Sample trimmed logistic on [-pi, pi]

Percentage Accurate: 99.0% → 99.0%

Time: 24.4s

Alternatives: 9

Speedup: 1.5×

Specification

\[\left(2.328306437 \cdot 10^{-10} \leq u \land u \leq 1\right) \land \left(0 \leq s \land s \leq 1.0651631\right)\]

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{1 + e^{\frac{\pi}{s}}}\\ \left(-s\right) \cdot \log \left(\frac{1}{u \cdot \left(\frac{1}{1 + e^{\frac{-\pi}{s}}} - t\_0\right) + t\_0} - 1\right) \end{array} \end{array} \]

FPCore

(FPCore (u s)
 :precision binary32
 (let* ((t_0 (/ 1.0 (+ 1.0 (exp (/ PI s))))))
   (*
    (- s)
    (log
     (-
      (/ 1.0 (+ (* u (- (/ 1.0 (+ 1.0 (exp (/ (- PI) s)))) t_0)) t_0))
      1.0)))))

C

float code(float u, float s) {
	float t_0 = 1.0f / (1.0f + expf((((float) M_PI) / s)));
	return -s * logf(((1.0f / ((u * ((1.0f / (1.0f + expf((-((float) M_PI) / s)))) - t_0)) + t_0)) - 1.0f));
}

Julia

function code(u, s)
	t_0 = Float32(Float32(1.0) / Float32(Float32(1.0) + exp(Float32(Float32(pi) / 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)))) - t_0)) + t_0)) - Float32(1.0))))
end

MATLAB

function tmp = code(u, s)
	t_0 = single(1.0) / (single(1.0) + exp((single(pi) / s)));
	tmp = -s * log(((single(1.0) / ((u * ((single(1.0) / (single(1.0) + exp((-single(pi) / s)))) - t_0)) + t_0)) - single(1.0)));
end

Initial Program: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{1 + e^{\frac{\pi}{s}}}\\ \left(-s\right) \cdot \log \left(\frac{1}{u \cdot \left(\frac{1}{1 + e^{\frac{-\pi}{s}}} - t\_0\right) + t\_0} - 1\right) \end{array} \end{array} \]

FPCore

(FPCore (u s)
 :precision binary32
 (let* ((t_0 (/ 1.0 (+ 1.0 (exp (/ PI s))))))
   (*
    (- s)
    (log
     (-
      (/ 1.0 (+ (* u (- (/ 1.0 (+ 1.0 (exp (/ (- PI) s)))) t_0)) t_0))
      1.0)))))

C

float code(float u, float s) {
	float t_0 = 1.0f / (1.0f + expf((((float) M_PI) / s)));
	return -s * logf(((1.0f / ((u * ((1.0f / (1.0f + expf((-((float) M_PI) / s)))) - t_0)) + t_0)) - 1.0f));
}

Julia

function code(u, s)
	t_0 = Float32(Float32(1.0) / Float32(Float32(1.0) + exp(Float32(Float32(pi) / 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)))) - t_0)) + t_0)) - Float32(1.0))))
end

MATLAB

function tmp = code(u, s)
	t_0 = single(1.0) / (single(1.0) + exp((single(pi) / s)));
	tmp = -s * log(((single(1.0) / ((u * ((single(1.0) / (single(1.0) + exp((-single(pi) / s)))) - t_0)) + t_0)) - single(1.0)));
end

Alternative 1: 99.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{-\frac{\pi}{s}}\\ \left(-s\right) \cdot \log \left(\frac{1 + t\_0}{\mathsf{fma}\left(1 - u, t\_0, u\right)} - 1\right) \end{array} \end{array} \]

FPCore

(FPCore (u s)
 :precision binary32
 (let* ((t_0 (exp (- (/ PI s)))))
   (* (- s) (log (- (/ (+ 1.0 t_0) (fma (- 1.0 u) t_0 u)) 1.0)))))

C

float code(float u, float s) {
	float t_0 = expf(-(((float) M_PI) / s));
	return -s * logf((((1.0f + t_0) / fmaf((1.0f - u), t_0, u)) - 1.0f));
}

Julia

function code(u, s)
	t_0 = exp(Float32(-Float32(Float32(pi) / s)))
	return Float32(Float32(-s) * log(Float32(Float32(Float32(Float32(1.0) + t_0) / fma(Float32(Float32(1.0) - u), t_0, u)) - Float32(1.0))))
end

