(FPCore (x y z t) :precision binary64 (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (- x (/ (log1p (* y (expm1 z))) t))))
(if (<= y -7.017489851709385e-155)
t_1
(if (<= y 7.647719248273216e-113) (- x (* y (/ (expm1 z) t))) t_1))))double code(double x, double y, double z, double t) {
return x - (log(((1.0 - y) + (y * exp(z)))) / t);
}
double code(double x, double y, double z, double t) {
double t_1 = x - (log1p((y * expm1(z))) / t);
double tmp;
if (y <= -7.017489851709385e-155) {
tmp = t_1;
} else if (y <= 7.647719248273216e-113) {
tmp = x - (y * (expm1(z) / t));
} else {
tmp = t_1;
}
return tmp;
}
public static double code(double x, double y, double z, double t) {
return x - (Math.log(((1.0 - y) + (y * Math.exp(z)))) / t);
}
public static double code(double x, double y, double z, double t) {
double t_1 = x - (Math.log1p((y * Math.expm1(z))) / t);
double tmp;
if (y <= -7.017489851709385e-155) {
tmp = t_1;
} else if (y <= 7.647719248273216e-113) {
tmp = x - (y * (Math.expm1(z) / t));
} else {
tmp = t_1;
}
return tmp;
}
def code(x, y, z, t): return x - (math.log(((1.0 - y) + (y * math.exp(z)))) / t)
def code(x, y, z, t): t_1 = x - (math.log1p((y * math.expm1(z))) / t) tmp = 0 if y <= -7.017489851709385e-155: tmp = t_1 elif y <= 7.647719248273216e-113: tmp = x - (y * (math.expm1(z) / t)) else: tmp = t_1 return tmp
function code(x, y, z, t) return Float64(x - Float64(log(Float64(Float64(1.0 - y) + Float64(y * exp(z)))) / t)) end
function code(x, y, z, t) t_1 = Float64(x - Float64(log1p(Float64(y * expm1(z))) / t)) tmp = 0.0 if (y <= -7.017489851709385e-155) tmp = t_1; elseif (y <= 7.647719248273216e-113) tmp = Float64(x - Float64(y * Float64(expm1(z) / t))); else tmp = t_1; end return tmp end
code[x_, y_, z_, t_] := N[(x - N[(N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[Log[1 + N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.017489851709385e-155], t$95$1, If[LessEqual[y, 7.647719248273216e-113], N[(x - N[(y * N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]
x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}
\begin{array}{l}
t_1 := x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}\\
\mathbf{if}\;y \leq -7.017489851709385 \cdot 10^{-155}:\\
\;\;\;\;t_1\\
\mathbf{elif}\;y \leq 7.647719248273216 \cdot 10^{-113}:\\
\;\;\;\;x - y \cdot \frac{\mathsf{expm1}\left(z\right)}{t}\\
\mathbf{else}:\\
\;\;\;\;t_1\\
\end{array}
Results
| Original | 25.7 |
|---|---|
| Target | 16.0 |
| Herbie | 0.6 |
if y < -7.01748985170938503e-155 or 7.6477192482732156e-113 < y Initial program 34.5
Simplified0.6
if -7.01748985170938503e-155 < y < 7.6477192482732156e-113Initial program 9.0
Simplified2.0
Taylor expanded in y around 0 4.3
Simplified0.4
Final simplification0.6
| Alternative 1 | |
|---|---|
| Error | 9.6 |
| Cost | 1348 |
| Alternative 2 | |
|---|---|
| Error | 19.4 |
| Cost | 912 |
| Alternative 3 | |
|---|---|
| Error | 18.2 |
| Cost | 64 |
herbie shell --seed 2022291
(FPCore (x y z t)
:name "System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2"
:precision binary64
:herbie-target
(if (< z -2.8874623088207947e+119) (- (- x (/ (/ (- 0.5) (* y t)) (* z z))) (* (/ (- 0.5) (* y t)) (/ (/ 2.0 z) (* z z)))) (- x (/ (log (+ 1.0 (* z y))) t)))
(- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))