Average Error: 0.2 → 0.0
Time: 12.8s
Precision: 64
\[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]
↓
\[\left(20 + \left(d2 + 10\right)\right) \cdot d1\]
\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20
↓
\left(20 + \left(d2 + 10\right)\right) \cdot d1
double f(double d1, double d2) {
        double r8952284 = d1;
        double r8952285 = 10.0;
        double r8952286 = r8952284 * r8952285;
        double r8952287 = d2;
        double r8952288 = r8952284 * r8952287;
        double r8952289 = r8952286 + r8952288;
        double r8952290 = 20.0;
        double r8952291 = r8952284 * r8952290;
        double r8952292 = r8952289 + r8952291;
        return r8952292;
}
↓
double f(double d1, double d2) {
        double r8952293 = 20.0;
        double r8952294 = d2;
        double r8952295 = 10.0;
        double r8952296 = r8952294 + r8952295;
        double r8952297 = r8952293 + r8952296;
        double r8952298 = d1;
        double r8952299 = r8952297 * r8952298;
        return r8952299;
}

Error

Bits error versus d1

Bits error versus d2

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Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.0
\[d1 \cdot \left(30 + d2\right)\]

Derivation

  1. Initial program 0.2

    \[\left(d1 \cdot 10 + d1 \cdot d2\right) + d1 \cdot 20\]

  2. Simplified0.0

    \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(10 + 20\right)\right)}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt32.1

    \[\leadsto \color{blue}{\left(\sqrt{d1} \cdot \sqrt{d1}\right)} \cdot \left(d2 + \left(10 + 20\right)\right)\]

  5. Applied associate-*l*32.1

    \[\leadsto \color{blue}{\sqrt{d1} \cdot \left(\sqrt{d1} \cdot \left(d2 + \left(10 + 20\right)\right)\right)}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity32.1

    \[\leadsto \color{blue}{\left(1 \cdot \sqrt{d1}\right)} \cdot \left(\sqrt{d1} \cdot \left(d2 + \left(10 + 20\right)\right)\right)\]

  8. Applied associate-*l*32.1

    \[\leadsto \color{blue}{1 \cdot \left(\sqrt{d1} \cdot \left(\sqrt{d1} \cdot \left(d2 + \left(10 + 20\right)\right)\right)\right)}\]

  9. Simplified0.0

    \[\leadsto 1 \cdot \color{blue}{\left(d1 \cdot \left(\left(10 + d2\right) + 20\right)\right)}\]

  10. Final simplification0.0

    \[\leadsto \left(20 + \left(d2 + 10\right)\right) \cdot d1\]

Reproduce

herbie shell --seed 2019171 
(FPCore (d1 d2)
  :name "FastMath test2"

  :herbie-target
  (* d1 (+ 30.0 d2))

  (+ (+ (* d1 10.0) (* d1 d2)) (* d1 20.0)))