Average Error: 0.0 → 0.1
Time: 5.1s
Precision: binary64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot e^{\log \left(\frac{\sinh y}{y}\right)}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot e^{\log \left(\frac{\sinh y}{y}\right)}
(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))
↓
(FPCore (x y) :precision binary64 (* (cos x) (exp (log (/ (sinh y) y)))))
double code(double x, double y) {
	return cos(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return cos(x) * exp(log(sinh(y) / y));
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-exp-log_binary64_250334.4

    \[\leadsto \cos x \cdot \frac{\sinh y}{\color{blue}{e^{\log y}}}\]

  4. Applied add-exp-log_binary64_250331.5

    \[\leadsto \cos x \cdot \frac{\color{blue}{e^{\log \sinh y}}}{e^{\log y}}\]

  5. Applied div-exp_binary64_251631.5

    \[\leadsto \cos x \cdot \color{blue}{e^{\log \sinh y - \log y}}\]

  6. Simplified0.1

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

  7. Final simplification0.1

    \[\leadsto \cos x \cdot e^{\log \left(\frac{\sinh y}{y}\right)}\]

Reproduce

herbie shell --seed 2021015 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))