Average Error: 0.3 → 0.3
Time: 10.4s
Precision: binary32
Cost: 13120
\[\left(\left(cosTheta_i > 0.9999 \land cosTheta_i \leq 1\right) \land \left(2.328306437 \cdot 10^{-10} \leq u1 \land u1 \leq 1\right)\right) \land \left(2.328306437 \cdot 10^{-10} \leq u2 \land u2 \leq 1\right)\]
\[\sqrt{\frac{u1}{1 - u1}} \cdot \cos \left(6.28318530718 \cdot u2\right) \]
↓
\[\sqrt{\frac{u1}{1 - u1}} \cdot \sqrt[3]{{\cos \left(6.28318530718 \cdot u2\right)}^{3}} \]
(FPCore (cosTheta_i u1 u2)
 :precision binary32
 (* (sqrt (/ u1 (- 1.0 u1))) (cos (* 6.28318530718 u2))))
↓
(FPCore (cosTheta_i u1 u2)
 :precision binary32
 (* (sqrt (/ u1 (- 1.0 u1))) (cbrt (pow (cos (* 6.28318530718 u2)) 3.0))))
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((u1 / (1.0f - u1))) * cbrtf(powf(cosf((6.28318530718f * u2)), 3.0f));
}

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(Float32(u1 / Float32(Float32(1.0) - u1))) * cbrt((cos(Float32(Float32(6.28318530718) * u2)) ^ Float32(3.0))))
end

\sqrt{\frac{u1}{1 - u1}} \cdot \cos \left(6.28318530718 \cdot u2\right)
↓
\sqrt{\frac{u1}{1 - u1}} \cdot \sqrt[3]{{\cos \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 0.3

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

  2. Applied egg-rr0.3

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

  3. Final simplification0.3

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

Alternatives

Alternative 1
Error3.2
Cost9892
\[\begin{array}{l} t_0 := \cos \left(6.28318530718 \cdot u2\right)\\ \mathbf{if}\;t_0 \leq 0.9999200105667114:\\ \;\;\;\;t_0 \cdot \sqrt{u1}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{u1}{1 - u1}}\\ \end{array} \]
Alternative 2
Error2.3
Cost6884
\[\begin{array}{l} \mathbf{if}\;\frac{u1}{1 - u1} \leq 0.0019000000320374966:\\ \;\;\;\;\cos \left(6.28318530718 \cdot u2\right) \cdot \sqrt{u1 \cdot \left(u1 + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{u1 \cdot \frac{1}{1 - u1}}\\ \end{array} \]
Alternative 3
Error0.3
Cost6688
\[\sqrt{\frac{u1}{1 - u1}} \cdot \cos \left(6.28318530718 \cdot u2\right) \]
Alternative 4
Error6.3
Cost3360
\[\sqrt{\frac{u1}{1 - u1}} \]
Alternative 5
Error11.7
Cost3232
\[\sqrt{u1} \]
Alternative 6
Error29.9
Cost32
\[0 \]

Error

Reproduce

herbie shell --seed 2022297 
(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))))