Average Error: 0.4 → 0.5
Time: 13.3s
Precision: 64
Internal Precision: 576
\[\sin x - 1\]
\[\frac{\left(\sin x \cdot \sin x\right) \cdot \sin x - 1}{\left(\sin x + 1\right) + \sin x \cdot \sin x}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\sin x - 1\]
  2. Using strategy rm
  3. Applied flip3--0.5

    \[\leadsto \color{blue}{\frac{{\left(\sin x\right)}^{3} - {1}^{3}}{\sin x \cdot \sin x + \left(1 \cdot 1 + \sin x \cdot 1\right)}}\]
  4. Applied simplify0.5

    \[\leadsto \frac{\color{blue}{{\left(\sin x\right)}^{3} - 1}}{\sin x \cdot \sin x + \left(1 \cdot 1 + \sin x \cdot 1\right)}\]
  5. Applied simplify0.5

    \[\leadsto \frac{{\left(\sin x\right)}^{3} - 1}{\color{blue}{\left(\sin x + 1\right) + \sin x \cdot \sin x}}\]
  6. Using strategy rm
  7. Applied add-cube-cbrt0.9

    \[\leadsto \frac{{\color{blue}{\left(\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right) \cdot \sqrt[3]{\sin x}\right)}}^{3} - 1}{\left(\sin x + 1\right) + \sin x \cdot \sin x}\]
  8. Applied unpow-prod-down0.9

    \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right)}^{3} \cdot {\left(\sqrt[3]{\sin x}\right)}^{3}} - 1}{\left(\sin x + 1\right) + \sin x \cdot \sin x}\]
  9. Applied simplify0.6

    \[\leadsto \frac{\color{blue}{\left(\sin x \cdot \sin x\right)} \cdot {\left(\sqrt[3]{\sin x}\right)}^{3} - 1}{\left(\sin x + 1\right) + \sin x \cdot \sin x}\]
  10. Applied simplify0.5

    \[\leadsto \frac{\left(\sin x \cdot \sin x\right) \cdot \color{blue}{\sin x} - 1}{\left(\sin x + 1\right) + \sin x \cdot \sin x}\]

Runtime

Time bar (total: 13.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "sin(x) -1"
  (- (sin x) 1))