Henrywood and Agarwal, Equation (13)

Percentage Accurate: 24.4% → 61.9%

Time: 34.3s

Precision: binary64

Cost: 44484

• could not determine a ground truth

  1. c0 = 1.3151336228713046e+289
  2. w = -7.570651180250974e-304
  3. h = 209050.5621829761
  4. D = -1.3944022307464933e-300
  5. d = 3.3922194564256224e+185
  6. M = 1.2806600203017494e+187

Math

\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

↓

\[\begin{array}{l} t_0 := \frac{c0}{w \cdot h}\\ t_1 := h \cdot \left(M \cdot M\right)\\ t_2 := t_0 \cdot {\left(\frac{d}{D}\right)}^{2}\\ t_3 := \frac{c0}{2 \cdot w}\\ t_4 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ t_5 := t_3 \cdot \left(t_4 + \sqrt{t_4 \cdot t_4 - M \cdot M}\right)\\ \mathbf{if}\;t_5 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;t_3 \cdot \mathsf{fma}\left(t_0, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{M + t_2} \cdot \sqrt{t_2 - M}\right)\\ \mathbf{elif}\;t_5 \leq 0:\\ \;\;\;\;0.25 \cdot \frac{D \cdot t_1}{d \cdot \frac{d}{D}}\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;\frac{{\left(c0 \cdot d\right)}^{2}}{w \cdot \left(w \cdot \left(D \cdot \left(h \cdot D\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \left(t_1 \cdot \left(\frac{D}{d} \cdot \frac{D}{d}\right)\right)\\ \end{array} \]

FPCore

(FPCore (c0 w h D d M)
 :precision binary64
 (*
  (/ c0 (* 2.0 w))
  (+
   (/ (* c0 (* d d)) (* (* w h) (* D D)))
   (sqrt
    (-
     (*
      (/ (* c0 (* d d)) (* (* w h) (* D D)))
      (/ (* c0 (* d d)) (* (* w h) (* D D))))
     (* M M))))))

↓

(FPCore (c0 w h D d M)
 :precision binary64
 (let* ((t_0 (/ c0 (* w h)))
        (t_1 (* h (* M M)))
        (t_2 (* t_0 (pow (/ d D) 2.0)))
        (t_3 (/ c0 (* 2.0 w)))
        (t_4 (/ (* c0 (* d d)) (* (* w h) (* D D))))
        (t_5 (* t_3 (+ t_4 (sqrt (- (* t_4 t_4) (* M M)))))))
   (if (<= t_5 -2e-304)
     (*
      t_3
      (fma t_0 (* (/ d D) (/ d D)) (* (sqrt (+ M t_2)) (sqrt (- t_2 M)))))
     (if (<= t_5 0.0)
       (* 0.25 (/ (* D t_1) (* d (/ d D))))
       (if (<= t_5 INFINITY)
         (/ (pow (* c0 d) 2.0) (* w (* w (* D (* h D)))))
         (* 0.25 (* t_1 (* (/ D d) (/ D d)))))))))

C

double code(double c0, double w, double h, double D, double d, double M) {
	return (c0 / (2.0 * w)) * (((c0 * (d * d)) / ((w * h) * (D * D))) + sqrt(((((c0 * (d * d)) / ((w * h) * (D * D))) * ((c0 * (d * d)) / ((w * h) * (D * D)))) - (M * M))));
}

↓

double code(double c0, double w, double h, double D, double d, double M) {
	double t_0 = c0 / (w * h);
	double t_1 = h * (M * M);
	double t_2 = t_0 * pow((d / D), 2.0);
	double t_3 = c0 / (2.0 * w);
	double t_4 = (c0 * (d * d)) / ((w * h) * (D * D));
	double t_5 = t_3 * (t_4 + sqrt(((t_4 * t_4) - (M * M))));
	double tmp;
	if (t_5 <= -2e-304) {
		tmp = t_3 * fma(t_0, ((d / D) * (d / D)), (sqrt((M + t_2)) * sqrt((t_2 - M))));
	} else if (t_5 <= 0.0) {
		tmp = 0.25 * ((D * t_1) / (d * (d / D)));
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = pow((c0 * d), 2.0) / (w * (w * (D * (h * D))));
	} else {
		tmp = 0.25 * (t_1 * ((D / d) * (D / d)));
	}
	return tmp;
}

Julia

function code(c0, w, h, D, d, M)
	return Float64(Float64(c0 / Float64(2.0 * w)) * Float64(Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D))) + sqrt(Float64(Float64(Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D))) * Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))) - Float64(M * M)))))
end

↓

function code(c0, w, h, D, d, M)
	t_0 = Float64(c0 / Float64(w * h))
	t_1 = Float64(h * Float64(M * M))
	t_2 = Float64(t_0 * (Float64(d / D) ^ 2.0))
	t_3 = Float64(c0 / Float64(2.0 * w))
	t_4 = Float64(Float64(c0 * Float64(d * d)) / Float64(Float64(w * h) * Float64(D * D)))
	t_5 = Float64(t_3 * Float64(t_4 + sqrt(Float64(Float64(t_4 * t_4) - Float64(M * M)))))
	tmp = 0.0
	if (t_5 <= -2e-304)
		tmp = Float64(t_3 * fma(t_0, Float64(Float64(d / D) * Float64(d / D)), Float64(sqrt(Float64(M + t_2)) * sqrt(Float64(t_2 - M)))));
	elseif (t_5 <= 0.0)
		tmp = Float64(0.25 * Float64(Float64(D * t_1) / Float64(d * Float64(d / D))));
	elseif (t_5 <= Inf)
		tmp = Float64((Float64(c0 * d) ^ 2.0) / Float64(w * Float64(w * Float64(D * Float64(h * D)))));
	else
		tmp = Float64(0.25 * Float64(t_1 * Float64(Float64(D / d) * Float64(D / d))));
	end
	return tmp
end

