(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 (log1p (* y (expm1 z)))))
(if (<= y -5e-34)
(+ x (* t_1 (/ -1.0 t)))
(if (<= y 4e-212) (- x (* (expm1 z) (/ y t))) (- x (/ t_1 t))))))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 = log1p((y * expm1(z)));
double tmp;
if (y <= -5e-34) {
tmp = x + (t_1 * (-1.0 / t));
} else if (y <= 4e-212) {
tmp = x - (expm1(z) * (y / t));
} else {
tmp = x - (t_1 / t);
}
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 = Math.log1p((y * Math.expm1(z)));
double tmp;
if (y <= -5e-34) {
tmp = x + (t_1 * (-1.0 / t));
} else if (y <= 4e-212) {
tmp = x - (Math.expm1(z) * (y / t));
} else {
tmp = x - (t_1 / t);
}
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 = math.log1p((y * math.expm1(z))) tmp = 0 if y <= -5e-34: tmp = x + (t_1 * (-1.0 / t)) elif y <= 4e-212: tmp = x - (math.expm1(z) * (y / t)) else: tmp = x - (t_1 / t) 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 = log1p(Float64(y * expm1(z))) tmp = 0.0 if (y <= -5e-34) tmp = Float64(x + Float64(t_1 * Float64(-1.0 / t))); elseif (y <= 4e-212) tmp = Float64(x - Float64(expm1(z) * Float64(y / t))); else tmp = Float64(x - Float64(t_1 / t)); 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[Log[1 + N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -5e-34], N[(x + N[(t$95$1 * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-212], N[(x - N[(N[(Exp[z] - 1), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision]]]]
x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}
\begin{array}{l}
t_1 := \mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)\\
\mathbf{if}\;y \leq -5 \cdot 10^{-34}:\\
\;\;\;\;x + t_1 \cdot \frac{-1}{t}\\
\mathbf{elif}\;y \leq 4 \cdot 10^{-212}:\\
\;\;\;\;x - \mathsf{expm1}\left(z\right) \cdot \frac{y}{t}\\
\mathbf{else}:\\
\;\;\;\;x - \frac{t_1}{t}\\
\end{array}
Results
| Original | 25.1 |
|---|---|
| Target | 16.6 |
| Herbie | 0.6 |
if y < -5.0000000000000003e-34Initial program 33.8
Simplified0.1
Applied egg-rr0.2
if -5.0000000000000003e-34 < y < 3.99999999999999982e-212Initial program 9.6
Simplified1.3
Taylor expanded in y around 0 4.5
Simplified0.0
Applied egg-rr0.0
if 3.99999999999999982e-212 < y Initial program 33.9
Simplified1.4
Final simplification0.6
| Alternative 1 | |
|---|---|
| Error | 0.6 |
| Cost | 13512 |
| Alternative 2 | |
|---|---|
| Error | 11.1 |
| Cost | 6980 |
| Alternative 3 | |
|---|---|
| Error | 9.6 |
| Cost | 6980 |
| Alternative 4 | |
|---|---|
| Error | 11.5 |
| Cost | 1092 |
| Alternative 5 | |
|---|---|
| Error | 13.8 |
| Cost | 580 |
| Alternative 6 | |
|---|---|
| Error | 11.7 |
| Cost | 580 |
| Alternative 7 | |
|---|---|
| Error | 18.4 |
| Cost | 64 |
herbie shell --seed 2022329
(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)))