Rust f32::asinh

Percentage Accurate: 37.8% → 98.1%

Time: 8.8s

Alternatives: 14

Speedup: 4.0×

Specification

Math

\[\begin{array}{l} \\ \sinh^{-1} x \end{array} \]

FPCore

(FPCore (x) :precision binary32 (asinh x))

C

float code(float x) {
	return asinhf(x);
}

Julia

function code(x)
	return asinh(x)
end

MATLAB

function tmp = code(x)
	tmp = asinh(x);
end

Initial Program: 37.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x))

C

float code(float x) {
	return copysignf(logf((fabsf(x) + sqrtf(((x * x) + 1.0f)))), x);
}

Julia

function code(x)
	return copysign(log(Float32(abs(x) + sqrt(Float32(Float32(x * x) + Float32(1.0))))), x)
end

MATLAB

function tmp = code(x)
	tmp = sign(x) * abs(log((abs(x) + sqrt(((x * x) + single(1.0))))));
end

Alternative 1: 98.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|x\right| + 1\\ t_1 := \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)\\ t_2 := \log \left(\frac{1}{x}\right)\\ t_3 := 1 + \left(\log 2 - t_2\right)\\ t_4 := \frac{1}{{t_3}^{2}}\\ \mathbf{if}\;t_1 \leq -1:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \mathbf{elif}\;t_1 \leq 0.019999999552965164:\\ \;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(\left|x\right|\right) + \mathsf{fma}\left(-0.041666666666666664, {x}^{4} \cdot \left(\frac{3}{t_0} + \frac{3}{{t_0}^{2}}\right), 0.5 \cdot \frac{{x}^{2}}{t_0}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log 2 + \left(\left(0.25 \cdot \frac{1}{{x}^{2}} + \frac{t_3 \cdot \left(-0.041666666666666664 \cdot \left(2.25 \cdot \frac{1}{t_3} + 0.75 \cdot t_4\right) + t_4 \cdot 0.03125\right)}{{x}^{4}}\right) - t_2\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (let* ((t_0 (+ (fabs x) 1.0))
        (t_1 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x))
        (t_2 (log (/ 1.0 x)))
        (t_3 (+ 1.0 (- (log 2.0) t_2)))
        (t_4 (/ 1.0 (pow t_3 2.0))))
   (if (<= t_1 -1.0)
     (copysign (log (+ (fabs x) (hypot 1.0 x))) x)
     (if (<= t_1 0.019999999552965164)
       (copysign
        (+
         (log1p (fabs x))
         (fma
          -0.041666666666666664
          (* (pow x 4.0) (+ (/ 3.0 t_0) (/ 3.0 (pow t_0 2.0))))
          (* 0.5 (/ (pow x 2.0) t_0))))
        x)
       (copysign
        (+
         (log 2.0)
         (-
          (+
           (* 0.25 (/ 1.0 (pow x 2.0)))
           (/
            (*
             t_3
             (+
              (* -0.041666666666666664 (+ (* 2.25 (/ 1.0 t_3)) (* 0.75 t_4)))
              (* t_4 0.03125)))
            (pow x 4.0)))
          t_2))
        x)))))

C

float code(float x) {
	float t_0 = fabsf(x) + 1.0f;
	float t_1 = copysignf(logf((fabsf(x) + sqrtf(((x * x) + 1.0f)))), x);
	float t_2 = logf((1.0f / x));
	float t_3 = 1.0f + (logf(2.0f) - t_2);
	float t_4 = 1.0f / powf(t_3, 2.0f);
	float tmp;
	if (t_1 <= -1.0f) {
		tmp = copysignf(logf((fabsf(x) + hypotf(1.0f, x))), x);
	} else if (t_1 <= 0.019999999552965164f) {
		tmp = copysignf((log1pf(fabsf(x)) + fmaf(-0.041666666666666664f, (powf(x, 4.0f) * ((3.0f / t_0) + (3.0f / powf(t_0, 2.0f)))), (0.5f * (powf(x, 2.0f) / t_0)))), x);
	} else {
		tmp = copysignf((logf(2.0f) + (((0.25f * (1.0f / powf(x, 2.0f))) + ((t_3 * ((-0.041666666666666664f * ((2.25f * (1.0f / t_3)) + (0.75f * t_4))) + (t_4 * 0.03125f))) / powf(x, 4.0f))) - t_2)), x);
	}
	return tmp;
}

