2-ancestry mixing, positive discriminant

Average Accuracy: 43.6% → 95.6%

Time: 19.3s

Precision: binary64

Cost: 52480

Math

\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]

↓

\[\frac{1}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{{\left(\sqrt{\mathsf{hypot}\left(g, h\right) - g}\right)}^{2}}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]

FPCore

(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 a)) (cbrt (pow (sqrt (- (hypot g h) g)) 2.0))))
  (* (cbrt (+ g (hypot g h))) (cbrt (/ -0.5 a)))))

C

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 + a)) / cbrt(pow(sqrt((hypot(g, h) - g)), 2.0)))) + (cbrt((g + hypot(g, h))) * cbrt((-0.5 / a)));
}

Java

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 + a)) / Math.cbrt(Math.pow(Math.sqrt((Math.hypot(g, h) - g)), 2.0)))) + (Math.cbrt((g + Math.hypot(g, h))) * Math.cbrt((-0.5 / a)));
}

Julia

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(Float64(a + a)) / cbrt((sqrt(Float64(hypot(g, h) - g)) ^ 2.0)))) + Float64(cbrt(Float64(g + hypot(g, h))) * cbrt(Float64(-0.5 / a))))
end

Wolfram

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[N[(a + a), $MachinePrecision], 1/3], $MachinePrecision] / N[Power[N[Power[N[Sqrt[N[(N[Sqrt[g ^ 2 + h ^ 2], $MachinePrecision] - g), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Power[N[(g + N[Sqrt[g ^ 2 + h ^ 2], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(-0.5 / a), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 43.6%

   \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]

2. Simplified 43.7%

   \[\leadsto \color{blue}{\sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)} - g\right)} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}}} \]
   Proof

   [Start] 43.6	\[ \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]
   associate-/r* [=>] 43.7	\[ \sqrt[3]{\color{blue}{\frac{\frac{1}{2}}{a}} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]
   metadata-eval [=>] 43.7	\[ \sqrt[3]{\frac{\color{blue}{0.5}}{a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]
   +-commutative [=>] 43.7	\[ \sqrt[3]{\frac{0.5}{a} \cdot \color{blue}{\left(\sqrt{g \cdot g - h \cdot h} + \left(-g\right)\right)}} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]
   unsub-neg [=>] 43.7	\[ \sqrt[3]{\frac{0.5}{a} \cdot \color{blue}{\left(\sqrt{g \cdot g - h \cdot h} - g\right)}} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]
   fma-neg [=>] 43.7	\[ \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\color{blue}{\mathsf{fma}\left(g, g, -h \cdot h\right)}} - g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]
   sub-neg [=>] 43.7	\[ \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)} - g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \color{blue}{\left(\left(-g\right) + \left(-\sqrt{g \cdot g - h \cdot h}\right)\right)}} \]
   distribute-neg-out [=>] 43.7	\[ \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)} - g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \color{blue}{\left(-\left(g + \sqrt{g \cdot g - h \cdot h}\right)\right)}} \]
   neg-mul-1 [=>] 43.7	\[ \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)} - g\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \color{blue}{\left(-1 \cdot \left(g + \sqrt{g \cdot g - h \cdot h}\right)\right)}} \]
   associate-*r* [=>] 43.7	\[ \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)} - g\right)} + \sqrt[3]{\color{blue}{\left(\frac{1}{2 \cdot a} \cdot -1\right) \cdot \left(g + \sqrt{g \cdot g - h \cdot h}\right)}} \]

3. Applied egg-rr 28.8%

   \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\sqrt[3]{0.5 \cdot \frac{\mathsf{hypot}\left(g, h\right) - g}{a}}\right)} - 1\right)} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]
   Proof

   [Start] 43.7	\[ \sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)} - g\right)} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]
   expm1-log1p-u [=>] 37.8	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)} - g\right)}\right)\right)} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]
   expm1-udef [=>] 28.8	\[ \color{blue}{\left(e^{\mathsf{log1p}\left(\sqrt[3]{\frac{0.5}{a} \cdot \left(\sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)} - g\right)}\right)} - 1\right)} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]

4. Simplified 43.4%

   \[\leadsto \color{blue}{\sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}}} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]
   Proof

