?

Average Error: 59.7 → 58.8
Time: 8.6s
Precision: binary64
Cost: 26304

?

\[\frac{\pi}{2} - 2 \cdot \sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right) \]
↓
\[\left(\sin^{-1} \left(\sqrt{0.5 + x \cdot -0.5}\right) \cdot -2 + \pi \cdot -0.5\right) + \pi \]
(FPCore (x)
 :precision binary64
 (- (/ PI 2.0) (* 2.0 (asin (sqrt (/ (- 1.0 x) 2.0))))))
↓
(FPCore (x)
 :precision binary64
 (+ (+ (* (asin (sqrt (+ 0.5 (* x -0.5)))) -2.0) (* PI -0.5)) PI))
double code(double x) {
	return (((double) M_PI) / 2.0) - (2.0 * asin(sqrt(((1.0 - x) / 2.0))));
}
↓
double code(double x) {
	return ((asin(sqrt((0.5 + (x * -0.5)))) * -2.0) + (((double) M_PI) * -0.5)) + ((double) M_PI);
}

public static double code(double x) {
	return (Math.PI / 2.0) - (2.0 * Math.asin(Math.sqrt(((1.0 - x) / 2.0))));
}
↓
public static double code(double x) {
	return ((Math.asin(Math.sqrt((0.5 + (x * -0.5)))) * -2.0) + (Math.PI * -0.5)) + Math.PI;
}

def code(x):
	return (math.pi / 2.0) - (2.0 * math.asin(math.sqrt(((1.0 - x) / 2.0))))
↓
def code(x):
	return ((math.asin(math.sqrt((0.5 + (x * -0.5)))) * -2.0) + (math.pi * -0.5)) + math.pi

function code(x)
	return Float64(Float64(pi / 2.0) - Float64(2.0 * asin(sqrt(Float64(Float64(1.0 - x) / 2.0)))))
end
↓
function code(x)
	return Float64(Float64(Float64(asin(sqrt(Float64(0.5 + Float64(x * -0.5)))) * -2.0) + Float64(pi * -0.5)) + pi)
end

function tmp = code(x)
	tmp = (pi / 2.0) - (2.0 * asin(sqrt(((1.0 - x) / 2.0))));
end
↓
function tmp = code(x)
	tmp = ((asin(sqrt((0.5 + (x * -0.5)))) * -2.0) + (pi * -0.5)) + pi;
end

code[x_] := N[(N[(Pi / 2.0), $MachinePrecision] - N[(2.0 * N[ArcSin[N[Sqrt[N[(N[(1.0 - x), $MachinePrecision] / 2.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(N[(N[(N[ArcSin[N[Sqrt[N[(0.5 + N[(x * -0.5), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * -2.0), $MachinePrecision] + N[(Pi * -0.5), $MachinePrecision]), $MachinePrecision] + Pi), $MachinePrecision]

\frac{\pi}{2} - 2 \cdot \sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right)
↓
\left(\sin^{-1} \left(\sqrt{0.5 + x \cdot -0.5}\right) \cdot -2 + \pi \cdot -0.5\right) + \pi

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original59.7
Target0
Herbie58.8
\[\sin^{-1} x \]

Derivation?

  1. Initial program 59.7

    \[\frac{\pi}{2} - 2 \cdot \sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right) \]

  2. Applied egg-rr58.8

    \[\leadsto \color{blue}{\left(\sin^{-1} \left(\sqrt{0.5 + x \cdot -0.5}\right) \cdot -2 + \pi \cdot -0.5\right) + \pi} \]

  3. Final simplification58.8

    \[\leadsto \left(\sin^{-1} \left(\sqrt{0.5 + x \cdot -0.5}\right) \cdot -2 + \pi \cdot -0.5\right) + \pi \]

Alternatives

Alternative 1
Error59.7
Cost19840
\[\frac{\pi}{2} - 2 \cdot \sin^{-1} \left(\sqrt{\frac{1 - x}{2}}\right) \]

Error

Reproduce?

herbie shell --seed 2023096 
(FPCore (x)
  :name "Ian Simplification"
  :precision binary64

  :herbie-target
  (asin x)

  (- (/ PI 2.0) (* 2.0 (asin (sqrt (/ (- 1.0 x) 2.0))))))