Average Error: 0.5 → 0.4
Time: 20.3s
Precision: binary32
Cost: 7072
\[\left(\left(\left(\left(\left(-1 \leq cosTheta_i \land cosTheta_i \leq 1\right) \land \left(-1 \leq cosTheta_O \land cosTheta_O \leq 1\right)\right) \land \left(-1 \leq sinTheta_i \land sinTheta_i \leq 1\right)\right) \land \left(-1 \leq sinTheta_O \land sinTheta_O \leq 1\right)\right) \land 0.1 < v\right) \land v \leq 1.5707964\]
\[\frac{e^{-\frac{sinTheta_i \cdot sinTheta_O}{v}} \cdot \frac{cosTheta_i \cdot cosTheta_O}{v}}{\left(\sinh \left(\frac{1}{v}\right) \cdot 2\right) \cdot v} \]
↓
\[cosTheta_O \cdot \left(\frac{\frac{\frac{cosTheta_i}{v}}{e^{\frac{sinTheta_O}{\frac{v}{sinTheta_i}}}} \cdot -0.5}{\sinh \left(\frac{1}{v}\right)} \cdot \frac{-1}{v}\right) \]
(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
 (*
  cosTheta_O
  (*
   (/
    (* (/ (/ cosTheta_i v) (exp (/ sinTheta_O (/ v sinTheta_i)))) -0.5)
    (sinh (/ 1.0 v)))
   (/ -1.0 v))))
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 cosTheta_O * (((((cosTheta_i / v) / expf((sinTheta_O / (v / sinTheta_i)))) * -0.5f) / sinhf((1.0f / v))) * (-1.0f / v));
}

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 = costheta_o * (((((costheta_i / v) / exp((sintheta_o / (v / sintheta_i)))) * (-0.5e0)) / sinh((1.0e0 / v))) * ((-1.0e0) / v))
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(cosTheta_O * Float32(Float32(Float32(Float32(Float32(cosTheta_i / v) / exp(Float32(sinTheta_O / Float32(v / sinTheta_i)))) * Float32(-0.5)) / sinh(Float32(Float32(1.0) / v))) * Float32(Float32(-1.0) / v)))
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 = cosTheta_O * (((((cosTheta_i / v) / exp((sinTheta_O / (v / sinTheta_i)))) * single(-0.5)) / sinh((single(1.0) / v))) * (single(-1.0) / v));
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}
↓
cosTheta_O \cdot \left(\frac{\frac{\frac{cosTheta_i}{v}}{e^{\frac{sinTheta_O}{\frac{v}{sinTheta_i}}}} \cdot -0.5}{\sinh \left(\frac{1}{v}\right)} \cdot \frac{-1}{v}\right)

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. Simplified0.4

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

  3. Applied egg-rr0.4

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

  4. Final simplification0.4

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

Alternatives

Alternative 1
Error0.4
Cost7072
\[\frac{\frac{1}{v}}{\sinh \left(\frac{1}{v}\right)} \cdot \left(0.5 \cdot \frac{cosTheta_O \cdot cosTheta_i}{v \cdot e^{\frac{sinTheta_O \cdot sinTheta_i}{v}}}\right) \]
Alternative 2
Error0.4
Cost7040
\[\frac{e^{\frac{sinTheta_O \cdot \left(-sinTheta_i\right)}{v}} \cdot \left(cosTheta_i \cdot \frac{cosTheta_O}{v}\right)}{v \cdot \left(\sinh \left(\frac{1}{v}\right) \cdot 2\right)} \]
Alternative 3
Error0.5
Cost7008
\[\frac{0.5 \cdot \frac{cosTheta_O \cdot cosTheta_i}{v \cdot e^{\frac{sinTheta_O \cdot sinTheta_i}{v}}}}{v \cdot \sinh \left(\frac{1}{v}\right)} \]
Alternative 4
Error0.5
Cost7008
\[cosTheta_O \cdot \left(\frac{\frac{\frac{cosTheta_i}{v}}{e^{\frac{sinTheta_O}{\frac{v}{sinTheta_i}}}}}{v} \cdot \frac{0.5}{\sinh \left(\frac{1}{v}\right)}\right) \]
Alternative 5
Error0.5
Cost7008
\[\frac{cosTheta_O}{v \cdot \left(\sinh \left(\frac{1}{v}\right) \cdot \left(2 \cdot \left(e^{\frac{sinTheta_O}{\frac{v}{sinTheta_i}}} \cdot \frac{v}{cosTheta_i}\right)\right)\right)} \]
Alternative 6
Error0.5
Cost6944
\[cosTheta_O \cdot \left(\frac{1}{v} \cdot \frac{\frac{cosTheta_i}{v}}{e^{\frac{1}{v}} - e^{\frac{-1}{v}}}\right) \]
Alternative 7
Error0.6
Cost3680
\[cosTheta_i \cdot \frac{1}{\frac{\sinh \left(\frac{1}{v}\right) \cdot \left(2 \cdot \left(v \cdot v\right)\right)}{cosTheta_O}} \]
Alternative 8
Error0.5
Cost3616
\[\frac{\frac{cosTheta_i}{v}}{v} \cdot \left(0.5 \cdot \frac{cosTheta_O}{\sinh \left(\frac{1}{v}\right)}\right) \]
Alternative 9
Error0.5
Cost3616
\[cosTheta_i \cdot \frac{cosTheta_O}{\sinh \left(\frac{1}{v}\right) \cdot \left(2 \cdot \left(v \cdot v\right)\right)} \]
Alternative 10
Error11.6
Cost352
\[\frac{cosTheta_O \cdot cosTheta_i}{\frac{0.3333333333333333}{v} + v \cdot 2} \]
Alternative 11
Error14.0
Cost224
\[cosTheta_i \cdot \left(v \cdot \left(cosTheta_O \cdot 3\right)\right) \]
Alternative 12
Error14.0
Cost224
\[3 \cdot \left(cosTheta_i \cdot \left(cosTheta_O \cdot v\right)\right) \]
Alternative 13
Error13.5
Cost224
\[\frac{cosTheta_O}{v \cdot \frac{2}{cosTheta_i}} \]
Alternative 14
Error13.4
Cost224
\[\frac{cosTheta_O \cdot cosTheta_i}{v \cdot 2} \]
Alternative 15
Error13.3
Cost224
\[\frac{0.5}{\frac{v}{cosTheta_O \cdot cosTheta_i}} \]

Error

Reproduce

herbie shell --seed 2022284 
(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)))