Average Error: 61.8 → 0.3
Time: 17.0s
Precision: 64
\[0.9000000000000000222044604925031308084726 \le t \le 1.100000000000000088817841970012523233891\]
\[\left(1 + t \cdot 1.999999999999999958195573448069207123682 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 1.999999999999999958195573448069207123682 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 1.999999999999999958195573448069207123682 \cdot 10^{-16}\right)\right)\]
↓
\[t \cdot \left(t \cdot 3.999999999999999676487027278085939408227 \cdot 10^{-32}\right)\]
\left(1 + t \cdot 1.999999999999999958195573448069207123682 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 1.999999999999999958195573448069207123682 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 1.999999999999999958195573448069207123682 \cdot 10^{-16}\right)\right)
↓
t \cdot \left(t \cdot 3.999999999999999676487027278085939408227 \cdot 10^{-32}\right)
double f(double t) {
        double r4049515 = 1.0;
        double r4049516 = t;
        double r4049517 = 2e-16;
        double r4049518 = r4049516 * r4049517;
        double r4049519 = r4049515 + r4049518;
        double r4049520 = r4049519 * r4049519;
        double r4049521 = -1.0;
        double r4049522 = 2.0;
        double r4049523 = r4049522 * r4049518;
        double r4049524 = r4049521 - r4049523;
        double r4049525 = r4049520 + r4049524;
        return r4049525;
}
↓
double f(double t) {
        double r4049526 = t;
        double r4049527 = 3.9999999999999997e-32;
        double r4049528 = r4049526 * r4049527;
        double r4049529 = r4049526 * r4049528;
        return r4049529;
}

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original61.8
Target50.6
Herbie0.3
\[\mathsf{fma}\left(1 + t \cdot 1.999999999999999958195573448069207123682 \cdot 10^{-16}, 1 + t \cdot 1.999999999999999958195573448069207123682 \cdot 10^{-16}, -1 - 2 \cdot \left(t \cdot 1.999999999999999958195573448069207123682 \cdot 10^{-16}\right)\right)\]

Derivation

  1. Initial program 61.8

    \[\left(1 + t \cdot 1.999999999999999958195573448069207123682 \cdot 10^{-16}\right) \cdot \left(1 + t \cdot 1.999999999999999958195573448069207123682 \cdot 10^{-16}\right) + \left(-1 - 2 \cdot \left(t \cdot 1.999999999999999958195573448069207123682 \cdot 10^{-16}\right)\right)\]

  2. Taylor expanded around 0 0.3

    \[\leadsto \color{blue}{3.999999999999999676487027278085939408227 \cdot 10^{-32} \cdot {t}^{2}}\]

  3. Simplified0.3

    \[\leadsto \color{blue}{\left(t \cdot t\right) \cdot 3.999999999999999676487027278085939408227 \cdot 10^{-32}}\]
  4. Using strategy rm

  5. Applied associate-*l*0.3

    \[\leadsto \color{blue}{t \cdot \left(t \cdot 3.999999999999999676487027278085939408227 \cdot 10^{-32}\right)}\]

  6. Final simplification0.3

    \[\leadsto t \cdot \left(t \cdot 3.999999999999999676487027278085939408227 \cdot 10^{-32}\right)\]

Reproduce

herbie shell --seed 2019172 
(FPCore (t)
  :name "fma_test1"
  :pre (<= 0.9 t 1.1)

  :herbie-target
  (fma (+ 1.0 (* t 2e-16)) (+ 1.0 (* t 2e-16)) (- -1.0 (* 2.0 (* t 2e-16))))

  (+ (* (+ 1.0 (* t 2e-16)) (+ 1.0 (* t 2e-16))) (- -1.0 (* 2.0 (* t 2e-16)))))