Average Error: 0.9 → 0.4
Time: 11.8s
Precision: binary32
\[0 \leq normAngle \land normAngle \leq \frac{\pi}{2} \land -1 \leq n0_i \land n0_i \leq 1 \land -1 \leq n1_i \land n1_i \leq 1 \land 2.328306437 \cdot 10^{-10} \leq u \land u \leq 1\]
\[\left(\sin \left(\left(1 - u\right) \cdot normAngle\right) \cdot \frac{1}{\sin normAngle}\right) \cdot n0_i + \left(\sin \left(u \cdot normAngle\right) \cdot \frac{1}{\sin normAngle}\right) \cdot n1_i\]
↓
\[\frac{\sin \left(normAngle \cdot \left(1 - u\right)\right)}{\sin normAngle} \cdot n0_i + \left(u + \left(0.16666666666666666 \cdot \left(normAngle \cdot normAngle\right)\right) \cdot \left(u - {u}^{3}\right)\right) \cdot n1_i\]
\left(\sin \left(\left(1 - u\right) \cdot normAngle\right) \cdot \frac{1}{\sin normAngle}\right) \cdot n0_i + \left(\sin \left(u \cdot normAngle\right) \cdot \frac{1}{\sin normAngle}\right) \cdot n1_i
↓
\frac{\sin \left(normAngle \cdot \left(1 - u\right)\right)}{\sin normAngle} \cdot n0_i + \left(u + \left(0.16666666666666666 \cdot \left(normAngle \cdot normAngle\right)\right) \cdot \left(u - {u}^{3}\right)\right) \cdot n1_i
(FPCore (normAngle u n0_i n1_i)
 :precision binary32
 (+
  (* (* (sin (* (- 1.0 u) normAngle)) (/ 1.0 (sin normAngle))) n0_i)
  (* (* (sin (* u normAngle)) (/ 1.0 (sin normAngle))) n1_i)))
↓
(FPCore (normAngle u n0_i n1_i)
 :precision binary32
 (+
  (* (/ (sin (* normAngle (- 1.0 u))) (sin normAngle)) n0_i)
  (*
   (+ u (* (* 0.16666666666666666 (* normAngle normAngle)) (- u (pow u 3.0))))
   n1_i)))
float code(float normAngle, float u, float n0_i, float n1_i) {
	return ((sinf((1.0f - u) * normAngle) * (1.0f / sinf(normAngle))) * n0_i) + ((sinf(u * normAngle) * (1.0f / sinf(normAngle))) * n1_i);
}
↓
float code(float normAngle, float u, float n0_i, float n1_i) {
	return ((sinf(normAngle * (1.0f - u)) / sinf(normAngle)) * n0_i) + ((u + ((0.16666666666666666f * (normAngle * normAngle)) * (u - powf(u, 3.0f)))) * n1_i);
}

Error

Bits error versus normAngle

Bits error versus u

Bits error versus n0_i

Bits error versus n1_i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.9

    \[\left(\sin \left(\left(1 - u\right) \cdot normAngle\right) \cdot \frac{1}{\sin normAngle}\right) \cdot n0_i + \left(\sin \left(u \cdot normAngle\right) \cdot \frac{1}{\sin normAngle}\right) \cdot n1_i\]

  2. Taylor expanded around 0 0.5

    \[\leadsto \left(\sin \left(\left(1 - u\right) \cdot normAngle\right) \cdot \frac{1}{\sin normAngle}\right) \cdot n0_i + \color{blue}{\left(\left(u + 0.16666666666666666 \cdot \left({normAngle}^{2} \cdot u\right)\right) - 0.16666666666666666 \cdot \left({normAngle}^{2} \cdot {u}^{3}\right)\right)} \cdot n1_i\]

  3. Simplified0.5

    \[\leadsto \left(\sin \left(\left(1 - u\right) \cdot normAngle\right) \cdot \frac{1}{\sin normAngle}\right) \cdot n0_i + \color{blue}{\left(u + \left(0.16666666666666666 \cdot \left(normAngle \cdot normAngle\right)\right) \cdot \left(u - {u}^{3}\right)\right)} \cdot n1_i\]
  4. Using strategy rm

  5. Applied *-un-lft-identity_binary320.5

    \[\leadsto \left(\color{blue}{\left(1 \cdot \sin \left(\left(1 - u\right) \cdot normAngle\right)\right)} \cdot \frac{1}{\sin normAngle}\right) \cdot n0_i + \left(u + \left(0.16666666666666666 \cdot \left(normAngle \cdot normAngle\right)\right) \cdot \left(u - {u}^{3}\right)\right) \cdot n1_i\]

  6. Applied associate-*l*_binary320.5

    \[\leadsto \color{blue}{\left(1 \cdot \left(\sin \left(\left(1 - u\right) \cdot normAngle\right) \cdot \frac{1}{\sin normAngle}\right)\right)} \cdot n0_i + \left(u + \left(0.16666666666666666 \cdot \left(normAngle \cdot normAngle\right)\right) \cdot \left(u - {u}^{3}\right)\right) \cdot n1_i\]

  7. Simplified0.4

    \[\leadsto \left(1 \cdot \color{blue}{\frac{\sin \left(normAngle \cdot \left(1 - u\right)\right)}{\sin normAngle}}\right) \cdot n0_i + \left(u + \left(0.16666666666666666 \cdot \left(normAngle \cdot normAngle\right)\right) \cdot \left(u - {u}^{3}\right)\right) \cdot n1_i\]

  8. Final simplification0.4

    \[\leadsto \frac{\sin \left(normAngle \cdot \left(1 - u\right)\right)}{\sin normAngle} \cdot n0_i + \left(u + \left(0.16666666666666666 \cdot \left(normAngle \cdot normAngle\right)\right) \cdot \left(u - {u}^{3}\right)\right) \cdot n1_i\]

Reproduce

herbie shell --seed 2021175 
(FPCore (normAngle u n0_i n1_i)
  :name "Curve intersection, scale width based on ribbon orientation"
  :precision binary32
  :pre (and (<= 0.0 normAngle (/ PI 2.0)) (<= -1.0 n0_i 1.0) (<= -1.0 n1_i 1.0) (<= 2.328306437e-10 u 1.0))
  (+ (* (* (sin (* (- 1.0 u) normAngle)) (/ 1.0 (sin normAngle))) n0_i) (* (* (sin (* u normAngle)) (/ 1.0 (sin normAngle))) n1_i)))