Julia

function code(x)
	t_0 = Float32(abs(x) + Float32(1.0))
	t_1 = copysign(log(Float32(abs(x) + sqrt(Float32(Float32(x * x) + Float32(1.0))))), x)
	t_2 = log(Float32(Float32(1.0) / x))
	t_3 = Float32(Float32(1.0) + Float32(log(Float32(2.0)) - t_2))
	t_4 = Float32(Float32(1.0) / (t_3 ^ Float32(2.0)))
	tmp = Float32(0.0)
	if (t_1 <= Float32(-1.0))
		tmp = copysign(log(Float32(abs(x) + hypot(Float32(1.0), x))), x);
	elseif (t_1 <= Float32(0.019999999552965164))
		tmp = copysign(Float32(log1p(abs(x)) + fma(Float32(-0.041666666666666664), Float32((x ^ Float32(4.0)) * Float32(Float32(Float32(3.0) / t_0) + Float32(Float32(3.0) / (t_0 ^ Float32(2.0))))), Float32(Float32(0.5) * Float32((x ^ Float32(2.0)) / t_0)))), x);
	else
		tmp = copysign(Float32(log(Float32(2.0)) + Float32(Float32(Float32(Float32(0.25) * Float32(Float32(1.0) / (x ^ Float32(2.0)))) + Float32(Float32(t_3 * Float32(Float32(Float32(-0.041666666666666664) * Float32(Float32(Float32(2.25) * Float32(Float32(1.0) / t_3)) + Float32(Float32(0.75) * t_4))) + Float32(t_4 * Float32(0.03125)))) / (x ^ Float32(4.0)))) - t_2)), x);
	end
	return tmp
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 97.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)\\ t_1 := \left|x\right| + 1\\ \mathbf{if}\;t_0 \leq -1:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \mathbf{elif}\;t_0 \leq 0.019999999552965164:\\ \;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(\left|x\right|\right) + \mathsf{fma}\left(-0.041666666666666664, {x}^{4} \cdot \left(\frac{3}{t_1} + \frac{3}{{t_1}^{2}}\right), 0.5 \cdot \frac{{x}^{2}}{t_1}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(0.3333333333333333 \cdot \left(3 \cdot \left(\log 2 + \log x\right)\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (let* ((t_0 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x))
        (t_1 (+ (fabs x) 1.0)))
   (if (<= t_0 -1.0)
     (copysign (log (+ (fabs x) (hypot 1.0 x))) x)
     (if (<= t_0 0.019999999552965164)
       (copysign
        (+
         (log1p (fabs x))
         (fma
          -0.041666666666666664
          (* (pow x 4.0) (+ (/ 3.0 t_1) (/ 3.0 (pow t_1 2.0))))
          (* 0.5 (/ (pow x 2.0) t_1))))
        x)
       (copysign (* 0.3333333333333333 (* 3.0 (+ (log 2.0) (log x)))) x)))))

C

float code(float x) {
	float t_0 = copysignf(logf((fabsf(x) + sqrtf(((x * x) + 1.0f)))), x);
	float t_1 = fabsf(x) + 1.0f;
	float tmp;
	if (t_0 <= -1.0f) {
		tmp = copysignf(logf((fabsf(x) + hypotf(1.0f, x))), x);
	} else if (t_0 <= 0.019999999552965164f) {
		tmp = copysignf((log1pf(fabsf(x)) + fmaf(-0.041666666666666664f, (powf(x, 4.0f) * ((3.0f / t_1) + (3.0f / powf(t_1, 2.0f)))), (0.5f * (powf(x, 2.0f) / t_1)))), x);
	} else {
		tmp = copysignf((0.3333333333333333f * (3.0f * (logf(2.0f) + logf(x)))), x);
	}
	return tmp;
}