   [Start] 28.8	\[ \left(e^{\mathsf{log1p}\left(\sqrt[3]{0.5 \cdot \frac{\mathsf{hypot}\left(g, h\right) - g}{a}}\right)} - 1\right) + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]
   expm1-def [=>] 37.7	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{0.5 \cdot \frac{\mathsf{hypot}\left(g, h\right) - g}{a}}\right)\right)} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]
   expm1-log1p [=>] 43.4	\[ \color{blue}{\sqrt[3]{0.5 \cdot \frac{\mathsf{hypot}\left(g, h\right) - g}{a}}} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]
   associate-*r/ [=>] 43.4	\[ \sqrt[3]{\color{blue}{\frac{0.5 \cdot \left(\mathsf{hypot}\left(g, h\right) - g\right)}{a}}} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]
   *-commutative [=>] 43.4	\[ \sqrt[3]{\frac{\color{blue}{\left(\mathsf{hypot}\left(g, h\right) - g\right) \cdot 0.5}}{a}} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]
   associate-/l* [=>] 43.4	\[ \sqrt[3]{\color{blue}{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}}} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]

5. Applied egg-rr 84.4%

   \[\leadsto \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \color{blue}{\sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}}} \]
   Proof

   [Start] 43.4	\[ \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \sqrt[3]{\frac{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}}{\frac{a}{-0.5}}} \]
   div-inv [=>] 43.4	\[ \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \sqrt[3]{\color{blue}{\left(g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}\right) \cdot \frac{1}{\frac{a}{-0.5}}}} \]
   cbrt-prod [=>] 46.6	\[ \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \color{blue}{\sqrt[3]{g + \sqrt{\mathsf{fma}\left(g, g, -h \cdot h\right)}} \cdot \sqrt[3]{\frac{1}{\frac{a}{-0.5}}}} \]
   fma-udef [=>] 46.6	\[ \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \sqrt[3]{g + \sqrt{\color{blue}{g \cdot g + \left(-h \cdot h\right)}}} \cdot \sqrt[3]{\frac{1}{\frac{a}{-0.5}}} \]
   add-sqr-sqrt [=>] 23.6	\[ \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \sqrt[3]{g + \sqrt{g \cdot g + \color{blue}{\sqrt{-h \cdot h} \cdot \sqrt{-h \cdot h}}}} \cdot \sqrt[3]{\frac{1}{\frac{a}{-0.5}}} \]
   sqrt-unprod [=>] 45.4	\[ \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \sqrt[3]{g + \sqrt{g \cdot g + \color{blue}{\sqrt{\left(-h \cdot h\right) \cdot \left(-h \cdot h\right)}}}} \cdot \sqrt[3]{\frac{1}{\frac{a}{-0.5}}} \]
   sqr-neg [=>] 45.4	\[ \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \sqrt[3]{g + \sqrt{g \cdot g + \sqrt{\color{blue}{\left(h \cdot h\right) \cdot \left(h \cdot h\right)}}}} \cdot \sqrt[3]{\frac{1}{\frac{a}{-0.5}}} \]
   sqrt-unprod [<=] 46.5	\[ \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \sqrt[3]{g + \sqrt{g \cdot g + \color{blue}{\sqrt{h \cdot h} \cdot \sqrt{h \cdot h}}}} \cdot \sqrt[3]{\frac{1}{\frac{a}{-0.5}}} \]
   add-sqr-sqrt [<=] 46.5	\[ \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \sqrt[3]{g + \sqrt{g \cdot g + \color{blue}{h \cdot h}}} \cdot \sqrt[3]{\frac{1}{\frac{a}{-0.5}}} \]
   hypot-udef [<=] 84.4	\[ \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \sqrt[3]{g + \color{blue}{\mathsf{hypot}\left(g, h\right)}} \cdot \sqrt[3]{\frac{1}{\frac{a}{-0.5}}} \]
   clear-num [<=] 84.4	\[ \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\color{blue}{\frac{-0.5}{a}}} \]

