| Alternative 1 | |
|---|---|
| Error | 2.6 |
| Cost | 20800 |
\[\frac{1}{\frac{\sqrt[3]{a}}{\sqrt[3]{-0.5 \cdot \left(g \cdot 2\right)}}} + \sqrt[3]{\left(g + \left(0.5 \cdot \frac{h}{\frac{g}{h}} - g\right)\right) \cdot \frac{-0.5}{a}}
\]
Error
(FPCore (g h a) :precision binary64 (+ (cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))
(FPCore (g h a) :precision binary64 (+ (/ 1.0 (/ (cbrt a) (cbrt (* -0.5 (* g 2.0))))) (/ (cbrt (* (* h (/ h g)) 0.25)) (cbrt (- a)))))
double code(double g, double h, double a) {
return cbrt(((1.0 / (2.0 * a)) * (-g + sqrt(((g * g) - (h * h)))))) + cbrt(((1.0 / (2.0 * a)) * (-g - sqrt(((g * g) - (h * h))))));
}
double code(double g, double h, double a) {
return (1.0 / (cbrt(a) / cbrt((-0.5 * (g * 2.0))))) + (cbrt(((h * (h / g)) * 0.25)) / cbrt(-a));
}
public static double code(double g, double h, double a) {
return Math.cbrt(((1.0 / (2.0 * a)) * (-g + Math.sqrt(((g * g) - (h * h)))))) + Math.cbrt(((1.0 / (2.0 * a)) * (-g - Math.sqrt(((g * g) - (h * h))))));
}
public static double code(double g, double h, double a) {
return (1.0 / (Math.cbrt(a) / Math.cbrt((-0.5 * (g * 2.0))))) + (Math.cbrt(((h * (h / g)) * 0.25)) / Math.cbrt(-a));
}
function code(g, h, a) return Float64(cbrt(Float64(Float64(1.0 / Float64(2.0 * a)) * Float64(Float64(-g) + sqrt(Float64(Float64(g * g) - Float64(h * h)))))) + cbrt(Float64(Float64(1.0 / Float64(2.0 * a)) * Float64(Float64(-g) - sqrt(Float64(Float64(g * g) - Float64(h * h))))))) end
function code(g, h, a) return Float64(Float64(1.0 / Float64(cbrt(a) / cbrt(Float64(-0.5 * Float64(g * 2.0))))) + Float64(cbrt(Float64(Float64(h * Float64(h / g)) * 0.25)) / cbrt(Float64(-a)))) end
code[g_, h_, a_] := N[(N[Power[N[(N[(1.0 / N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * N[((-g) + N[Sqrt[N[(N[(g * g), $MachinePrecision] - N[(h * h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[Power[N[(N[(1.0 / N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * N[((-g) - N[Sqrt[N[(N[(g * g), $MachinePrecision] - N[(h * h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]
code[g_, h_, a_] := N[(N[(1.0 / N[(N[Power[a, 1/3], $MachinePrecision] / N[Power[N[(-0.5 * N[(g * 2.0), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Power[N[(N[(h * N[(h / g), $MachinePrecision]), $MachinePrecision] * 0.25), $MachinePrecision], 1/3], $MachinePrecision] / N[Power[(-a), 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}
\frac{1}{\frac{\sqrt[3]{a}}{\sqrt[3]{-0.5 \cdot \left(g \cdot 2\right)}}} + \frac{\sqrt[3]{\left(h \cdot \frac{h}{g}\right) \cdot 0.25}}{\sqrt[3]{-a}}
Results
Initial program 36.1
Simplified36.1
Applied egg-rr34.1
Taylor expanded in g around -inf 44.0
Simplified44.0
Taylor expanded in g around -inf 6.0
Simplified2.6
Applied egg-rr1.4
Final simplification1.4
| Alternative 1 | |
|---|---|
| Error | 2.6 |
| Cost | 20800 |
| Alternative 2 | |
|---|---|
| Error | 2.8 |
| Cost | 19968 |
| Alternative 3 | |
|---|---|
| Error | 17.1 |
| Cost | 13696 |
| Alternative 4 | |
|---|---|
| Error | 17.5 |
| Cost | 13568 |
herbie shell --seed 2022294
(FPCore (g h a)
:name "2-ancestry mixing, positive discriminant"
:precision binary64
(+ (cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))