Average Error: 13.9 → 0.8
Time: 30.3s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(\sqrt[3]{x \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right)} \cdot \sqrt[3]{x \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right)}\right) \cdot \sqrt[3]{x \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right)}\right) \cdot \sqrt[3]{\frac{y}{z}} \le -5.940110676760339 \cdot 10^{+297}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\left(\left(\sqrt[3]{x \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right)} \cdot \sqrt[3]{x \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right)}\right) \cdot \sqrt[3]{x \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right)}\right) \cdot \sqrt[3]{\frac{y}{z}} \le -4.374671639145726 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;\left(\left(\sqrt[3]{x \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right)} \cdot \sqrt[3]{x \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right)}\right) \cdot \sqrt[3]{x \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right)}\right) \cdot \sqrt[3]{\frac{y}{z}} \le 0.0:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\left(\left(\sqrt[3]{x \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right)} \cdot \sqrt[3]{x \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right)}\right) \cdot \sqrt[3]{x \cdot \left(\sqrt[3]{\frac{y}{z}} \cdot \sqrt[3]{\frac{y}{z}}\right)}\right) \cdot \sqrt[3]{\frac{y}{z}} \le 1.835979574020469 \cdot 10^{+267}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Split input into 2 regimes

  2. if (* (* (* (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z))))) (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z)))))) (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z)))))) (cbrt (/ y z))) < -5.940110676760339e+297 or -4.374671639145726e-305 < (* (* (* (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z))))) (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z)))))) (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z)))))) (cbrt (/ y z))) < 0.0 or 1.835979574020469e+267 < (* (* (* (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z))))) (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z)))))) (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z)))))) (cbrt (/ y z)))

    1. Initial program 19.1

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Applied simplify18.2

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
    3. Using strategy rm

    4. Applied associate-*r/1.4

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]

    if -5.940110676760339e+297 < (* (* (* (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z))))) (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z)))))) (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z)))))) (cbrt (/ y z))) < -4.374671639145726e-305 or 0.0 < (* (* (* (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z))))) (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z)))))) (cbrt (* x (* (cbrt (/ y z)) (cbrt (/ y z)))))) (cbrt (/ y z))) < 1.835979574020469e+267

    1. Initial program 11.6

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Applied simplify0.5

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
  3. Recombined 2 regimes into one program.

Runtime

Time bar (total: 30.3s)Debug logProfile

herbie shell --seed '#(1070960995 739739648 2531964651 3069671617 351857262 3877178482)' +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))