Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1

Average Accuracy: 27.3% → 31.4%

Time: 28.8s

Precision: binary64

Cost: 87556

Math

\[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]

↓

\[\begin{array}{l} t_1 := z \cdot \mathsf{fma}\left(0.125, y, 0.0625\right)\\ \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 4 \cdot 10^{+283}:\\ \;\;\;\;\frac{x \cdot {\left(\sqrt[3]{\cos \left(t \cdot \left(b \cdot 0.0625\right)\right) \cdot \cos \left(\mathsf{fma}\left(0.125, y, 0.0625\right) \cdot \left(z \cdot t\right)\right)}\right)}^{2}}{\frac{\sqrt[3]{2}}{\sqrt[3]{\cos \left(t \cdot \left(b \cdot 0.0625 + t_1\right)\right) + \cos \left(t \cdot \left(t_1 + b \cdot -0.0625\right)\right)}}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (*
  (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
  (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (fma 0.125 y 0.0625))))
   (if (<=
        (*
         (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
         (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
        4e+283)
     (/
      (*
       x
       (pow
        (cbrt
         (* (cos (* t (* b 0.0625))) (cos (* (fma 0.125 y 0.0625) (* z t)))))
        2.0))
      (/
       (cbrt 2.0)
       (cbrt
        (+
         (cos (* t (+ (* b 0.0625) t_1)))
         (cos (* t (+ t_1 (* b -0.0625))))))))
     x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * fma(0.125, y, 0.0625);
	double tmp;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 4e+283) {
		tmp = (x * pow(cbrt((cos((t * (b * 0.0625))) * cos((fma(0.125, y, 0.0625) * (z * t))))), 2.0)) / (cbrt(2.0) / cbrt((cos((t * ((b * 0.0625) + t_1))) + cos((t * (t_1 + (b * -0.0625)))))));
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(Float64(Float64(Float64(a * 2.0) + 1.0) * b) * t) / 16.0)))
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(z * fma(0.125, y, 0.0625))
	tmp = 0.0
	if (Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 4e+283)
		tmp = Float64(Float64(x * (cbrt(Float64(cos(Float64(t * Float64(b * 0.0625))) * cos(Float64(fma(0.125, y, 0.0625) * Float64(z * t))))) ^ 2.0)) / Float64(cbrt(2.0) / cbrt(Float64(cos(Float64(t * Float64(Float64(b * 0.0625) + t_1))) + cos(Float64(t * Float64(t_1 + Float64(b * -0.0625))))))));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(N[(N[(N[(a * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * b), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(0.125 * y + 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * N[(N[(1.0 + N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 4e+283], N[(N[(x * N[Power[N[Power[N[(N[Cos[N[(t * N[(b * 0.0625), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(N[(0.125 * y + 0.0625), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(N[Power[2.0, 1/3], $MachinePrecision] / N[Power[N[(N[Cos[N[(t * N[(N[(b * 0.0625), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[Cos[N[(t * N[(t$95$1 + N[(b * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Target

Original	27.3%
Target	30.0%
Herbie	31.4%

\[x \cdot \cos \left(\frac{b}{16} \cdot \frac{t}{\left(1 - a \cdot 2\right) + {\left(a \cdot 2\right)}^{2}}\right) \]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16))) < 3.99999999999999982e283

   1. Initial program 46.7%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]

   2. Simplified 46.7%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(\left(t \cdot b\right) \cdot \left(\frac{a}{8} + 0.0625\right)\right)\right)} \]
      Proof

      [Start] 46.7	\[ \left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
      associate-*l* [=>] 46.7	\[ \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

   3. Taylor expanded in a around 0 46.2%

      \[\leadsto x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \color{blue}{\cos \left(0.0625 \cdot \left(t \cdot b\right)\right)}\right) \]

   4. Simplified 46.2%

      \[\leadsto x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \color{blue}{\cos \left(t \cdot \left(0.0625 \cdot b\right)\right)}\right) \]
      Proof

      [Start] 46.2	\[ x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(0.0625 \cdot \left(t \cdot b\right)\right)\right) \]
      *-commutative [=>] 46.2	\[ x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \color{blue}{\left(\left(t \cdot b\right) \cdot 0.0625\right)}\right) \]
      associate-*l* [=>] 46.2	\[ x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \color{blue}{\left(t \cdot \left(b \cdot 0.0625\right)\right)}\right) \]
      *-commutative [<=] 46.2	\[ x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \color{blue}{\left(0.0625 \cdot b\right)}\right)\right) \]

