Disney BSSRDF, sample scattering profile, lower

Percentage Accurate: 61.6% → 99.4%

Time: 10.5s

Alternatives: 13

Speedup: 21.8×

Specification

\[\left(0 \leq s \land s \leq 256\right) \land \left(2.328306437 \cdot 10^{-10} \leq u \land u \leq 0.25\right)\]

Math

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

FPCore

(FPCore (s u) :precision binary32 (* s (log (/ 1.0 (- 1.0 (* 4.0 u))))))

C

float code(float s, float u) {
	return s * logf((1.0f / (1.0f - (4.0f * u))));
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = s * log((1.0e0 / (1.0e0 - (4.0e0 * u))))
end function

Julia

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

MATLAB

function tmp = code(s, u)
	tmp = s * log((single(1.0) / (single(1.0) - (single(4.0) * u))));
end

Initial Program: 61.6% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (s u) :precision binary32 (* s (log (/ 1.0 (- 1.0 (* 4.0 u))))))

C

float code(float s, float u) {
	return s * logf((1.0f / (1.0f - (4.0f * u))));
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = s * log((1.0e0 / (1.0e0 - (4.0e0 * u))))
end function

Julia

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

MATLAB

function tmp = code(s, u)
	tmp = s * log((single(1.0) / (single(1.0) - (single(4.0) * u))));
end

Alternative 1: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ s \cdot \left(-\mathsf{log1p}\left(u \cdot -4\right)\right) \end{array} \]

FPCore

(FPCore (s u) :precision binary32 (* s (- (log1p (* u -4.0)))))

C

float code(float s, float u) {
	return s * -log1pf((u * -4.0f));
}

Julia

function code(s, u)
	return Float32(s * Float32(-log1p(Float32(u * Float32(-4.0)))))
end

Derivation

1. Initial program 64.4%

   \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
2. Step-by-step derivation

   1. log-rec 66.9%

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

   2. sub-neg 66.9%

      \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4 \cdot u\right)\right)}\right) \]

   3. distribute-rgt-neg-out 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{4 \cdot \left(-u\right)}\right)\right) \]

   4. log1p-def 99.5%

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

   5. distribute-rgt-neg-in 99.5%

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

   6. *-commutative 99.5%

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

   7. distribute-rgt-neg-in 99.5%

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

   8. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 2: 91.0% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ s \cdot \left(u \cdot \left(4 + u \cdot \left(8 - u \cdot -21.333333333333332\right)\right)\right) \end{array} \]

FPCore

(FPCore (s u)
 :precision binary32
 (* s (* u (+ 4.0 (* u (- 8.0 (* u -21.333333333333332)))))))

C

float code(float s, float u) {
	return s * (u * (4.0f + (u * (8.0f - (u * -21.333333333333332f)))));
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = s * (u * (4.0e0 + (u * (8.0e0 - (u * (-21.333333333333332e0))))))
end function

Julia

function code(s, u)
	return Float32(s * Float32(u * Float32(Float32(4.0) + Float32(u * Float32(Float32(8.0) - Float32(u * Float32(-21.333333333333332)))))))
end

MATLAB

function tmp = code(s, u)
	tmp = s * (u * (single(4.0) + (u * (single(8.0) - (u * single(-21.333333333333332))))));
end

Derivation

1. Initial program 64.4%

   \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
2. Step-by-step derivation

   1. log-rec 66.9%

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

   2. remove-double-neg 66.9%

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

   3. cancel-sign-sub-inv 66.9%

      \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

   4. remove-double-neg 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

   5. metadata-eval 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

3. Simplified 66.9%

   \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

4. Taylor expanded in u around 0 90.5%

   \[\leadsto s \cdot \left(-\color{blue}{\left(-21.333333333333332 \cdot {u}^{3} + \left(-8 \cdot {u}^{2} + -4 \cdot u\right)\right)}\right) \]
5. Step-by-step derivation

   1. associate-+r+ 90.6%

      \[\leadsto s \cdot \left(-\color{blue}{\left(\left(-21.333333333333332 \cdot {u}^{3} + -8 \cdot {u}^{2}\right) + -4 \cdot u\right)}\right) \]

   2. +-commutative 90.6%

      \[\leadsto s \cdot \left(-\color{blue}{\left(-4 \cdot u + \left(-21.333333333333332 \cdot {u}^{3} + -8 \cdot {u}^{2}\right)\right)}\right) \]

