\[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
Test:
simple fma test
Bits:
128 bits
Bits error versus x
Bits error versus y
Bits error versus z
Time: 28.8 s
Input Error: 43.9
Output Error: 11.2
Log: ⚲
Profile: 🕒
\(\begin{cases} \sqrt[3]{{\left(\left((x * y + z)_* - z\right) - \left(y \cdot x + 1\right)\right)}^3} & \text{when } z \le -4.7058626500647184 \cdot 10^{+222} \\ (\left(\frac{1}{x}\right) * \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - 1 & \text{when } z \le -1.2056317072164634 \cdot 10^{+131} \\ {\left(\sqrt[3]{\left((x * y + z)_* - z\right) - \left(y \cdot x + 1\right)}\right)}^3 & \text{when } z \le -1.1169983808143004 \cdot 10^{+51} \\ (\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - \frac{\left(\frac{2}{y \cdot \left(z \cdot x\right)} - \frac{\frac{\frac{1}{y}}{y}}{x \cdot x}\right) - \left(\frac{\frac{1}{z}}{z} - 1\right)}{\left(\frac{1}{z} + 1\right) - \frac{1}{y \cdot x}} & \text{when } z \le -76168393706.3139 \\ \left((x * y + z)_* - y \cdot x\right) - \left(1 + z\right) & \text{when } z \le 3.1224846592363346 \cdot 10^{+28} \\ (\left(\frac{1}{x}\right) * \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - 1 & \text{otherwise} \end{cases}\)

    if z < -4.7058626500647184e+222

    1. Started with
      \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
      62.2
    2. Using strategy rm
      62.2
    3. Applied flip-+ to get
      \[(x * y + z)_* - \color{red}{\left(1 + \left(x \cdot y + z\right)\right)} \leadsto (x * y + z)_* - \color{blue}{\frac{{1}^2 - {\left(x \cdot y + z\right)}^2}{1 - \left(x \cdot y + z\right)}}\]
      63.6
    4. Using strategy rm
      63.6
    5. Applied clear-num to get
      \[(x * y + z)_* - \color{red}{\frac{{1}^2 - {\left(x \cdot y + z\right)}^2}{1 - \left(x \cdot y + z\right)}} \leadsto (x * y + z)_* - \color{blue}{\frac{1}{\frac{1 - \left(x \cdot y + z\right)}{{1}^2 - {\left(x \cdot y + z\right)}^2}}}\]
      63.6
    6. Applied simplify to get
      \[(x * y + z)_* - \frac{1}{\color{red}{\frac{1 - \left(x \cdot y + z\right)}{{1}^2 - {\left(x \cdot y + z\right)}^2}}} \leadsto (x * y + z)_* - \frac{1}{\color{blue}{\frac{1}{x \cdot y + \left(z + 1\right)} \cdot 1}}\]
      62.3
    7. Using strategy rm
      62.3
    8. Applied add-cbrt-cube to get
      \[\color{red}{(x * y + z)_* - \frac{1}{\frac{1}{x \cdot y + \left(z + 1\right)} \cdot 1}} \leadsto \color{blue}{\sqrt[3]{{\left((x * y + z)_* - \frac{1}{\frac{1}{x \cdot y + \left(z + 1\right)} \cdot 1}\right)}^3}}\]
      62.4
    9. Applied simplify to get
      \[\sqrt[3]{\color{red}{{\left((x * y + z)_* - \frac{1}{\frac{1}{x \cdot y + \left(z + 1\right)} \cdot 1}\right)}^3}} \leadsto \sqrt[3]{\color{blue}{{\left(\left((x * y + z)_* - z\right) - \left(y \cdot x + 1\right)\right)}^3}}\]
      30.9

    if -4.7058626500647184e+222 < z < -1.2056317072164634e+131 or 3.1224846592363346e+28 < z

