Average Error: 12.4 → 0.2
Time: 13.5s
Precision: binary32
Cost: 3392
\[\left(0 \leq s \land s \leq 256\right) \land \left(2.328306437 \cdot 10^{-10} \leq u \land u \leq 0.25\right)\]
\[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
↓
\[s \cdot \left(-\mathsf{log1p}\left(u \cdot -4\right)\right) \]
(FPCore (s u) :precision binary32 (* s (log (/ 1.0 (- 1.0 (* 4.0 u))))))
↓
(FPCore (s u) :precision binary32 (* s (- (log1p (* u -4.0)))))
float code(float s, float u) {
	return s * logf((1.0f / (1.0f - (4.0f * u))));
}
↓
float code(float s, float u) {
	return s * -log1pf((u * -4.0f));
}

function code(s, u)
	return Float32(s * log(Float32(Float32(1.0) / Float32(Float32(1.0) - Float32(Float32(4.0) * u)))))
end
↓
function code(s, u)
	return Float32(s * Float32(-log1p(Float32(u * Float32(-4.0)))))
end

s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right)
↓
s \cdot \left(-\mathsf{log1p}\left(u \cdot -4\right)\right)

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.4

    \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]

  2. Simplified0.2

    \[\leadsto \color{blue}{s \cdot \left(-\mathsf{log1p}\left(u \cdot -4\right)\right)} \]
    Proof
    (*.f32 s (neg.f32 (log1p.f32 (*.f32 u -4)))): 0 points increase in error, 0 points decrease in error
    (*.f32 s (neg.f32 (log1p.f32 (*.f32 u (Rewrite<= metadata-eval (neg.f32 4)))))): 0 points increase in error, 0 points decrease in error
    (*.f32 s (neg.f32 (log1p.f32 (Rewrite<= distribute-rgt-neg-in_binary32 (neg.f32 (*.f32 u 4)))))): 0 points increase in error, 0 points decrease in error
    (*.f32 s (neg.f32 (log1p.f32 (neg.f32 (Rewrite<= *-commutative_binary32 (*.f32 4 u)))))): 0 points increase in error, 0 points decrease in error
    (*.f32 s (neg.f32 (Rewrite<= log1p-def_binary32 (log.f32 (+.f32 1 (neg.f32 (*.f32 4 u))))))): 234 points increase in error, 1 points decrease in error
    (*.f32 s (neg.f32 (log.f32 (Rewrite<= sub-neg_binary32 (-.f32 1 (*.f32 4 u)))))): 0 points increase in error, 0 points decrease in error
    (*.f32 s (Rewrite<= log-rec_binary32 (log.f32 (/.f32 1 (-.f32 1 (*.f32 4 u)))))): 144 points increase in error, 43 points decrease in error

  3. Final simplification0.2

    \[\leadsto s \cdot \left(-\mathsf{log1p}\left(u \cdot -4\right)\right) \]

Alternatives

Alternative 1
Error2.7
Cost480
\[s \cdot \left(u \cdot 4 + \left(u \cdot u\right) \cdot \left(u \cdot 21.333333333333332 + 8\right)\right) \]
Alternative 2
Error4.2
Cost352
\[u \cdot \left(s \cdot 4 + 8 \cdot \left(s \cdot u\right)\right) \]
Alternative 3
Error4.2
Cost352
\[s \cdot \left(u \cdot 4 + \left(u \cdot u\right) \cdot 8\right) \]
Alternative 4
Error4.3
Cost288
\[\left(s \cdot u\right) \cdot \left(4 + u \cdot 8\right) \]
Alternative 5
Error4.2
Cost288
\[u \cdot \left(s \cdot \left(4 + u \cdot 8\right)\right) \]
Alternative 6
Error8.3
Cost160
\[s \cdot \left(u \cdot 4\right) \]

Error

Reproduce

herbie shell --seed 2022318 
(FPCore (s u)
  :name "Disney BSSRDF, sample scattering profile, lower"
  :precision binary32
  :pre (and (and (<= 0.0 s) (<= s 256.0)) (and (<= 2.328306437e-10 u) (<= u 0.25)))
  (* s (log (/ 1.0 (- 1.0 (* 4.0 u))))))