   3. *-commutative 90.6%

      \[\leadsto s \cdot \left(-\left(\color{blue}{u \cdot -4} + \left(-21.333333333333332 \cdot {u}^{3} + -8 \cdot {u}^{2}\right)\right)\right) \]

   4. unpow3 90.6%

      \[\leadsto s \cdot \left(-\left(u \cdot -4 + \left(-21.333333333333332 \cdot \color{blue}{\left(\left(u \cdot u\right) \cdot u\right)} + -8 \cdot {u}^{2}\right)\right)\right) \]

   5. unpow2 90.6%

      \[\leadsto s \cdot \left(-\left(u \cdot -4 + \left(-21.333333333333332 \cdot \left(\color{blue}{{u}^{2}} \cdot u\right) + -8 \cdot {u}^{2}\right)\right)\right) \]

   6. associate-*r* 90.6%

      \[\leadsto s \cdot \left(-\left(u \cdot -4 + \left(\color{blue}{\left(-21.333333333333332 \cdot {u}^{2}\right) \cdot u} + -8 \cdot {u}^{2}\right)\right)\right) \]

   7. *-commutative 90.6%

      \[\leadsto s \cdot \left(-\left(u \cdot -4 + \left(\color{blue}{u \cdot \left(-21.333333333333332 \cdot {u}^{2}\right)} + -8 \cdot {u}^{2}\right)\right)\right) \]

   8. *-commutative 90.6%

      \[\leadsto s \cdot \left(-\left(u \cdot -4 + \left(u \cdot \left(-21.333333333333332 \cdot {u}^{2}\right) + \color{blue}{{u}^{2} \cdot -8}\right)\right)\right) \]

   9. unpow2 90.6%

      \[\leadsto s \cdot \left(-\left(u \cdot -4 + \left(u \cdot \left(-21.333333333333332 \cdot {u}^{2}\right) + \color{blue}{\left(u \cdot u\right)} \cdot -8\right)\right)\right) \]

   10. associate-*l* 90.6%

       \[\leadsto s \cdot \left(-\left(u \cdot -4 + \left(u \cdot \left(-21.333333333333332 \cdot {u}^{2}\right) + \color{blue}{u \cdot \left(u \cdot -8\right)}\right)\right)\right) \]

   11. distribute-lft-out 90.6%

       \[\leadsto s \cdot \left(-\left(u \cdot -4 + \color{blue}{u \cdot \left(-21.333333333333332 \cdot {u}^{2} + u \cdot -8\right)}\right)\right) \]

   12. distribute-lft-out 90.4%

       \[\leadsto s \cdot \left(-\color{blue}{u \cdot \left(-4 + \left(-21.333333333333332 \cdot {u}^{2} + u \cdot -8\right)\right)}\right) \]

   13. +-commutative 90.4%

       \[\leadsto s \cdot \left(-u \cdot \left(-4 + \color{blue}{\left(u \cdot -8 + -21.333333333333332 \cdot {u}^{2}\right)}\right)\right) \]

   14. *-commutative 90.4%

       \[\leadsto s \cdot \left(-u \cdot \left(-4 + \left(\color{blue}{-8 \cdot u} + -21.333333333333332 \cdot {u}^{2}\right)\right)\right) \]

   15. unpow2 90.4%

       \[\leadsto s \cdot \left(-u \cdot \left(-4 + \left(-8 \cdot u + -21.333333333333332 \cdot \color{blue}{\left(u \cdot u\right)}\right)\right)\right) \]

   16. associate-*r* 90.4%

       \[\leadsto s \cdot \left(-u \cdot \left(-4 + \left(-8 \cdot u + \color{blue}{\left(-21.333333333333332 \cdot u\right) \cdot u}\right)\right)\right) \]

   17. distribute-rgt-out 90.4%

       \[\leadsto s \cdot \left(-u \cdot \left(-4 + \color{blue}{u \cdot \left(-8 + -21.333333333333332 \cdot u\right)}\right)\right) \]

   18. *-commutative 90.4%

       \[\leadsto s \cdot \left(-u \cdot \left(-4 + u \cdot \left(-8 + \color{blue}{u \cdot -21.333333333333332}\right)\right)\right) \]

6. Simplified 90.4%

   \[\leadsto s \cdot \left(-\color{blue}{u \cdot \left(-4 + u \cdot \left(-8 + u \cdot -21.333333333333332\right)\right)}\right) \]

7. Final simplification 90.4%

   \[\leadsto s \cdot \left(u \cdot \left(4 + u \cdot \left(8 - u \cdot -21.333333333333332\right)\right)\right) \]