6. Applied egg-rr 95.6%

   \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   Proof

   [Start] 84.4	\[ \sqrt[3]{\frac{\mathsf{hypot}\left(g, h\right) - g}{\frac{a}{0.5}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   cbrt-div [=>] 95.6	\[ \color{blue}{\frac{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}{\sqrt[3]{\frac{a}{0.5}}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   clear-num [=>] 95.6	\[ \color{blue}{\frac{1}{\frac{\sqrt[3]{\frac{a}{0.5}}}{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   add-log-exp [=>] 28.3	\[ \frac{1}{\frac{\sqrt[3]{\color{blue}{\log \left(e^{\frac{a}{0.5}}\right)}}}{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   div-inv [=>] 28.3	\[ \frac{1}{\frac{\sqrt[3]{\log \left(e^{\color{blue}{a \cdot \frac{1}{0.5}}}\right)}}{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   metadata-eval [=>] 28.3	\[ \frac{1}{\frac{\sqrt[3]{\log \left(e^{a \cdot \color{blue}{2}}\right)}}{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   exp-lft-sqr [=>] 28.2	\[ \frac{1}{\frac{\sqrt[3]{\log \color{blue}{\left(e^{a} \cdot e^{a}\right)}}}{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   log-prod [=>] 28.2	\[ \frac{1}{\frac{\sqrt[3]{\color{blue}{\log \left(e^{a}\right) + \log \left(e^{a}\right)}}}{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   add-log-exp [<=] 56.0	\[ \frac{1}{\frac{\sqrt[3]{\color{blue}{a} + \log \left(e^{a}\right)}}{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   add-log-exp [<=] 95.6	\[ \frac{1}{\frac{\sqrt[3]{a + \color{blue}{a}}}{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]

7. Applied egg-rr 95.6%

   \[\leadsto \frac{1}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{\color{blue}{{\left(\sqrt{\mathsf{hypot}\left(g, h\right) - g}\right)}^{2}}}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   Proof

   [Start] 95.6	\[ \frac{1}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   add-sqr-sqrt [=>] 95.6	\[ \frac{1}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{\color{blue}{\sqrt{\mathsf{hypot}\left(g, h\right) - g} \cdot \sqrt{\mathsf{hypot}\left(g, h\right) - g}}}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]
   pow2 [=>] 95.6	\[ \frac{1}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{\color{blue}{{\left(\sqrt{\mathsf{hypot}\left(g, h\right) - g}\right)}^{2}}}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]

8. Final simplification 95.6%

   \[\leadsto \frac{1}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{{\left(\sqrt{\mathsf{hypot}\left(g, h\right) - g}\right)}^{2}}}} + \sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} \]

Alternatives

Alternative 1
Accuracy	95.6%
Cost	39616

\[\sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} + \frac{1}{\frac{\sqrt[3]{a + a}}{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}} \]

Alternative 2
Accuracy	95.7%
Cost	39488

\[\sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} + \sqrt[3]{\mathsf{hypot}\left(g, h\right) - g} \cdot \sqrt[3]{\frac{0.5}{a}} \]

Alternative 3
Accuracy	95.6%
Cost	39488

\[\sqrt[3]{g + \mathsf{hypot}\left(g, h\right)} \cdot \sqrt[3]{\frac{-0.5}{a}} + \frac{\sqrt[3]{\mathsf{hypot}\left(g, h\right) - g}}{\sqrt[3]{a + a}} \]

Alternative 4
Accuracy	95.9%
Cost	19968

\[\sqrt[3]{\frac{-0.5}{a} \cdot \left(g - g\right)} + \frac{\sqrt[3]{g}}{\sqrt[3]{-a}} \]

Alternative 5
Accuracy	72.9%
Cost	13760

\[\sqrt[3]{\frac{-0.5}{a} \cdot \left(g - g\right)} + \sqrt[3]{\frac{-0.5}{a} \cdot \left(g + g\right)} \]

Alternative 6
Accuracy	73.0%
Cost	13568

\[\sqrt[3]{\frac{-0.5}{a} \cdot \left(g - g\right)} + \sqrt[3]{\frac{-g}{a}} \]

Alternative 7
Accuracy	1.3%
Cost	13504

\[\sqrt[3]{\frac{-0.5}{a} \cdot \left(g - g\right)} + \sqrt[3]{\frac{g}{a}} \]

Reproduce

herbie shell --seed 2023151 
(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))))))))