    1. Started with
      \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
      62.5
    2. Using strategy rm
      62.5
    3. Applied flip-+ to get
      \[(x * y + z)_* - \color{red}{\left(1 + \left(x \cdot y + z\right)\right)} \leadsto (x * y + z)_* - \color{blue}{\frac{{1}^2 - {\left(x \cdot y + z\right)}^2}{1 - \left(x \cdot y + z\right)}}\]
      62.5
    4. Using strategy rm
      62.5
    5. Applied clear-num to get
      \[(x * y + z)_* - \color{red}{\frac{{1}^2 - {\left(x \cdot y + z\right)}^2}{1 - \left(x \cdot y + z\right)}} \leadsto (x * y + z)_* - \color{blue}{\frac{1}{\frac{1 - \left(x \cdot y + z\right)}{{1}^2 - {\left(x \cdot y + z\right)}^2}}}\]
      62.5
    6. Applied simplify to get
      \[(x * y + z)_* - \frac{1}{\color{red}{\frac{1 - \left(x \cdot y + z\right)}{{1}^2 - {\left(x \cdot y + z\right)}^2}}} \leadsto (x * y + z)_* - \frac{1}{\color{blue}{\frac{1}{x \cdot y + \left(z + 1\right)} \cdot 1}}\]
      62.4
    7. Using strategy rm
      62.4
    8. Applied add-cube-cbrt to get
      \[(x * y + z)_* - \frac{1}{\color{red}{\frac{1}{x \cdot y + \left(z + 1\right)}} \cdot 1} \leadsto (x * y + z)_* - \frac{1}{\color{blue}{{\left(\sqrt[3]{\frac{1}{x \cdot y + \left(z + 1\right)}}\right)}^3} \cdot 1}\]
      62.2
    9. Applied taylor to get
      \[(x * y + z)_* - \frac{1}{{\left(\sqrt[3]{\frac{1}{x \cdot y + \left(z + 1\right)}}\right)}^3 \cdot 1} \leadsto (\left(\frac{1}{x}\right) * \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - 1\]
      0.2
    10. Taylor expanded around inf to get
      \[\color{red}{(\left(\frac{1}{x}\right) * \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - 1} \leadsto \color{blue}{(\left(\frac{1}{x}\right) * \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - 1}\]
      0.2
    11. Applied simplify to get
      \[(\left(\frac{1}{x}\right) * \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - 1 \leadsto (\left(\frac{1}{x}\right) * \left(\frac{1}{y}\right) + \left(\frac{1}{z}\right))_* - 1\]
      0.2
    12. Applied final simplification

    if -1.2056317072164634e+131 < z < -1.1169983808143004e+51

    1. Started with
      \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
      62.2
    2. Using strategy rm
      62.2
    3. Applied flip-+ to get
      \[(x * y + z)_* - \color{red}{\left(1 + \left(x \cdot y + z\right)\right)} \leadsto (x * y + z)_* - \color{blue}{\frac{{1}^2 - {\left(x \cdot y + z\right)}^2}{1 - \left(x \cdot y + z\right)}}\]
      62.3
    4. Using strategy rm
      62.3
    5. Applied clear-num to get
      \[(x * y + z)_* - \color{red}{\frac{{1}^2 - {\left(x \cdot y + z\right)}^2}{1 - \left(x \cdot y + z\right)}} \leadsto (x * y + z)_* - \color{blue}{\frac{1}{\frac{1 - \left(x \cdot y + z\right)}{{1}^2 - {\left(x \cdot y + z\right)}^2}}}\]
      62.2
    6. Applied simplify to get
      \[(x * y + z)_* - \frac{1}{\color{red}{\frac{1 - \left(x \cdot y + z\right)}{{1}^2 - {\left(x \cdot y + z\right)}^2}}} \leadsto (x * y + z)_* - \frac{1}{\color{blue}{\frac{1}{x \cdot y + \left(z + 1\right)} \cdot 1}}\]
      62.1
    7. Using strategy rm
      62.1
    8. Applied add-cube-cbrt to get
      \[\color{red}{(x * y + z)_* - \frac{1}{\frac{1}{x \cdot y + \left(z + 1\right)} \cdot 1}} \leadsto \color{blue}{{\left(\sqrt[3]{(x * y + z)_* - \frac{1}{\frac{1}{x \cdot y + \left(z + 1\right)} \cdot 1}}\right)}^3}\]
      62.1
    9. Applied simplify to get
      \[{\color{red}{\left(\sqrt[3]{(x * y + z)_* - \frac{1}{\frac{1}{x \cdot y + \left(z + 1\right)} \cdot 1}}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{\left((x * y + z)_* - z\right) - \left(y \cdot x + 1\right)}\right)}}^3\]
      33.8