Alternative 3: 88.5% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \frac{16 \cdot \left(s \cdot u\right)}{4 + u \cdot -8} \end{array} \]

FPCore

(FPCore (s u) :precision binary32 (/ (* 16.0 (* s u)) (+ 4.0 (* u -8.0))))

C

float code(float s, float u) {
	return (16.0f * (s * u)) / (4.0f + (u * -8.0f));
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = (16.0e0 * (s * u)) / (4.0e0 + (u * (-8.0e0)))
end function

Julia

function code(s, u)
	return Float32(Float32(Float32(16.0) * Float32(s * u)) / Float32(Float32(4.0) + Float32(u * Float32(-8.0))))
end

MATLAB

function tmp = code(s, u)
	tmp = (single(16.0) * (s * u)) / (single(4.0) + (u * single(-8.0)));
end

Derivation

1. Initial program 64.4%

   \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
2. Step-by-step derivation

   1. log-rec 66.9%

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

   2. remove-double-neg 66.9%

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

   3. cancel-sign-sub-inv 66.9%

      \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

   4. remove-double-neg 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

   5. metadata-eval 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

3. Simplified 66.9%

   \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

4. Taylor expanded in u around 0 84.8%

   \[\leadsto \color{blue}{4 \cdot \left(s \cdot u\right) + 8 \cdot \left(s \cdot {u}^{2}\right)} \]
5. Step-by-step derivation

   1. unpow2 84.8%

      \[\leadsto 4 \cdot \left(s \cdot u\right) + 8 \cdot \left(s \cdot \color{blue}{\left(u \cdot u\right)}\right) \]

   2. associate-*r* 84.8%

      \[\leadsto 4 \cdot \left(s \cdot u\right) + 8 \cdot \color{blue}{\left(\left(s \cdot u\right) \cdot u\right)} \]

   3. *-commutative 84.8%

      \[\leadsto 4 \cdot \left(s \cdot u\right) + 8 \cdot \color{blue}{\left(u \cdot \left(s \cdot u\right)\right)} \]

   4. associate-*r* 84.9%

      \[\leadsto 4 \cdot \left(s \cdot u\right) + \color{blue}{\left(8 \cdot u\right) \cdot \left(s \cdot u\right)} \]

   5. distribute-rgt-out 84.7%

      \[\leadsto \color{blue}{\left(s \cdot u\right) \cdot \left(4 + 8 \cdot u\right)} \]

   6. *-commutative 84.7%

      \[\leadsto \color{blue}{\left(u \cdot s\right)} \cdot \left(4 + 8 \cdot u\right) \]

   7. *-commutative 84.7%

      \[\leadsto \left(u \cdot s\right) \cdot \left(4 + \color{blue}{u \cdot 8}\right) \]

6. Simplified 84.7%

   \[\leadsto \color{blue}{\left(u \cdot s\right) \cdot \left(4 + u \cdot 8\right)} \]
7. Step-by-step derivation

   1. *-commutative 84.7%

      \[\leadsto \color{blue}{\left(4 + u \cdot 8\right) \cdot \left(u \cdot s\right)} \]

   2. flip-+ 84.7%

      \[\leadsto \color{blue}{\frac{4 \cdot 4 - \left(u \cdot 8\right) \cdot \left(u \cdot 8\right)}{4 - u \cdot 8}} \cdot \left(u \cdot s\right) \]

   3. associate-*l/ 84.9%

      \[\leadsto \color{blue}{\frac{\left(4 \cdot 4 - \left(u \cdot 8\right) \cdot \left(u \cdot 8\right)\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8}} \]

   4. metadata-eval 84.9%

      \[\leadsto \frac{\left(\color{blue}{16} - \left(u \cdot 8\right) \cdot \left(u \cdot 8\right)\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8} \]

   5. *-commutative 84.9%

      \[\leadsto \frac{\left(16 - \color{blue}{\left(8 \cdot u\right)} \cdot \left(u \cdot 8\right)\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8} \]

   6. *-commutative 84.9%

      \[\leadsto \frac{\left(16 - \left(8 \cdot u\right) \cdot \color{blue}{\left(8 \cdot u\right)}\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8} \]

   7. swap-sqr 84.9%

      \[\leadsto \frac{\left(16 - \color{blue}{\left(8 \cdot 8\right) \cdot \left(u \cdot u\right)}\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8} \]

   8. metadata-eval 84.9%

      \[\leadsto \frac{\left(16 - \color{blue}{64} \cdot \left(u \cdot u\right)\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8} \]

