Average Error: 0.1 → 0.1
Time: 45.4s
Precision: 64
Internal precision: 384
\[-\left(\left(\left(1.0 \cdot e^{-\left(\left(3.0 \cdot \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) + 10.0 \cdot \left(\left(x2 - 0.117\right) \cdot \left(x2 - 0.117\right)\right)\right) + 30.0 \cdot \left(\left(x3 - 0.2673\right) \cdot \left(x3 - 0.2673\right)\right)\right)} + 1.2 \cdot e^{-\left(\left(0.1 \cdot \left(\left(x1 - 0.4699\right) \cdot \left(x1 - 0.4699\right)\right) + 10.0 \cdot \left(\left(x2 - 0.4387\right) \cdot \left(x2 - 0.4387\right)\right)\right) + 35.0 \cdot \left(\left(x3 - 0.747\right) \cdot \left(x3 - 0.747\right)\right)\right)}\right) + 3.0 \cdot e^{-\left(\left(3.0 \cdot \left(\left(x1 - 0.1091\right) \cdot \left(x1 - 0.1091\right)\right) + 10.0 \cdot \left(\left(x2 - 0.8732\right) \cdot \left(x2 - 0.8732\right)\right)\right) + 30.0 \cdot \left(\left(x3 - 0.5547\right) \cdot \left(x3 - 0.5547\right)\right)\right)}\right) + 3.2 \cdot e^{-\left(\left(0.1 \cdot \left(\left(x1 - 0.03815\right) \cdot \left(x1 - 0.03815\right)\right) + 10.0 \cdot \left(\left(x2 - 0.5743\right) \cdot \left(x2 - 0.5743\right)\right)\right) + 35.0 \cdot \left(\left(x3 - 0.8828\right) \cdot \left(x3 - 0.8828\right)\right)\right)}\right)\]
⬇
\[-\left(\left(e^{\left(-10.0\right) \cdot \left(\left(x2 - 0.117\right) \cdot \left(x2 - 0.117\right)\right) + \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) \cdot \left(-3.0\right)} \cdot \frac{1.0}{{\left(e^{1}\right)}^{\left(\left(x3 - 0.2673\right) \cdot \left(30.0 \cdot \left(x3 - 0.2673\right)\right)\right)}} + e^{\left(\left(x2 - 0.4387\right) \cdot \left(x2 - 0.4387\right)\right) \cdot \left(-10.0\right) + \left(\left(x1 - 0.4699\right) \cdot \left(x1 - 0.4699\right)\right) \cdot \left(-0.1\right)} \cdot \frac{1.2}{\sqrt[3]{{\left({\left(e^{35.0}\right)}^{\left({\left(x3 - 0.747\right)}^2\right)}\right)}^3}}\right) + \left(e^{\left(3.0 \cdot \left(x1 - 0.1091\right)\right) \cdot \left(-\left(x1 - 0.1091\right)\right) + \left(\left(x2 - 0.8732\right) \cdot \left(x2 - 0.8732\right)\right) \cdot \left(-10.0\right)} \cdot \frac{3.0}{{\left(e^{x3 - 0.5547}\right)}^{\left(30.0 \cdot \left(x3 - 0.5547\right)\right)}} + e^{\left(-0.1\right) \cdot {\left(x1 - 0.03815\right)}^2 + {\left(x2 - 0.5743\right)}^2 \cdot \left(-10.0\right)} \cdot \frac{3.2}{{\left(e^{35.0}\right)}^{\left(\left(x3 - 0.8828\right) \cdot \left(x3 - 0.8828\right)\right)}}\right)\right)\]