    if -1.1169983808143004e+51 < z < -76168393706.3139

    1. Started with
      \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
      57.1
    2. Using strategy rm
      57.1
    3. Applied flip-+ to get
      \[(x * y + z)_* - \color{red}{\left(1 + \left(x \cdot y + z\right)\right)} \leadsto (x * y + z)_* - \color{blue}{\frac{{1}^2 - {\left(x \cdot y + z\right)}^2}{1 - \left(x \cdot y + z\right)}}\]
      57.4
    4. Using strategy rm
      57.4
    5. Applied add-cube-cbrt to get
      \[(x * y + z)_* - \frac{{1}^2 - {\left(x \cdot y + z\right)}^2}{\color{red}{1 - \left(x \cdot y + z\right)}} \leadsto (x * y + z)_* - \frac{{1}^2 - {\left(x \cdot y + z\right)}^2}{\color{blue}{{\left(\sqrt[3]{1 - \left(x \cdot y + z\right)}\right)}^3}}\]
      59.3
    6. Applied add-cube-cbrt to get
      \[(x * y + z)_* - \frac{\color{red}{{1}^2 - {\left(x \cdot y + z\right)}^2}}{{\left(\sqrt[3]{1 - \left(x \cdot y + z\right)}\right)}^3} \leadsto (x * y + z)_* - \frac{\color{blue}{{\left(\sqrt[3]{{1}^2 - {\left(x \cdot y + z\right)}^2}\right)}^3}}{{\left(\sqrt[3]{1 - \left(x \cdot y + z\right)}\right)}^3}\]
      59.7
    7. Applied cube-undiv to get
      \[(x * y + z)_* - \color{red}{\frac{{\left(\sqrt[3]{{1}^2 - {\left(x \cdot y + z\right)}^2}\right)}^3}{{\left(\sqrt[3]{1 - \left(x \cdot y + z\right)}\right)}^3}} \leadsto (x * y + z)_* - \color{blue}{{\left(\frac{\sqrt[3]{{1}^2 - {\left(x \cdot y + z\right)}^2}}{\sqrt[3]{1 - \left(x \cdot y + z\right)}}\right)}^3}\]
      59.3
    8. Applied taylor to get
      \[(x * y + z)_* - {\left(\frac{\sqrt[3]{{1}^2 - {\left(x \cdot y + z\right)}^2}}{\sqrt[3]{1 - \left(x \cdot y + z\right)}}\right)}^3 \leadsto (\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - {\left(\frac{\sqrt[3]{\left(1 + 2 \cdot \frac{1}{y \cdot \left(x \cdot z\right)}\right) - \left(\frac{1}{{z}^2} + \frac{1}{{y}^2 \cdot {x}^2}\right)}}{\sqrt[3]{\left(\frac{1}{z} + 1\right) - \frac{1}{y \cdot x}}}\right)}^3\]
      35.7
    9. Taylor expanded around -inf to get
      \[\color{red}{(\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - {\left(\frac{\sqrt[3]{\left(1 + 2 \cdot \frac{1}{y \cdot \left(x \cdot z\right)}\right) - \left(\frac{1}{{z}^2} + \frac{1}{{y}^2 \cdot {x}^2}\right)}}{\sqrt[3]{\left(\frac{1}{z} + 1\right) - \frac{1}{y \cdot x}}}\right)}^3} \leadsto \color{blue}{(\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - {\left(\frac{\sqrt[3]{\left(1 + 2 \cdot \frac{1}{y \cdot \left(x \cdot z\right)}\right) - \left(\frac{1}{{z}^2} + \frac{1}{{y}^2 \cdot {x}^2}\right)}}{\sqrt[3]{\left(\frac{1}{z} + 1\right) - \frac{1}{y \cdot x}}}\right)}^3}\]
      35.7
    10. Applied simplify to get
      \[(\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - {\left(\frac{\sqrt[3]{\left(1 + 2 \cdot \frac{1}{y \cdot \left(x \cdot z\right)}\right) - \left(\frac{1}{{z}^2} + \frac{1}{{y}^2 \cdot {x}^2}\right)}}{\sqrt[3]{\left(\frac{1}{z} + 1\right) - \frac{1}{y \cdot x}}}\right)}^3 \leadsto (\left(\frac{-1}{x}\right) * \left(\frac{-1}{y}\right) + \left(\frac{-1}{z}\right))_* - \frac{\left(\frac{2}{y \cdot \left(z \cdot x\right)} - \frac{\frac{\frac{1}{y}}{y}}{x \cdot x}\right) - \left(\frac{\frac{1}{z}}{z} - 1\right)}{\left(\frac{1}{z} + 1\right) - \frac{1}{y \cdot x}}\]
      35.7
    11. Applied final simplification

