Average Error: 0.3 → 0.3
Time: 5.4s
Precision: binary32
\[\left(\left(cosTheta_i > 0.9999 \land cosTheta_i \leq 1\right) \land \left(2.328306437 \cdot 10^{-10} \leq u1 \land u1 \leq 1\right)\right) \land \left(2.328306437 \cdot 10^{-10} \leq u2 \land u2 \leq 1\right)\]
\[\sqrt{\frac{u1}{1 - u1}} \cdot \cos \left(6.28318530718 \cdot u2\right) \]
↓
\[\sqrt{\sqrt{{\left(\frac{u1}{1 - u1}\right)}^{2}}} \cdot \cos \log \left({\left(e^{6.28318530718}\right)}^{u2}\right) \]
(FPCore (cosTheta_i u1 u2)
 :precision binary32
 (* (sqrt (/ u1 (- 1.0 u1))) (cos (* 6.28318530718 u2))))
↓
(FPCore (cosTheta_i u1 u2)
 :precision binary32
 (*
  (sqrt (sqrt (pow (/ u1 (- 1.0 u1)) 2.0)))
  (cos (log (pow (exp 6.28318530718) u2)))))
float code(float cosTheta_i, float u1, float u2) {
	return sqrtf((u1 / (1.0f - u1))) * cosf((6.28318530718f * u2));
}
↓
float code(float cosTheta_i, float u1, float u2) {
	return sqrtf(sqrtf(powf((u1 / (1.0f - u1)), 2.0f))) * cosf(logf(powf(expf(6.28318530718f), u2)));
}

real(4) function code(costheta_i, u1, u2)
    real(4), intent (in) :: costheta_i
    real(4), intent (in) :: u1
    real(4), intent (in) :: u2
    code = sqrt((u1 / (1.0e0 - u1))) * cos((6.28318530718e0 * u2))
end function
↓
real(4) function code(costheta_i, u1, u2)
    real(4), intent (in) :: costheta_i
    real(4), intent (in) :: u1
    real(4), intent (in) :: u2
    code = sqrt(sqrt(((u1 / (1.0e0 - u1)) ** 2.0e0))) * cos(log((exp(6.28318530718e0) ** u2)))
end function

function code(cosTheta_i, u1, u2)
	return Float32(sqrt(Float32(u1 / Float32(Float32(1.0) - u1))) * cos(Float32(Float32(6.28318530718) * u2)))
end
↓
function code(cosTheta_i, u1, u2)
	return Float32(sqrt(sqrt((Float32(u1 / Float32(Float32(1.0) - u1)) ^ Float32(2.0)))) * cos(log((exp(Float32(6.28318530718)) ^ u2))))
end

function tmp = code(cosTheta_i, u1, u2)
	tmp = sqrt((u1 / (single(1.0) - u1))) * cos((single(6.28318530718) * u2));
end
↓
function tmp = code(cosTheta_i, u1, u2)
	tmp = sqrt(sqrt(((u1 / (single(1.0) - u1)) ^ single(2.0)))) * cos(log((exp(single(6.28318530718)) ^ u2)));
end

\sqrt{\frac{u1}{1 - u1}} \cdot \cos \left(6.28318530718 \cdot u2\right)
↓
\sqrt{\sqrt{{\left(\frac{u1}{1 - u1}\right)}^{2}}} \cdot \cos \log \left({\left(e^{6.28318530718}\right)}^{u2}\right)

Error

Bits error versus cosTheta_i

Bits error versus u1

Bits error versus u2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\sqrt{\frac{u1}{1 - u1}} \cdot \cos \left(6.28318530718 \cdot u2\right) \]

  2. Applied egg-rr0.3

    \[\leadsto \sqrt{\frac{u1}{1 - u1}} \cdot \cos \color{blue}{\log \left({\left(e^{6.28318530718}\right)}^{u2}\right)} \]

  3. Applied egg-rr0.4

    \[\leadsto \sqrt{\color{blue}{\frac{1}{1 - u1} \cdot u1}} \cdot \cos \log \left({\left(e^{6.28318530718}\right)}^{u2}\right) \]

  4. Applied egg-rr0.3

    \[\leadsto \sqrt{\color{blue}{\sqrt{{\left(\frac{u1}{1 - u1}\right)}^{2}}}} \cdot \cos \log \left({\left(e^{6.28318530718}\right)}^{u2}\right) \]

  5. Final simplification0.3

    \[\leadsto \sqrt{\sqrt{{\left(\frac{u1}{1 - u1}\right)}^{2}}} \cdot \cos \log \left({\left(e^{6.28318530718}\right)}^{u2}\right) \]

Reproduce

herbie shell --seed 2022171 
(FPCore (cosTheta_i u1 u2)
  :name "Trowbridge-Reitz Sample, near normal, slope_x"
  :precision binary32
  :pre (and (and (and (> cosTheta_i 0.9999) (<= cosTheta_i 1.0)) (and (<= 2.328306437e-10 u1) (<= u1 1.0))) (and (<= 2.328306437e-10 u2) (<= u2 1.0)))
  (* (sqrt (/ u1 (- 1.0 u1))) (cos (* 6.28318530718 u2))))