Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, K

Average Error: 20.6 → 16.4

Time: 25.0s

Precision: binary64

Cost: 34120

Math

\[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]

↓

\[\begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{\frac{a}{-3}}{b}\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+160}:\\ \;\;\;\;t_1 \cdot \left(\cos y \cdot \cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) - \sin y \cdot \sin \left(\left(z \cdot t\right) \cdot -0.3333333333333333\right)\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \cos y - \frac{\frac{a}{b}}{3}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= (* z t) -5e+158)
     (fma 2.0 (sqrt x) (/ (/ a -3.0) b))
     (if (<= (* z t) 5e+160)
       (-
        (*
         t_1
         (-
          (* (cos y) (cos (* t (* z -0.3333333333333333))))
          (* (sin y) (sin (* (* z t) -0.3333333333333333)))))
        (/ a (* b 3.0)))
       (- (* t_1 (cos y)) (/ (/ a b) 3.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double tmp;
	if ((z * t) <= -5e+158) {
		tmp = fma(2.0, sqrt(x), ((a / -3.0) / b));
	} else if ((z * t) <= 5e+160) {
		tmp = (t_1 * ((cos(y) * cos((t * (z * -0.3333333333333333)))) - (sin(y) * sin(((z * t) * -0.3333333333333333))))) - (a / (b * 3.0));
	} else {
		tmp = (t_1 * cos(y)) - ((a / b) / 3.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0)))
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(z * t) <= -5e+158)
		tmp = fma(2.0, sqrt(x), Float64(Float64(a / -3.0) / b));
	elseif (Float64(z * t) <= 5e+160)
		tmp = Float64(Float64(t_1 * Float64(Float64(cos(y) * cos(Float64(t * Float64(z * -0.3333333333333333)))) - Float64(sin(y) * sin(Float64(Float64(z * t) * -0.3333333333333333))))) - Float64(a / Float64(b * 3.0)));
	else
		tmp = Float64(Float64(t_1 * cos(y)) - Float64(Float64(a / b) / 3.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -5e+158], N[(2.0 * N[Sqrt[x], $MachinePrecision] + N[(N[(a / -3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+160], N[(N[(t$95$1 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(t * N[(z * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(N[(z * t), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	20.6
Target	18.9
Herbie	16.4

\[\begin{array}{l} \mathbf{if}\;z < -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1}{y} - \frac{\frac{0.3333333333333333}{z}}{t}\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{elif}\;z < 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.3333333333333333}{z}}{t}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3}\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.9999999999999996e158

   1. Initial program 46.8

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]

   2. Simplified 46.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(2, \sqrt{x} \cdot \cos \left(\mathsf{fma}\left(z, t \cdot -0.3333333333333333, y\right)\right), \frac{\frac{a}{-3}}{b}\right)} \]
      Proof
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (*.f64 t (Rewrite<= metadata-eval (/.f64 -1 3))) y))) (/.f64 (/.f64 a -3) b)): 20 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (Rewrite=> *-commutative_binary64 (*.f64 (/.f64 -1 3) t)) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 20 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (Rewrite<= associate-/r/_binary64 (/.f64 -1 (/.f64 3 t))) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 -1 t) 3)) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (/.f64 (Rewrite=> mul-1-neg_binary64 (neg.f64 t)) 3) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (/.f64 (neg.f64 t) 3)) y)))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 z (neg.f64 t)) 3)) y))) (/.f64 (/.f64 a -3) b)): 20 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (+.f64 (/.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 z t))) 3) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 20 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (+.f64 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (*.f64 z t) 3))) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (Rewrite<= +-commutative_binary64 (+.f64 y (neg.f64 (/.f64 (*.f64 z t) 3)))))) (/.f64 (/.f64 a -3) b)): 20 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (Rewrite<= sub-neg_binary64 (-.f64 y (/.f64 (*.f64 z t) 3))))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 20 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 (/.f64 a (Rewrite<= metadata-eval (/.f64 3 -1))) b)): 16 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 a -1) 3)) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1 a)) 3) b)): 0 points increase in error, 16 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 a)) 3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (Rewrite=> associate-/l/_binary64 (/.f64 (neg.f64 a) (*.f64 b 3)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 a (*.f64 b 3))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))) (/.f64 a (*.f64 b 3)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))) (/.f64 a (*.f64 b 3))): 16 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around 0 33.6

      \[\leadsto \mathsf{fma}\left(2, \sqrt{x} \cdot \color{blue}{\cos y}, \frac{\frac{a}{-3}}{b}\right) \]

   4. Taylor expanded in y around 0 33.5

      \[\leadsto \mathsf{fma}\left(2, \color{blue}{\sqrt{x}}, \frac{\frac{a}{-3}}{b}\right) \]

   if -4.9999999999999996e158 < (*.f64 z t) < 5.0000000000000002e160

   1. Initial program 10.5

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]