Julia

function code(x)
	t_0 = copysign(log(Float32(abs(x) + sqrt(Float32(Float32(x * x) + Float32(1.0))))), x)
	t_1 = Float32(abs(x) + Float32(1.0))
	tmp = Float32(0.0)
	if (t_0 <= Float32(-1.0))
		tmp = copysign(log(Float32(abs(x) + hypot(Float32(1.0), x))), x);
	elseif (t_0 <= Float32(0.019999999552965164))
		tmp = copysign(Float32(log1p(abs(x)) + fma(Float32(-0.041666666666666664), Float32((x ^ Float32(4.0)) * Float32(Float32(Float32(3.0) / t_1) + Float32(Float32(3.0) / (t_1 ^ Float32(2.0))))), Float32(Float32(0.5) * Float32((x ^ Float32(2.0)) / t_1)))), x);
	else
		tmp = copysign(Float32(Float32(0.3333333333333333) * Float32(Float32(3.0) * Float32(log(Float32(2.0)) + log(x)))), x);
	end
	return tmp
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 97.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)\\ \mathbf{if}\;t_0 \leq -1:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \mathbf{elif}\;t_0 \leq 0.019999999552965164:\\ \;\;\;\;\mathsf{copysign}\left(\mathsf{fma}\left(0.5, \frac{{x}^{2}}{x + 1}, \mathsf{log1p}\left(x\right)\right) + \left(\frac{3}{x + 1} + \frac{3}{{\left(x + 1\right)}^{2}}\right) \cdot \left(-0.041666666666666664 \cdot {x}^{4}\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(0.3333333333333333 \cdot \left(3 \cdot \left(\log 2 + \log x\right)\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (let* ((t_0 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x)))
   (if (<= t_0 -1.0)
     (copysign (log (+ (fabs x) (hypot 1.0 x))) x)
     (if (<= t_0 0.019999999552965164)
       (copysign
        (+
         (fma 0.5 (/ (pow x 2.0) (+ x 1.0)) (log1p x))
         (*
          (+ (/ 3.0 (+ x 1.0)) (/ 3.0 (pow (+ x 1.0) 2.0)))
          (* -0.041666666666666664 (pow x 4.0))))
        x)
       (copysign (* 0.3333333333333333 (* 3.0 (+ (log 2.0) (log x)))) x)))))

C

float code(float x) {
	float t_0 = copysignf(logf((fabsf(x) + sqrtf(((x * x) + 1.0f)))), x);
	float tmp;
	if (t_0 <= -1.0f) {
		tmp = copysignf(logf((fabsf(x) + hypotf(1.0f, x))), x);
	} else if (t_0 <= 0.019999999552965164f) {
		tmp = copysignf((fmaf(0.5f, (powf(x, 2.0f) / (x + 1.0f)), log1pf(x)) + (((3.0f / (x + 1.0f)) + (3.0f / powf((x + 1.0f), 2.0f))) * (-0.041666666666666664f * powf(x, 4.0f)))), x);
	} else {
		tmp = copysignf((0.3333333333333333f * (3.0f * (logf(2.0f) + logf(x)))), x);
	}
	return tmp;
}

