
(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 7 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 (fma (- y x) (/ z t) x))
double code(double x, double y, double z, double t) {
return fma((y - x), (z / t), x);
}
function code(x, y, z, t) return fma(Float64(y - x), Float64(z / t), x) end
code[x_, y_, z_, t_] := N[(N[(y - x), $MachinePrecision] * N[(z / t), $MachinePrecision] + x), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(y - x, \frac{z}{t}, x\right)
\end{array}
Initial program 97.8%
+-commutative97.8%
fma-define97.8%
Simplified97.8%
Final simplification97.8%
(FPCore (x y z t) :precision binary64 (if (or (<= z -4.9e-178) (not (<= z 1.8e-192))) (+ x (* z (/ (- y x) t))) (+ x (/ (* y z) t))))
double code(double x, double y, double z, double t) {
double tmp;
if ((z <= -4.9e-178) || !(z <= 1.8e-192)) {
tmp = x + (z * ((y - x) / 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 ((z <= (-4.9d-178)) .or. (.not. (z <= 1.8d-192))) then
tmp = x + (z * ((y - x) / 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 ((z <= -4.9e-178) || !(z <= 1.8e-192)) {
tmp = x + (z * ((y - x) / t));
} else {
tmp = x + ((y * z) / t);
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (z <= -4.9e-178) or not (z <= 1.8e-192): tmp = x + (z * ((y - x) / t)) else: tmp = x + ((y * z) / t) return tmp
function code(x, y, z, t) tmp = 0.0 if ((z <= -4.9e-178) || !(z <= 1.8e-192)) tmp = Float64(x + Float64(z * Float64(Float64(y - x) / t))); else tmp = Float64(x + Float64(Float64(y * z) / t)); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((z <= -4.9e-178) || ~((z <= 1.8e-192))) tmp = x + (z * ((y - x) / t)); else tmp = x + ((y * z) / t); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.9e-178], N[Not[LessEqual[z, 1.8e-192]], $MachinePrecision]], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -4.9 \cdot 10^{-178} \lor \neg \left(z \leq 1.8 \cdot 10^{-192}\right):\\
\;\;\;\;x + z \cdot \frac{y - x}{t}\\
\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot z}{t}\\
\end{array}
\end{array}
if z < -4.9000000000000002e-178 or 1.7999999999999999e-192 < z Initial program 97.8%
Taylor expanded in y around 0 86.1%
+-commutative86.1%
mul-1-neg86.1%
unsub-neg86.1%
associate-*r/85.4%
associate-/l*89.0%
distribute-rgt-out--97.8%
associate-*l/93.5%
associate-/l*96.2%
Simplified96.2%
if -4.9000000000000002e-178 < z < 1.7999999999999999e-192Initial program 97.8%
Taylor expanded in y around inf 98.1%
Final simplification96.5%
(FPCore (x y z t) :precision binary64 (if (or (<= y -4.4e+64) (not (<= y 3.4e-80))) (+ x (* y (/ z t))) (* x (- 1.0 (/ z t)))))
double code(double x, double y, double z, double t) {
double tmp;
if ((y <= -4.4e+64) || !(y <= 3.4e-80)) {
tmp = x + (y * (z / t));
} else {
tmp = x * (1.0 - (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 ((y <= (-4.4d+64)) .or. (.not. (y <= 3.4d-80))) then
tmp = x + (y * (z / t))
else
tmp = x * (1.0d0 - (z / t))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((y <= -4.4e+64) || !(y <= 3.4e-80)) {
tmp = x + (y * (z / t));
} else {
tmp = x * (1.0 - (z / t));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (y <= -4.4e+64) or not (y <= 3.4e-80): tmp = x + (y * (z / t)) else: tmp = x * (1.0 - (z / t)) return tmp
function code(x, y, z, t) tmp = 0.0 if ((y <= -4.4e+64) || !(y <= 3.4e-80)) tmp = Float64(x + Float64(y * Float64(z / t))); else tmp = Float64(x * Float64(1.0 - Float64(z / t))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((y <= -4.4e+64) || ~((y <= 3.4e-80))) tmp = x + (y * (z / t)); else tmp = x * (1.0 - (z / t)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.4e+64], N[Not[LessEqual[y, 3.4e-80]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -4.4 \cdot 10^{+64} \lor \neg \left(y \leq 3.4 \cdot 10^{-80}\right):\\
\;\;\;\;x + y \cdot \frac{z}{t}\\
\mathbf{else}:\\
\;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\
\end{array}
\end{array}
if y < -4.40000000000000004e64 or 3.4000000000000001e-80 < y Initial program 97.9%
Taylor expanded in y around inf 87.2%
associate-*r/92.0%
Simplified92.0%
if -4.40000000000000004e64 < y < 3.4000000000000001e-80Initial program 97.7%
Taylor expanded in x around inf 89.0%
mul-1-neg89.0%
unsub-neg89.0%
Simplified89.0%
Final simplification90.5%
(FPCore (x y z t) :precision binary64 (if (or (<= z -5.2e-56) (not (<= z 17.0))) (* x (/ z (- t))) x))
double code(double x, double y, double z, double t) {
double tmp;
if ((z <= -5.2e-56) || !(z <= 17.0)) {
tmp = x * (z / -t);
} else {
tmp = x;
}
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 <= (-5.2d-56)) .or. (.not. (z <= 17.0d0))) then
tmp = x * (z / -t)
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if ((z <= -5.2e-56) || !(z <= 17.0)) {
tmp = x * (z / -t);
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (z <= -5.2e-56) or not (z <= 17.0): tmp = x * (z / -t) else: tmp = x return tmp
function code(x, y, z, t) tmp = 0.0 if ((z <= -5.2e-56) || !(z <= 17.0)) tmp = Float64(x * Float64(z / Float64(-t))); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((z <= -5.2e-56) || ~((z <= 17.0))) tmp = x * (z / -t); else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e-56], N[Not[LessEqual[z, 17.0]], $MachinePrecision]], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], x]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -5.2 \cdot 10^{-56} \lor \neg \left(z \leq 17\right):\\
\;\;\;\;x \cdot \frac{z}{-t}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
if z < -5.19999999999999994e-56 or 17 < z Initial program 97.7%
Taylor expanded in x around inf 63.8%
mul-1-neg63.8%
unsub-neg63.8%
Simplified63.8%
Taylor expanded in z around inf 46.9%
mul-1-neg46.9%
distribute-frac-neg246.9%
associate-*r/53.7%
Simplified53.7%
if -5.19999999999999994e-56 < z < 17Initial program 97.9%
Taylor expanded in z around 0 64.1%
Final simplification58.7%
(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 97.8%
Final simplification97.8%
(FPCore (x y z t) :precision binary64 (* x (- 1.0 (/ z t))))
double code(double x, double y, double z, double t) {
return x * (1.0 - (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 * (1.0d0 - (z / t))
end function
public static double code(double x, double y, double z, double t) {
return x * (1.0 - (z / t));
}
def code(x, y, z, t): return x * (1.0 - (z / t))
function code(x, y, z, t) return Float64(x * Float64(1.0 - Float64(z / t))) end
function tmp = code(x, y, z, t) tmp = x * (1.0 - (z / t)); end
code[x_, y_, z_, t_] := N[(x * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \left(1 - \frac{z}{t}\right)
\end{array}
Initial program 97.8%
Taylor expanded in x around inf 68.7%
mul-1-neg68.7%
unsub-neg68.7%
Simplified68.7%
Final simplification68.7%
(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 97.8%
Taylor expanded in z around 0 37.5%
Final simplification37.5%
(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 2024059
(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))))