Error

Bits error versus x1

Bits error versus x2

Bits error versus x3

Derivation

  1. Initial program 0.1

    \[-\left(\left(\left(1.0 \cdot e^{-\left(\left(3.0 \cdot \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) + 10.0 \cdot \left(\left(x2 - 0.117\right) \cdot \left(x2 - 0.117\right)\right)\right) + 30.0 \cdot \left(\left(x3 - 0.2673\right) \cdot \left(x3 - 0.2673\right)\right)\right)} + 1.2 \cdot e^{-\left(\left(0.1 \cdot \left(\left(x1 - 0.4699\right) \cdot \left(x1 - 0.4699\right)\right) + 10.0 \cdot \left(\left(x2 - 0.4387\right) \cdot \left(x2 - 0.4387\right)\right)\right) + 35.0 \cdot \left(\left(x3 - 0.747\right) \cdot \left(x3 - 0.747\right)\right)\right)}\right) + 3.0 \cdot e^{-\left(\left(3.0 \cdot \left(\left(x1 - 0.1091\right) \cdot \left(x1 - 0.1091\right)\right) + 10.0 \cdot \left(\left(x2 - 0.8732\right) \cdot \left(x2 - 0.8732\right)\right)\right) + 30.0 \cdot \left(\left(x3 - 0.5547\right) \cdot \left(x3 - 0.5547\right)\right)\right)}\right) + 3.2 \cdot e^{-\left(\left(0.1 \cdot \left(\left(x1 - 0.03815\right) \cdot \left(x1 - 0.03815\right)\right) + 10.0 \cdot \left(\left(x2 - 0.5743\right) \cdot \left(x2 - 0.5743\right)\right)\right) + 35.0 \cdot \left(\left(x3 - 0.8828\right) \cdot \left(x3 - 0.8828\right)\right)\right)}\right)\]

  2. Applied simplify 1.9

    \[\leadsto \color{blue}{-\left(\left(e^{\left(-10.0\right) \cdot \left(\left(x2 - 0.117\right) \cdot \left(x2 - 0.117\right)\right) + \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) \cdot \left(-3.0\right)} \cdot \frac{1.0}{{\left(e^{x3 - 0.2673}\right)}^{\left(30.0 \cdot \left(x3 - 0.2673\right)\right)}} + e^{\left(\left(x2 - 0.4387\right) \cdot \left(x2 - 0.4387\right)\right) \cdot \left(-10.0\right) + \left(\left(x1 - 0.4699\right) \cdot \left(x1 - 0.4699\right)\right) \cdot \left(-0.1\right)} \cdot \frac{1.2}{{\left(e^{35.0}\right)}^{\left({\left(x3 - 0.747\right)}^2\right)}}\right) + \left(e^{\left(3.0 \cdot \left(x1 - 0.1091\right)\right) \cdot \left(-\left(x1 - 0.1091\right)\right) + \left(\left(x2 - 0.8732\right) \cdot \left(x2 - 0.8732\right)\right) \cdot \left(-10.0\right)} \cdot \frac{3.0}{{\left(e^{x3 - 0.5547}\right)}^{\left(30.0 \cdot \left(x3 - 0.5547\right)\right)}} + e^{\left(-0.1\right) \cdot {\left(x1 - 0.03815\right)}^2 + {\left(x2 - 0.5743\right)}^2 \cdot \left(-10.0\right)} \cdot \frac{3.2}{{\left(e^{35.0}\right)}^{\left(\left(x3 - 0.8828\right) \cdot \left(x3 - 0.8828\right)\right)}}\right)\right)}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity 1.9

