?

Average Error: 0.5 → 0.4
Time: 18.6s
Precision: binary32
Cost: 10336

?

\[\left(\left(\left(\left(\left(-1 \leq cosTheta_i \land cosTheta_i \leq 1\right) \land \left(-1 \leq cosTheta_O \land cosTheta_O \leq 1\right)\right) \land \left(-1 \leq sinTheta_i \land sinTheta_i \leq 1\right)\right) \land \left(-1 \leq sinTheta_O \land sinTheta_O \leq 1\right)\right) \land 0.1 < v\right) \land v \leq 1.5707964\]
\[ \begin{array}{c}[cosTheta_i, cosTheta_O] = \mathsf{sort}([cosTheta_i, cosTheta_O])\\ \end{array} \]
\[\frac{e^{-\frac{sinTheta_i \cdot sinTheta_O}{v}} \cdot \frac{cosTheta_i \cdot cosTheta_O}{v}}{\left(\sinh \left(\frac{1}{v}\right) \cdot 2\right) \cdot v} \]
↓
\[\frac{e^{\frac{sinTheta_O \cdot \left(-sinTheta_i\right)}{v}} \cdot \left(cosTheta_i \cdot \left(cosTheta_O \cdot \frac{1}{v}\right)\right)}{{\left(\frac{\frac{0.5}{v}}{\sinh \left(\frac{1}{v}\right)}\right)}^{-1}} \]
(FPCore (cosTheta_i cosTheta_O sinTheta_i sinTheta_O v)
 :precision binary32
 (/
  (* (exp (- (/ (* sinTheta_i sinTheta_O) v))) (/ (* cosTheta_i cosTheta_O) v))
  (* (* (sinh (/ 1.0 v)) 2.0) v)))
↓
(FPCore (cosTheta_i cosTheta_O sinTheta_i sinTheta_O v)
 :precision binary32
 (/
  (*
   (exp (/ (* sinTheta_O (- sinTheta_i)) v))
   (* cosTheta_i (* cosTheta_O (/ 1.0 v))))
  (pow (/ (/ 0.5 v) (sinh (/ 1.0 v))) -1.0)))
float code(float cosTheta_i, float cosTheta_O, float sinTheta_i, float sinTheta_O, float v) {
	return (expf(-((sinTheta_i * sinTheta_O) / v)) * ((cosTheta_i * cosTheta_O) / v)) / ((sinhf((1.0f / v)) * 2.0f) * v);
}
↓
float code(float cosTheta_i, float cosTheta_O, float sinTheta_i, float sinTheta_O, float v) {
	return (expf(((sinTheta_O * -sinTheta_i) / v)) * (cosTheta_i * (cosTheta_O * (1.0f / v)))) / powf(((0.5f / v) / sinhf((1.0f / v))), -1.0f);
}

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(-((sintheta_i * sintheta_o) / v)) * ((costheta_i * costheta_o) / v)) / ((sinh((1.0e0 / v)) * 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
    code = (exp(((sintheta_o * -sintheta_i) / v)) * (costheta_i * (costheta_o * (1.0e0 / v)))) / (((0.5e0 / v) / sinh((1.0e0 / v))) ** (-1.0e0))
end function

function code(cosTheta_i, cosTheta_O, sinTheta_i, sinTheta_O, v)
	return Float32(Float32(exp(Float32(-Float32(Float32(sinTheta_i * sinTheta_O) / v))) * Float32(Float32(cosTheta_i * cosTheta_O) / v)) / Float32(Float32(sinh(Float32(Float32(1.0) / v)) * Float32(2.0)) * v))
end
↓
function code(cosTheta_i, cosTheta_O, sinTheta_i, sinTheta_O, v)
	return Float32(Float32(exp(Float32(Float32(sinTheta_O * Float32(-sinTheta_i)) / v)) * Float32(cosTheta_i * Float32(cosTheta_O * Float32(Float32(1.0) / v)))) / (Float32(Float32(Float32(0.5) / v) / sinh(Float32(Float32(1.0) / v))) ^ Float32(-1.0)))
end

function tmp = code(cosTheta_i, cosTheta_O, sinTheta_i, sinTheta_O, v)
	tmp = (exp(-((sinTheta_i * sinTheta_O) / v)) * ((cosTheta_i * cosTheta_O) / v)) / ((sinh((single(1.0) / v)) * single(2.0)) * v);
end
↓
function tmp = code(cosTheta_i, cosTheta_O, sinTheta_i, sinTheta_O, v)
	tmp = (exp(((sinTheta_O * -sinTheta_i) / v)) * (cosTheta_i * (cosTheta_O * (single(1.0) / v)))) / (((single(0.5) / v) / sinh((single(1.0) / v))) ^ single(-1.0));
end