   9. unpow2 84.9%

      \[\leadsto \frac{\left(16 - 64 \cdot \color{blue}{{u}^{2}}\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8} \]

   10. *-commutative 84.9%

       \[\leadsto \frac{\left(16 - 64 \cdot {u}^{2}\right) \cdot \left(u \cdot s\right)}{4 - \color{blue}{8 \cdot u}} \]

   11. cancel-sign-sub-inv 84.9%

       \[\leadsto \frac{\left(16 - 64 \cdot {u}^{2}\right) \cdot \left(u \cdot s\right)}{\color{blue}{4 + \left(-8\right) \cdot u}} \]

   12. metadata-eval 84.9%

       \[\leadsto \frac{\left(16 - 64 \cdot {u}^{2}\right) \cdot \left(u \cdot s\right)}{4 + \color{blue}{-8} \cdot u} \]

   13. *-commutative 84.9%

       \[\leadsto \frac{\left(16 - 64 \cdot {u}^{2}\right) \cdot \left(u \cdot s\right)}{4 + \color{blue}{u \cdot -8}} \]

8. Applied egg-rr 84.9%

   \[\leadsto \color{blue}{\frac{\left(16 - 64 \cdot {u}^{2}\right) \cdot \left(u \cdot s\right)}{4 + u \cdot -8}} \]

9. Taylor expanded in u around 0 87.1%

   \[\leadsto \frac{\color{blue}{16 \cdot \left(s \cdot u\right)}}{4 + u \cdot -8} \]

10. Final simplification 87.1%

    \[\leadsto \frac{16 \cdot \left(s \cdot u\right)}{4 + u \cdot -8} \]

Alternative 4: 88.7% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \frac{s \cdot \left(u \cdot 16\right)}{4 + u \cdot -8} \end{array} \]

FPCore

(FPCore (s u) :precision binary32 (/ (* s (* u 16.0)) (+ 4.0 (* u -8.0))))

C

float code(float s, float u) {
	return (s * (u * 16.0f)) / (4.0f + (u * -8.0f));
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = (s * (u * 16.0e0)) / (4.0e0 + (u * (-8.0e0)))
end function

Julia

function code(s, u)
	return Float32(Float32(s * Float32(u * Float32(16.0))) / Float32(Float32(4.0) + Float32(u * Float32(-8.0))))
end

MATLAB

function tmp = code(s, u)
	tmp = (s * (u * single(16.0))) / (single(4.0) + (u * single(-8.0)));
end

Derivation

1. Initial program 64.4%

   \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
2. Step-by-step derivation

   1. log-rec 66.9%

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

   2. remove-double-neg 66.9%

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

   3. cancel-sign-sub-inv 66.9%

      \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

   4. remove-double-neg 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

   5. metadata-eval 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

3. Simplified 66.9%

   \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

4. Taylor expanded in u around 0 84.8%

   \[\leadsto \color{blue}{4 \cdot \left(s \cdot u\right) + 8 \cdot \left(s \cdot {u}^{2}\right)} \]
5. Step-by-step derivation

   1. unpow2 84.8%

      \[\leadsto 4 \cdot \left(s \cdot u\right) + 8 \cdot \left(s \cdot \color{blue}{\left(u \cdot u\right)}\right) \]

   2. associate-*r* 84.8%

      \[\leadsto 4 \cdot \left(s \cdot u\right) + 8 \cdot \color{blue}{\left(\left(s \cdot u\right) \cdot u\right)} \]

   3. *-commutative 84.8%

      \[\leadsto 4 \cdot \left(s \cdot u\right) + 8 \cdot \color{blue}{\left(u \cdot \left(s \cdot u\right)\right)} \]

   4. associate-*r* 84.9%

      \[\leadsto 4 \cdot \left(s \cdot u\right) + \color{blue}{\left(8 \cdot u\right) \cdot \left(s \cdot u\right)} \]

   5. distribute-rgt-out 84.7%

      \[\leadsto \color{blue}{\left(s \cdot u\right) \cdot \left(4 + 8 \cdot u\right)} \]

   6. *-commutative 84.7%

      \[\leadsto \color{blue}{\left(u \cdot s\right)} \cdot \left(4 + 8 \cdot u\right) \]

   7. *-commutative 84.7%

      \[\leadsto \left(u \cdot s\right) \cdot \left(4 + \color{blue}{u \cdot 8}\right) \]

6. Simplified 84.7%

   \[\leadsto \color{blue}{\left(u \cdot s\right) \cdot \left(4 + u \cdot 8\right)} \]
7. Step-by-step derivation