    if -76168393706.3139 < z < 3.1224846592363346e+28

    1. Started with
      \[(x * y + z)_* - \left(1 + \left(x \cdot y + z\right)\right)\]
      30.5
    2. Using strategy rm
      30.5
    3. Applied flip-+ to get
      \[(x * y + z)_* - \color{red}{\left(1 + \left(x \cdot y + z\right)\right)} \leadsto (x * y + z)_* - \color{blue}{\frac{{1}^2 - {\left(x \cdot y + z\right)}^2}{1 - \left(x \cdot y + z\right)}}\]
      30.7
    4. Using strategy rm
      30.7
    5. Applied clear-num to get
      \[(x * y + z)_* - \color{red}{\frac{{1}^2 - {\left(x \cdot y + z\right)}^2}{1 - \left(x \cdot y + z\right)}} \leadsto (x * y + z)_* - \color{blue}{\frac{1}{\frac{1 - \left(x \cdot y + z\right)}{{1}^2 - {\left(x \cdot y + z\right)}^2}}}\]
      30.9
    6. Applied simplify to get
      \[(x * y + z)_* - \frac{1}{\color{red}{\frac{1 - \left(x \cdot y + z\right)}{{1}^2 - {\left(x \cdot y + z\right)}^2}}} \leadsto (x * y + z)_* - \frac{1}{\color{blue}{\frac{1}{x \cdot y + \left(z + 1\right)} \cdot 1}}\]
      30.6
    7. Applied taylor to get
      \[(x * y + z)_* - \frac{1}{\frac{1}{x \cdot y + \left(z + 1\right)} \cdot 1} \leadsto (x * y + z)_* - \frac{1}{\frac{1}{y \cdot x + \left(1 + z\right)} \cdot 1}\]
      30.6
    8. Taylor expanded around 0 to get
      \[(x * y + z)_* - \frac{1}{\frac{1}{\color{red}{y \cdot x + \left(1 + z\right)}} \cdot 1} \leadsto (x * y + z)_* - \frac{1}{\frac{1}{\color{blue}{y \cdot x + \left(1 + z\right)}} \cdot 1}\]
      30.6
    9. Applied simplify to get
      \[\color{red}{(x * y + z)_* - \frac{1}{\frac{1}{y \cdot x + \left(1 + z\right)} \cdot 1}} \leadsto \color{blue}{\left((x * y + z)_* - y \cdot x\right) - \left(1 + z\right)}\]
      10.4
  1. Removed slow pow expressions

Original test:


(lambda ((x default) (y default) (z default))
  #:name "simple fma test"
  (- (fma x y z) (+ 1 (+ (* x y) z)))
  #:target
  -1)