Julia

function code(x)
	t_0 = copysign(log(Float32(abs(x) + sqrt(Float32(Float32(x * x) + Float32(1.0))))), x)
	tmp = Float32(0.0)
	if (t_0 <= Float32(-1.0))
		tmp = copysign(log(Float32(abs(x) + hypot(Float32(1.0), x))), x);
	elseif (t_0 <= Float32(0.019999999552965164))
		tmp = copysign(Float32(fma(Float32(0.5), Float32((x ^ Float32(2.0)) / Float32(x + Float32(1.0))), log1p(x)) + Float32(Float32(Float32(Float32(3.0) / Float32(x + Float32(1.0))) + Float32(Float32(3.0) / (Float32(x + Float32(1.0)) ^ Float32(2.0)))) * Float32(Float32(-0.041666666666666664) * (x ^ Float32(4.0))))), x);
	else
		tmp = copysign(Float32(Float32(0.3333333333333333) * Float32(Float32(3.0) * Float32(log(Float32(2.0)) + log(x)))), x);
	end
	return tmp
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 97.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)\\ \mathbf{if}\;t_0 \leq -0.019999999552965164:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \mathbf{elif}\;t_0 \leq 0.019999999552965164:\\ \;\;\;\;\mathsf{copysign}\left(\mathsf{fma}\left(0.5, \frac{{x}^{2}}{x + 1}, \mathsf{log1p}\left(x\right)\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(0.3333333333333333 \cdot \left(3 \cdot \left(\log 2 + \log x\right)\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (let* ((t_0 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x)))
   (if (<= t_0 -0.019999999552965164)
     (copysign (log (+ (fabs x) (hypot 1.0 x))) x)
     (if (<= t_0 0.019999999552965164)
       (copysign (fma 0.5 (/ (pow x 2.0) (+ x 1.0)) (log1p x)) x)
       (copysign (* 0.3333333333333333 (* 3.0 (+ (log 2.0) (log x)))) x)))))

C

float code(float x) {
	float t_0 = copysignf(logf((fabsf(x) + sqrtf(((x * x) + 1.0f)))), x);
	float tmp;
	if (t_0 <= -0.019999999552965164f) {
		tmp = copysignf(logf((fabsf(x) + hypotf(1.0f, x))), x);
	} else if (t_0 <= 0.019999999552965164f) {
		tmp = copysignf(fmaf(0.5f, (powf(x, 2.0f) / (x + 1.0f)), log1pf(x)), x);
	} else {
		tmp = copysignf((0.3333333333333333f * (3.0f * (logf(2.0f) + logf(x)))), x);
	}
	return tmp;
}

Julia

function code(x)
	t_0 = copysign(log(Float32(abs(x) + sqrt(Float32(Float32(x * x) + Float32(1.0))))), x)
	tmp = Float32(0.0)
	if (t_0 <= Float32(-0.019999999552965164))
		tmp = copysign(log(Float32(abs(x) + hypot(Float32(1.0), x))), x);
	elseif (t_0 <= Float32(0.019999999552965164))
		tmp = copysign(fma(Float32(0.5), Float32((x ^ Float32(2.0)) / Float32(x + Float32(1.0))), log1p(x)), x);
	else
		tmp = copysign(Float32(Float32(0.3333333333333333) * Float32(Float32(3.0) * Float32(log(Float32(2.0)) + log(x)))), x);
	end
	return tmp
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 99.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{copysign}\left(\log \left(\left|x\right| + \sqrt{x \cdot x + 1}\right), x\right)\\ \mathbf{if}\;t_0 \leq -0.019999999552965164:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left|x\right| + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \mathbf{elif}\;t_0 \leq 0.0010000000474974513:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (let* ((t_0 (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x)))
   (if (<= t_0 -0.019999999552965164)
     (copysign (log (+ (fabs x) (hypot 1.0 x))) x)
     (if (<= t_0 0.0010000000474974513)
       (copysign x x)
       (copysign (log (+ x (hypot 1.0 x))) x)))))

C

float code(float x) {
	float t_0 = copysignf(logf((fabsf(x) + sqrtf(((x * x) + 1.0f)))), x);
	float tmp;
	if (t_0 <= -0.019999999552965164f) {
		tmp = copysignf(logf((fabsf(x) + hypotf(1.0f, x))), x);
	} else if (t_0 <= 0.0010000000474974513f) {
		tmp = copysignf(x, x);
	} else {
		tmp = copysignf(logf((x + hypotf(1.0f, x))), x);
	}
	return tmp;
}

