Average Error: 0.5 → 0.5
Time: 15.9s
Precision: binary32
Cost: 13152
\[\left(\left(cosTheta_i > 0.9999 \land cosTheta_i \leq 1\right) \land \left(2.328306437 \cdot 10^{-10} \leq u1 \land u1 \leq 1\right)\right) \land \left(2.328306437 \cdot 10^{-10} \leq u2 \land u2 \leq 1\right)\]
\[\sqrt{\frac{u1}{1 - u1}} \cdot \sin \left(6.28318530718 \cdot u2\right) \]
↓
\[\sqrt[3]{{\left(\frac{1}{u1} + -1\right)}^{-1.5} \cdot {\sin \left(6.28318530718 \cdot u2\right)}^{3}} \]
(FPCore (cosTheta_i u1 u2)
 :precision binary32
 (* (sqrt (/ u1 (- 1.0 u1))) (sin (* 6.28318530718 u2))))
↓
(FPCore (cosTheta_i u1 u2)
 :precision binary32
 (cbrt
  (* (pow (+ (/ 1.0 u1) -1.0) -1.5) (pow (sin (* 6.28318530718 u2)) 3.0))))
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) {
	return cbrtf((powf(((1.0f / u1) + -1.0f), -1.5f) * powf(sinf((6.28318530718f * u2)), 3.0f)));
}

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)
	return cbrt(Float32((Float32(Float32(Float32(1.0) / u1) + Float32(-1.0)) ^ Float32(-1.5)) * (sin(Float32(Float32(6.28318530718) * u2)) ^ Float32(3.0))))
end

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

Error

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-rr0.6

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

  3. Applied egg-rr0.5

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

  4. Final simplification0.5

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

Alternatives

Alternative 1
Error1.9
Cost6820
\[\begin{array}{l} \mathbf{if}\;6.28318530718 \cdot u2 \leq 0.005799999926239252:\\ \;\;\;\;\sqrt{\frac{1}{\frac{1}{u1} + -1} \cdot \left(39.47841760436263 \cdot \left(u2 \cdot u2\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sin \left(6.28318530718 \cdot u2\right) \cdot \sqrt{u1 + u1 \cdot u1}\\ \end{array} \]
Alternative 2
Error0.6
Cost6720
\[\sin \left(6.28318530718 \cdot u2\right) \cdot {\left(\frac{1}{u1} + -1\right)}^{-0.5} \]
Alternative 3
Error3.1
Cost6692
\[\begin{array}{l} \mathbf{if}\;6.28318530718 \cdot u2 \leq 0.011599999852478504:\\ \;\;\;\;\sqrt{\frac{1}{\frac{1}{u1} + -1} \cdot \left(39.47841760436263 \cdot \left(u2 \cdot u2\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sin \left(6.28318530718 \cdot u2\right) \cdot \sqrt{u1}\\ \end{array} \]
Alternative 4
Error0.5
Cost6688
\[\sin \left(6.28318530718 \cdot u2\right) \cdot \sqrt{\frac{u1}{1 - u1}} \]
Alternative 5
Error6.0
Cost3616
\[\sqrt{\frac{1}{\frac{1}{u1} + -1} \cdot \left(39.47841760436263 \cdot \left(u2 \cdot u2\right)\right)} \]
Alternative 6
Error6.0
Cost3552
\[\sqrt{\frac{u2 \cdot \left(u2 \cdot 39.47841760436263\right)}{\frac{1}{u1} + -1}} \]
Alternative 7
Error5.9
Cost3552
\[\sqrt{39.47841760436263 \cdot \frac{u2 \cdot u2}{\frac{1}{u1} + -1}} \]
Alternative 8
Error6.1
Cost3520
\[6.28318530718 \cdot \left(u2 \cdot {\left(\frac{1}{u1} + -1\right)}^{-0.5}\right) \]
Alternative 9
Error8.6
Cost3488
\[6.28318530718 \cdot \left(u2 \cdot \sqrt{u1 \cdot \left(1 + u1\right)}\right) \]
Alternative 10
Error6.1
Cost3488
\[\left(6.28318530718 \cdot u2\right) \cdot \sqrt{\frac{u1}{1 - u1}} \]
Alternative 11
Error6.0
Cost3488
\[6.28318530718 \cdot \left(u2 \cdot \sqrt{\frac{u1}{1 - u1}}\right) \]
Alternative 12
Error11.3
Cost3424
\[6.28318530718 \cdot \sqrt{u1 \cdot \left(u2 \cdot u2\right)} \]
Alternative 13
Error25.7
Cost3360
\[u1 \cdot \sin \left(6.28318530718 \cdot u2\right) \]
Alternative 14
Error11.3
Cost3360
\[6.28318530718 \cdot \left(u2 \cdot \sqrt{u1}\right) \]
Alternative 15
Error25.8
Cost160
\[6.28318530718 \cdot \left(u1 \cdot u2\right) \]

Error

Reproduce

herbie shell --seed 2022294 
(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))))