Average Error: 2.0 → 2.0
Time: 7.5s
Precision: binary64
Cost: 7168
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{a}{\frac{1 + k \cdot \left(k + 10\right)}{{k}^{m}}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{a}{\frac{1 + k \cdot \left(k + 10\right)}{{k}^{m}}}
(FPCore (a k m)
 :precision binary64
 (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))
↓
(FPCore (a k m)
 :precision binary64
 (/ a (/ (+ 1.0 (* k (+ k 10.0))) (pow k m))))
double code(double a, double k, double m) {
	return (a * pow(k, m)) / ((1.0 + (10.0 * k)) + (k * k));
}
↓
double code(double a, double k, double m) {
	return a / ((1.0 + (k * (k + 10.0))) / pow(k, m));
}

Error

Bits error versus a

Bits error versus k

Bits error versus m

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error2.8
Cost7040
\[a \cdot \frac{{k}^{m}}{1 + k \cdot k}\]
Alternative 2
Error2.6
Cost7361
\[\begin{array}{l} \mathbf{if}\;m \leq -1.7860706643506695 \cdot 10^{-12}:\\ \;\;\;\;\frac{a}{\frac{1 + k \cdot 10}{{k}^{m}}}\\ \mathbf{elif}\;m \leq 3.2477976376559465 \cdot 10^{-05}:\\ \;\;\;\;\frac{a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot {k}^{m}\\ \end{array}\]
Alternative 3
Error2.6
Cost7361
\[\begin{array}{l} \mathbf{if}\;m \leq -3.1948433370395285 \cdot 10^{-09}:\\ \;\;\;\;\frac{a \cdot {k}^{m}}{1 + k \cdot 10}\\ \mathbf{elif}\;m \leq 4.278985884150029 \cdot 10^{-06}:\\ \;\;\;\;\frac{a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot {k}^{m}\\ \end{array}\]
Alternative 4
Error2.6
Cost7298
\[\begin{array}{l} \mathbf{if}\;m \leq -4.571640876378084 \cdot 10^{-09}:\\ \;\;\;\;\frac{a}{{k}^{\left(-m\right)}}\\ \mathbf{elif}\;m \leq 2.176032748255031 \cdot 10^{-06}:\\ \;\;\;\;\frac{a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;a \cdot {k}^{m}\\ \end{array}\]
Alternative 5
Error2.7
Cost6984
\[\begin{array}{l} \mathbf{if}\;m \leq -3.067743449350231 \cdot 10^{-10} \lor \neg \left(m \leq 6.745266197517147 \cdot 10^{-07}\right):\\ \;\;\;\;a \cdot {k}^{m}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{1 + k \cdot \left(k + 10\right)}\\ \end{array}\]
Alternative 6
Error3.0
Cost1218
\[\begin{array}{l} \mathbf{if}\;m \leq -9.968841800700799 \cdot 10^{+19}:\\ \;\;\;\;0\\ \mathbf{elif}\;m \leq 0.33590269322317595:\\ \;\;\;\;\frac{a}{1 + k \cdot \left(k + 10\right)}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 7
Error23.6
Cost64
\[0\]
Alternative 8
Error61.9
Cost64
\[1\]

Error

Derivation

  1. Initial program 2.0

    \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

  2. Simplified2.0

    \[\leadsto \color{blue}{\frac{a \cdot {k}^{m}}{1 + k \cdot \left(k + 10\right)}}\]
  3. Using strategy rm

  4. Applied associate-/l*_binary64_17282.0

    \[\leadsto \color{blue}{\frac{a}{\frac{1 + k \cdot \left(k + 10\right)}{{k}^{m}}}}\]

  5. Simplified2.0

    \[\leadsto \color{blue}{\frac{a}{\frac{1 + k \cdot \left(k + 10\right)}{{k}^{m}}}}\]

  6. Final simplification2.0

    \[\leadsto \frac{a}{\frac{1 + k \cdot \left(k + 10\right)}{{k}^{m}}}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))