   1. *-commutative 84.7%

      \[\leadsto \color{blue}{\left(4 + u \cdot 8\right) \cdot \left(u \cdot s\right)} \]

   2. flip-+ 84.7%

      \[\leadsto \color{blue}{\frac{4 \cdot 4 - \left(u \cdot 8\right) \cdot \left(u \cdot 8\right)}{4 - u \cdot 8}} \cdot \left(u \cdot s\right) \]

   3. associate-*l/ 84.9%

      \[\leadsto \color{blue}{\frac{\left(4 \cdot 4 - \left(u \cdot 8\right) \cdot \left(u \cdot 8\right)\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8}} \]

   4. metadata-eval 84.9%

      \[\leadsto \frac{\left(\color{blue}{16} - \left(u \cdot 8\right) \cdot \left(u \cdot 8\right)\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8} \]

   5. *-commutative 84.9%

      \[\leadsto \frac{\left(16 - \color{blue}{\left(8 \cdot u\right)} \cdot \left(u \cdot 8\right)\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8} \]

   6. *-commutative 84.9%

      \[\leadsto \frac{\left(16 - \left(8 \cdot u\right) \cdot \color{blue}{\left(8 \cdot u\right)}\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8} \]

   7. swap-sqr 84.9%

      \[\leadsto \frac{\left(16 - \color{blue}{\left(8 \cdot 8\right) \cdot \left(u \cdot u\right)}\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8} \]

   8. metadata-eval 84.9%

      \[\leadsto \frac{\left(16 - \color{blue}{64} \cdot \left(u \cdot u\right)\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8} \]

   9. unpow2 84.9%

      \[\leadsto \frac{\left(16 - 64 \cdot \color{blue}{{u}^{2}}\right) \cdot \left(u \cdot s\right)}{4 - u \cdot 8} \]

   10. *-commutative 84.9%

       \[\leadsto \frac{\left(16 - 64 \cdot {u}^{2}\right) \cdot \left(u \cdot s\right)}{4 - \color{blue}{8 \cdot u}} \]

   11. cancel-sign-sub-inv 84.9%

       \[\leadsto \frac{\left(16 - 64 \cdot {u}^{2}\right) \cdot \left(u \cdot s\right)}{\color{blue}{4 + \left(-8\right) \cdot u}} \]

   12. metadata-eval 84.9%

       \[\leadsto \frac{\left(16 - 64 \cdot {u}^{2}\right) \cdot \left(u \cdot s\right)}{4 + \color{blue}{-8} \cdot u} \]

   13. *-commutative 84.9%

       \[\leadsto \frac{\left(16 - 64 \cdot {u}^{2}\right) \cdot \left(u \cdot s\right)}{4 + \color{blue}{u \cdot -8}} \]

8. Applied egg-rr 84.9%

   \[\leadsto \color{blue}{\frac{\left(16 - 64 \cdot {u}^{2}\right) \cdot \left(u \cdot s\right)}{4 + u \cdot -8}} \]

9. Taylor expanded in u around 0 87.1%

   \[\leadsto \frac{\color{blue}{16 \cdot \left(s \cdot u\right)}}{4 + u \cdot -8} \]
10. Step-by-step derivation

    1. *-commutative 87.1%

       \[\leadsto \frac{\color{blue}{\left(s \cdot u\right) \cdot 16}}{4 + u \cdot -8} \]

    2. associate-*l* 87.4%

       \[\leadsto \frac{\color{blue}{s \cdot \left(u \cdot 16\right)}}{4 + u \cdot -8} \]

11. Simplified 87.4%

    \[\leadsto \frac{\color{blue}{s \cdot \left(u \cdot 16\right)}}{4 + u \cdot -8} \]

12. Final simplification 87.4%

    \[\leadsto \frac{s \cdot \left(u \cdot 16\right)}{4 + u \cdot -8} \]

Alternative 5: 86.7% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ s \cdot \left(u \cdot \left(4 + u \cdot 8\right)\right) \end{array} \]

FPCore

(FPCore (s u) :precision binary32 (* s (* u (+ 4.0 (* u 8.0)))))

C

float code(float s, float u) {
	return s * (u * (4.0f + (u * 8.0f)));
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = s * (u * (4.0e0 + (u * 8.0e0)))
end function

Julia

function code(s, u)
	return Float32(s * Float32(u * Float32(Float32(4.0) + Float32(u * Float32(8.0)))))
end

MATLAB

function tmp = code(s, u)
	tmp = s * (u * (single(4.0) + (u * single(8.0))));
end

