From Warwick Tucker's Validated Numerics

Percentage Accurate: 9.2% → 100.0%
Time: 1.6s
Alternatives: 1
Speedup: N/A×

Specification

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\[\begin{array}{l} t_0 := {33096}^{6}\\ t_1 := 77617 \cdot 77617\\ \left(\left(333.75 \cdot t_0 + t_1 \cdot \left(\left(\left(\left(11 \cdot t_1\right) \cdot \left(33096 \cdot 33096\right) + \left(-t_0\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \end{array} \]

Your Program's Arguments

    Results

    Enter valid numbers for all inputs

    Local Percentage Accuracy vs ?

    The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

    Accuracy vs Speed?

    Herbie found 1 alternatives:

    AlternativeAccuracySpeedup
    The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

    Alternative 1: 100.0% accurate, 440.0× speedup?

    \[-0.8273960599468214 \]
    Derivation

    1. Initial program 9.2%

      \[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
    2. Step-by-step derivation

      1. Simplified100.0%

        \[\leadsto \color{blue}{-0.8273960599468214} \]

      2. Final simplification100.0%

        \[\leadsto -0.8273960599468214 \]

      Reproduce

      ?
      herbie shell --seed 2023167 
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  :precision binary64
  (+ (+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0))) (/ 77617.0 (* 2.0 33096.0))))