    \[\leadsto -\left(\left(e^{\left(-10.0\right) \cdot \left(\left(x2 - 0.117\right) \cdot \left(x2 - 0.117\right)\right) + \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) \cdot \left(-3.0\right)} \cdot \frac{1.0}{{\left(e^{\color{blue}{1 \cdot \left(x3 - 0.2673\right)}}\right)}^{\left(30.0 \cdot \left(x3 - 0.2673\right)\right)}} + e^{\left(\left(x2 - 0.4387\right) \cdot \left(x2 - 0.4387\right)\right) \cdot \left(-10.0\right) + \left(\left(x1 - 0.4699\right) \cdot \left(x1 - 0.4699\right)\right) \cdot \left(-0.1\right)} \cdot \frac{1.2}{{\left(e^{35.0}\right)}^{\left({\left(x3 - 0.747\right)}^2\right)}}\right) + \left(e^{\left(3.0 \cdot \left(x1 - 0.1091\right)\right) \cdot \left(-\left(x1 - 0.1091\right)\right) + \left(\left(x2 - 0.8732\right) \cdot \left(x2 - 0.8732\right)\right) \cdot \left(-10.0\right)} \cdot \frac{3.0}{{\left(e^{x3 - 0.5547}\right)}^{\left(30.0 \cdot \left(x3 - 0.5547\right)\right)}} + e^{\left(-0.1\right) \cdot {\left(x1 - 0.03815\right)}^2 + {\left(x2 - 0.5743\right)}^2 \cdot \left(-10.0\right)} \cdot \frac{3.2}{{\left(e^{35.0}\right)}^{\left(\left(x3 - 0.8828\right) \cdot \left(x3 - 0.8828\right)\right)}}\right)\right)\]

  5. Applied exp-prod 1.9

    \[\leadsto -\left(\left(e^{\left(-10.0\right) \cdot \left(\left(x2 - 0.117\right) \cdot \left(x2 - 0.117\right)\right) + \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) \cdot \left(-3.0\right)} \cdot \frac{1.0}{{\color{blue}{\left({\left(e^{1}\right)}^{\left(x3 - 0.2673\right)}\right)}}^{\left(30.0 \cdot \left(x3 - 0.2673\right)\right)}} + e^{\left(\left(x2 - 0.4387\right) \cdot \left(x2 - 0.4387\right)\right) \cdot \left(-10.0\right) + \left(\left(x1 - 0.4699\right) \cdot \left(x1 - 0.4699\right)\right) \cdot \left(-0.1\right)} \cdot \frac{1.2}{{\left(e^{35.0}\right)}^{\left({\left(x3 - 0.747\right)}^2\right)}}\right) + \left(e^{\left(3.0 \cdot \left(x1 - 0.1091\right)\right) \cdot \left(-\left(x1 - 0.1091\right)\right) + \left(\left(x2 - 0.8732\right) \cdot \left(x2 - 0.8732\right)\right) \cdot \left(-10.0\right)} \cdot \frac{3.0}{{\left(e^{x3 - 0.5547}\right)}^{\left(30.0 \cdot \left(x3 - 0.5547\right)\right)}} + e^{\left(-0.1\right) \cdot {\left(x1 - 0.03815\right)}^2 + {\left(x2 - 0.5743\right)}^2 \cdot \left(-10.0\right)} \cdot \frac{3.2}{{\left(e^{35.0}\right)}^{\left(\left(x3 - 0.8828\right) \cdot \left(x3 - 0.8828\right)\right)}}\right)\right)\]

  6. Applied pow-pow 0.1

    \[\leadsto -\left(\left(e^{\left(-10.0\right) \cdot \left(\left(x2 - 0.117\right) \cdot \left(x2 - 0.117\right)\right) + \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) \cdot \left(-3.0\right)} \cdot \frac{1.0}{\color{blue}{{\left(e^{1}\right)}^{\left(\left(x3 - 0.2673\right) \cdot \left(30.0 \cdot \left(x3 - 0.2673\right)\right)\right)}}} + e^{\left(\left(x2 - 0.4387\right) \cdot \left(x2 - 0.4387\right)\right) \cdot \left(-10.0\right) + \left(\left(x1 - 0.4699\right) \cdot \left(x1 - 0.4699\right)\right) \cdot \left(-0.1\right)} \cdot \frac{1.2}{{\left(e^{35.0}\right)}^{\left({\left(x3 - 0.747\right)}^2\right)}}\right) + \left(e^{\left(3.0 \cdot \left(x1 - 0.1091\right)\right) \cdot \left(-\left(x1 - 0.1091\right)\right) + \left(\left(x2 - 0.8732\right) \cdot \left(x2 - 0.8732\right)\right) \cdot \left(-10.0\right)} \cdot \frac{3.0}{{\left(e^{x3 - 0.5547}\right)}^{\left(30.0 \cdot \left(x3 - 0.5547\right)\right)}} + e^{\left(-0.1\right) \cdot {\left(x1 - 0.03815\right)}^2 + {\left(x2 - 0.5743\right)}^2 \cdot \left(-10.0\right)} \cdot \frac{3.2}{{\left(e^{35.0}\right)}^{\left(\left(x3 - 0.8828\right) \cdot \left(x3 - 0.8828\right)\right)}}\right)\right)\]
  7. Using strategy rm