Derivation

1. Initial program 64.4%

   \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
2. Step-by-step derivation

   1. log-rec 66.9%

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

   2. remove-double-neg 66.9%

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

   3. cancel-sign-sub-inv 66.9%

      \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

   4. remove-double-neg 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

   5. metadata-eval 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

3. Simplified 66.9%

   \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

4. Taylor expanded in u around 0 84.8%

   \[\leadsto \color{blue}{4 \cdot \left(s \cdot u\right) + 8 \cdot \left(s \cdot {u}^{2}\right)} \]
5. Step-by-step derivation

   1. unpow2 84.8%

      \[\leadsto 4 \cdot \left(s \cdot u\right) + 8 \cdot \left(s \cdot \color{blue}{\left(u \cdot u\right)}\right) \]

   2. associate-*r* 84.8%

      \[\leadsto 4 \cdot \left(s \cdot u\right) + 8 \cdot \color{blue}{\left(\left(s \cdot u\right) \cdot u\right)} \]

   3. *-commutative 84.8%

      \[\leadsto 4 \cdot \left(s \cdot u\right) + 8 \cdot \color{blue}{\left(u \cdot \left(s \cdot u\right)\right)} \]

   4. associate-*r* 84.9%

      \[\leadsto 4 \cdot \left(s \cdot u\right) + \color{blue}{\left(8 \cdot u\right) \cdot \left(s \cdot u\right)} \]

   5. distribute-rgt-out 84.7%

      \[\leadsto \color{blue}{\left(s \cdot u\right) \cdot \left(4 + 8 \cdot u\right)} \]

   6. *-commutative 84.7%

      \[\leadsto \color{blue}{\left(u \cdot s\right)} \cdot \left(4 + 8 \cdot u\right) \]

   7. *-commutative 84.7%

      \[\leadsto \left(u \cdot s\right) \cdot \left(4 + \color{blue}{u \cdot 8}\right) \]

6. Simplified 84.7%

   \[\leadsto \color{blue}{\left(u \cdot s\right) \cdot \left(4 + u \cdot 8\right)} \]

7. Taylor expanded in s around 0 85.1%

   \[\leadsto \color{blue}{s \cdot \left(u \cdot \left(4 + 8 \cdot u\right)\right)} \]

8. Final simplification 85.1%

   \[\leadsto s \cdot \left(u \cdot \left(4 + u \cdot 8\right)\right) \]

Alternative 6: 22.8% accurate, 21.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;s \leq 4.000000094968912 \cdot 10^{-32}:\\ \;\;\;\;s \cdot 0\\ \mathbf{else}:\\ \;\;\;\;s \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (s u)
 :precision binary32
 (if (<= s 4.000000094968912e-32) (* s 0.0) (* s 0.5)))

C

float code(float s, float u) {
	float tmp;
	if (s <= 4.000000094968912e-32f) {
		tmp = s * 0.0f;
	} else {
		tmp = s * 0.5f;
	}
	return tmp;
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    real(4) :: tmp
    if (s <= 4.000000094968912e-32) then
        tmp = s * 0.0e0
    else
        tmp = s * 0.5e0
    end if
    code = tmp
end function

Julia

function code(s, u)
	tmp = Float32(0.0)
	if (s <= Float32(4.000000094968912e-32))
		tmp = Float32(s * Float32(0.0));
	else
		tmp = Float32(s * Float32(0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(s, u)
	tmp = single(0.0);
	if (s <= single(4.000000094968912e-32))
		tmp = s * single(0.0);
	else
		tmp = s * single(0.5);
	end
	tmp_2 = tmp;
end

Derivation

1. Split input into 2 regimes

2. if s < 4.00000009e-32

   1. Initial program 80.6%

      \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
   2. Step-by-step derivation

      1. log-rec 83.4%

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

      2. remove-double-neg 83.4%

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

      3. cancel-sign-sub-inv 83.4%

         \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

      4. remove-double-neg 83.4%

         \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

      5. metadata-eval 83.4%

         \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

   3. Simplified 83.4%

      \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

   5. Applied egg-rr 48.9%

      \[\leadsto s \cdot \left(-\color{blue}{0}\right) \]

   if 4.00000009e-32 < s

   1. Initial program 60.5%

      \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
   2. Step-by-step derivation