Wolfram

code[c0_, w_, h_, D_, d_, M_] := N[(N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[Sqrt[N[(N[(N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[c0_, w_, h_, D_, d_, M_] := Block[{t$95$0 = N[(c0 / N[(w * h), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(h * N[(M * M), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 * N[Power[N[(d / D), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c0 / N[(2.0 * w), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(c0 * N[(d * d), $MachinePrecision]), $MachinePrecision] / N[(N[(w * h), $MachinePrecision] * N[(D * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 * N[(t$95$4 + N[Sqrt[N[(N[(t$95$4 * t$95$4), $MachinePrecision] - N[(M * M), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, -2e-304], N[(t$95$3 * N[(t$95$0 * N[(N[(d / D), $MachinePrecision] * N[(d / D), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(M + t$95$2), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(t$95$2 - M), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, 0.0], N[(0.25 * N[(N[(D * t$95$1), $MachinePrecision] / N[(d * N[(d / D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, Infinity], N[(N[Power[N[(c0 * d), $MachinePrecision], 2.0], $MachinePrecision] / N[(w * N[(w * N[(D * N[(h * D), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.25 * N[(t$95$1 * N[(N[(D / d), $MachinePrecision] * N[(D / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))) < -1.99999999999999994e-304

   1. Initial program 84.6%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   2. Simplified 82.7%

      \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\left(d \cdot d\right) \cdot \frac{c0}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M\right)}\right)} \]
      Step-by-step derivation

      [Start] 84.6%	\[ \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
      times-frac [=>] 82.6%	\[ \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0}{w \cdot h} \cdot \frac{d \cdot d}{D \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
      fma-def [=>] 82.6%	\[ \frac{c0}{2 \cdot w} \cdot \color{blue}{\mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d \cdot d}{D \cdot D}, \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]
      times-frac [=>] 82.6%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \color{blue}{\frac{d}{D} \cdot \frac{d}{D}}, \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
      difference-of-squares [=>] 82.6%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\color{blue}{\left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + M\right) \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M\right)}}\right) \]

   3. Applied egg-rr 77.4%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\color{blue}{\frac{\frac{\frac{c0}{h}}{w} \cdot \left(d \cdot \frac{d}{D}\right)}{D}} - M\right)}\right) \]
      Step-by-step derivation

      [Start] 82.7%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\left(d \cdot d\right) \cdot \frac{c0}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M\right)}\right) \]
      associate-*r/ [=>] 82.7%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\color{blue}{\frac{\left(d \cdot d\right) \cdot c0}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M\right)}\right) \]
      *-commutative [<=] 82.7%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M\right)}\right) \]
      times-frac [=>] 82.7%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\color{blue}{\frac{c0}{w \cdot h} \cdot \frac{d \cdot d}{D \cdot D}} - M\right)}\right) \]
      associate-/l/ [<=] 85.0%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{c0}{w \cdot h} \cdot \color{blue}{\frac{\frac{d \cdot d}{D}}{D}} - M\right)}\right) \]
      associate-*r/ [=>] 85.0%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\color{blue}{\frac{\frac{c0}{w \cdot h} \cdot \frac{d \cdot d}{D}}{D}} - M\right)}\right) \]
      associate-/l/ [<=] 77.5%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\color{blue}{\frac{\frac{c0}{h}}{w}} \cdot \frac{d \cdot d}{D}}{D} - M\right)}\right) \]
      associate-/l* [=>] 77.5%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\frac{\frac{c0}{h}}{w} \cdot \color{blue}{\frac{d}{\frac{D}{d}}}}{D} - M\right)}\right) \]
      div-inv [=>] 77.4%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\frac{\frac{c0}{h}}{w} \cdot \color{blue}{\left(d \cdot \frac{1}{\frac{D}{d}}\right)}}{D} - M\right)}\right) \]
      clear-num [<=] 77.4%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\frac{\frac{c0}{h}}{w} \cdot \left(d \cdot \color{blue}{\frac{d}{D}}\right)}{D} - M\right)}\right) \]

   4. Simplified 84.9%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\color{blue}{\frac{\frac{c0}{w \cdot h}}{\frac{D}{d \cdot \frac{d}{D}}}} - M\right)}\right) \]
      Step-by-step derivation

      [Start] 77.4%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\frac{\frac{c0}{h}}{w} \cdot \left(d \cdot \frac{d}{D}\right)}{D} - M\right)}\right) \]
      associate-/l* [=>] 77.4%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\color{blue}{\frac{\frac{\frac{c0}{h}}{w}}{\frac{D}{d \cdot \frac{d}{D}}}} - M\right)}\right) \]
      associate-/l/ [=>] 84.9%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\color{blue}{\frac{c0}{w \cdot h}}}{\frac{D}{d \cdot \frac{d}{D}}} - M\right)}\right) \]

   5. Applied egg-rr 90.4%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \color{blue}{\sqrt{\frac{c0}{w \cdot h} \cdot {\left(\frac{d}{D}\right)}^{2} + M} \cdot \sqrt{\frac{c0}{w \cdot h} \cdot {\left(\frac{d}{D}\right)}^{2} - M}}\right) \]
      Step-by-step derivation

