Average Error: 2.8 → 1.0
Time: 4.1s
Precision: binary64
\[\]
\[\]
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) (((double) sin(y)) / y)))) / z));
}
double code(double x, double y, double z) {
	double VAR;
	if (((z <= -1.2486964666857625e-98) || !(z <= 3.47399387577626e-196))) {
		VAR = ((double) (((double) (((double) sin(y)) / y)) * ((double) (x / z))));
	} else {
		VAR = ((double) (x / ((double) (y * ((double) (z / ((double) sin(y))))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.8
Target0.3
Herbie1.0
\[\]

Derivation

  1. Split input into 2 regimes
  2. if z < -1.2486964666857625e-98 or 3.4739938757762599e-196 < z

    1. Initial program 1.0

      \[\]
    2. Using strategy rm
    3. Applied associate-/l*3.6

      \[\leadsto \]
    4. Simplified10.8

      \[\leadsto \]
    5. Using strategy rm
    6. Applied *-un-lft-identity10.8

      \[\leadsto \]
    7. Applied times-frac11.5

      \[\leadsto \]
    8. Simplified7.5

      \[\leadsto \]
    9. Using strategy rm
    10. Applied associate-*r*1.3

      \[\leadsto \]
    11. Simplified1.3

      \[\leadsto \]

    if -1.2486964666857625e-98 < z < 3.4739938757762599e-196

    1. Initial program 9.2

      \[\]
    2. Using strategy rm
    3. Applied associate-/l*0.2

      \[\leadsto \]
    4. Simplified0.3

      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification1.0

    \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (x y z)
  :name "Linear.Quaternion:$ctanh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< z -4.2173720203427147e-29) (/ (* x (/ 1.0 (/ y (sin y)))) z) (if (< z 4.446702369113811e+64) (/ x (* z (/ y (sin y)))) (/ (* x (/ 1.0 (/ y (sin y)))) z)))

  (/ (* x (/ (sin y) y)) z))