Average Error: 10.0 → 0.4
Time: 36.3s
Precision: 64
Internal Precision: 1344
\[\sin \left(3 \cdot x\right) + \left(21 \cdot 56\right) \cdot xy\]
\[3 \cdot \sin x - \left(4 \cdot \left(\left(\sin x \cdot \sin x\right) \cdot \sin x\right) - \left(21 \cdot 56\right) \cdot xy\right)\]

Error

Bits error versus x

Bits error versus xy

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 10.0

    \[\sin \left(3 \cdot x\right) + \left(21 \cdot 56\right) \cdot xy\]
  2. Using strategy rm
  3. Applied sin-30.4

    \[\leadsto \color{blue}{\left(3 \cdot \sin x - 4 \cdot {\left(\sin x\right)}^{3}\right)} + \left(21 \cdot 56\right) \cdot xy\]
  4. Applied associate-+l-0.4

    \[\leadsto \color{blue}{3 \cdot \sin x - \left(4 \cdot {\left(\sin x\right)}^{3} - \left(21 \cdot 56\right) \cdot xy\right)}\]
  5. Using strategy rm
  6. Applied add-cube-cbrt0.8

    \[\leadsto 3 \cdot \sin x - \left(4 \cdot {\color{blue}{\left(\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right) \cdot \sqrt[3]{\sin x}\right)}}^{3} - \left(21 \cdot 56\right) \cdot xy\right)\]
  7. Applied unpow-prod-down0.8

    \[\leadsto 3 \cdot \sin x - \left(4 \cdot \color{blue}{\left({\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}\right)}^{3} \cdot {\left(\sqrt[3]{\sin x}\right)}^{3}\right)} - \left(21 \cdot 56\right) \cdot xy\right)\]
  8. Applied simplify0.6

    \[\leadsto 3 \cdot \sin x - \left(4 \cdot \left(\color{blue}{\left(\sin x \cdot \sin x\right)} \cdot {\left(\sqrt[3]{\sin x}\right)}^{3}\right) - \left(21 \cdot 56\right) \cdot xy\right)\]
  9. Applied simplify0.4

    \[\leadsto 3 \cdot \sin x - \left(4 \cdot \left(\left(\sin x \cdot \sin x\right) \cdot \color{blue}{\sin x}\right) - \left(21 \cdot 56\right) \cdot xy\right)\]

Runtime

Time bar (total: 36.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x xy)
  :name "sin(3x) + 21 * 56xy"
  (+ (sin (* 3 x)) (* (* 21 56) xy)))