
(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 (+ 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 98.4%
clear-num98.3%
un-div-inv98.5%
Applied egg-rr98.5%
(FPCore (x y z t) :precision binary64 (if (or (<= y -3.2e-104) (not (<= y 5.6e-135))) (+ x (* y (/ z t))) (* x (- 1.0 (/ z t)))))
double code(double x, double y, double z, double t) {
double tmp;
if ((y <= -3.2e-104) || !(y <= 5.6e-135)) {
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 <= (-3.2d-104)) .or. (.not. (y <= 5.6d-135))) 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 <= -3.2e-104) || !(y <= 5.6e-135)) {
tmp = x + (y * (z / t));
} else {
tmp = x * (1.0 - (z / t));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (y <= -3.2e-104) or not (y <= 5.6e-135): 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 <= -3.2e-104) || !(y <= 5.6e-135)) 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 <= -3.2e-104) || ~((y <= 5.6e-135))) 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, -3.2e-104], N[Not[LessEqual[y, 5.6e-135]], $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 -3.2 \cdot 10^{-104} \lor \neg \left(y \leq 5.6 \cdot 10^{-135}\right):\\
\;\;\;\;x + y \cdot \frac{z}{t}\\
\mathbf{else}:\\
\;\;\;\;x \cdot \left(1 - \frac{z}{t}\right)\\
\end{array}
\end{array}
if y < -3.19999999999999989e-104 or 5.60000000000000047e-135 < y Initial program 98.7%
Taylor expanded in y around inf 82.7%
associate-*r/90.9%
Simplified90.9%
if -3.19999999999999989e-104 < y < 5.60000000000000047e-135Initial program 97.6%
Taylor expanded in x around inf 94.9%
mul-1-neg94.9%
unsub-neg94.9%
Simplified94.9%
Final simplification92.2%
(FPCore (x y z t) :precision binary64 (if (or (<= z -1.05e+154) (not (<= z 8.6e+63))) (* x (/ z (- t))) x))
double code(double x, double y, double z, double t) {
double tmp;
if ((z <= -1.05e+154) || !(z <= 8.6e+63)) {
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 <= (-1.05d+154)) .or. (.not. (z <= 8.6d+63))) 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 <= -1.05e+154) || !(z <= 8.6e+63)) {
tmp = x * (z / -t);
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (z <= -1.05e+154) or not (z <= 8.6e+63): tmp = x * (z / -t) else: tmp = x return tmp
function code(x, y, z, t) tmp = 0.0 if ((z <= -1.05e+154) || !(z <= 8.6e+63)) 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 <= -1.05e+154) || ~((z <= 8.6e+63))) tmp = x * (z / -t); else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.05e+154], N[Not[LessEqual[z, 8.6e+63]], $MachinePrecision]], N[(x * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], x]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -1.05 \cdot 10^{+154} \lor \neg \left(z \leq 8.6 \cdot 10^{+63}\right):\\
\;\;\;\;x \cdot \frac{z}{-t}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
if z < -1.04999999999999997e154 or 8.6000000000000001e63 < z Initial program 96.3%
Taylor expanded in x around inf 54.8%
mul-1-neg54.8%
unsub-neg54.8%
Simplified54.8%
Taylor expanded in z around inf 49.6%
associate-*r/49.6%
mul-1-neg49.6%
Simplified49.6%
if -1.04999999999999997e154 < z < 8.6000000000000001e63Initial program 99.3%
Taylor expanded in z around 0 58.4%
Final simplification55.7%
(FPCore (x y z t) :precision binary64 (if (or (<= z -6.6e+154) (not (<= z 1.8e+65))) (- (/ z (/ t x))) x))
double code(double x, double y, double z, double t) {
double tmp;
if ((z <= -6.6e+154) || !(z <= 1.8e+65)) {
tmp = -(z / (t / x));
} 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 <= (-6.6d+154)) .or. (.not. (z <= 1.8d+65))) then
tmp = -(z / (t / x))
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 <= -6.6e+154) || !(z <= 1.8e+65)) {
tmp = -(z / (t / x));
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if (z <= -6.6e+154) or not (z <= 1.8e+65): tmp = -(z / (t / x)) else: tmp = x return tmp
function code(x, y, z, t) tmp = 0.0 if ((z <= -6.6e+154) || !(z <= 1.8e+65)) tmp = Float64(-Float64(z / Float64(t / x))); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if ((z <= -6.6e+154) || ~((z <= 1.8e+65))) tmp = -(z / (t / x)); else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.6e+154], N[Not[LessEqual[z, 1.8e+65]], $MachinePrecision]], (-N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), x]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -6.6 \cdot 10^{+154} \lor \neg \left(z \leq 1.8 \cdot 10^{+65}\right):\\
\;\;\;\;-\frac{z}{\frac{t}{x}}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
if z < -6.6e154 or 1.79999999999999989e65 < z Initial program 96.3%
Taylor expanded in x around inf 54.8%
mul-1-neg54.8%
unsub-neg54.8%
Simplified54.8%
Taylor expanded in z around inf 49.6%
associate-*r/49.6%
mul-1-neg49.6%
Simplified49.6%
*-commutative49.6%
distribute-frac-neg49.6%
distribute-lft-neg-in49.6%
associate-/r/43.7%
Applied egg-rr43.7%
if -6.6e154 < z < 1.79999999999999989e65Initial program 99.3%
Taylor expanded in z around 0 58.4%
Final simplification53.9%
(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 98.4%
(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 98.4%
Taylor expanded in x around inf 64.1%
mul-1-neg64.1%
unsub-neg64.1%
Simplified64.1%
(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 98.4%
Taylor expanded in z around 0 42.7%
(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 2024170
(FPCore (x y z t)
:name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
:precision binary64
:alt
(! :herbie-platform default (if (< (* (- y x) (/ z t)) -10136466924358867/10000) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) 0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z))))))
(+ x (* (- y x) (/ z t))))