Average Error: 3.7 → 0.3
Time: 1.2m
Precision: 64
Internal Precision: 576
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\frac{1}{\frac{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}{\sin ky}} \cdot \sin th\]

Error

Bits error versus kx

Bits error versus ky

Bits error versus th

Derivation

  1. Initial program 3.7

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

  3. Applied clear-num3.7

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}}} \cdot \sin th\]

  4. Applied simplify0.3

    \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt{\left(\sin kx\right)^2 + \left(\sin ky\right)^2}^*}{\sin ky}}} \cdot \sin th\]

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed '#(1072107073 2127697367 3936270018 2300570620 2134894798 4023771849)' +o rules:numerics
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))