(FPCore (x y) :precision binary64 (- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))
(FPCore (x y)
:precision binary64
(if (<= y -10000000000.0)
(log (/ (* y E) (+ x -1.0)))
(if (<= y 1.98)
(- 1.0 (log1p (/ (- x y) (+ y -1.0))))
(log (/ (* y E) x)))))double code(double x, double y) {
return 1.0 - log((1.0 - ((x - y) / (1.0 - y))));
}
double code(double x, double y) {
double tmp;
if (y <= -10000000000.0) {
tmp = log(((y * ((double) M_E)) / (x + -1.0)));
} else if (y <= 1.98) {
tmp = 1.0 - log1p(((x - y) / (y + -1.0)));
} else {
tmp = log(((y * ((double) M_E)) / x));
}
return tmp;
}
public static double code(double x, double y) {
return 1.0 - Math.log((1.0 - ((x - y) / (1.0 - y))));
}
public static double code(double x, double y) {
double tmp;
if (y <= -10000000000.0) {
tmp = Math.log(((y * Math.E) / (x + -1.0)));
} else if (y <= 1.98) {
tmp = 1.0 - Math.log1p(((x - y) / (y + -1.0)));
} else {
tmp = Math.log(((y * Math.E) / x));
}
return tmp;
}
def code(x, y): return 1.0 - math.log((1.0 - ((x - y) / (1.0 - y))))
def code(x, y): tmp = 0 if y <= -10000000000.0: tmp = math.log(((y * math.e) / (x + -1.0))) elif y <= 1.98: tmp = 1.0 - math.log1p(((x - y) / (y + -1.0))) else: tmp = math.log(((y * math.e) / x)) return tmp
function code(x, y) return Float64(1.0 - log(Float64(1.0 - Float64(Float64(x - y) / Float64(1.0 - y))))) end
function code(x, y) tmp = 0.0 if (y <= -10000000000.0) tmp = log(Float64(Float64(y * exp(1)) / Float64(x + -1.0))); elseif (y <= 1.98) tmp = Float64(1.0 - log1p(Float64(Float64(x - y) / Float64(y + -1.0)))); else tmp = log(Float64(Float64(y * exp(1)) / x)); end return tmp end
code[x_, y_] := N[(1.0 - N[Log[N[(1.0 - N[(N[(x - y), $MachinePrecision] / N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
code[x_, y_] := If[LessEqual[y, -10000000000.0], N[Log[N[(N[(y * E), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[y, 1.98], N[(1.0 - N[Log[1 + N[(N[(x - y), $MachinePrecision] / N[(y + -1.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Log[N[(N[(y * E), $MachinePrecision] / x), $MachinePrecision]], $MachinePrecision]]]
1 - \log \left(1 - \frac{x - y}{1 - y}\right)
\begin{array}{l}
\mathbf{if}\;y \leq -10000000000:\\
\;\;\;\;\log \left(\frac{y \cdot e}{x + -1}\right)\\
\mathbf{elif}\;y \leq 1.98:\\
\;\;\;\;1 - \mathsf{log1p}\left(\frac{x - y}{y + -1}\right)\\
\mathbf{else}:\\
\;\;\;\;\log \left(\frac{y \cdot e}{x}\right)\\
\end{array}
Results
| Original | 18.0 |
|---|---|
| Target | 0.1 |
| Herbie | 0.3 |
if y < -1e10Initial program 51.8
Simplified51.8
Applied egg-rr51.8
Taylor expanded in y around inf 0.1
if -1e10 < y < 1.98Initial program 0.1
Simplified0.1
if 1.98 < y Initial program 30.3
Simplified30.3
Applied egg-rr30.3
Taylor expanded in y around inf 1.2
Taylor expanded in x around -inf 2.0
Final simplification0.3
| Alternative 1 | |
|---|---|
| Error | 0.3 |
| Cost | 13320 |
| Alternative 2 | |
|---|---|
| Error | 0.1 |
| Cost | 7492 |
| Alternative 3 | |
|---|---|
| Error | 1.1 |
| Cost | 7112 |
| Alternative 4 | |
|---|---|
| Error | 9.8 |
| Cost | 7048 |
| Alternative 5 | |
|---|---|
| Error | 10.2 |
| Cost | 6984 |
| Alternative 6 | |
|---|---|
| Error | 25.1 |
| Cost | 6788 |
| Alternative 7 | |
|---|---|
| Error | 13.3 |
| Cost | 6788 |
| Alternative 8 | |
|---|---|
| Error | 36.0 |
| Cost | 192 |
| Alternative 9 | |
|---|---|
| Error | 36.2 |
| Cost | 64 |
herbie shell --seed 2022316
(FPCore (x y)
:name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, B"
:precision binary64
:herbie-target
(if (< y -81284752.61947241) (- 1.0 (log (- (/ x (* y y)) (- (/ 1.0 y) (/ x y))))) (if (< y 3.0094271212461764e+25) (log (/ (exp 1.0) (- 1.0 (/ (- x y) (- 1.0 y))))) (- 1.0 (log (- (/ x (* y y)) (- (/ 1.0 y) (/ x y)))))))
(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y))))))