?

Average Accuracy: 99.0% → 99.0%
Time: 16.5s
Precision: binary32
Cost: 20000

?

\[\left(2.328306437 \cdot 10^{-10} \leq u \land u \leq 1\right) \land \left(0 \leq s \land s \leq 1.0651631\right)\]
\[\left(-s\right) \cdot \log \left(\frac{1}{u \cdot \left(\frac{1}{1 + e^{\frac{-\pi}{s}}} - \frac{1}{1 + e^{\frac{\pi}{s}}}\right) + \frac{1}{1 + e^{\frac{\pi}{s}}}} - 1\right) \]
↓
\[s \cdot \left(-\log \left(-1 + \frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} + \frac{1 - u}{1 + \sqrt[3]{e^{\frac{\frac{\pi}{0.3333333333333333}}{s}}}}}\right)\right) \]
(FPCore (u s)
 :precision binary32
 (*
  (- s)
  (log
   (-
    (/
     1.0
     (+
      (*
       u
       (- (/ 1.0 (+ 1.0 (exp (/ (- PI) s)))) (/ 1.0 (+ 1.0 (exp (/ PI s))))))
      (/ 1.0 (+ 1.0 (exp (/ PI s))))))
    1.0))))
↓
(FPCore (u s)
 :precision binary32
 (*
  s
  (-
   (log
    (+
     -1.0
     (/
      1.0
      (+
       (/ u (+ 1.0 (exp (/ (- PI) s))))
       (/
        (- 1.0 u)
        (+ 1.0 (cbrt (exp (/ (/ PI 0.3333333333333333) s))))))))))))
float code(float u, float s) {
	return -s * logf(((1.0f / ((u * ((1.0f / (1.0f + expf((-((float) M_PI) / s)))) - (1.0f / (1.0f + expf((((float) M_PI) / s)))))) + (1.0f / (1.0f + expf((((float) M_PI) / s)))))) - 1.0f));
}
↓
float code(float u, float s) {
	return s * -logf((-1.0f + (1.0f / ((u / (1.0f + expf((-((float) M_PI) / s)))) + ((1.0f - u) / (1.0f + cbrtf(expf(((((float) M_PI) / 0.3333333333333333f) / s)))))))));
}

function code(u, s)
	return Float32(Float32(-s) * log(Float32(Float32(Float32(1.0) / Float32(Float32(u * Float32(Float32(Float32(1.0) / Float32(Float32(1.0) + exp(Float32(Float32(-Float32(pi)) / s)))) - Float32(Float32(1.0) / Float32(Float32(1.0) + exp(Float32(Float32(pi) / s)))))) + Float32(Float32(1.0) / Float32(Float32(1.0) + exp(Float32(Float32(pi) / s)))))) - Float32(1.0))))
end
↓
function code(u, s)
	return Float32(s * Float32(-log(Float32(Float32(-1.0) + Float32(Float32(1.0) / Float32(Float32(u / Float32(Float32(1.0) + exp(Float32(Float32(-Float32(pi)) / s)))) + Float32(Float32(Float32(1.0) - u) / Float32(Float32(1.0) + cbrt(exp(Float32(Float32(Float32(pi) / Float32(0.3333333333333333)) / s)))))))))))
end

\left(-s\right) \cdot \log \left(\frac{1}{u \cdot \left(\frac{1}{1 + e^{\frac{-\pi}{s}}} - \frac{1}{1 + e^{\frac{\pi}{s}}}\right) + \frac{1}{1 + e^{\frac{\pi}{s}}}} - 1\right)
↓
s \cdot \left(-\log \left(-1 + \frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} + \frac{1 - u}{1 + \sqrt[3]{e^{\frac{\frac{\pi}{0.3333333333333333}}{s}}}}}\right)\right)

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 99.0%

    \[\left(-s\right) \cdot \log \left(\frac{1}{u \cdot \left(\frac{1}{1 + e^{\frac{-\pi}{s}}} - \frac{1}{1 + e^{\frac{\pi}{s}}}\right) + \frac{1}{1 + e^{\frac{\pi}{s}}}} - 1\right) \]

  2. Simplified99.0%

    \[\leadsto \color{blue}{\left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + e^{\frac{\pi}{s}}}} + -1\right)} \]
    Proof

    [Start]99.0

    \[ \left(-s\right) \cdot \log \left(\frac{1}{u \cdot \left(\frac{1}{1 + e^{\frac{-\pi}{s}}} - \frac{1}{1 + e^{\frac{\pi}{s}}}\right) + \frac{1}{1 + e^{\frac{\pi}{s}}}} - 1\right) \]

    sub-neg [=>]99.0

    \[ \left(-s\right) \cdot \log \color{blue}{\left(\frac{1}{u \cdot \left(\frac{1}{1 + e^{\frac{-\pi}{s}}} - \frac{1}{1 + e^{\frac{\pi}{s}}}\right) + \frac{1}{1 + e^{\frac{\pi}{s}}}} + \left(-1\right)\right)} \]

  3. Applied egg-rr99.0%

    \[\leadsto \left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + \color{blue}{\sqrt[3]{e^{\frac{\pi}{s} \cdot 3}}}}} + -1\right) \]
    Proof

