Average Error: 1.9 → 0.6
Time: 16.5s
Precision: binary64
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double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (x * ((double) exp(((double) (((double) (y * ((double) (((double) log(z)) - t)))) + ((double) (a * ((double) (((double) log(((double) (1.0 - z)))) - b))))))))));
}
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (x * ((double) (((double) sqrt(((double) exp(((double) (((double) (y * ((double) (((double) log(z)) - t)))) + ((double) (a * ((double) (((double) log(1.0)) + ((double) (((double) (((double) (z / 1.0)) * ((double) (((double) (z / 1.0)) * -0.5)))) - ((double) (((double) (z * 1.0)) + b)))))))))))))) * ((double) sqrt(((double) exp(((double) (((double) (y * ((double) (((double) log(z)) - t)))) + ((double) (a * ((double) (((double) log(1.0)) + ((double) (((double) (((double) (z / 1.0)) * ((double) (((double) (z / 1.0)) * -0.5)))) - ((double) (((double) (z * 1.0)) + b))))))))))))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.9

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  2. Taylor expanded around 0 0.6

    \[\leadsto \]
  3. Simplified0.6

    \[\leadsto \]
  4. Using strategy rm
  5. Applied add-sqr-sqrt0.6

    \[\leadsto \]
  6. Simplified0.6

    \[\leadsto \]
  7. Simplified0.6

    \[\leadsto \]
  8. Final simplification0.6

    \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))