Average Error: 12.9 → 0.2
Time: 38.7s
Precision: binary64
Cost: 45696
\[\left(x = 0 \lor 0.5884142 \leq x \land x \leq 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \leq y \land y \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq y \land y \leq 1.7512240000000001 \cdot 10^{+308}\right) \land \left(-1.7767070000000002 \cdot 10^{+308} \leq z \land z \leq -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \leq z \land z \leq 1.725154 \cdot 10^{+308}\right) \land \left(-1.796658 \cdot 10^{+308} \leq a \land a \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq a \land a \leq 1.7512240000000001 \cdot 10^{+308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\tan y + \tan z}{1 - \sqrt[3]{{\left(\tan y \cdot \tan z\right)}^{3}}} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\tan y + \tan z}{1 - \sqrt[3]{{\left(\tan y \cdot \tan z\right)}^{3}}} - \tan a\right)
(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))
↓
(FPCore (x y z a)
 :precision binary64
 (+
  x
  (-
   (/ (+ (tan y) (tan z)) (- 1.0 (cbrt (pow (* (tan y) (tan z)) 3.0))))
   (tan a))))
double code(double x, double y, double z, double a) {
	return x + (tan(y + z) - tan(a));
}
↓
double code(double x, double y, double z, double a) {
	return x + (((tan(y) + tan(z)) / (1.0 - cbrt(pow((tan(y) * tan(z)), 3.0)))) - tan(a));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.2
Cost32832
\[x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right)\]
Alternative 2
Error0.2
Cost32832
\[\left(x + \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\right) - \tan a\]
Alternative 3
Error12.9
Cost13248
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
Alternative 4
Error13.0
Cost13248
\[\left(x + \tan \left(y + z\right)\right) - \tan a\]
Alternative 5
Error37.3
Cost6592
\[x - \tan a\]
Alternative 6
Error43.9
Cost64
\[x\]
Alternative 7
Error54.5
Cost64
\[1\]

Error

Derivation

  1. Initial program 12.9

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  2. Using strategy rm

  3. Applied tan-sum_binary640.2

    \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right)\]
  4. Using strategy rm

  5. Applied add-cbrt-cube_binary640.2

    \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\sqrt[3]{\left(\left(\tan y \cdot \tan z\right) \cdot \left(\tan y \cdot \tan z\right)\right) \cdot \left(\tan y \cdot \tan z\right)}}} - \tan a\right)\]

  6. Simplified0.2

    \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \sqrt[3]{\color{blue}{{\left(\tan y \cdot \tan z\right)}^{3}}}} - \tan a\right)\]

  7. Simplified0.2

    \[\leadsto \color{blue}{x + \left(\frac{\tan y + \tan z}{1 - \sqrt[3]{{\left(\tan y \cdot \tan z\right)}^{3}}} - \tan a\right)}\]

  8. Final simplification0.2

    \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \sqrt[3]{{\left(\tan y \cdot \tan z\right)}^{3}}} - \tan a\right)\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z a)
  :name "tan-example"
  :precision binary64
  :pre (and (or (== x 0.0) (<= 0.5884142 x 505.5909)) (or (<= -1.796658e+308 y -9.425585e-310) (<= 1.284938e-309 y 1.7512240000000001e+308)) (or (<= -1.7767070000000002e+308 z -8.599796e-310) (<= 3.293145e-311 z 1.725154e+308)) (or (<= -1.796658e+308 a -9.425585e-310) (<= 1.284938e-309 a 1.7512240000000001e+308)))
  (+ x (- (tan (+ y z)) (tan a))))