      [Start] 84.9%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\frac{c0}{w \cdot h}}{\frac{D}{d \cdot \frac{d}{D}}} - M\right)}\right) \]
      sqrt-prod [=>] 88.7%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \color{blue}{\sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right)} \cdot \sqrt{\frac{\frac{c0}{w \cdot h}}{\frac{D}{d \cdot \frac{d}{D}}} - M}}\right) \]

   if -1.99999999999999994e-304 < (*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))) < 0.0

   1. Initial program 62.7%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   2. Taylor expanded in c0 around -inf 61.6%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(0.5 \cdot \frac{{D}^{2} \cdot \left(w \cdot \left({M}^{2} \cdot h\right)\right)}{{d}^{2} \cdot c0} + -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right)} \]

   3. Simplified 61.4%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\mathsf{fma}\left(0.5, \frac{D \cdot D}{d \cdot d} \cdot \frac{w \cdot \left(h \cdot \left(M \cdot M\right)\right)}{c0}, c0 \cdot 0\right)} \]
      Step-by-step derivation

      [Start] 61.6%	\[ \frac{c0}{2 \cdot w} \cdot \left(0.5 \cdot \frac{{D}^{2} \cdot \left(w \cdot \left({M}^{2} \cdot h\right)\right)}{{d}^{2} \cdot c0} + -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right) \]
      fma-def [=>] 61.6%	\[ \frac{c0}{2 \cdot w} \cdot \color{blue}{\mathsf{fma}\left(0.5, \frac{{D}^{2} \cdot \left(w \cdot \left({M}^{2} \cdot h\right)\right)}{{d}^{2} \cdot c0}, -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right)} \]
      times-frac [=>] 61.4%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(0.5, \color{blue}{\frac{{D}^{2}}{{d}^{2}} \cdot \frac{w \cdot \left({M}^{2} \cdot h\right)}{c0}}, -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right) \]
      unpow2 [=>] 61.4%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(0.5, \frac{\color{blue}{D \cdot D}}{{d}^{2}} \cdot \frac{w \cdot \left({M}^{2} \cdot h\right)}{c0}, -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right) \]
      unpow2 [=>] 61.4%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(0.5, \frac{D \cdot D}{\color{blue}{d \cdot d}} \cdot \frac{w \cdot \left({M}^{2} \cdot h\right)}{c0}, -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right) \]
      *-commutative [=>] 61.4%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(0.5, \frac{D \cdot D}{d \cdot d} \cdot \frac{w \cdot \color{blue}{\left(h \cdot {M}^{2}\right)}}{c0}, -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right) \]
      unpow2 [=>] 61.4%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(0.5, \frac{D \cdot D}{d \cdot d} \cdot \frac{w \cdot \left(h \cdot \color{blue}{\left(M \cdot M\right)}\right)}{c0}, -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right) \]
      associate-*r* [=>] 61.4%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(0.5, \frac{D \cdot D}{d \cdot d} \cdot \frac{w \cdot \left(h \cdot \left(M \cdot M\right)\right)}{c0}, \color{blue}{\left(-1 \cdot \left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right)\right) \cdot c0}\right) \]

   4. Taylor expanded in c0 around 0 66.9%

      \[\leadsto \color{blue}{0.25 \cdot \frac{{D}^{2} \cdot \left(h \cdot {M}^{2}\right)}{{d}^{2}}} \]

   5. Simplified 78.2%

      \[\leadsto \color{blue}{0.25 \cdot \left(\frac{D}{d \cdot \frac{d}{D}} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right)} \]
      Step-by-step derivation

      [Start] 66.9%	\[ 0.25 \cdot \frac{{D}^{2} \cdot \left(h \cdot {M}^{2}\right)}{{d}^{2}} \]
      unpow2 [=>] 66.9%	\[ 0.25 \cdot \frac{{D}^{2} \cdot \left(h \cdot {M}^{2}\right)}{\color{blue}{d \cdot d}} \]
      associate-/l* [=>] 61.9%	\[ 0.25 \cdot \color{blue}{\frac{{D}^{2}}{\frac{d \cdot d}{h \cdot {M}^{2}}}} \]
      unpow2 [=>] 61.9%	\[ 0.25 \cdot \frac{{D}^{2}}{\frac{d \cdot d}{h \cdot \color{blue}{\left(M \cdot M\right)}}} \]
      associate-/r/ [=>] 66.7%	\[ 0.25 \cdot \color{blue}{\left(\frac{{D}^{2}}{d \cdot d} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right)} \]
      unpow2 [=>] 66.7%	\[ 0.25 \cdot \left(\frac{\color{blue}{D \cdot D}}{d \cdot d} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]
      associate-/l* [=>] 72.3%	\[ 0.25 \cdot \left(\color{blue}{\frac{D}{\frac{d \cdot d}{D}}} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]
      associate-*r/ [<=] 78.2%	\[ 0.25 \cdot \left(\frac{D}{\color{blue}{d \cdot \frac{d}{D}}} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]

   6. Applied egg-rr 78.8%

      \[\leadsto 0.25 \cdot \color{blue}{\frac{D \cdot \left(h \cdot \left(M \cdot M\right)\right)}{d \cdot \frac{d}{D}}} \]
      Step-by-step derivation

      [Start] 78.2%	\[ 0.25 \cdot \left(\frac{D}{d \cdot \frac{d}{D}} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]
      associate-*l/ [=>] 78.8%	\[ 0.25 \cdot \color{blue}{\frac{D \cdot \left(h \cdot \left(M \cdot M\right)\right)}{d \cdot \frac{d}{D}}} \]

   if 0.0 < (*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M))))) < +inf.0

   1. Initial program 72.0%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   2. Simplified 71.9%

      \[\leadsto \color{blue}{\frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\left(d \cdot d\right) \cdot \frac{c0}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M\right)}\right)} \]
      Step-by-step derivation