      1. log-rec 62.9%

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

      2. remove-double-neg 62.9%

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

      3. cancel-sign-sub-inv 62.9%

         \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

      4. remove-double-neg 62.9%

         \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

      5. metadata-eval 62.9%

         \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

   3. Simplified 62.9%

      \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

   5. Applied egg-rr 18.2%

      \[\leadsto s \cdot \left(-\color{blue}{-0.5}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 24.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;s \leq 4.000000094968912 \cdot 10^{-32}:\\ \;\;\;\;s \cdot 0\\ \mathbf{else}:\\ \;\;\;\;s \cdot 0.5\\ \end{array} \]

Alternative 7: 73.6% accurate, 21.8× speedup

Math

\[\begin{array}{l} \\ 4 \cdot \left(s \cdot u\right) \end{array} \]

FPCore

(FPCore (s u) :precision binary32 (* 4.0 (* s u)))

C

float code(float s, float u) {
	return 4.0f * (s * u);
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = 4.0e0 * (s * u)
end function

Julia

function code(s, u)
	return Float32(Float32(4.0) * Float32(s * u))
end

MATLAB

function tmp = code(s, u)
	tmp = single(4.0) * (s * u);
end

Derivation

1. Initial program 64.4%

   \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
2. Step-by-step derivation

   1. log-rec 66.9%

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

   2. remove-double-neg 66.9%

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

   3. cancel-sign-sub-inv 66.9%

      \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

   4. remove-double-neg 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

   5. metadata-eval 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

3. Simplified 66.9%

   \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

4. Taylor expanded in u around 0 71.8%

   \[\leadsto \color{blue}{4 \cdot \left(s \cdot u\right)} \]
5. Step-by-step derivation

   1. *-commutative 71.8%

      \[\leadsto 4 \cdot \color{blue}{\left(u \cdot s\right)} \]

6. Simplified 71.8%

   \[\leadsto \color{blue}{4 \cdot \left(u \cdot s\right)} \]

7. Final simplification 71.8%

   \[\leadsto 4 \cdot \left(s \cdot u\right) \]

Alternative 8: 73.8% accurate, 21.8× speedup

Math

\[\begin{array}{l} \\ u \cdot \left(s \cdot 4\right) \end{array} \]

FPCore

(FPCore (s u) :precision binary32 (* u (* s 4.0)))

C

float code(float s, float u) {
	return u * (s * 4.0f);
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = u * (s * 4.0e0)
end function

Julia

function code(s, u)
	return Float32(u * Float32(s * Float32(4.0)))
end

MATLAB

function tmp = code(s, u)
	tmp = u * (s * single(4.0));
end

Derivation

1. Initial program 64.4%

   \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
2. Step-by-step derivation

   1. log-rec 66.9%

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

   2. remove-double-neg 66.9%

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

   3. cancel-sign-sub-inv 66.9%

      \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

   4. remove-double-neg 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

   5. metadata-eval 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

3. Simplified 66.9%

   \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

4. Taylor expanded in u around 0 71.8%

   \[\leadsto \color{blue}{4 \cdot \left(s \cdot u\right)} \]
5. Step-by-step derivation

   1. associate-*r* 72.0%

      \[\leadsto \color{blue}{\left(4 \cdot s\right) \cdot u} \]

   2. *-commutative 72.0%

      \[\leadsto \color{blue}{u \cdot \left(4 \cdot s\right)} \]

6. Simplified 72.0%

   \[\leadsto \color{blue}{u \cdot \left(4 \cdot s\right)} \]

7. Final simplification 72.0%

   \[\leadsto u \cdot \left(s \cdot 4\right) \]

Alternative 9: 16.3% accurate, 36.3× speedup

Math

\[\begin{array}{l} \\ s \cdot 8 \end{array} \]

FPCore

(FPCore (s u) :precision binary32 (* s 8.0))

C

float code(float s, float u) {
	return s * 8.0f;
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = s * 8.0e0
end function

Julia

function code(s, u)
	return Float32(s * Float32(8.0))
end

MATLAB

function tmp = code(s, u)
	tmp = s * single(8.0);
end

Derivation

1. Initial program 64.4%

   \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
2. Step-by-step derivation

   1. log-rec 66.9%

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

   2. remove-double-neg 66.9%

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

   3. cancel-sign-sub-inv 66.9%

      \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

   4. remove-double-neg 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

   5. metadata-eval 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

3. Simplified 66.9%

   \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

5. Applied egg-rr 16.6%

   \[\leadsto s \cdot \left(-\color{blue}{-8}\right) \]

6. Final simplification 16.6%

   \[\leadsto s \cdot 8 \]

Alternative 10: 16.8% accurate, 36.3× speedup

Math

\[\begin{array}{l} \\ s \cdot 4 \end{array} \]

