Average Error: 0.0 → 0.0
Time: 3.3s
Precision: binary64
\[-\left(\left(\left(1 \cdot e^{-\left(\left(3 \cdot \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) + 10 \cdot \left(\left(x2 - 0.117000000000000007\right) \cdot \left(x2 - 0.117000000000000007\right)\right)\right) + 30 \cdot \left(\left(x3 - 0.26729999999999998\right) \cdot \left(x3 - 0.26729999999999998\right)\right)\right)} + 1.19999999999999996 \cdot e^{-\left(\left(0.10000000000000001 \cdot \left(\left(x1 - 0.46989999999999998\right) \cdot \left(x1 - 0.46989999999999998\right)\right) + 10 \cdot \left(\left(x2 - 0.43869999999999998\right) \cdot \left(x2 - 0.43869999999999998\right)\right)\right) + 35 \cdot \left(\left(x3 - 0.746999999999999997\right) \cdot \left(x3 - 0.746999999999999997\right)\right)\right)}\right) + 3 \cdot e^{-\left(\left(3 \cdot \left(\left(x1 - 0.1091\right) \cdot \left(x1 - 0.1091\right)\right) + 10 \cdot \left(\left(x2 - 0.87319999999999998\right) \cdot \left(x2 - 0.87319999999999998\right)\right)\right) + 30 \cdot \left(\left(x3 - 0.55469999999999997\right) \cdot \left(x3 - 0.55469999999999997\right)\right)\right)}\right) + 3.2000000000000002 \cdot e^{-\left(\left(0.10000000000000001 \cdot \left(\left(x1 - 0.038150000000000003\right) \cdot \left(x1 - 0.038150000000000003\right)\right) + 10 \cdot \left(\left(x2 - 0.57430000000000003\right) \cdot \left(x2 - 0.57430000000000003\right)\right)\right) + 35 \cdot \left(\left(x3 - 0.88280000000000003\right) \cdot \left(x3 - 0.88280000000000003\right)\right)\right)}\right)\]
↓
\[\frac{-3.2000000000000002}{e^{\left(0.10000000000000001 \cdot \left(\left(x1 - 0.038150000000000003\right) \cdot \left(x1 - 0.038150000000000003\right)\right) + 10 \cdot \left(\left(x2 - 0.57430000000000003\right) \cdot \left(x2 - 0.57430000000000003\right)\right)\right) + 35 \cdot \left(\left(x3 - 0.88280000000000003\right) \cdot \left(x3 - 0.88280000000000003\right)\right)}} - \left(\left(1 \cdot e^{-\left(\left(3 \cdot \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) + 10 \cdot \left(\left(x2 - 0.117000000000000007\right) \cdot \left(x2 - 0.117000000000000007\right)\right)\right) + 30 \cdot \left(\left(x3 - 0.26729999999999998\right) \cdot \left(x3 - 0.26729999999999998\right)\right)\right)} + 1.19999999999999996 \cdot e^{-\left(\left(0.10000000000000001 \cdot \left(\left(x1 - 0.46989999999999998\right) \cdot \left(x1 - 0.46989999999999998\right)\right) + 10 \cdot \left(\left(x2 - 0.43869999999999998\right) \cdot \left(x2 - 0.43869999999999998\right)\right)\right) + 35 \cdot \left(\left(x3 - 0.746999999999999997\right) \cdot \left(x3 - 0.746999999999999997\right)\right)\right)}\right) + 3 \cdot e^{-\left(\left(3 \cdot \left(\left(x1 - 0.1091\right) \cdot \left(x1 - 0.1091\right)\right) + 10 \cdot \left(\left(x2 - 0.87319999999999998\right) \cdot \left(x2 - 0.87319999999999998\right)\right)\right) + 30 \cdot \left(\left(x3 - 0.55469999999999997\right) \cdot \left(x3 - 0.55469999999999997\right)\right)\right)}\right)\]

