(- (+ (* 0.362 (exp (* (* (- 0.5) t1) t1))) (* 1.056 (exp (* (* (- 0.5) t2) t2)))) (* 0.065 (exp (* (* (- 0.5) t3) t3))))

Average Error: 0.3 → 0.3

Time: 2.4s

Precision: binary64

Math

\[\left(0.36199999999999999 \cdot e^{\left(\left(-0.5\right) \cdot t1\right) \cdot t1} + 1.056 \cdot e^{\left(\left(-0.5\right) \cdot t2\right) \cdot t2}\right) - 0.065000000000000002 \cdot e^{\left(\left(-0.5\right) \cdot t3\right) \cdot t3}\]

↓

\[\left(0.36199999999999999 \cdot e^{\left(\left(-0.5\right) \cdot t1\right) \cdot t1} + 1.056 \cdot e^{\left(\left(-0.5\right) \cdot t2\right) \cdot t2}\right) - 0.065000000000000002 \cdot e^{\left(\left(-0.5\right) \cdot t3\right) \cdot t3}\]

Error

Bits error versus t1

Bits error versus t2

Bits error versus t3

Derivation

1. Initial program 0.3

   \[\left(0.36199999999999999 \cdot e^{\left(\left(-0.5\right) \cdot t1\right) \cdot t1} + 1.056 \cdot e^{\left(\left(-0.5\right) \cdot t2\right) \cdot t2}\right) - 0.065000000000000002 \cdot e^{\left(\left(-0.5\right) \cdot t3\right) \cdot t3}\]

2. Final simplification 0.3

   \[\leadsto \left(0.36199999999999999 \cdot e^{\left(\left(-0.5\right) \cdot t1\right) \cdot t1} + 1.056 \cdot e^{\left(\left(-0.5\right) \cdot t2\right) \cdot t2}\right) - 0.065000000000000002 \cdot e^{\left(\left(-0.5\right) \cdot t3\right) \cdot t3}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (t1 t2 t3)
  :name "(- (+ (* 0.362 (exp (* (* (- 0.5) t1) t1))) (* 1.056 (exp (* (* (- 0.5) t2) t2)))) (* 0.065 (exp (* (* (- 0.5) t3) t3))))"
  :precision binary64
  (- (+ (* 0.362 (exp (* (* (neg 0.5) t1) t1))) (* 1.056 (exp (* (* (neg 0.5) t2) t2)))) (* 0.065 (exp (* (* (neg 0.5) t3) t3)))))