Derivation

1. Initial program 99.0%

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

3. Applied rewrites 99.0%

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

5. Applied rewrites 99.0%

   \[\leadsto \left(-s\right) \cdot \log \left(\color{blue}{\frac{1 + e^{-\frac{\pi}{s}}}{\mathsf{fma}\left(1 - u, e^{-\frac{\pi}{s}}, u\right)}} - 1\right) \]
6. Add Preprocessing

Alternative 2: 98.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{-\frac{\pi}{s}}\\ \left(-s\right) \cdot \log \left(\frac{1 + t\_0}{\mathsf{fma}\left(1, t\_0, u\right)} - 1\right) \end{array} \end{array} \]

FPCore

(FPCore (u s)
 :precision binary32
 (let* ((t_0 (exp (- (/ PI s)))))
   (* (- s) (log (- (/ (+ 1.0 t_0) (fma 1.0 t_0 u)) 1.0)))))

C

float code(float u, float s) {
	float t_0 = expf(-(((float) M_PI) / s));
	return -s * logf((((1.0f + t_0) / fmaf(1.0f, t_0, u)) - 1.0f));
}

Julia

function code(u, s)
	t_0 = exp(Float32(-Float32(Float32(pi) / s)))
	return Float32(Float32(-s) * log(Float32(Float32(Float32(Float32(1.0) + t_0) / fma(Float32(1.0), t_0, u)) - Float32(1.0))))
end

Derivation

1. Initial program 99.0%

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

3. Applied rewrites 99.0%

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

5. Applied rewrites 99.0%

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

6. Taylor expanded in u around 0

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

8. Applied rewrites 98.7%

   \[\leadsto \left(-s\right) \cdot \log \left(\frac{1 + e^{-\frac{\pi}{s}}}{\mathsf{fma}\left(\color{blue}{1}, e^{-\frac{\pi}{s}}, u\right)} - 1\right) \]
9. Add Preprocessing

Alternative 3: 97.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -\frac{\pi}{s}\\ \left(-s\right) \cdot \log \left(\frac{1 + e^{t\_0}}{-1 \cdot \left(u \cdot \mathsf{expm1}\left(t\_0\right)\right)} - 1\right) \end{array} \end{array} \]

FPCore

(FPCore (u s)
 :precision binary32
 (let* ((t_0 (- (/ PI s))))
   (* (- s) (log (- (/ (+ 1.0 (exp t_0)) (* -1.0 (* u (expm1 t_0)))) 1.0)))))

C

float code(float u, float s) {
	float t_0 = -(((float) M_PI) / s);
	return -s * logf((((1.0f + expf(t_0)) / (-1.0f * (u * expm1f(t_0)))) - 1.0f));
}

Julia

function code(u, s)
	t_0 = Float32(-Float32(Float32(pi) / s))
	return Float32(Float32(-s) * log(Float32(Float32(Float32(Float32(1.0) + exp(t_0)) / Float32(Float32(-1.0) * Float32(u * expm1(t_0)))) - Float32(1.0))))
end

Derivation

1. Initial program 99.0%

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

3. Applied rewrites 99.0%

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

5. Applied rewrites 99.0%

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

6. Taylor expanded in u around -inf

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

8. Applied rewrites 97.8%

   \[\leadsto \left(-s\right) \cdot \log \left(\frac{1 + e^{-\frac{\pi}{s}}}{\color{blue}{-1 \cdot \left(u \cdot \mathsf{expm1}\left(-\frac{\pi}{s}\right)\right)}} - 1\right) \]
9. Add Preprocessing

Alternative 4: 25.1% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \left(-s\right) \cdot \log \left(1 + -1 \cdot \frac{\pi - 2 \cdot \pi}{s}\right) \end{array} \]

FPCore

(FPCore (u s)
 :precision binary32
 (* (- s) (log (+ 1.0 (* -1.0 (/ (- PI (* 2.0 PI)) s))))))

C

float code(float u, float s) {
	return -s * logf((1.0f + (-1.0f * ((((float) M_PI) - (2.0f * ((float) M_PI))) / s))));
}

Julia

function code(u, s)
	return Float32(Float32(-s) * log(Float32(Float32(1.0) + Float32(Float32(-1.0) * Float32(Float32(Float32(pi) - Float32(Float32(2.0) * Float32(pi))) / s)))))
end

