(tan (/ (pow x y) z))

Average Error: 14.3 → 14.3

Time: 6.5s

Precision: binary64

• could not determine a ground truth for program body

  1. x = -10629.839558496014
  2. y = 4.595974795218958e-11
  3. z = 5.439533459030745e-36

Math

\[\tan \left(\frac{{x}^{y}}{z}\right)\]

↓

\[\tan \left(\frac{{x}^{y}}{z}\right)\]

C

double code(double x, double y, double z) {
	return ((double) tan(((double) (((double) pow(x, y)) / z))));
}

↓

double code(double x, double y, double z) {
	return ((double) tan(((double) (((double) pow(x, y)) / z))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 14.3

   \[\tan \left(\frac{{x}^{y}}{z}\right)\]

2. Final simplification 14.3

   \[\leadsto \tan \left(\frac{{x}^{y}}{z}\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y z)
  :name "(tan (/ (pow x y) z))"
  :precision binary64
  (tan (/ (pow x y) z)))