Julia

function code(x)
	t_0 = copysign(log(Float32(abs(x) + sqrt(Float32(Float32(x * x) + Float32(1.0))))), x)
	tmp = Float32(0.0)
	if (t_0 <= Float32(-0.019999999552965164))
		tmp = copysign(log(Float32(abs(x) + hypot(Float32(1.0), x))), x);
	elseif (t_0 <= Float32(0.0010000000474974513))
		tmp = copysign(x, x);
	else
		tmp = copysign(log(Float32(x + hypot(Float32(1.0), x))), x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = sign(x) * abs(log((abs(x) + sqrt(((x * x) + single(1.0))))));
	tmp = single(0.0);
	if (t_0 <= single(-0.019999999552965164))
		tmp = sign(x) * abs(log((abs(x) + hypot(single(1.0), x))));
	elseif (t_0 <= single(0.0010000000474974513))
		tmp = sign(x) * abs(x);
	else
		tmp = sign(x) * abs(log((x + hypot(single(1.0), x))));
	end
	tmp_2 = tmp;
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 99.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.019999999552965164:\\ \;\;\;\;\mathsf{copysign}\left(0.3333333333333333 \cdot \left(3 \cdot \log \left(\frac{1}{\mathsf{hypot}\left(1, x\right) - x}\right)\right), x\right)\\ \mathbf{elif}\;x \leq 0.0010000000474974513:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (if (<= x -0.019999999552965164)
   (copysign
    (* 0.3333333333333333 (* 3.0 (log (/ 1.0 (- (hypot 1.0 x) x)))))
    x)
   (if (<= x 0.0010000000474974513)
     (copysign x x)
     (copysign (log (+ x (hypot 1.0 x))) x))))

C

float code(float x) {
	float tmp;
	if (x <= -0.019999999552965164f) {
		tmp = copysignf((0.3333333333333333f * (3.0f * logf((1.0f / (hypotf(1.0f, x) - x))))), x);
	} else if (x <= 0.0010000000474974513f) {
		tmp = copysignf(x, x);
	} else {
		tmp = copysignf(logf((x + hypotf(1.0f, x))), x);
	}
	return tmp;
}

Julia

function code(x)
	tmp = Float32(0.0)
	if (x <= Float32(-0.019999999552965164))
		tmp = copysign(Float32(Float32(0.3333333333333333) * Float32(Float32(3.0) * log(Float32(Float32(1.0) / Float32(hypot(Float32(1.0), x) - x))))), x);
	elseif (x <= Float32(0.0010000000474974513))
		tmp = copysign(x, x);
	else
		tmp = copysign(log(Float32(x + hypot(Float32(1.0), x))), x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = single(0.0);
	if (x <= single(-0.019999999552965164))
		tmp = sign(x) * abs((single(0.3333333333333333) * (single(3.0) * log((single(1.0) / (hypot(single(1.0), x) - x))))));
	elseif (x <= single(0.0010000000474974513))
		tmp = sign(x) * abs(x);
	else
		tmp = sign(x) * abs(log((x + hypot(single(1.0), x))));
	end
	tmp_2 = tmp;
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 98.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\left(\left|x\right| - x\right) + \frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;x \leq 0.0010000000474974513:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (if (<= x -1.0)
   (copysign (log (+ (- (fabs x) x) (/ -0.5 x))) x)
   (if (<= x 0.0010000000474974513)
     (copysign x x)
     (copysign (log (+ x (hypot 1.0 x))) x))))

C

float code(float x) {
	float tmp;
	if (x <= -1.0f) {
		tmp = copysignf(logf(((fabsf(x) - x) + (-0.5f / x))), x);
	} else if (x <= 0.0010000000474974513f) {
		tmp = copysignf(x, x);
	} else {
		tmp = copysignf(logf((x + hypotf(1.0f, x))), x);
	}
	return tmp;
}

Julia

function code(x)
	tmp = Float32(0.0)
	if (x <= Float32(-1.0))
		tmp = copysign(log(Float32(Float32(abs(x) - x) + Float32(Float32(-0.5) / x))), x);
	elseif (x <= Float32(0.0010000000474974513))
		tmp = copysign(x, x);
	else
		tmp = copysign(log(Float32(x + hypot(Float32(1.0), x))), x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = single(0.0);
	if (x <= single(-1.0))
		tmp = sign(x) * abs(log(((abs(x) - x) + (single(-0.5) / x))));
	elseif (x <= single(0.0010000000474974513))
		tmp = sign(x) * abs(x);
	else
		tmp = sign(x) * abs(log((x + hypot(single(1.0), x))));
	end
	tmp_2 = tmp;
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 98.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;x \leq 0.0010000000474974513:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + \mathsf{hypot}\left(1, x\right)\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (if (<= x -1.0)
   (copysign (log (/ -0.5 x)) x)
   (if (<= x 0.0010000000474974513)
     (copysign x x)
     (copysign (log (+ x (hypot 1.0 x))) x))))

