exp neg sub

Average Error: 0.0 → 0.0

Time: 2.1s

Precision: 64

Math

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

↓

\[{\left(e^{-\sqrt{1}} \cdot e^{-x}\right)}^{\left(\sqrt{1} - x\right)}\]

C

double f(double x) {
        double r26344 = 1.0;
        double r26345 = x;
        double r26346 = r26345 * r26345;
        double r26347 = r26344 - r26346;
        double r26348 = -r26347;
        double r26349 = exp(r26348);
        return r26349;
}

↓

double f(double x) {
        double r26350 = 1.0;
        double r26351 = sqrt(r26350);
        double r26352 = -r26351;
        double r26353 = exp(r26352);
        double r26354 = x;
        double r26355 = -r26354;
        double r26356 = exp(r26355);
        double r26357 = r26353 * r26356;
        double r26358 = r26351 - r26354;
        double r26359 = pow(r26357, r26358);
        return r26359;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[e^{-\left(1 - x \cdot x\right)}\]
2. Using strategy rm

3. Applied add-sqr-sqrt 0.0

   \[\leadsto e^{-\left(\color{blue}{\sqrt{1} \cdot \sqrt{1}} - x \cdot x\right)}\]

4. Applied difference-of-squares 0.0

   \[\leadsto e^{-\color{blue}{\left(\sqrt{1} + x\right) \cdot \left(\sqrt{1} - x\right)}}\]

5. Applied distribute-lft-neg-in 0.0

   \[\leadsto e^{\color{blue}{\left(-\left(\sqrt{1} + x\right)\right) \cdot \left(\sqrt{1} - x\right)}}\]

6. Applied exp-prod 0.0

   \[\leadsto \color{blue}{{\left(e^{-\left(\sqrt{1} + x\right)}\right)}^{\left(\sqrt{1} - x\right)}}\]
7. Using strategy rm

8. Applied distribute-neg-in 0.0

   \[\leadsto {\left(e^{\color{blue}{\left(-\sqrt{1}\right) + \left(-x\right)}}\right)}^{\left(\sqrt{1} - x\right)}\]

9. Applied exp-sum 0.0

   \[\leadsto {\color{blue}{\left(e^{-\sqrt{1}} \cdot e^{-x}\right)}}^{\left(\sqrt{1} - x\right)}\]

10. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020002 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))