Error

Bits error versus x1

Bits error versus x2

Bits error versus x3

Derivation

  1. Initial program 0.0

    \[-\left(\left(\left(1 \cdot e^{-\left(\left(3 \cdot \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) + 10 \cdot \left(\left(x2 - 0.117000000000000007\right) \cdot \left(x2 - 0.117000000000000007\right)\right)\right) + 30 \cdot \left(\left(x3 - 0.26729999999999998\right) \cdot \left(x3 - 0.26729999999999998\right)\right)\right)} + 1.19999999999999996 \cdot e^{-\left(\left(0.10000000000000001 \cdot \left(\left(x1 - 0.46989999999999998\right) \cdot \left(x1 - 0.46989999999999998\right)\right) + 10 \cdot \left(\left(x2 - 0.43869999999999998\right) \cdot \left(x2 - 0.43869999999999998\right)\right)\right) + 35 \cdot \left(\left(x3 - 0.746999999999999997\right) \cdot \left(x3 - 0.746999999999999997\right)\right)\right)}\right) + 3 \cdot e^{-\left(\left(3 \cdot \left(\left(x1 - 0.1091\right) \cdot \left(x1 - 0.1091\right)\right) + 10 \cdot \left(\left(x2 - 0.87319999999999998\right) \cdot \left(x2 - 0.87319999999999998\right)\right)\right) + 30 \cdot \left(\left(x3 - 0.55469999999999997\right) \cdot \left(x3 - 0.55469999999999997\right)\right)\right)}\right) + 3.2000000000000002 \cdot e^{-\left(\left(0.10000000000000001 \cdot \left(\left(x1 - 0.038150000000000003\right) \cdot \left(x1 - 0.038150000000000003\right)\right) + 10 \cdot \left(\left(x2 - 0.57430000000000003\right) \cdot \left(x2 - 0.57430000000000003\right)\right)\right) + 35 \cdot \left(\left(x3 - 0.88280000000000003\right) \cdot \left(x3 - 0.88280000000000003\right)\right)\right)}\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{-3.2000000000000002}{e^{\left(0.10000000000000001 \cdot \left(\left(x1 - 0.038150000000000003\right) \cdot \left(x1 - 0.038150000000000003\right)\right) + 10 \cdot \left(\left(x2 - 0.57430000000000003\right) \cdot \left(x2 - 0.57430000000000003\right)\right)\right) + 35 \cdot \left(\left(x3 - 0.88280000000000003\right) \cdot \left(x3 - 0.88280000000000003\right)\right)}} - \left(\left(1 \cdot e^{-\left(\left(3 \cdot \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) + 10 \cdot \left(\left(x2 - 0.117000000000000007\right) \cdot \left(x2 - 0.117000000000000007\right)\right)\right) + 30 \cdot \left(\left(x3 - 0.26729999999999998\right) \cdot \left(x3 - 0.26729999999999998\right)\right)\right)} + 1.19999999999999996 \cdot e^{-\left(\left(0.10000000000000001 \cdot \left(\left(x1 - 0.46989999999999998\right) \cdot \left(x1 - 0.46989999999999998\right)\right) + 10 \cdot \left(\left(x2 - 0.43869999999999998\right) \cdot \left(x2 - 0.43869999999999998\right)\right)\right) + 35 \cdot \left(\left(x3 - 0.746999999999999997\right) \cdot \left(x3 - 0.746999999999999997\right)\right)\right)}\right) + 3 \cdot e^{-\left(\left(3 \cdot \left(\left(x1 - 0.1091\right) \cdot \left(x1 - 0.1091\right)\right) + 10 \cdot \left(\left(x2 - 0.87319999999999998\right) \cdot \left(x2 - 0.87319999999999998\right)\right)\right) + 30 \cdot \left(\left(x3 - 0.55469999999999997\right) \cdot \left(x3 - 0.55469999999999997\right)\right)\right)}\right)}\]

  3. Final simplification0.0

    \[\leadsto \frac{-3.2000000000000002}{e^{\left(0.10000000000000001 \cdot \left(\left(x1 - 0.038150000000000003\right) \cdot \left(x1 - 0.038150000000000003\right)\right) + 10 \cdot \left(\left(x2 - 0.57430000000000003\right) \cdot \left(x2 - 0.57430000000000003\right)\right)\right) + 35 \cdot \left(\left(x3 - 0.88280000000000003\right) \cdot \left(x3 - 0.88280000000000003\right)\right)}} - \left(\left(1 \cdot e^{-\left(\left(3 \cdot \left(\left(x1 - 0.3689\right) \cdot \left(x1 - 0.3689\right)\right) + 10 \cdot \left(\left(x2 - 0.117000000000000007\right) \cdot \left(x2 - 0.117000000000000007\right)\right)\right) + 30 \cdot \left(\left(x3 - 0.26729999999999998\right) \cdot \left(x3 - 0.26729999999999998\right)\right)\right)} + 1.19999999999999996 \cdot e^{-\left(\left(0.10000000000000001 \cdot \left(\left(x1 - 0.46989999999999998\right) \cdot \left(x1 - 0.46989999999999998\right)\right) + 10 \cdot \left(\left(x2 - 0.43869999999999998\right) \cdot \left(x2 - 0.43869999999999998\right)\right)\right) + 35 \cdot \left(\left(x3 - 0.746999999999999997\right) \cdot \left(x3 - 0.746999999999999997\right)\right)\right)}\right) + 3 \cdot e^{-\left(\left(3 \cdot \left(\left(x1 - 0.1091\right) \cdot \left(x1 - 0.1091\right)\right) + 10 \cdot \left(\left(x2 - 0.87319999999999998\right) \cdot \left(x2 - 0.87319999999999998\right)\right)\right) + 30 \cdot \left(\left(x3 - 0.55469999999999997\right) \cdot \left(x3 - 0.55469999999999997\right)\right)\right)}\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x1 x2 x3)
  :name "(- (+ (+ (+ (* 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)))))))))"
  :precision binary64
  (neg (+ (+ (+ (* 1.0 (exp (neg (+ (+ (* 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 (neg (+ (+ (* 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 (neg (+ (+ (* 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 (neg (+ (+ (* 0.1 (* (- x1 0.03815) (- x1 0.03815))) (* 10.0 (* (- x2 0.5743) (- x2 0.5743)))) (* 35.0 (* (- x3 0.8828) (- x3 0.8828))))))))))