C

float code(float x) {
	float tmp;
	if (x <= -1.0f) {
		tmp = copysignf(logf((-0.5f / x)), x);
	} else if (x <= 0.0010000000474974513f) {
		tmp = copysignf(x, x);
	} else {
		tmp = copysignf(logf((x + hypotf(1.0f, x))), x);
	}
	return tmp;
}

Julia

function code(x)
	tmp = Float32(0.0)
	if (x <= Float32(-1.0))
		tmp = copysign(log(Float32(Float32(-0.5) / x)), x);
	elseif (x <= Float32(0.0010000000474974513))
		tmp = copysign(x, x);
	else
		tmp = copysign(log(Float32(x + hypot(Float32(1.0), x))), x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = single(0.0);
	if (x <= single(-1.0))
		tmp = sign(x) * abs(log((single(-0.5) / x)));
	elseif (x <= single(0.0010000000474974513))
		tmp = sign(x) * abs(x);
	else
		tmp = sign(x) * abs(log((x + hypot(single(1.0), x))));
	end
	tmp_2 = tmp;
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 97.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;x \leq 0.019999999552965164:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{0.5}{x} + \left(x + x\right)\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (if (<= x -1.0)
   (copysign (log (/ -0.5 x)) x)
   (if (<= x 0.019999999552965164)
     (copysign x x)
     (copysign (log (+ (/ 0.5 x) (+ x x))) x))))

C

float code(float x) {
	float tmp;
	if (x <= -1.0f) {
		tmp = copysignf(logf((-0.5f / x)), x);
	} else if (x <= 0.019999999552965164f) {
		tmp = copysignf(x, x);
	} else {
		tmp = copysignf(logf(((0.5f / x) + (x + x))), x);
	}
	return tmp;
}

Julia

function code(x)
	tmp = Float32(0.0)
	if (x <= Float32(-1.0))
		tmp = copysign(log(Float32(Float32(-0.5) / x)), x);
	elseif (x <= Float32(0.019999999552965164))
		tmp = copysign(x, x);
	else
		tmp = copysign(log(Float32(Float32(Float32(0.5) / x) + Float32(x + x))), x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = single(0.0);
	if (x <= single(-1.0))
		tmp = sign(x) * abs(log((single(-0.5) / x)));
	elseif (x <= single(0.019999999552965164))
		tmp = sign(x) * abs(x);
	else
		tmp = sign(x) * abs(log(((single(0.5) / x) + (x + x))));
	end
	tmp_2 = tmp;
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 96.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(\frac{-0.5}{x}\right), x\right)\\ \mathbf{elif}\;x \leq 0.019999999552965164:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + x\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (if (<= x -1.0)
   (copysign (log (/ -0.5 x)) x)
   (if (<= x 0.019999999552965164) (copysign x x) (copysign (log (+ x x)) x))))

C

float code(float x) {
	float tmp;
	if (x <= -1.0f) {
		tmp = copysignf(logf((-0.5f / x)), x);
	} else if (x <= 0.019999999552965164f) {
		tmp = copysignf(x, x);
	} else {
		tmp = copysignf(logf((x + x)), x);
	}
	return tmp;
}

Julia

function code(x)
	tmp = Float32(0.0)
	if (x <= Float32(-1.0))
		tmp = copysign(log(Float32(Float32(-0.5) / x)), x);
	elseif (x <= Float32(0.019999999552965164))
		tmp = copysign(x, x);
	else
		tmp = copysign(log(Float32(x + x)), x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = single(0.0);
	if (x <= single(-1.0))
		tmp = sign(x) * abs(log((single(-0.5) / x)));
	elseif (x <= single(0.019999999552965164))
		tmp = sign(x) * abs(x);
	else
		tmp = sign(x) * abs(log((x + x)));
	end
	tmp_2 = tmp;
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 62.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.019999999552965164:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + 1\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (if (<= x 0.019999999552965164) (copysign x x) (copysign (log (+ x 1.0)) x)))