      [Start] 72.0%	\[ \frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
      times-frac [=>] 71.9%	\[ \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0}{w \cdot h} \cdot \frac{d \cdot d}{D \cdot D}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
      fma-def [=>] 71.9%	\[ \frac{c0}{2 \cdot w} \cdot \color{blue}{\mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d \cdot d}{D \cdot D}, \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)} \]
      times-frac [=>] 71.9%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \color{blue}{\frac{d}{D} \cdot \frac{d}{D}}, \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
      difference-of-squares [=>] 71.9%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\color{blue}{\left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + M\right) \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M\right)}}\right) \]

   3. Applied egg-rr 68.7%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\color{blue}{\frac{\frac{\frac{c0}{h}}{w} \cdot \left(d \cdot \frac{d}{D}\right)}{D}} - M\right)}\right) \]
      Step-by-step derivation

      [Start] 71.9%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\left(d \cdot d\right) \cdot \frac{c0}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M\right)}\right) \]
      associate-*r/ [=>] 71.9%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\color{blue}{\frac{\left(d \cdot d\right) \cdot c0}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}} - M\right)}\right) \]
      *-commutative [<=] 71.9%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\color{blue}{c0 \cdot \left(d \cdot d\right)}}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M\right)}\right) \]
      times-frac [=>] 71.9%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\color{blue}{\frac{c0}{w \cdot h} \cdot \frac{d \cdot d}{D \cdot D}} - M\right)}\right) \]
      associate-/l/ [<=] 71.9%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{c0}{w \cdot h} \cdot \color{blue}{\frac{\frac{d \cdot d}{D}}{D}} - M\right)}\right) \]
      associate-*r/ [=>] 71.9%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\color{blue}{\frac{\frac{c0}{w \cdot h} \cdot \frac{d \cdot d}{D}}{D}} - M\right)}\right) \]
      associate-/l/ [<=] 68.7%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\color{blue}{\frac{\frac{c0}{h}}{w}} \cdot \frac{d \cdot d}{D}}{D} - M\right)}\right) \]
      associate-/l* [=>] 68.7%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\frac{\frac{c0}{h}}{w} \cdot \color{blue}{\frac{d}{\frac{D}{d}}}}{D} - M\right)}\right) \]
      div-inv [=>] 68.7%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\frac{\frac{c0}{h}}{w} \cdot \color{blue}{\left(d \cdot \frac{1}{\frac{D}{d}}\right)}}{D} - M\right)}\right) \]
      clear-num [<=] 68.7%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\frac{\frac{c0}{h}}{w} \cdot \left(d \cdot \color{blue}{\frac{d}{D}}\right)}{D} - M\right)}\right) \]

   4. Simplified 71.9%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\color{blue}{\frac{\frac{c0}{w \cdot h}}{\frac{D}{d \cdot \frac{d}{D}}}} - M\right)}\right) \]
      Step-by-step derivation

      [Start] 68.7%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\frac{\frac{c0}{h}}{w} \cdot \left(d \cdot \frac{d}{D}\right)}{D} - M\right)}\right) \]
      associate-/l* [=>] 68.7%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\color{blue}{\frac{\frac{\frac{c0}{h}}{w}}{\frac{D}{d \cdot \frac{d}{D}}}} - M\right)}\right) \]
      associate-/l/ [=>] 71.9%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{\mathsf{fma}\left(\frac{c0}{\left(w \cdot h\right) \cdot D}, \frac{d}{\frac{D}{d}}, M\right) \cdot \left(\frac{\color{blue}{\frac{c0}{w \cdot h}}}{\frac{D}{d \cdot \frac{d}{D}}} - M\right)}\right) \]

   5. Taylor expanded in c0 around inf 61.8%

      \[\leadsto \color{blue}{\frac{{d}^{2} \cdot {c0}^{2}}{{D}^{2} \cdot \left({w}^{2} \cdot h\right)}} \]

   6. Simplified 80.9%

      \[\leadsto \color{blue}{\frac{{\left(d \cdot c0\right)}^{2}}{D \cdot \left(D \cdot \left(\left(w \cdot h\right) \cdot w\right)\right)}} \]
      Step-by-step derivation

      [Start] 61.8%	\[ \frac{{d}^{2} \cdot {c0}^{2}}{{D}^{2} \cdot \left({w}^{2} \cdot h\right)} \]
      unpow2 [=>] 61.8%	\[ \frac{\color{blue}{\left(d \cdot d\right)} \cdot {c0}^{2}}{{D}^{2} \cdot \left({w}^{2} \cdot h\right)} \]
      unpow2 [=>] 61.8%	\[ \frac{\left(d \cdot d\right) \cdot \color{blue}{\left(c0 \cdot c0\right)}}{{D}^{2} \cdot \left({w}^{2} \cdot h\right)} \]
      swap-sqr [<=] 77.7%	\[ \frac{\color{blue}{\left(d \cdot c0\right) \cdot \left(d \cdot c0\right)}}{{D}^{2} \cdot \left({w}^{2} \cdot h\right)} \]
      unpow2 [<=] 77.7%	\[ \frac{\color{blue}{{\left(d \cdot c0\right)}^{2}}}{{D}^{2} \cdot \left({w}^{2} \cdot h\right)} \]
      *-commutative [=>] 77.7%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{{D}^{2} \cdot \color{blue}{\left(h \cdot {w}^{2}\right)}} \]
      unpow2 [=>] 77.7%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{\color{blue}{\left(D \cdot D\right)} \cdot \left(h \cdot {w}^{2}\right)} \]
      unpow2 [=>] 77.7%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{\left(D \cdot D\right) \cdot \left(h \cdot \color{blue}{\left(w \cdot w\right)}\right)} \]
      associate-*l* [=>] 77.7%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{\color{blue}{D \cdot \left(D \cdot \left(h \cdot \left(w \cdot w\right)\right)\right)}} \]
      associate-*r* [=>] 80.9%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{D \cdot \left(D \cdot \color{blue}{\left(\left(h \cdot w\right) \cdot w\right)}\right)} \]
      *-commutative [<=] 80.9%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{D \cdot \left(D \cdot \left(\color{blue}{\left(w \cdot h\right)} \cdot w\right)\right)} \]

