Error

Derivation

1. Split input into 3 regimes

2. if (/ y z) < -4.042168375717475e+238 or -2.83183872683271e-291 < (/ y z) < 2.1410747010905e-315

   1. Initial program 25.7

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

   2. Applied simplify21.4

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

   4. Applied div-inv21.4

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

   5. Applied associate-*r*0.3

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

   7. Applied pow10.3

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

   8. Applied pow10.3

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

   9. Applied pow-prod-down0.3

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

   10. Applied simplify0.2

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

   12. Applied div-inv0.3

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

   13. Applied simplify0.2

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

   if -4.042168375717475e+238 < (/ y z) < -2.83183872683271e-291 or 2.1410747010905e-315 < (/ y z) < 2.231852696675739e+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/8.3

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

   6. Applied associate-/l*0.3

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

   if 2.231852696675739e+189 < (/ y z)

   1. Initial program 38.4

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

   2. Applied simplify23.6

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

   4. Applied div-inv23.6

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

   5. Applied associate-*r*0.8

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

   7. Applied pow10.8

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

   8. Applied pow10.8

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

   9. Applied pow-prod-down0.8

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

   10. Applied simplify1.7

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

   12. Applied div-inv1.9

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

   13. Applied simplify1.8

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

4. Applied simplify0.4

   \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.042168375717475 \cdot 10^{+238}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{if}\;\frac{y}{z} \le -2.83183872683271 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\frac{y}{z} \le 2.1410747010905 \cdot 10^{-315}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{if}\;\frac{y}{z} \le 2.231852696675739 \cdot 10^{+189}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}}\]

Runtime

Time bar (total: 13.5s)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)))