Error

Derivation

1. Split input into 3 regimes

2. if (/ y z) < -1.5879954155334042e+238 or 2.232900212470126e+189 < (/ y z)

   1. Initial program 40.5

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

   2. Applied simplify25.7

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

   4. Applied div-inv25.8

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]

   5. Applied associate-*r*0.9

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
   6. Using strategy rm

   7. Applied pow10.9

      \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{{\left(\frac{1}{z}\right)}^{1}}\]

   8. Applied pow10.9

      \[\leadsto \color{blue}{{\left(x \cdot y\right)}^{1}} \cdot {\left(\frac{1}{z}\right)}^{1}\]

   9. Applied pow-prod-down0.9

      \[\leadsto \color{blue}{{\left(\left(x \cdot y\right) \cdot \frac{1}{z}\right)}^{1}}\]

   10. Applied simplify1.2

       \[\leadsto {\color{blue}{\left(\frac{y}{\frac{z}{x}}\right)}}^{1}\]
   11. Using strategy rm

   12. Applied div-inv1.4

       \[\leadsto {\color{blue}{\left(y \cdot \frac{1}{\frac{z}{x}}\right)}}^{1}\]

   13. Applied simplify1.3

       \[\leadsto {\left(y \cdot \color{blue}{\frac{x}{z}}\right)}^{1}\]

   if -1.5879954155334042e+238 < (/ y z) < -3.6573980275164494e-291 or 2.3601614122087e-315 < (/ y z) < 2.232900212470126e+189

   1. Initial program 9.2

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

   2. Applied simplify0.2

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

   4. Applied associate-*r/8.4

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

   6. Applied associate-/l*0.3

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

   if -3.6573980275164494e-291 < (/ y z) < 2.3601614122087e-315

   1. Initial program 20.5

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

   2. Applied simplify19.1

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

   4. Applied div-inv19.1

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]

   5. Applied associate-*r*0.1

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
   6. Using strategy rm

   7. Applied pow10.1

      \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{{\left(\frac{1}{z}\right)}^{1}}\]

   8. Applied pow10.1

      \[\leadsto \color{blue}{{\left(x \cdot y\right)}^{1}} \cdot {\left(\frac{1}{z}\right)}^{1}\]

   9. Applied pow-prod-down0.1

      \[\leadsto \color{blue}{{\left(\left(x \cdot y\right) \cdot \frac{1}{z}\right)}^{1}}\]

   10. Applied simplify0.1

       \[\leadsto {\color{blue}{\left(\frac{y}{\frac{z}{x}}\right)}}^{1}\]
3. Recombined 3 regimes into one program.

4. Applied simplify0.4

   \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.5879954155334042 \cdot 10^{+238}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{if}\;\frac{y}{z} \le -3.6573980275164494 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\frac{y}{z} \le 2.3601614122087 \cdot 10^{-315}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{if}\;\frac{y}{z} \le 2.232900212470126 \cdot 10^{+189}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}}\]

Runtime

Time bar (total: 13.0s)Debug logProfile

herbie shell --seed '#(1071821486 549052472 3784827256 1559736200 3548510075 881134285)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))