FPCore

(FPCore (s u) :precision binary32 (* s 4.0))

C

float code(float s, float u) {
	return s * 4.0f;
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = s * 4.0e0
end function

Julia

function code(s, u)
	return Float32(s * Float32(4.0))
end

MATLAB

function tmp = code(s, u)
	tmp = s * single(4.0);
end

Derivation

1. Initial program 64.4%

   \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
2. Step-by-step derivation

   1. log-rec 66.9%

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

   2. remove-double-neg 66.9%

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

   3. cancel-sign-sub-inv 66.9%

      \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

   4. remove-double-neg 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

   5. metadata-eval 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

3. Simplified 66.9%

   \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

5. Applied egg-rr 17.2%

   \[\leadsto s \cdot \left(-\color{blue}{-4}\right) \]

6. Final simplification 17.2%

   \[\leadsto s \cdot 4 \]

Alternative 11: 17.3% accurate, 36.3× speedup

Math

\[\begin{array}{l} \\ s \cdot 2 \end{array} \]

FPCore

(FPCore (s u) :precision binary32 (* s 2.0))

C

float code(float s, float u) {
	return s * 2.0f;
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = s * 2.0e0
end function

Julia

function code(s, u)
	return Float32(s * Float32(2.0))
end

MATLAB

function tmp = code(s, u)
	tmp = s * single(2.0);
end

Derivation

1. Initial program 64.4%

   \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
2. Step-by-step derivation

   1. log-rec 66.9%

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

   2. remove-double-neg 66.9%

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

   3. cancel-sign-sub-inv 66.9%

      \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

   4. remove-double-neg 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

   5. metadata-eval 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

3. Simplified 66.9%

   \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

5. Applied egg-rr 17.6%

   \[\leadsto s \cdot \left(-\color{blue}{-2}\right) \]

6. Final simplification 17.6%

   \[\leadsto s \cdot 2 \]

Alternative 12: 18.5% accurate, 36.3× speedup

Math

\[\begin{array}{l} \\ s \cdot 0.5 \end{array} \]

FPCore

(FPCore (s u) :precision binary32 (* s 0.5))

C

float code(float s, float u) {
	return s * 0.5f;
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = s * 0.5e0
end function

Julia

function code(s, u)
	return Float32(s * Float32(0.5))
end

MATLAB

function tmp = code(s, u)
	tmp = s * single(0.5);
end

Derivation

1. Initial program 64.4%

   \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
2. Step-by-step derivation

   1. log-rec 66.9%

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

   2. remove-double-neg 66.9%

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

   3. cancel-sign-sub-inv 66.9%

      \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

   4. remove-double-neg 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

   5. metadata-eval 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

3. Simplified 66.9%

   \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

5. Applied egg-rr 18.8%

   \[\leadsto s \cdot \left(-\color{blue}{-0.5}\right) \]

6. Final simplification 18.8%

   \[\leadsto s \cdot 0.5 \]

Alternative 13: 17.9% accurate, 109.0× speedup

Math

\[\begin{array}{l} \\ s \end{array} \]

FPCore

(FPCore (s u) :precision binary32 s)

C

float code(float s, float u) {
	return s;
}

Fortran

real(4) function code(s, u)
    real(4), intent (in) :: s
    real(4), intent (in) :: u
    code = s
end function

Julia

function code(s, u)
	return s
end

MATLAB

function tmp = code(s, u)
	tmp = s;
end

Derivation

1. Initial program 64.4%

   \[s \cdot \log \left(\frac{1}{1 - 4 \cdot u}\right) \]
2. Step-by-step derivation

   1. log-rec 66.9%

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

   2. remove-double-neg 66.9%

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

   3. cancel-sign-sub-inv 66.9%

      \[\leadsto s \cdot \left(-\log \color{blue}{\left(1 + \left(-4\right) \cdot \left(-\left(-u\right)\right)\right)}\right) \]

   4. remove-double-neg 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \left(-4\right) \cdot \color{blue}{u}\right)\right) \]

   5. metadata-eval 66.9%

      \[\leadsto s \cdot \left(-\log \left(1 + \color{blue}{-4} \cdot u\right)\right) \]

3. Simplified 66.9%

   \[\leadsto \color{blue}{s \cdot \left(-\log \left(1 + -4 \cdot u\right)\right)} \]

5. Applied egg-rr 18.2%

   \[\leadsto s \cdot \left(-\color{blue}{-1}\right) \]

6. Final simplification 18.2%

   \[\leadsto s \]

Reproduce

herbie shell --seed 2023301 
(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))))))