MATLAB

function tmp = code(u, s)
	tmp = -s * log((single(1.0) + (single(-1.0) * ((single(pi) - (single(2.0) * single(pi))) / s))));
end

Derivation

1. Initial program 99.0%

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

3. Applied rewrites 99.0%

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

5. Applied rewrites 99.0%

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

6. Taylor expanded in s around -inf

   \[\leadsto \left(-s\right) \cdot \log \color{blue}{\left(1 + -1 \cdot \frac{\mathsf{PI}\left(\right) - 2 \cdot \left(\mathsf{PI}\left(\right) \cdot \left(1 - u\right)\right)}{s}\right)} \]

8. Applied rewrites 24.9%

   \[\leadsto \left(-s\right) \cdot \log \color{blue}{\left(1 + -1 \cdot \frac{\pi - 2 \cdot \left(\pi \cdot \left(1 - u\right)\right)}{s}\right)} \]

9. Taylor expanded in u around 0

   \[\leadsto \left(-s\right) \cdot \log \left(1 + -1 \cdot \frac{\pi - 2 \cdot \mathsf{PI}\left(\right)}{s}\right) \]

11. Applied rewrites 25.1%

    \[\leadsto \left(-s\right) \cdot \log \left(1 + -1 \cdot \frac{\pi - 2 \cdot \pi}{s}\right) \]
12. Add Preprocessing

Alternative 5: 14.4% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \frac{s}{u \cdot \left(0.5 - \left(0.5 + 0.25 \cdot \frac{\pi}{s}\right)\right)} \end{array} \]

FPCore

(FPCore (u s)
 :precision binary32
 (/ s (* u (- 0.5 (+ 0.5 (* 0.25 (/ PI s)))))))

C

float code(float u, float s) {
	return s / (u * (0.5f - (0.5f + (0.25f * (((float) M_PI) / s)))));
}

Julia

function code(u, s)
	return Float32(s / Float32(u * Float32(Float32(0.5) - Float32(Float32(0.5) + Float32(Float32(0.25) * Float32(Float32(pi) / s))))))
end

MATLAB

function tmp = code(u, s)
	tmp = s / (u * (single(0.5) - (single(0.5) + (single(0.25) * (single(pi) / s)))));
end

Derivation

1. Initial program 99.0%

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

3. Applied rewrites 99.0%

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

4. Taylor expanded in u around -inf

   \[\leadsto \color{blue}{\frac{s}{u \cdot \left(\frac{1}{1 + e^{\frac{\mathsf{PI}\left(\right)}{s}}} - \frac{1}{1 + e^{\mathsf{neg}\left(\frac{\mathsf{PI}\left(\right)}{s}\right)}}\right)}} \]

6. Applied rewrites 17.3%

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

7. Taylor expanded in s around inf

   \[\leadsto \frac{s}{u \cdot \left(\frac{1}{1 + e^{\frac{\pi}{s}}} - \left(\frac{1}{2} + \color{blue}{\frac{1}{4} \cdot \frac{\mathsf{PI}\left(\right)}{s}}\right)\right)} \]

9. Applied rewrites 14.4%

   \[\leadsto \frac{s}{u \cdot \left(\frac{1}{1 + e^{\frac{\pi}{s}}} - \left(0.5 + \color{blue}{0.25 \cdot \frac{\pi}{s}}\right)\right)} \]

10. Taylor expanded in s around inf

    \[\leadsto \frac{s}{u \cdot \left(\frac{1}{2} - \left(\color{blue}{\frac{1}{2}} + \frac{1}{4} \cdot \frac{\pi}{s}\right)\right)} \]

12. Applied rewrites 14.4%

    \[\leadsto \frac{s}{u \cdot \left(0.5 - \left(\color{blue}{0.5} + 0.25 \cdot \frac{\pi}{s}\right)\right)} \]
13. Add Preprocessing

Alternative 6: 11.4% accurate, 6.9× speedup

Math

\[\begin{array}{l} \\ u \cdot \left(\left(\pi + \pi\right) - \frac{\pi}{u}\right) \end{array} \]

FPCore

(FPCore (u s) :precision binary32 (* u (- (+ PI PI) (/ PI u))))

C

float code(float u, float s) {
	return u * ((((float) M_PI) + ((float) M_PI)) - (((float) M_PI) / u));
}

Julia

function code(u, s)
	return Float32(u * Float32(Float32(Float32(pi) + Float32(pi)) - Float32(Float32(pi) / u)))
end

