Average Error: 0.1 → 0.1
Time: 12.9s
Precision: binary32
Cost: 36096
\[\left(\left(\left(\left(-1 \leq cosTheta_i \land cosTheta_i \leq 1\right) \land \left(-1 \leq cosTheta_O \land cosTheta_O \leq 1\right)\right) \land \left(-1 \leq sinTheta_i \land sinTheta_i \leq 1\right)\right) \land \left(-1 \leq sinTheta_O \land sinTheta_O \leq 1\right)\right) \land \left(-1.5707964 \leq v \land v \leq 0.1\right)\]
\[e^{\left(\left(\left(\frac{cosTheta_i \cdot cosTheta_O}{v} - \frac{sinTheta_i \cdot sinTheta_O}{v}\right) - \frac{1}{v}\right) + 0.6931\right) + \log \left(\frac{1}{2 \cdot v}\right)} \]
↓
\[\begin{array}{l} t_0 := {\left(\sqrt{{\left(0.6931 + \log \left(\frac{0.5}{v}\right)\right)}^{0.16666666666666666}}\right)}^{3}\\ e^{\frac{\left(cosTheta_i \cdot cosTheta_O - sinTheta_i \cdot sinTheta_O\right) + -1}{v}} \cdot e^{{\left(t_0 \cdot t_0\right)}^{2}} \end{array} \]
(FPCore (cosTheta_i cosTheta_O sinTheta_i sinTheta_O v)
 :precision binary32
 (exp
  (+
   (+
    (-
     (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v))
     (/ 1.0 v))
    0.6931)
   (log (/ 1.0 (* 2.0 v))))))
↓
(FPCore (cosTheta_i cosTheta_O sinTheta_i sinTheta_O v)
 :precision binary32
 (let* ((t_0
         (pow
          (sqrt (pow (+ 0.6931 (log (/ 0.5 v))) 0.16666666666666666))
          3.0)))
   (*
    (exp
     (/ (+ (- (* cosTheta_i cosTheta_O) (* sinTheta_i sinTheta_O)) -1.0) v))
    (exp (pow (* t_0 t_0) 2.0)))))
float code(float cosTheta_i, float cosTheta_O, float sinTheta_i, float sinTheta_O, float v) {
	return expf(((((((cosTheta_i * cosTheta_O) / v) - ((sinTheta_i * sinTheta_O) / v)) - (1.0f / v)) + 0.6931f) + logf((1.0f / (2.0f * v)))));
}
↓
float code(float cosTheta_i, float cosTheta_O, float sinTheta_i, float sinTheta_O, float v) {
	float t_0 = powf(sqrtf(powf((0.6931f + logf((0.5f / v))), 0.16666666666666666f)), 3.0f);
	return expf(((((cosTheta_i * cosTheta_O) - (sinTheta_i * sinTheta_O)) + -1.0f) / v)) * expf(powf((t_0 * t_0), 2.0f));
}

real(4) function code(costheta_i, costheta_o, sintheta_i, sintheta_o, v)
    real(4), intent (in) :: costheta_i
    real(4), intent (in) :: costheta_o
    real(4), intent (in) :: sintheta_i
    real(4), intent (in) :: sintheta_o
    real(4), intent (in) :: v
    code = exp(((((((costheta_i * costheta_o) / v) - ((sintheta_i * sintheta_o) / v)) - (1.0e0 / v)) + 0.6931e0) + log((1.0e0 / (2.0e0 * v)))))
end function
↓
real(4) function code(costheta_i, costheta_o, sintheta_i, sintheta_o, v)
    real(4), intent (in) :: costheta_i
    real(4), intent (in) :: costheta_o
    real(4), intent (in) :: sintheta_i
    real(4), intent (in) :: sintheta_o
    real(4), intent (in) :: v
    real(4) :: t_0
    t_0 = sqrt(((0.6931e0 + log((0.5e0 / v))) ** 0.16666666666666666e0)) ** 3.0e0
    code = exp(((((costheta_i * costheta_o) - (sintheta_i * sintheta_o)) + (-1.0e0)) / v)) * exp(((t_0 * t_0) ** 2.0e0))
end function

function code(cosTheta_i, cosTheta_O, sinTheta_i, sinTheta_O, v)
	return exp(Float32(Float32(Float32(Float32(Float32(Float32(cosTheta_i * cosTheta_O) / v) - Float32(Float32(sinTheta_i * sinTheta_O) / v)) - Float32(Float32(1.0) / v)) + Float32(0.6931)) + log(Float32(Float32(1.0) / Float32(Float32(2.0) * v)))))
end
↓
function code(cosTheta_i, cosTheta_O, sinTheta_i, sinTheta_O, v)
	t_0 = sqrt((Float32(Float32(0.6931) + log(Float32(Float32(0.5) / v))) ^ Float32(0.16666666666666666))) ^ Float32(3.0)
	return Float32(exp(Float32(Float32(Float32(Float32(cosTheta_i * cosTheta_O) - Float32(sinTheta_i * sinTheta_O)) + Float32(-1.0)) / v)) * exp((Float32(t_0 * t_0) ^ Float32(2.0))))
end

