Average Error: 0.0 → 0.0
Time: 26.3s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\frac{\cos x}{\sqrt{\frac{y}{\sinh y}}}}{\sqrt{\frac{y}{\sinh y}}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\frac{\frac{\cos x}{\sqrt{\frac{y}{\sinh y}}}}{\sqrt{\frac{y}{\sinh y}}}
double f(double x, double y) {
        double r200307 = x;
        double r200308 = cos(r200307);
        double r200309 = y;
        double r200310 = sinh(r200309);
        double r200311 = r200310 / r200309;
        double r200312 = r200308 * r200311;
        return r200312;
}
↓
double f(double x, double y) {
        double r200313 = x;
        double r200314 = cos(r200313);
        double r200315 = y;
        double r200316 = sinh(r200315);
        double r200317 = r200315 / r200316;
        double r200318 = sqrt(r200317);
        double r200319 = r200314 / r200318;
        double r200320 = r200319 / r200318;
        return r200320;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\cos x \cdot \frac{\sinh y}{y}\]
  2. Using strategy rm

  3. Applied pow10.0

    \[\leadsto \cos x \cdot \color{blue}{{\left(\frac{\sinh y}{y}\right)}^{1}}\]

  4. Applied pow10.0

    \[\leadsto \color{blue}{{\left(\cos x\right)}^{1}} \cdot {\left(\frac{\sinh y}{y}\right)}^{1}\]

  5. Applied pow-prod-down0.0

    \[\leadsto \color{blue}{{\left(\cos x \cdot \frac{\sinh y}{y}\right)}^{1}}\]

  6. Simplified0.0

    \[\leadsto {\color{blue}{\left(\frac{\cos x}{\frac{y}{\sinh y}}\right)}}^{1}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.0

    \[\leadsto {\left(\frac{\cos x}{\color{blue}{\sqrt{\frac{y}{\sinh y}} \cdot \sqrt{\frac{y}{\sinh y}}}}\right)}^{1}\]

  9. Applied associate-/r*0.0

    \[\leadsto {\color{blue}{\left(\frac{\frac{\cos x}{\sqrt{\frac{y}{\sinh y}}}}{\sqrt{\frac{y}{\sinh y}}}\right)}}^{1}\]

  10. Final simplification0.0

    \[\leadsto \frac{\frac{\cos x}{\sqrt{\frac{y}{\sinh y}}}}{\sqrt{\frac{y}{\sinh y}}}\]

Reproduce

herbie shell --seed 2019350 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))