\frac{e^{-\frac{sinTheta_i \cdot sinTheta_O}{v}} \cdot \frac{cosTheta_i \cdot cosTheta_O}{v}}{\left(\sinh \left(\frac{1}{v}\right) \cdot 2\right) \cdot v}
↓
\frac{e^{\frac{sinTheta_O \cdot \left(-sinTheta_i\right)}{v}} \cdot \left(cosTheta_i \cdot \left(cosTheta_O \cdot \frac{1}{v}\right)\right)}{{\left(\frac{\frac{0.5}{v}}{\sinh \left(\frac{1}{v}\right)}\right)}^{-1}}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.5

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

  2. Applied egg-rr0.4

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

  3. Applied egg-rr0.4

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

  4. Applied egg-rr0.4

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

  5. Final simplification0.4

    \[\leadsto \frac{e^{\frac{sinTheta_O \cdot \left(-sinTheta_i\right)}{v}} \cdot \left(cosTheta_i \cdot \left(cosTheta_O \cdot \frac{1}{v}\right)\right)}{{\left(\frac{\frac{0.5}{v}}{\sinh \left(\frac{1}{v}\right)}\right)}^{-1}} \]

Alternatives

Alternative 1
Error0.4
Cost7168
\[\frac{e^{\frac{sinTheta_O \cdot \left(-sinTheta_i\right)}{v}} \cdot \left(cosTheta_i \cdot \left(cosTheta_O \cdot \frac{1}{v}\right)\right)}{\frac{\sinh \left(\frac{1}{v}\right) \cdot 2}{\frac{1}{v}}} \]
Alternative 2
Error0.4
Cost7104
\[\frac{e^{\frac{sinTheta_O \cdot \left(-sinTheta_i\right)}{v}} \cdot \left(cosTheta_i \cdot \left(cosTheta_O \cdot \frac{1}{v}\right)\right)}{v \cdot \left(\sinh \left(\frac{1}{v}\right) \cdot 2\right)} \]
Alternative 3
Error0.4
Cost7072
\[\left(cosTheta_i \cdot \frac{cosTheta_O}{v}\right) \cdot \left(\frac{1}{v} \cdot \frac{\frac{0.5}{\sinh \left(\frac{1}{v}\right)}}{e^{\frac{sinTheta_i \cdot sinTheta_O}{v}}}\right) \]
Alternative 4
Error0.5
Cost6944
\[\frac{\frac{1}{v} \cdot \left(cosTheta_O \cdot \frac{cosTheta_i}{v}\right)}{e^{\frac{1}{v}} - e^{\frac{-1}{v}}} \]
Alternative 5
Error0.5
Cost6880
\[\frac{cosTheta_i}{v \cdot v} \cdot \frac{cosTheta_O}{e^{\frac{1}{v}} - e^{\frac{-1}{v}}} \]
Alternative 6
Error0.5
Cost6880
\[\frac{cosTheta_i \cdot \frac{cosTheta_O}{v \cdot v}}{e^{\frac{1}{v}} - e^{\frac{-1}{v}}} \]
Alternative 7
Error0.6
Cost3616
\[\frac{0.5}{\sinh \left(\frac{1}{v}\right)} \cdot \frac{\frac{cosTheta_i \cdot cosTheta_O}{v}}{v} \]
Alternative 8
Error13.2
Cost288
\[\frac{\frac{0.5}{v}}{\frac{\frac{1}{cosTheta_O}}{cosTheta_i}} \]
Alternative 9
Error13.4
Cost224
\[0.5 \cdot \frac{cosTheta_i}{\frac{v}{cosTheta_O}} \]
Alternative 10
Error13.4
Cost224
\[0.5 \cdot \left(cosTheta_i \cdot \frac{cosTheta_O}{v}\right) \]
Alternative 11
Error13.4
Cost224
\[\frac{0.5}{v} \cdot \left(cosTheta_i \cdot cosTheta_O\right) \]
Alternative 12
Error13.3
Cost224
\[\frac{0.5}{\frac{v}{cosTheta_i \cdot cosTheta_O}} \]

Error

Reproduce?

herbie shell --seed 2023046 
(FPCore (cosTheta_i cosTheta_O sinTheta_i sinTheta_O v)
  :name "HairBSDF, Mp, upper"
  :precision binary32
  :pre (and (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))) (< 0.1 v)) (<= v 1.5707964))
  (/ (* (exp (- (/ (* sinTheta_i sinTheta_O) v))) (/ (* cosTheta_i cosTheta_O) v)) (* (* (sinh (/ 1.0 v)) 2.0) v)))