(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
(+
(+
(*
(* u (+ (* 0.5 n0_i) (* 0.16666666666666666 (- n1_i n0_i))))
(pow normAngle 2.0))
(* n0_i (- 1.0 u)))
(* n1_i u)))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 (((u * ((0.5f * n0_i) + (0.16666666666666666f * (n1_i - n0_i)))) * powf(normAngle, 2.0f)) + (n0_i * (1.0f - u))) + (n1_i * u);
}
real(4) function code(normangle, u, n0_i, n1_i)
real(4), intent (in) :: normangle
real(4), intent (in) :: u
real(4), intent (in) :: n0_i
real(4), intent (in) :: n1_i
code = ((sin(((1.0e0 - u) * normangle)) * (1.0e0 / sin(normangle))) * n0_i) + ((sin((u * normangle)) * (1.0e0 / sin(normangle))) * n1_i)
end function
real(4) function code(normangle, u, n0_i, n1_i)
real(4), intent (in) :: normangle
real(4), intent (in) :: u
real(4), intent (in) :: n0_i
real(4), intent (in) :: n1_i
code = (((u * ((0.5e0 * n0_i) + (0.16666666666666666e0 * (n1_i - n0_i)))) * (normangle ** 2.0e0)) + (n0_i * (1.0e0 - u))) + (n1_i * u)
end function
function code(normAngle, u, n0_i, n1_i) return Float32(Float32(Float32(sin(Float32(Float32(Float32(1.0) - u) * normAngle)) * Float32(Float32(1.0) / sin(normAngle))) * n0_i) + Float32(Float32(sin(Float32(u * normAngle)) * Float32(Float32(1.0) / sin(normAngle))) * n1_i)) end
function code(normAngle, u, n0_i, n1_i) return Float32(Float32(Float32(Float32(u * Float32(Float32(Float32(0.5) * n0_i) + Float32(Float32(0.16666666666666666) * Float32(n1_i - n0_i)))) * (normAngle ^ Float32(2.0))) + Float32(n0_i * Float32(Float32(1.0) - u))) + Float32(n1_i * u)) end
function tmp = code(normAngle, u, n0_i, n1_i) tmp = ((sin(((single(1.0) - u) * normAngle)) * (single(1.0) / sin(normAngle))) * n0_i) + ((sin((u * normAngle)) * (single(1.0) / sin(normAngle))) * n1_i); end
function tmp = code(normAngle, u, n0_i, n1_i) tmp = (((u * ((single(0.5) * n0_i) + (single(0.16666666666666666) * (n1_i - n0_i)))) * (normAngle ^ single(2.0))) + (n0_i * (single(1.0) - u))) + (n1_i * u); end
\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
\left(\left(u \cdot \left(0.5 \cdot n0_i + 0.16666666666666666 \cdot \left(n1_i - n0_i\right)\right)\right) \cdot {normAngle}^{2} + n0_i \cdot \left(1 - u\right)\right) + n1_i \cdot u
Results
Initial program 0.9
Simplified8.1
Taylor expanded in u around 0 8.1
Simplified8.1
Taylor expanded in normAngle around 0 0.4
Taylor expanded in u around 0 0.5
Simplified0.5
Final simplification0.5
| Alternative 1 | |
|---|---|
| Error | 9.6 |
| Cost | 296 |
| Alternative 2 | |
|---|---|
| Error | 4.4 |
| Cost | 296 |
| Alternative 3 | |
|---|---|
| Error | 4.4 |
| Cost | 296 |
| Alternative 4 | |
|---|---|
| Error | 13.1 |
| Cost | 232 |
| Alternative 5 | |
|---|---|
| Error | 0.6 |
| Cost | 224 |
| Alternative 6 | |
|---|---|
| Error | 17.1 |
| Cost | 32 |
herbie shell --seed 2022335
(FPCore (normAngle u n0_i n1_i)
:name "Curve intersection, scale width based on ribbon orientation"
:precision binary32
:pre (and (and (and (and (<= 0.0 normAngle) (<= normAngle (/ PI 2.0))) (and (<= -1.0 n0_i) (<= n0_i 1.0))) (and (<= -1.0 n1_i) (<= n1_i 1.0))) (and (<= 2.328306437e-10 u) (<= u 1.0)))
(+ (* (* (sin (* (- 1.0 u) normAngle)) (/ 1.0 (sin normAngle))) n0_i) (* (* (sin (* u normAngle)) (/ 1.0 (sin normAngle))) n1_i)))