Error

Target

Derivation

1. Split input into 2 regimes.

2. if z < -6.793618503523319e-17 or 1.6241870003327005e+17 < z

   1. Initial program 61.6

      \[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
   2. Using strategy rm

   3. Applied add-cbrt-cube 62.2

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

   4. Applied taylor 55.5

      \[\leadsto (\left(\frac{1}{x}\right) \cdot \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - \left(1 + e^{-\left(\log y + \log x\right)}\right)\]

   5. Taylor expanded around inf 55.5

      \[\leadsto \color{blue}{(\left(\frac{1}{x}\right) \cdot \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - \left(1 + e^{-\left(\log y + \log x\right)}\right)}\]

   6. Applied simplify 29.6

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

   8. Applied add-log-exp 31.0

      \[\leadsto (\left(\frac{1}{x}\right) \cdot \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - \color{blue}{\log \left(e^{\frac{1}{y \cdot x} + 1}\right)}\]

   9. Applied add-log-exp 31.6

      \[\leadsto \color{blue}{\log \left(e^{(\left(\frac{1}{x}\right) \cdot \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_*}\right)} - \log \left(e^{\frac{1}{y \cdot x} + 1}\right)\]

   10. Applied diff-log 31.7

       \[\leadsto \color{blue}{\log \left(\frac{e^{(\left(\frac{1}{x}\right) \cdot \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_*}}{e^{\frac{1}{y \cdot x} + 1}}\right)}\]

   11. Applied simplify 18.9

       \[\leadsto \log \color{blue}{\left(e^{\left((\left(\frac{1}{x}\right) \cdot \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - \frac{1}{y \cdot x}\right) - 1}\right)}\]

   if -6.793618503523319e-17 < z < 1.6241870003327005e+17

   1. Initial program 29.4

      \[(x \cdot y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
   2. Using strategy rm

   3. Applied add-cbrt-cube 30.0

      \[\leadsto (x \cdot y + z)_* - \left(1 + \color{blue}{\sqrt[3]{{\left(x \cdot y + z\right)}^3}}\right)\]
   4. Using strategy rm

   5. Applied cube-mult 30.0

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

   6. Applied cbrt-prod 30.1

      \[\leadsto (x \cdot y + z)_* - \left(1 + \color{blue}{\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot \left(x \cdot y + z\right)}}\right)\]
3. Recombined 2 regimes into one program.
4. Removed slow pow expressions

Runtime

Time bar (total: 16.2s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (x y z)
  :name "simple fma test"

  :target
  -1

  (- (fma x y z) (+ 1 (+ (* x y) z))))