore (x y z t)
:name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
:precision binary64
:herbie-target
(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))))