   5. Applied egg-rr 45.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot {\left(\sqrt[3]{\cos \left(t \cdot \left(0.0625 \cdot b\right)\right) \cdot \cos \left(z \cdot \left(t \cdot \mathsf{fma}\left(y, 0.125, 0.0625\right)\right)\right)}\right)}^{2}\right) \cdot \sqrt[3]{\cos \left(\mathsf{fma}\left(z, t \cdot \mathsf{fma}\left(y, 0.125, 0.0625\right), t \cdot \left(0.0625 \cdot b\right)\right)\right) + \cos \left(\mathsf{fma}\left(t \cdot z, \mathsf{fma}\left(y, 0.125, 0.0625\right), -t \cdot \left(0.0625 \cdot b\right)\right)\right)}}{\sqrt[3]{2}}} \]
      Proof

      [Start] 46.2	\[ x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right)\right) \]
      add-cube-cbrt [=>] 46.2	\[ x \cdot \color{blue}{\left(\left(\sqrt[3]{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right)} \cdot \sqrt[3]{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right)}\right) \cdot \sqrt[3]{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right)}\right)} \]
      associate-*r* [=>] 46.2	\[ \color{blue}{\left(x \cdot \left(\sqrt[3]{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right)} \cdot \sqrt[3]{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right)}\right)\right) \cdot \sqrt[3]{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right)}} \]
      cos-mult [=>] 46.2	\[ \left(x \cdot \left(\sqrt[3]{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right)} \cdot \sqrt[3]{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right)}\right)\right) \cdot \sqrt[3]{\color{blue}{\frac{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right) + t \cdot \left(0.0625 \cdot b\right)\right) + \cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right) - t \cdot \left(0.0625 \cdot b\right)\right)}{2}}} \]
      cbrt-div [=>] 46.2	\[ \left(x \cdot \left(\sqrt[3]{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right)} \cdot \sqrt[3]{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \left(0.0625 \cdot b\right)\right)}\right)\right) \cdot \color{blue}{\frac{\sqrt[3]{\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right) + t \cdot \left(0.0625 \cdot b\right)\right) + \cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right) - t \cdot \left(0.0625 \cdot b\right)\right)}}{\sqrt[3]{2}}} \]

   6. Simplified 46.2%

      \[\leadsto \color{blue}{\frac{x \cdot {\left(\sqrt[3]{\cos \left(t \cdot \left(b \cdot 0.0625\right)\right) \cdot \cos \left(\mathsf{fma}\left(0.125, y, 0.0625\right) \cdot \left(t \cdot z\right)\right)}\right)}^{2}}{\frac{\sqrt[3]{2}}{\sqrt[3]{\cos \left(t \cdot \left(\mathsf{fma}\left(0.125, y, 0.0625\right) \cdot z + b \cdot 0.0625\right)\right) + \cos \left(t \cdot \left(\mathsf{fma}\left(0.125, y, 0.0625\right) \cdot z + b \cdot -0.0625\right)\right)}}}} \]
      Proof

      [Start] 45.7

      \[ \frac{\left(x \cdot {\left(\sqrt[3]{\cos \left(t \cdot \left(0.0625 \cdot b\right)\right) \cdot \cos \left(z \cdot \left(t \cdot \mathsf{fma}\left(y, 0.125, 0.0625\right)\right)\right)}\right)}^{2}\right) \cdot \sqrt[3]{\cos \left(\mathsf{fma}\left(z, t \cdot \mathsf{fma}\left(y, 0.125, 0.0625\right), t \cdot \left(0.0625 \cdot b\right)\right)\right) + \cos \left(\mathsf{fma}\left(t \cdot z, \mathsf{fma}\left(y, 0.125, 0.0625\right), -t \cdot \left(0.0625 \cdot b\right)\right)\right)}}{\sqrt[3]{2}} \]

      associate-/l* [=>] 45.8

      \[ \color{blue}{\frac{x \cdot {\left(\sqrt[3]{\cos \left(t \cdot \left(0.0625 \cdot b\right)\right) \cdot \cos \left(z \cdot \left(t \cdot \mathsf{fma}\left(y, 0.125, 0.0625\right)\right)\right)}\right)}^{2}}{\frac{\sqrt[3]{2}}{\sqrt[3]{\cos \left(\mathsf{fma}\left(z, t \cdot \mathsf{fma}\left(y, 0.125, 0.0625\right), t \cdot \left(0.0625 \cdot b\right)\right)\right) + \cos \left(\mathsf{fma}\left(t \cdot z, \mathsf{fma}\left(y, 0.125, 0.0625\right), -t \cdot \left(0.0625 \cdot b\right)\right)\right)}}}} \]

   if 3.99999999999999982e283 < (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16)))