   7. Taylor expanded in d around 0 61.8%

      \[\leadsto \color{blue}{\frac{{d}^{2} \cdot {c0}^{2}}{{D}^{2} \cdot \left({w}^{2} \cdot h\right)}} \]

   8. Simplified 80.9%

      \[\leadsto \color{blue}{\frac{{\left(d \cdot c0\right)}^{2}}{\left(w \cdot w\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}} \]
      Step-by-step derivation

      [Start] 61.8%	\[ \frac{{d}^{2} \cdot {c0}^{2}}{{D}^{2} \cdot \left({w}^{2} \cdot h\right)} \]
      unpow2 [=>] 61.8%	\[ \frac{\color{blue}{\left(d \cdot d\right)} \cdot {c0}^{2}}{{D}^{2} \cdot \left({w}^{2} \cdot h\right)} \]
      unpow2 [=>] 61.8%	\[ \frac{\left(d \cdot d\right) \cdot \color{blue}{\left(c0 \cdot c0\right)}}{{D}^{2} \cdot \left({w}^{2} \cdot h\right)} \]
      swap-sqr [<=] 77.7%	\[ \frac{\color{blue}{\left(d \cdot c0\right) \cdot \left(d \cdot c0\right)}}{{D}^{2} \cdot \left({w}^{2} \cdot h\right)} \]
      unpow2 [<=] 77.7%	\[ \frac{\color{blue}{{\left(d \cdot c0\right)}^{2}}}{{D}^{2} \cdot \left({w}^{2} \cdot h\right)} \]
      unpow2 [=>] 77.7%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{{D}^{2} \cdot \left(\color{blue}{\left(w \cdot w\right)} \cdot h\right)} \]
      associate-*r* [<=] 80.9%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{{D}^{2} \cdot \color{blue}{\left(w \cdot \left(w \cdot h\right)\right)}} \]
      *-commutative [=>] 80.9%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{\color{blue}{\left(w \cdot \left(w \cdot h\right)\right) \cdot {D}^{2}}} \]
      associate-*r* [=>] 77.7%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{\color{blue}{\left(\left(w \cdot w\right) \cdot h\right)} \cdot {D}^{2}} \]
      unpow2 [<=] 77.7%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{\left(\color{blue}{{w}^{2}} \cdot h\right) \cdot {D}^{2}} \]
      associate-*l* [=>] 80.9%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{\color{blue}{{w}^{2} \cdot \left(h \cdot {D}^{2}\right)}} \]
      unpow2 [=>] 80.9%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{\color{blue}{\left(w \cdot w\right)} \cdot \left(h \cdot {D}^{2}\right)} \]
      *-commutative [<=] 80.9%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{\left(w \cdot w\right) \cdot \color{blue}{\left({D}^{2} \cdot h\right)}} \]
      unpow2 [=>] 80.9%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{\left(w \cdot w\right) \cdot \left(\color{blue}{\left(D \cdot D\right)} \cdot h\right)} \]

   9. Applied egg-rr 84.1%

      \[\leadsto \color{blue}{1 \cdot \frac{{\left(d \cdot c0\right)}^{2}}{w \cdot \left(w \cdot \left(D \cdot \left(D \cdot h\right)\right)\right)}} \]
      Step-by-step derivation

      [Start] 80.9%	\[ \frac{{\left(d \cdot c0\right)}^{2}}{\left(w \cdot w\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)} \]
      *-un-lft-identity [=>] 80.9%	\[ \color{blue}{1 \cdot \frac{{\left(d \cdot c0\right)}^{2}}{\left(w \cdot w\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}} \]
      associate-*l* [=>] 84.1%	\[ 1 \cdot \frac{{\left(d \cdot c0\right)}^{2}}{\color{blue}{w \cdot \left(w \cdot \left(\left(D \cdot D\right) \cdot h\right)\right)}} \]
      associate-*l* [=>] 84.1%	\[ 1 \cdot \frac{{\left(d \cdot c0\right)}^{2}}{w \cdot \left(w \cdot \color{blue}{\left(D \cdot \left(D \cdot h\right)\right)}\right)} \]

   if +inf.0 < (*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))

   1. Initial program 0.0%

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]

   2. Taylor expanded in c0 around -inf 1.3%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(0.5 \cdot \frac{{D}^{2} \cdot \left(w \cdot \left({M}^{2} \cdot h\right)\right)}{{d}^{2} \cdot c0} + -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right)} \]

   3. Simplified 29.1%

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\mathsf{fma}\left(0.5, \frac{D \cdot D}{d \cdot d} \cdot \frac{w \cdot \left(h \cdot \left(M \cdot M\right)\right)}{c0}, c0 \cdot 0\right)} \]
      Step-by-step derivation