  8. Applied add-cbrt-cube 0.1

    \[\leadsto -\left(\left(e^{\left(-10.0\right) \cdot \left(\left(x2 - 0.117\right) \cdot \left(x2 - 0.117\right)\right) + \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) \cdot \left(-3.0\right)} \cdot \frac{1.0}{{\left(e^{1}\right)}^{\left(\left(x3 - 0.2673\right) \cdot \left(30.0 \cdot \left(x3 - 0.2673\right)\right)\right)}} + e^{\left(\left(x2 - 0.4387\right) \cdot \left(x2 - 0.4387\right)\right) \cdot \left(-10.0\right) + \left(\left(x1 - 0.4699\right) \cdot \left(x1 - 0.4699\right)\right) \cdot \left(-0.1\right)} \cdot \frac{1.2}{\color{blue}{\sqrt[3]{{\left({\left(e^{35.0}\right)}^{\left({\left(x3 - 0.747\right)}^2\right)}\right)}^3}}}\right) + \left(e^{\left(3.0 \cdot \left(x1 - 0.1091\right)\right) \cdot \left(-\left(x1 - 0.1091\right)\right) + \left(\left(x2 - 0.8732\right) \cdot \left(x2 - 0.8732\right)\right) \cdot \left(-10.0\right)} \cdot \frac{3.0}{{\left(e^{x3 - 0.5547}\right)}^{\left(30.0 \cdot \left(x3 - 0.5547\right)\right)}} + e^{\left(-0.1\right) \cdot {\left(x1 - 0.03815\right)}^2 + {\left(x2 - 0.5743\right)}^2 \cdot \left(-10.0\right)} \cdot \frac{3.2}{{\left(e^{35.0}\right)}^{\left(\left(x3 - 0.8828\right) \cdot \left(x3 - 0.8828\right)\right)}}\right)\right)\]
  9. Removed slow pow expressions

Runtime

Time bar (total: 45.4s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3052192724 3812927732 3686175817 630908657 2373248591 511094450)'
(FPCore (x1 x2 x3)
  :name "hartman3"
  :pre (and (<= 0 x1 1) (<= 0 x2 1) (<= 0 x3 1))
  (- (+ (+ (+ (* 1.0 (exp (- (+ (+ (* 3.0 (* (- x1 0.3689) (- x1 0.3689))) (* 10.0 (* (- x2 0.117) (- x2 0.117)))) (* 30.0 (* (- x3 0.2673) (- x3 0.2673))))))) (* 1.2 (exp (- (+ (+ (* 0.1 (* (- x1 0.4699) (- x1 0.4699))) (* 10.0 (* (- x2 0.4387) (- x2 0.4387)))) (* 35.0 (* (- x3 0.747) (- x3 0.747)))))))) (* 3.0 (exp (- (+ (+ (* 3.0 (* (- x1 0.1091) (- x1 0.1091))) (* 10.0 (* (- x2 0.8732) (- x2 0.8732)))) (* 30.0 (* (- x3 0.5547) (- x3 0.5547)))))))) (* 3.2 (exp (- (+ (+ (* 0.1 (* (- x1 0.03815) (- x1 0.03815))) (* 10.0 (* (- x2 0.5743) (- x2 0.5743)))) (* 35.0 (* (- x3 0.8828) (- x3 0.8828))))))))))