    [Start]99.0

    \[ \left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + e^{\frac{\pi}{s}}}} + -1\right) \]

    add-cbrt-cube [=>]99.0

    \[ \left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + \color{blue}{\sqrt[3]{\left(e^{\frac{\pi}{s}} \cdot e^{\frac{\pi}{s}}\right) \cdot e^{\frac{\pi}{s}}}}}} + -1\right) \]

    unpow3 [<=]99.0

    \[ \left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + \sqrt[3]{\color{blue}{{\left(e^{\frac{\pi}{s}}\right)}^{3}}}}} + -1\right) \]

    pow-exp [=>]99.0

    \[ \left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + \sqrt[3]{\color{blue}{e^{\frac{\pi}{s} \cdot 3}}}}} + -1\right) \]

  4. Applied egg-rr99.0%

    \[\leadsto \left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + \sqrt[3]{e^{\color{blue}{\frac{\frac{\pi}{0.3333333333333333}}{s}}}}}} + -1\right) \]
    Proof

    [Start]99.0

    \[ \left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + \sqrt[3]{e^{\frac{\pi}{s} \cdot 3}}}} + -1\right) \]

    associate-*l/ [=>]99.0

    \[ \left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + \sqrt[3]{e^{\color{blue}{\frac{\pi \cdot 3}{s}}}}}} + -1\right) \]

    *-un-lft-identity [=>]99.0

    \[ \left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + \sqrt[3]{e^{\frac{\pi \cdot 3}{\color{blue}{1 \cdot s}}}}}} + -1\right) \]

    associate-/r* [=>]99.0

    \[ \left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + \sqrt[3]{e^{\color{blue}{\frac{\frac{\pi \cdot 3}{1}}{s}}}}}} + -1\right) \]

    associate-/l* [=>]99.0

    \[ \left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + \sqrt[3]{e^{\frac{\color{blue}{\frac{\pi}{\frac{1}{3}}}}{s}}}}} + -1\right) \]

    metadata-eval [=>]99.0

    \[ \left(-s\right) \cdot \log \left(\frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} - \frac{u + -1}{1 + \sqrt[3]{e^{\frac{\frac{\pi}{\color{blue}{0.3333333333333333}}}{s}}}}} + -1\right) \]

  5. Final simplification99.0%

    \[\leadsto s \cdot \left(-\log \left(-1 + \frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} + \frac{1 - u}{1 + \sqrt[3]{e^{\frac{\frac{\pi}{0.3333333333333333}}{s}}}}}\right)\right) \]

Alternatives

Alternative 1
Accuracy99.0%
Cost19936
\[\left(-s\right) \cdot \log \left(-1 + \frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} + \frac{1 - u}{1 + {e}^{\left(\frac{\pi}{s}\right)}}}\right) \]
Alternative 2
Accuracy99.0%
Cost16800
\[s \cdot \left(-\log \left(-1 + \frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} + \frac{1 - u}{1 + e^{\pi \cdot \frac{1}{s}}}}\right)\right) \]
Alternative 3
Accuracy99.0%
Cost16736
\[\left(-s\right) \cdot \log \left(-1 + \frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} + \frac{1 - u}{1 + e^{\frac{\pi}{s}}}}\right) \]
Alternative 4
Accuracy86.3%
Cost13600
\[\left(-s\right) \cdot \log \left(-1 + \frac{1}{\frac{u}{1 + e^{\frac{-\pi}{s}}} + \frac{1 - u}{1 + \left(1 + \frac{\pi}{s}\right)}}\right) \]
Alternative 5
Accuracy37.1%
Cost10176
\[s \cdot \left(-\log \left(-1 + \frac{\frac{1}{u}}{\frac{1}{1 + e^{\frac{-\pi}{s}}} + -0.5}\right)\right) \]
Alternative 6
Accuracy16.2%
Cost6848
\[s \cdot \left(-4 \cdot \left(u \cdot \left(0.5 + \frac{-1}{1 + e^{\frac{\pi}{s}}}\right)\right)\right) \]
Alternative 7
Accuracy11.6%
Cost3584
\[4 \cdot \frac{1}{\frac{1}{\pi \cdot \left(-0.25 + u \cdot 0.5\right)}} \]
Alternative 8
Accuracy11.6%
Cost3456
\[4 \cdot \left(\pi \cdot \left(-0.25 + u \cdot 0.5\right)\right) \]
Alternative 9
Accuracy11.4%
Cost3232
\[-\pi \]

Error

Reproduce?

herbie shell --seed 2023137 
(FPCore (u s)
  :name "Sample trimmed logistic on [-pi, pi]"
  :precision binary32
  :pre (and (and (<= 2.328306437e-10 u) (<= u 1.0)) (and (<= 0.0 s) (<= s 1.0651631)))
  (* (- s) (log (- (/ 1.0 (+ (* u (- (/ 1.0 (+ 1.0 (exp (/ (- PI) s)))) (/ 1.0 (+ 1.0 (exp (/ PI s)))))) (/ 1.0 (+ 1.0 (exp (/ PI s)))))) 1.0))))