Average Error: 0.5 → 0.5
Time: 8.8s
Precision: binary32
\[\left(\left(cosTheta_i > 0.9999 \land cosTheta_i \leq 1\right) \land \left(2.328306437 \cdot 10^{-10} \leq u1 \land u1 \leq 1\right)\right) \land \left(2.328306437 \cdot 10^{-10} \leq u2 \land u2 \leq 1\right)\]
\[\sqrt{\frac{u1}{1 - u1}} \cdot \sin \left(6.28318530718 \cdot u2\right) \]
↓
\[\begin{array}{l} t_0 := \sqrt[3]{\sin \left(6.28318530718 \cdot u2\right)}\\ \sqrt[3]{{\left(\frac{u1}{1 - u1}\right)}^{1.5} \cdot \left({t_0}^{2} \cdot \left(t_0 \cdot {\sin \left(\sqrt{39.47841760436263 \cdot \left(u2 \cdot u2\right)}\right)}^{2}\right)\right)} \end{array} \]
(FPCore (cosTheta_i u1 u2)
 :precision binary32
 (* (sqrt (/ u1 (- 1.0 u1))) (sin (* 6.28318530718 u2))))
↓
(FPCore (cosTheta_i u1 u2)
 :precision binary32
 (let* ((t_0 (cbrt (sin (* 6.28318530718 u2)))))
   (cbrt
    (*
     (pow (/ u1 (- 1.0 u1)) 1.5)
     (*
      (pow t_0 2.0)
      (* t_0 (pow (sin (sqrt (* 39.47841760436263 (* u2 u2)))) 2.0)))))))
float code(float cosTheta_i, float u1, float u2) {
	return sqrtf((u1 / (1.0f - u1))) * sinf((6.28318530718f * u2));
}
↓
float code(float cosTheta_i, float u1, float u2) {
	float t_0 = cbrtf(sinf((6.28318530718f * u2)));
	return cbrtf((powf((u1 / (1.0f - u1)), 1.5f) * (powf(t_0, 2.0f) * (t_0 * powf(sinf(sqrtf((39.47841760436263f * (u2 * u2)))), 2.0f)))));
}

function code(cosTheta_i, u1, u2)
	return Float32(sqrt(Float32(u1 / Float32(Float32(1.0) - u1))) * sin(Float32(Float32(6.28318530718) * u2)))
end
↓
function code(cosTheta_i, u1, u2)
	t_0 = cbrt(sin(Float32(Float32(6.28318530718) * u2)))
	return cbrt(Float32((Float32(u1 / Float32(Float32(1.0) - u1)) ^ Float32(1.5)) * Float32((t_0 ^ Float32(2.0)) * Float32(t_0 * (sin(sqrt(Float32(Float32(39.47841760436263) * Float32(u2 * u2)))) ^ Float32(2.0))))))
end

\sqrt{\frac{u1}{1 - u1}} \cdot \sin \left(6.28318530718 \cdot u2\right)
↓
\begin{array}{l}
t_0 := \sqrt[3]{\sin \left(6.28318530718 \cdot u2\right)}\\
\sqrt[3]{{\left(\frac{u1}{1 - u1}\right)}^{1.5} \cdot \left({t_0}^{2} \cdot \left(t_0 \cdot {\sin \left(\sqrt{39.47841760436263 \cdot \left(u2 \cdot u2\right)}\right)}^{2}\right)\right)}
\end{array}

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 0.5

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

  2. Applied egg-rr0.5

    \[\leadsto \color{blue}{\sqrt[3]{{\left(\frac{u1}{1 - u1}\right)}^{1.5} \cdot {\sin \left(6.28318530718 \cdot u2\right)}^{3}}} \]

  3. Applied egg-rr0.6

    \[\leadsto \sqrt[3]{{\left(\frac{u1}{1 - u1}\right)}^{1.5} \cdot \color{blue}{\left({\left(\sqrt[3]{\sin \left(6.28318530718 \cdot u2\right)}\right)}^{2} \cdot \left(\sqrt[3]{\sin \left(6.28318530718 \cdot u2\right)} \cdot {\sin \left(6.28318530718 \cdot u2\right)}^{2}\right)\right)}} \]

  4. Applied egg-rr0.5

    \[\leadsto \sqrt[3]{{\left(\frac{u1}{1 - u1}\right)}^{1.5} \cdot \left({\left(\sqrt[3]{\sin \left(6.28318530718 \cdot u2\right)}\right)}^{2} \cdot \left(\sqrt[3]{\sin \left(6.28318530718 \cdot u2\right)} \cdot {\sin \color{blue}{\left(\sqrt{39.47841760436263 \cdot \left(u2 \cdot u2\right)}\right)}}^{2}\right)\right)} \]

  5. Final simplification0.5

    \[\leadsto \sqrt[3]{{\left(\frac{u1}{1 - u1}\right)}^{1.5} \cdot \left({\left(\sqrt[3]{\sin \left(6.28318530718 \cdot u2\right)}\right)}^{2} \cdot \left(\sqrt[3]{\sin \left(6.28318530718 \cdot u2\right)} \cdot {\sin \left(\sqrt{39.47841760436263 \cdot \left(u2 \cdot u2\right)}\right)}^{2}\right)\right)} \]

Reproduce

herbie shell --seed 2022133 
(FPCore (cosTheta_i u1 u2)
  :name "Trowbridge-Reitz Sample, near normal, slope_y"
  :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))) (sin (* 6.28318530718 u2))))