   1. Initial program 1.4%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]

   2. Simplified 3.6%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(\left(t \cdot b\right) \cdot \left(\frac{a}{8} + 0.0625\right)\right)\right)} \]
      Proof

      [Start] 1.4	\[ \left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
      associate-*l* [=>] 1.4	\[ \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

   3. Taylor expanded in a around 0 5.1%

      \[\leadsto x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \color{blue}{\cos \left(0.0625 \cdot \left(t \cdot b\right)\right)}\right) \]

   4. Simplified 5.1%

      \[\leadsto x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \color{blue}{\cos \left(t \cdot \left(0.0625 \cdot b\right)\right)}\right) \]
      Proof

      [Start] 5.1	\[ x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(0.0625 \cdot \left(t \cdot b\right)\right)\right) \]
      *-commutative [=>] 5.1	\[ x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \color{blue}{\left(\left(t \cdot b\right) \cdot 0.0625\right)}\right) \]
      associate-*l* [=>] 5.1	\[ x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \color{blue}{\left(t \cdot \left(b \cdot 0.0625\right)\right)}\right) \]
      *-commutative [<=] 5.1	\[ x \cdot \left(\cos \left(\left(z \cdot t\right) \cdot \left(0.0625 + \frac{y}{8}\right)\right) \cdot \cos \left(t \cdot \color{blue}{\left(0.0625 \cdot b\right)}\right)\right) \]

   5. Taylor expanded in t around 0 11.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 4 \cdot 10^{+283}:\\ \;\;\;\;\frac{x \cdot {\left(\sqrt[3]{\cos \left(t \cdot \left(b \cdot 0.0625\right)\right) \cdot \cos \left(\mathsf{fma}\left(0.125, y, 0.0625\right) \cdot \left(z \cdot t\right)\right)}\right)}^{2}}{\frac{\sqrt[3]{2}}{\sqrt[3]{\cos \left(t \cdot \left(b \cdot 0.0625 + z \cdot \mathsf{fma}\left(0.125, y, 0.0625\right)\right)\right) + \cos \left(t \cdot \left(z \cdot \mathsf{fma}\left(0.125, y, 0.0625\right) + b \cdot -0.0625\right)\right)}}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	31.4%
Cost	41796

\[\begin{array}{l} t_1 := z \cdot \mathsf{fma}\left(0.125, y, 0.0625\right)\\ \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 4 \cdot 10^{+283}:\\ \;\;\;\;\frac{x}{2} \cdot \left(\cos \left(t \cdot \left(b \cdot 0.0625 + t_1\right)\right) + \cos \left(t \cdot \left(b \cdot 0.0625 - t_1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Accuracy	31.5%
Cost	41412

\[\begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 6 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \left(\cos \left(\frac{z \cdot \mathsf{fma}\left(y, 2, 1\right)}{\frac{16}{t}}\right) \cdot \cos \left(\frac{b \cdot \mathsf{fma}\left(a, 2, 1\right)}{\frac{16}{t}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	31.4%
Cost	34756

\[\begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 4 \cdot 10^{+283}:\\ \;\;\;\;x \cdot \left(\cos \left(t \cdot \left(b \cdot 0.0625\right)\right) \cdot \cos \left(\frac{z \cdot \mathsf{fma}\left(y, 2, 1\right)}{\frac{16}{t}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Accuracy	31.4%
Cost	28484

\[\begin{array}{l} t_1 := x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\\ \mathbf{if}\;t_1 \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 4 \cdot 10^{+283}:\\ \;\;\;\;t_1 \cdot \cos \left(\frac{t \cdot b}{16}\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5
Accuracy	30.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023138 
(FPCore (x y z t a b)
  :name "Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1"
  :precision binary64

  :herbie-target
  (* x (cos (* (/ b 16.0) (/ t (+ (- 1.0 (* a 2.0)) (pow (* a 2.0) 2.0))))))

  (* (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0))) (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))