(/ (* x (- 1 (exp (* (- y) z)))) y)

Average Error: 30.7 → 30.7

Time: 2.2s

Precision: binary64

Math

\[\frac{x \cdot \left(1 - e^{\left(-y\right) \cdot z}\right)}{y}\]

↓

\[\frac{x \cdot \left(1 - e^{\left(-y\right) \cdot z}\right)}{y}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 30.7

   \[\frac{x \cdot \left(1 - e^{\left(-y\right) \cdot z}\right)}{y}\]

2. Final simplification 30.7

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x y z)
  :name "(/ (* x (- 1 (exp (* (- y) z)))) y)"
  :precision binary64
  (/ (* x (- 1.0 (exp (* (neg y) z)))) y))