   2. Simplified 10.5

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{3} \cdot t\right) - \frac{a}{3 \cdot b}} \]
      Proof
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (*.f64 t -1/3) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (*.f64 t (Rewrite<= metadata-eval (/.f64 -1 3))) y))) (/.f64 (/.f64 a -3) b)): 20 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (Rewrite=> *-commutative_binary64 (*.f64 (/.f64 -1 3) t)) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 20 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (Rewrite<= associate-/r/_binary64 (/.f64 -1 (/.f64 3 t))) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 -1 t) 3)) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (fma.f64 z (/.f64 (Rewrite=> mul-1-neg_binary64 (neg.f64 t)) 3) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (/.f64 (neg.f64 t) 3)) y)))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 z (neg.f64 t)) 3)) y))) (/.f64 (/.f64 a -3) b)): 20 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (+.f64 (/.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 z t))) 3) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 20 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (+.f64 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (*.f64 z t) 3))) y))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (Rewrite<= +-commutative_binary64 (+.f64 y (neg.f64 (/.f64 (*.f64 z t) 3)))))) (/.f64 (/.f64 a -3) b)): 20 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (Rewrite<= sub-neg_binary64 (-.f64 y (/.f64 (*.f64 z t) 3))))) (/.f64 (/.f64 a -3) b)): 0 points increase in error, 20 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 (/.f64 a (Rewrite<= metadata-eval (/.f64 3 -1))) b)): 16 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 a -1) 3)) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1 a)) 3) b)): 0 points increase in error, 16 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 a)) 3) b)): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (Rewrite=> associate-/l/_binary64 (/.f64 (neg.f64 a) (*.f64 b 3)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 a (*.f64 b 3))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 2 (*.f64 (sqrt.f64 x) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))) (/.f64 a (*.f64 b 3)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))) (/.f64 a (*.f64 b 3))): 16 points increase in error, 0 points decrease in error

   3. Applied egg-rr 9.8

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) - \sin y \cdot \sin \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right)\right)} - \frac{a}{3 \cdot b} \]

   4. Taylor expanded in t around inf 9.8

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) - \sin y \cdot \color{blue}{\sin \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)}\right) - \frac{a}{3 \cdot b} \]

   if 5.0000000000000002e160 < (*.f64 z t)

   1. Initial program 47.6

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]

   2. Taylor expanded in z around 0 33.9

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

   3. Applied egg-rr 33.9

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{\left(3 \cdot \frac{b}{a}\right)}^{-1}} \]

   4. Applied egg-rr 33.9

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{a}{b}}{3}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 16.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+158}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{\frac{a}{-3}}{b}\right)\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+160}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) - \sin y \cdot \sin \left(\left(z \cdot t\right) \cdot -0.3333333333333333\right)\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{a}{b}}{3}\\ \end{array} \]

Alternatives

Alternative 1
Error	16.8
Cost	27720

\[\begin{array}{l} t_1 := \frac{\frac{a}{b}}{3}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;z \cdot t \leq -200000000000:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;z \cdot t \leq 20000000000:\\ \;\;\;\;t_2 \cdot \left(\cos y \cdot \cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) - \sin y \cdot \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right)\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \cos y - t_1\\ \end{array} \]

Alternative 2
Error	20.5
Cost	13896

\[\begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-110}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-142}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 - \frac{\frac{a}{b}}{3}\\ \end{array} \]

Alternative 3
Error	20.5
Cost	13896

\[\begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-110}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x}, \frac{\frac{a}{-3}}{b}\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-142}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{b}}{3}\\ \end{array} \]

Alternative 4
Error	17.2
Cost	13504

\[\left(2 \cdot \sqrt{x}\right) \cdot \cos y - a \cdot \frac{0.3333333333333333}{b} \]

Alternative 5
Error	17.2
Cost	13504

\[\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{b \cdot 3} \]

Alternative 6
Error	17.2
Cost	13504

\[\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{a}{b}}{3} \]

Alternative 7
Error	25.3
Cost	6976

\[2 \cdot \sqrt{x} + -0.3333333333333333 \cdot \frac{a}{b} \]

Alternative 8
Error	25.3
Cost	6976

\[2 \cdot \sqrt{x} - \frac{a}{b \cdot 3} \]

Alternative 9
Error	25.3
Cost	6976

\[2 \cdot \sqrt{x} - \frac{\frac{a}{b}}{3} \]

Alternative 10
Error	36.3
Cost	320

\[-0.3333333333333333 \cdot \frac{a}{b} \]

Alternative 11
Error	36.3
Cost	320

\[\frac{\frac{a}{-3}}{b} \]

Reproduce

herbie shell --seed 2022343 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :herbie-target
  (if (< z -1.3793337487235141e+129) (- (* (* 2.0 (sqrt x)) (cos (- (/ 1.0 y) (/ (/ 0.3333333333333333 z) t)))) (/ (/ a 3.0) b)) (if (< z 3.516290613555987e+106) (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) (/ (/ a 3.0) b)) (- (* (cos (- y (/ (/ 0.3333333333333333 z) t))) (* 2.0 (sqrt x))) (/ (/ a b) 3.0))))

  (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))