Average Error: 0.5 → 0.5
Time: 11.9s
Precision: binary32
\[\left(\left(cosTheta_i > 0.9999 \land cosTheta_i \leq 1\right) \land \left(2.328306437 \cdot 10^{-10} \leq u1 \land u1 \leq 1\right)\right) \land \left(2.328306437 \cdot 10^{-10} \leq u2 \land u2 \leq 1\right)\]
\[\sqrt{\frac{u1}{1 - u1}} \cdot \sin \left(6.28318530718 \cdot u2\right) \]
↓
\[\frac{\sin \left(\sqrt{\left(u2 \cdot u2\right) \cdot \sqrt[3]{61528.90838884378}}\right)}{\sqrt{\frac{1 - u1}{u1}}} \]
\sqrt{\frac{u1}{1 - u1}} \cdot \sin \left(6.28318530718 \cdot u2\right)
↓
\frac{\sin \left(\sqrt{\left(u2 \cdot u2\right) \cdot \sqrt[3]{61528.90838884378}}\right)}{\sqrt{\frac{1 - u1}{u1}}}

(FPCore (cosTheta_i u1 u2)
 :precision binary32
 (* (sqrt (/ u1 (- 1.0 u1))) (sin (* 6.28318530718 u2))))
↓
(FPCore (cosTheta_i u1 u2)
 :precision binary32
 (/
  (sin (sqrt (* (* u2 u2) (cbrt 61528.90838884378))))
  (sqrt (/ (- 1.0 u1) u1))))
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) {
	return sinf(sqrtf((u2 * u2) * cbrtf(61528.90838884378f))) / sqrtf((1.0f - u1) / u1);
}

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 egg0.5

    \[\leadsto \sqrt{\frac{u1}{1 - u1}} \cdot \sin \color{blue}{\left(\sqrt[3]{248.05021344244753 \cdot {u2}^{3}}\right)} \]

  3. Applied egg0.6

    \[\leadsto \color{blue}{\frac{\sqrt{u1}}{\sqrt{1 - u1}}} \cdot \sin \left(\sqrt[3]{248.05021344244753 \cdot {u2}^{3}}\right) \]

  4. Applied egg0.5

    \[\leadsto \color{blue}{\frac{\sin \left(u2 \cdot \sqrt[3]{248.05021344244753}\right)}{\sqrt{\frac{1 - u1}{u1}}}} \]

  5. Applied egg0.5

    \[\leadsto \frac{\sin \color{blue}{\left(\sqrt{\left(u2 \cdot u2\right) \cdot \sqrt[3]{61528.90838884378}}\right)}}{\sqrt{\frac{1 - u1}{u1}}} \]

  6. Final simplification0.5

    \[\leadsto \frac{\sin \left(\sqrt{\left(u2 \cdot u2\right) \cdot \sqrt[3]{61528.90838884378}}\right)}{\sqrt{\frac{1 - u1}{u1}}} \]

Reproduce

herbie shell --seed 2022125 
(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))))