?

Average Accuracy: 43.8% → 95.7%
Time: 21.0s
Precision: binary64
Cost: 19968

?

\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]
↓
\[\sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \frac{\sqrt[3]{g}}{\sqrt[3]{-a}} \]
(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
 (+ (cbrt (* (- g g) (/ -0.5 a))) (/ (cbrt g) (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 cbrt(((g - g) * (-0.5 / a))) + (cbrt(g) / 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 Math.cbrt(((g - g) * (-0.5 / a))) + (Math.cbrt(g) / 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(cbrt(Float64(Float64(g - g) * Float64(-0.5 / a))) + Float64(cbrt(g) / 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[Power[N[(N[(g - g), $MachinePrecision] * N[(-0.5 / a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[(N[Power[g, 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)}
↓
\sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \frac{\sqrt[3]{g}}{\sqrt[3]{-a}}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 47.0%

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

  2. Simplified47.0%

    \[\leadsto \color{blue}{\sqrt[3]{\left(g - \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right) \cdot \frac{-0.5}{a}} + \sqrt[3]{\left(g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right) \cdot \frac{-0.5}{a}}} \]
    Step-by-step derivation

    [Start]47.0

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

  3. Taylor expanded in g around inf 27.1%

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

  4. Taylor expanded in g around inf 72.1%

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

  5. Simplified72.1%

    \[\leadsto \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \sqrt[3]{\color{blue}{\frac{-g}{a}}} \]
    Step-by-step derivation

    [Start]72.1

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

    associate-*r/ [=>]72.1

    \[ \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \sqrt[3]{\color{blue}{\frac{-1 \cdot g}{a}}} \]

    mul-1-neg [=>]72.1

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

  6. Applied egg-rr96.4%

    \[\leadsto \sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{-a}}} \]
    Step-by-step derivation

    [Start]72.1

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

    frac-2neg [=>]72.1

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

    cbrt-div [=>]96.4

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

    remove-double-neg [=>]96.4

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

  7. Final simplification96.4%

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

Alternatives

Alternative 1
Accuracy73.2%
Cost13568
\[\sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \sqrt[3]{-\frac{g}{a}} \]
Alternative 2
Accuracy1.4%
Cost13504
\[\sqrt[3]{\left(g - g\right) \cdot \frac{-0.5}{a}} + \sqrt[3]{\frac{g}{a}} \]

Error

Reproduce?

herbie shell --seed 2023159 
(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))))))))