Average Error: 3.8 → 4.1
Time: 1.4m
Precision: 64
Internal Precision: 384
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + \left(\sqrt[3]{{\left(\sin ky\right)}^{2}} \cdot \sqrt[3]{{\left(\sin ky\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\sin ky\right)}^{2}}}} \cdot \sin th\]

Error

Bits error versus kx

Bits error versus ky

Bits error versus th

Derivation

  1. Initial program 3.8

    \[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
  2. Using strategy rm

  3. Applied add-cube-cbrt4.1

    \[\leadsto \frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + \color{blue}{\left(\sqrt[3]{{\left(\sin ky\right)}^{2}} \cdot \sqrt[3]{{\left(\sin ky\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\sin ky\right)}^{2}}}}} \cdot \sin th\]
  4. Removed slow pow expressions.

Runtime

Time bar (total: 1.4m)Debug logProfile

herbie shell --seed '#(1063185673 2139736501 2393378123 1907444849 1070993796 1007244912)' 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))