MATLAB

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

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. Taylor expanded in s around inf

   \[\leadsto \color{blue}{4 \cdot \left(u \cdot \left(\frac{1}{4} \cdot \mathsf{PI}\left(\right) - \frac{-1}{4} \cdot \mathsf{PI}\left(\right)\right) - \frac{1}{4} \cdot \mathsf{PI}\left(\right)\right)} \]

4. Applied rewrites 11.4%

   \[\leadsto \color{blue}{4 \cdot \left(u \cdot \left(0.25 \cdot \pi - -0.25 \cdot \pi\right) - 0.25 \cdot \pi\right)} \]

6. Applied rewrites 11.4%

   \[\leadsto 4 \cdot \left(\left(0.25 - -0.25\right) \cdot \left(u \cdot \pi\right) - \color{blue}{0.25} \cdot \pi\right) \]

7. Taylor expanded in u around inf

   \[\leadsto u \cdot \color{blue}{\left(-1 \cdot \frac{\mathsf{PI}\left(\right)}{u} + 2 \cdot \mathsf{PI}\left(\right)\right)} \]

9. Applied rewrites 11.4%

   \[\leadsto u \cdot \color{blue}{\mathsf{fma}\left(-1, \frac{\pi}{u}, 2 \cdot \pi\right)} \]

11. Applied rewrites 11.4%

    \[\leadsto \color{blue}{u \cdot \left(\left(\pi + \pi\right) - \frac{\pi}{u}\right)} \]
12. Add Preprocessing

Alternative 7: 11.4% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \pi - 2 \cdot \left(\pi \cdot \left(1 - u\right)\right) \end{array} \]

FPCore

(FPCore (u s) :precision binary32 (- PI (* 2.0 (* PI (- 1.0 u)))))

C

float code(float u, float s) {
	return ((float) M_PI) - (2.0f * (((float) M_PI) * (1.0f - u)));
}

Julia

function code(u, s)
	return Float32(Float32(pi) - Float32(Float32(2.0) * Float32(Float32(pi) * Float32(Float32(1.0) - u))))
end

MATLAB

function tmp = code(u, s)
	tmp = single(pi) - (single(2.0) * (single(pi) * (single(1.0) - u)));
end

Derivation

1. Initial program 99.0%

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

3. Applied rewrites 99.0%

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

5. Applied rewrites 99.0%

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

6. Taylor expanded in s around -inf

   \[\leadsto \color{blue}{\mathsf{PI}\left(\right) - 2 \cdot \left(\mathsf{PI}\left(\right) \cdot \left(1 - u\right)\right)} \]

8. Applied rewrites 11.4%

   \[\leadsto \color{blue}{\pi - 2 \cdot \left(\pi \cdot \left(1 - u\right)\right)} \]
9. Add Preprocessing

Alternative 8: 11.2% accurate, 10.3× speedup

Math

\[\begin{array}{l} \\ \left(-s\right) \cdot \frac{\pi}{s} \end{array} \]

FPCore

(FPCore (u s) :precision binary32 (* (- s) (/ PI s)))

C

float code(float u, float s) {
	return -s * (((float) M_PI) / s);
}

Julia

function code(u, s)
	return Float32(Float32(-s) * Float32(Float32(pi) / s))
end

MATLAB

function tmp = code(u, s)
	tmp = -s * (single(pi) / s);
end

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. Taylor expanded in u around 0

   \[\leadsto \left(-s\right) \cdot \color{blue}{\frac{\mathsf{PI}\left(\right)}{s}} \]

4. Applied rewrites 11.2%

   \[\leadsto \left(-s\right) \cdot \color{blue}{\frac{\pi}{s}} \]
5. Add Preprocessing

Alternative 9: 11.2% accurate, 46.3× speedup

Math

\[\begin{array}{l} \\ -\pi \end{array} \]

FPCore

(FPCore (u s) :precision binary32 (- PI))

C

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

Julia

function code(u, s)
	return Float32(-Float32(pi))
end

MATLAB

function tmp = code(u, s)
	tmp = -single(pi);
end

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. Taylor expanded in u around 0

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

4. Applied rewrites 11.2%

   \[\leadsto \color{blue}{-1 \cdot \pi} \]

6. Applied rewrites 11.2%

   \[\leadsto -\pi \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2025153 
(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))))