      [Start] 1.3%	\[ \frac{c0}{2 \cdot w} \cdot \left(0.5 \cdot \frac{{D}^{2} \cdot \left(w \cdot \left({M}^{2} \cdot h\right)\right)}{{d}^{2} \cdot c0} + -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right) \]
      fma-def [=>] 1.3%	\[ \frac{c0}{2 \cdot w} \cdot \color{blue}{\mathsf{fma}\left(0.5, \frac{{D}^{2} \cdot \left(w \cdot \left({M}^{2} \cdot h\right)\right)}{{d}^{2} \cdot c0}, -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right)} \]
      times-frac [=>] 2.6%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(0.5, \color{blue}{\frac{{D}^{2}}{{d}^{2}} \cdot \frac{w \cdot \left({M}^{2} \cdot h\right)}{c0}}, -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right) \]
      unpow2 [=>] 2.6%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(0.5, \frac{\color{blue}{D \cdot D}}{{d}^{2}} \cdot \frac{w \cdot \left({M}^{2} \cdot h\right)}{c0}, -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right) \]
      unpow2 [=>] 2.6%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(0.5, \frac{D \cdot D}{\color{blue}{d \cdot d}} \cdot \frac{w \cdot \left({M}^{2} \cdot h\right)}{c0}, -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right) \]
      *-commutative [=>] 2.6%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(0.5, \frac{D \cdot D}{d \cdot d} \cdot \frac{w \cdot \color{blue}{\left(h \cdot {M}^{2}\right)}}{c0}, -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right) \]
      unpow2 [=>] 2.6%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(0.5, \frac{D \cdot D}{d \cdot d} \cdot \frac{w \cdot \left(h \cdot \color{blue}{\left(M \cdot M\right)}\right)}{c0}, -1 \cdot \left(\left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right) \cdot c0\right)\right) \]
      associate-*r* [=>] 2.6%	\[ \frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(0.5, \frac{D \cdot D}{d \cdot d} \cdot \frac{w \cdot \left(h \cdot \left(M \cdot M\right)\right)}{c0}, \color{blue}{\left(-1 \cdot \left(\frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)} + -1 \cdot \frac{{d}^{2}}{{D}^{2} \cdot \left(w \cdot h\right)}\right)\right) \cdot c0}\right) \]

   4. Taylor expanded in c0 around 0 41.3%

      \[\leadsto \color{blue}{0.25 \cdot \frac{{D}^{2} \cdot \left(h \cdot {M}^{2}\right)}{{d}^{2}}} \]

   5. Simplified 52.3%

      \[\leadsto \color{blue}{0.25 \cdot \left(\frac{D}{d \cdot \frac{d}{D}} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right)} \]
      Step-by-step derivation

      [Start] 41.3%	\[ 0.25 \cdot \frac{{D}^{2} \cdot \left(h \cdot {M}^{2}\right)}{{d}^{2}} \]
      unpow2 [=>] 41.3%	\[ 0.25 \cdot \frac{{D}^{2} \cdot \left(h \cdot {M}^{2}\right)}{\color{blue}{d \cdot d}} \]
      associate-/l* [=>] 40.7%	\[ 0.25 \cdot \color{blue}{\frac{{D}^{2}}{\frac{d \cdot d}{h \cdot {M}^{2}}}} \]
      unpow2 [=>] 40.7%	\[ 0.25 \cdot \frac{{D}^{2}}{\frac{d \cdot d}{h \cdot \color{blue}{\left(M \cdot M\right)}}} \]
      associate-/r/ [=>] 41.3%	\[ 0.25 \cdot \color{blue}{\left(\frac{{D}^{2}}{d \cdot d} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right)} \]
      unpow2 [=>] 41.3%	\[ 0.25 \cdot \left(\frac{\color{blue}{D \cdot D}}{d \cdot d} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]
      associate-/l* [=>] 47.8%	\[ 0.25 \cdot \left(\color{blue}{\frac{D}{\frac{d \cdot d}{D}}} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]
      associate-*r/ [<=] 52.3%	\[ 0.25 \cdot \left(\frac{D}{\color{blue}{d \cdot \frac{d}{D}}} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]

   6. Taylor expanded in D around 0 41.3%

      \[\leadsto 0.25 \cdot \left(\color{blue}{\frac{{D}^{2}}{{d}^{2}}} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]

   7. Simplified 54.9%

      \[\leadsto 0.25 \cdot \left(\color{blue}{\left(\frac{D}{d} \cdot \frac{D}{d}\right)} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]
      Step-by-step derivation

      [Start] 41.3%	\[ 0.25 \cdot \left(\frac{{D}^{2}}{{d}^{2}} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]
      unpow2 [=>] 41.3%	\[ 0.25 \cdot \left(\frac{\color{blue}{D \cdot D}}{{d}^{2}} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]
      unpow2 [=>] 41.3%	\[ 0.25 \cdot \left(\frac{D \cdot D}{\color{blue}{d \cdot d}} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]
      times-frac [=>] 54.9%	\[ 0.25 \cdot \left(\color{blue}{\left(\frac{D}{d} \cdot \frac{D}{d}\right)} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right) \]