function tmp = code(cosTheta_i, cosTheta_O, sinTheta_i, sinTheta_O, v)
	tmp = exp(((((((cosTheta_i * cosTheta_O) / v) - ((sinTheta_i * sinTheta_O) / v)) - (single(1.0) / v)) + single(0.6931)) + log((single(1.0) / (single(2.0) * v)))));
end
↓
function tmp = code(cosTheta_i, cosTheta_O, sinTheta_i, sinTheta_O, v)
	t_0 = sqrt(((single(0.6931) + log((single(0.5) / v))) ^ single(0.16666666666666666))) ^ single(3.0);
	tmp = exp(((((cosTheta_i * cosTheta_O) - (sinTheta_i * sinTheta_O)) + single(-1.0)) / v)) * exp(((t_0 * t_0) ^ single(2.0)));
end

e^{\left(\left(\left(\frac{cosTheta_i \cdot cosTheta_O}{v} - \frac{sinTheta_i \cdot sinTheta_O}{v}\right) - \frac{1}{v}\right) + 0.6931\right) + \log \left(\frac{1}{2 \cdot v}\right)}
↓
\begin{array}{l}
t_0 := {\left(\sqrt{{\left(0.6931 + \log \left(\frac{0.5}{v}\right)\right)}^{0.16666666666666666}}\right)}^{3}\\
e^{\frac{\left(cosTheta_i \cdot cosTheta_O - sinTheta_i \cdot sinTheta_O\right) + -1}{v}} \cdot e^{{\left(t_0 \cdot t_0\right)}^{2}}
\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[e^{\left(\left(\left(\frac{cosTheta_i \cdot cosTheta_O}{v} - \frac{sinTheta_i \cdot sinTheta_O}{v}\right) - \frac{1}{v}\right) + 0.6931\right) + \log \left(\frac{1}{2 \cdot v}\right)} \]

  2. Applied egg-rr0.1

    \[\leadsto \color{blue}{e^{\frac{\left(cosTheta_i \cdot cosTheta_O - sinTheta_i \cdot sinTheta_O\right) - 1}{v}} \cdot e^{0.6931 + \log \left(\frac{0.5}{v}\right)}} \]

  3. Applied egg-rr0.1

    \[\leadsto e^{\frac{\left(cosTheta_i \cdot cosTheta_O - sinTheta_i \cdot sinTheta_O\right) - 1}{v}} \cdot e^{\color{blue}{{\left(\sqrt{0.6931 + \log \left(\frac{0.5}{v}\right)}\right)}^{2}}} \]

  4. Applied egg-rr0.1

    \[\leadsto e^{\frac{\left(cosTheta_i \cdot cosTheta_O - sinTheta_i \cdot sinTheta_O\right) - 1}{v}} \cdot e^{{\color{blue}{\left({\left(\sqrt{{\left(0.6931 + \log \left(\frac{0.5}{v}\right)\right)}^{0.16666666666666666}}\right)}^{3} \cdot {\left(\sqrt{{\left(0.6931 + \log \left(\frac{0.5}{v}\right)\right)}^{0.16666666666666666}}\right)}^{3}\right)}}^{2}} \]

  5. Final simplification0.1

    \[\leadsto e^{\frac{\left(cosTheta_i \cdot cosTheta_O - sinTheta_i \cdot sinTheta_O\right) + -1}{v}} \cdot e^{{\left({\left(\sqrt{{\left(0.6931 + \log \left(\frac{0.5}{v}\right)\right)}^{0.16666666666666666}}\right)}^{3} \cdot {\left(\sqrt{{\left(0.6931 + \log \left(\frac{0.5}{v}\right)\right)}^{0.16666666666666666}}\right)}^{3}\right)}^{2}} \]

Alternatives

Alternative 1
Error0.1
Cost6816
\[e^{\frac{cosTheta_i \cdot cosTheta_O + -1}{v}} \cdot \frac{0.5 \cdot e^{0.6931}}{v} \]
Alternative 2
Error0.1
Cost3616
\[\frac{0.5 \cdot e^{0.6931 + \frac{cosTheta_i \cdot cosTheta_O + -1}{v}}}{v} \]
Alternative 3
Error0.1
Cost3488
\[\frac{0.5}{v} \cdot e^{0.6931 + \frac{-1}{v}} \]
Alternative 4
Error0.7
Cost3296
\[e^{\frac{-1}{v}} \]
Alternative 5
Error29.9
Cost32
\[1 \]

Error

Reproduce

herbie shell --seed 2022284 
(FPCore (cosTheta_i cosTheta_O sinTheta_i sinTheta_O v)
  :name "HairBSDF, Mp, lower"
  :precision binary32
  :pre (and (and (and (and (and (<= -1.0 cosTheta_i) (<= cosTheta_i 1.0)) (and (<= -1.0 cosTheta_O) (<= cosTheta_O 1.0))) (and (<= -1.0 sinTheta_i) (<= sinTheta_i 1.0))) (and (<= -1.0 sinTheta_O) (<= sinTheta_O 1.0))) (and (<= -1.5707964 v) (<= v 0.1)))
  (exp (+ (+ (- (- (/ (* cosTheta_i cosTheta_O) v) (/ (* sinTheta_i sinTheta_O) v)) (/ 1.0 v)) 0.6931) (log (/ 1.0 (* 2.0 v))))))