C

float code(float x) {
	float tmp;
	if (x <= 0.019999999552965164f) {
		tmp = copysignf(x, x);
	} else {
		tmp = copysignf(logf((x + 1.0f)), x);
	}
	return tmp;
}

Julia

function code(x)
	tmp = Float32(0.0)
	if (x <= Float32(0.019999999552965164))
		tmp = copysign(x, x);
	else
		tmp = copysign(log(Float32(x + Float32(1.0))), x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = single(0.0);
	if (x <= single(0.019999999552965164))
		tmp = sign(x) * abs(x);
	else
		tmp = sign(x) * abs(log((x + single(1.0))));
	end
	tmp_2 = tmp;
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 75.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.019999999552965164:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\log \left(x + x\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (if (<= x 0.019999999552965164) (copysign x x) (copysign (log (+ x x)) x)))

C

float code(float x) {
	float tmp;
	if (x <= 0.019999999552965164f) {
		tmp = copysignf(x, x);
	} else {
		tmp = copysignf(logf((x + x)), x);
	}
	return tmp;
}

Julia

function code(x)
	tmp = Float32(0.0)
	if (x <= Float32(0.019999999552965164))
		tmp = copysign(x, x);
	else
		tmp = copysign(log(Float32(x + x)), x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = single(0.0);
	if (x <= single(0.019999999552965164))
		tmp = sign(x) * abs(x);
	else
		tmp = sign(x) * abs(log((x + x)));
	end
	tmp_2 = tmp;
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 62.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.019999999552965164:\\ \;\;\;\;\mathsf{copysign}\left(x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{copysign}\left(\mathsf{log1p}\left(x\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (if (<= x 0.019999999552965164) (copysign x x) (copysign (log1p x) x)))

C

float code(float x) {
	float tmp;
	if (x <= 0.019999999552965164f) {
		tmp = copysignf(x, x);
	} else {
		tmp = copysignf(log1pf(x), x);
	}
	return tmp;
}

Julia

function code(x)
	tmp = Float32(0.0)
	if (x <= Float32(0.019999999552965164))
		tmp = copysign(x, x);
	else
		tmp = copysign(log1p(x), x);
	end
	return tmp
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 54.7% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{copysign}\left(x, x\right) \end{array} \]

FPCore

(FPCore (x) :precision binary32 (copysign x x))

C

float code(float x) {
	return copysignf(x, x);
}

Julia

function code(x)
	return copysign(x, x)
end

MATLAB

function tmp = code(x)
	tmp = sign(x) * abs(x);
end

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 99.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\left|x\right|}\\ \mathsf{copysign}\left(\mathsf{log1p}\left(\left|x\right| + \frac{\left|x\right|}{\mathsf{hypot}\left(1, t_0\right) + t_0}\right), x\right) \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary32
 (let* ((t_0 (/ 1.0 (fabs x))))
   (copysign (log1p (+ (fabs x) (/ (fabs x) (+ (hypot 1.0 t_0) t_0)))) x)))

C

float code(float x) {
	float t_0 = 1.0f / fabsf(x);
	return copysignf(log1pf((fabsf(x) + (fabsf(x) / (hypotf(1.0f, t_0) + t_0)))), x);
}

Julia

function code(x)
	t_0 = Float32(Float32(1.0) / abs(x))
	return copysign(log1p(Float32(abs(x) + Float32(abs(x) / Float32(hypot(Float32(1.0), t_0) + t_0)))), x)
end

Reproduce

herbie shell --seed 2023343 
(FPCore (x)
  :name "Rust f32::asinh"
  :precision binary32

  :herbie-target
  (copysign (log1p (+ (fabs x) (/ (fabs x) (+ (hypot 1.0 (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))))) x)

  (copysign (log (+ (fabs x) (sqrt (+ (* x x) 1.0)))) x))