3. Recombined 4 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \mathsf{fma}\left(\frac{c0}{w \cdot h}, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{M + \frac{c0}{w \cdot h} \cdot {\left(\frac{d}{D}\right)}^{2}} \cdot \sqrt{\frac{c0}{w \cdot h} \cdot {\left(\frac{d}{D}\right)}^{2} - M}\right)\\ \mathbf{elif}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \leq 0:\\ \;\;\;\;0.25 \cdot \frac{D \cdot \left(h \cdot \left(M \cdot M\right)\right)}{d \cdot \frac{d}{D}}\\ \mathbf{elif}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \leq \infty:\\ \;\;\;\;\frac{{\left(c0 \cdot d\right)}^{2}}{w \cdot \left(w \cdot \left(D \cdot \left(h \cdot D\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \left(\left(h \cdot \left(M \cdot M\right)\right) \cdot \left(\frac{D}{d} \cdot \frac{D}{d}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	61.9%
Cost	44484

\[\begin{array}{l} t_0 := \frac{c0}{w \cdot h}\\ t_1 := h \cdot \left(M \cdot M\right)\\ t_2 := t_0 \cdot {\left(\frac{d}{D}\right)}^{2}\\ t_3 := \frac{c0}{2 \cdot w}\\ t_4 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ t_5 := t_3 \cdot \left(t_4 + \sqrt{t_4 \cdot t_4 - M \cdot M}\right)\\ \mathbf{if}\;t_5 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;t_3 \cdot \mathsf{fma}\left(t_0, \frac{d}{D} \cdot \frac{d}{D}, \sqrt{M + t_2} \cdot \sqrt{t_2 - M}\right)\\ \mathbf{elif}\;t_5 \leq 0:\\ \;\;\;\;0.25 \cdot \frac{D \cdot t_1}{d \cdot \frac{d}{D}}\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;\frac{{\left(c0 \cdot d\right)}^{2}}{w \cdot \left(w \cdot \left(D \cdot \left(h \cdot D\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \left(t_1 \cdot \left(\frac{D}{d} \cdot \frac{D}{d}\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	62.0%
Cost	36492

\[\begin{array}{l} t_0 := \frac{c0}{2 \cdot w}\\ t_1 := h \cdot \left(M \cdot M\right)\\ t_2 := \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ t_3 := t_0 \cdot \left(t_2 + \sqrt{t_2 \cdot t_2 - M \cdot M}\right)\\ \mathbf{if}\;t_3 \leq -2 \cdot 10^{-304}:\\ \;\;\;\;t_0 \cdot \left(2 \cdot \left(\frac{c0}{w \cdot h} \cdot {\left(\frac{d}{D}\right)}^{2}\right)\right)\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;0.25 \cdot \frac{D \cdot t_1}{d \cdot \frac{d}{D}}\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;\frac{{\left(c0 \cdot d\right)}^{2}}{w \cdot \left(w \cdot \left(D \cdot \left(h \cdot D\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \left(t_1 \cdot \left(\frac{D}{d} \cdot \frac{D}{d}\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	41.8%
Cost	7825

\[\begin{array}{l} t_0 := h \cdot \left(M \cdot M\right)\\ t_1 := d \cdot \frac{d}{D}\\ \mathbf{if}\;h \leq -2.3 \cdot 10^{+99}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(d \cdot \left(d \cdot \frac{c0}{w \cdot \left(h \cdot \left(D \cdot D\right)\right)}\right) + \frac{\frac{c0}{w \cdot h}}{D} \cdot \frac{d \cdot d}{D}\right)\\ \mathbf{elif}\;h \leq -5.1 \cdot 10^{+81}:\\ \;\;\;\;0.25 \cdot \left(t_0 \cdot \frac{D}{t_1}\right)\\ \mathbf{elif}\;h \leq 4.3 \cdot 10^{-225} \lor \neg \left(h \leq 4.6 \cdot 10^{+172}\right):\\ \;\;\;\;\frac{{\left(c0 \cdot d\right)}^{2}}{D \cdot \left(\left(w \cdot h\right) \cdot \left(w \cdot D\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \frac{D \cdot t_0}{t_1}\\ \end{array} \]

Alternative 4
Accuracy	41.0%
Cost	7824

\[\begin{array}{l} t_0 := \left(c0 \cdot d\right) \cdot \left(c0 \cdot d\right)\\ t_1 := D \cdot \left(w \cdot \left(w \cdot h\right)\right)\\ t_2 := h \cdot \left(M \cdot M\right)\\ t_3 := d \cdot \frac{d}{D}\\ t_4 := \frac{\frac{t_0}{D}}{t_1}\\ \mathbf{if}\;h \leq -1.6 \cdot 10^{+97}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(d \cdot \left(d \cdot \frac{c0}{w \cdot \left(h \cdot \left(D \cdot D\right)\right)}\right) + \frac{\frac{c0}{w \cdot h}}{D} \cdot \frac{d \cdot d}{D}\right)\\ \mathbf{elif}\;h \leq -8 \cdot 10^{+81}:\\ \;\;\;\;0.25 \cdot \left(t_2 \cdot \frac{D}{t_3}\right)\\ \mathbf{elif}\;h \leq -8 \cdot 10^{+57}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;h \leq -1.05 \cdot 10^{-184}:\\ \;\;\;\;\frac{{\left(\frac{d}{D}\right)}^{2}}{w} \cdot \frac{c0 \cdot c0}{w \cdot h}\\ \mathbf{elif}\;h \leq 7.8 \cdot 10^{-225}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;h \leq 2.7 \cdot 10^{+172}:\\ \;\;\;\;0.25 \cdot \frac{D \cdot t_2}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{D \cdot t_1}\\ \end{array} \]

Alternative 5
Accuracy	44.2%
Cost	2389

\[\begin{array}{l} t_0 := h \cdot \left(M \cdot M\right)\\ t_1 := \left(\frac{d}{D} \cdot \frac{d}{D}\right) \cdot \left(\frac{c0}{h} \cdot \frac{c0}{w \cdot w}\right)\\ \mathbf{if}\;M \cdot M \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;0\\ \mathbf{elif}\;M \cdot M \leq 6.2 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;M \cdot M \leq 1.5 \cdot 10^{+137}:\\ \;\;\;\;0.25 \cdot \frac{D \cdot t_0}{d \cdot \frac{d}{D}}\\ \mathbf{elif}\;M \cdot M \leq 1.2 \cdot 10^{+189} \lor \neg \left(M \cdot M \leq 1.25 \cdot 10^{+269}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \left(t_0 \cdot \left(\frac{D}{d} \cdot \frac{D}{d}\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	41.5%
Cost	2244

\[\begin{array}{l} t_0 := \left(c0 \cdot d\right) \cdot \left(c0 \cdot d\right)\\ t_1 := D \cdot \left(w \cdot \left(w \cdot h\right)\right)\\ t_2 := h \cdot \left(M \cdot M\right)\\ t_3 := d \cdot \frac{d}{D}\\ \mathbf{if}\;h \leq -1.55 \cdot 10^{+100}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(d \cdot \left(d \cdot \frac{c0}{w \cdot \left(h \cdot \left(D \cdot D\right)\right)}\right) + \frac{\frac{c0}{w \cdot h}}{D} \cdot \frac{d \cdot d}{D}\right)\\ \mathbf{elif}\;h \leq -6.5 \cdot 10^{+81}:\\ \;\;\;\;0.25 \cdot \left(t_2 \cdot \frac{D}{t_3}\right)\\ \mathbf{elif}\;h \leq 3.5 \cdot 10^{-224}:\\ \;\;\;\;\frac{\frac{t_0}{D}}{t_1}\\ \mathbf{elif}\;h \leq 3.8 \cdot 10^{+172}:\\ \;\;\;\;0.25 \cdot \frac{D \cdot t_2}{t_3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{D \cdot t_1}\\ \end{array} \]

Alternative 7
Accuracy	41.2%
Cost	1616

\[\begin{array}{l} t_0 := d \cdot \frac{d}{D}\\ t_1 := \left(c0 \cdot d\right) \cdot \left(c0 \cdot d\right)\\ t_2 := D \cdot \left(w \cdot \left(w \cdot h\right)\right)\\ t_3 := h \cdot \left(M \cdot M\right)\\ \mathbf{if}\;h \leq -2.1 \cdot 10^{+99}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(2 \cdot \left(\frac{c0}{w \cdot h} \cdot \frac{d \cdot d}{D \cdot D}\right)\right)\\ \mathbf{elif}\;h \leq -1.25 \cdot 10^{+82}:\\ \;\;\;\;0.25 \cdot \left(t_3 \cdot \frac{D}{t_0}\right)\\ \mathbf{elif}\;h \leq 3.8 \cdot 10^{-225}:\\ \;\;\;\;\frac{\frac{t_1}{D}}{t_2}\\ \mathbf{elif}\;h \leq 3.6 \cdot 10^{+172}:\\ \;\;\;\;0.25 \cdot \frac{D \cdot t_3}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{D \cdot t_2}\\ \end{array} \]

Alternative 8
Accuracy	41.1%
Cost	1616

\[\begin{array}{l} t_0 := d \cdot \frac{d}{D}\\ t_1 := \left(c0 \cdot d\right) \cdot \left(c0 \cdot d\right)\\ t_2 := D \cdot \left(w \cdot \left(w \cdot h\right)\right)\\ t_3 := h \cdot \left(M \cdot M\right)\\ \mathbf{if}\;h \leq -9 \cdot 10^{+96}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \frac{2 \cdot \left(c0 \cdot \left(d \cdot d\right)\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}\\ \mathbf{elif}\;h \leq -5.1 \cdot 10^{+81}:\\ \;\;\;\;0.25 \cdot \left(t_3 \cdot \frac{D}{t_0}\right)\\ \mathbf{elif}\;h \leq 5.8 \cdot 10^{-227}:\\ \;\;\;\;\frac{\frac{t_1}{D}}{t_2}\\ \mathbf{elif}\;h \leq 2.8 \cdot 10^{+172}:\\ \;\;\;\;0.25 \cdot \frac{D \cdot t_3}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{D \cdot t_2}\\ \end{array} \]

Alternative 9
Accuracy	41.7%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;h \leq 1.05 \cdot 10^{-226} \lor \neg \left(h \leq 2.2 \cdot 10^{+172}\right):\\ \;\;\;\;\frac{\left(c0 \cdot d\right) \cdot \left(c0 \cdot d\right)}{D \cdot \left(D \cdot \left(w \cdot \left(w \cdot h\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \frac{D \cdot \left(h \cdot \left(M \cdot M\right)\right)}{d \cdot \frac{d}{D}}\\ \end{array} \]

Alternative 10
Accuracy	42.2%
Cost	1352

\[\begin{array}{l} t_0 := D \cdot \left(w \cdot \left(w \cdot h\right)\right)\\ t_1 := \left(c0 \cdot d\right) \cdot \left(c0 \cdot d\right)\\ \mathbf{if}\;h \leq 1.95 \cdot 10^{-225}:\\ \;\;\;\;\frac{\frac{t_1}{D}}{t_0}\\ \mathbf{elif}\;h \leq 4.4 \cdot 10^{+172}:\\ \;\;\;\;0.25 \cdot \frac{D \cdot \left(h \cdot \left(M \cdot M\right)\right)}{d \cdot \frac{d}{D}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{D \cdot t_0}\\ \end{array} \]

Alternative 11
Accuracy	41.4%
Cost	960

\[0.25 \cdot \left(\left(h \cdot \left(M \cdot M\right)\right) \cdot \left(\frac{D}{d} \cdot \frac{D}{d}\right)\right) \]

Alternative 12
Accuracy	32.4%
Cost	64

\[0 \]

Reproduce

herbie shell --seed 2023165 
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  :precision binary64
  (* (/ c0 (* 2.0 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))))