Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Average Error: 6.3 → 1.6

Time: 40.3s

Precision: binary64

Cost: 2504

Math

\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

↓

\[\begin{array}{l} t_1 := a + b \cdot c\\ t_2 := \left(t_1 \cdot c\right) \cdot i\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(t_1 \cdot i\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t_2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - \frac{c}{\frac{1}{b \cdot \left(c \cdot i\right)}}\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))

↓

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ a (* b c))) (t_2 (* (* t_1 c) i)))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (+ (* x y) (- (* z t) (* c (* t_1 i)))))
     (if (<= t_2 5e+299)
       (* 2.0 (- (+ (* x y) (* z t)) t_2))
       (* 2.0 (+ (* x y) (- (* z t) (/ c (/ 1.0 (* b (* c i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (t_1 * c) * i;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (t_1 * i))));
	} else if (t_2 <= 5e+299) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	} else {
		tmp = 2.0 * ((x * y) + ((z * t) - (c / (1.0 / (b * (c * i))))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = a + (b * c);
	double t_2 = (t_1 * c) * i;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (t_1 * i))));
	} else if (t_2 <= 5e+299) {
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	} else {
		tmp = 2.0 * ((x * y) + ((z * t) - (c / (1.0 / (b * (c * i))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	return 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))

↓

def code(x, y, z, t, a, b, c, i):
	t_1 = a + (b * c)
	t_2 = (t_1 * c) * i
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (t_1 * i))))
	elif t_2 <= 5e+299:
		tmp = 2.0 * (((x * y) + (z * t)) - t_2)
	else:
		tmp = 2.0 * ((x * y) + ((z * t) - (c / (1.0 / (b * (c * i))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
end

↓

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(a + Float64(b * c))
	t_2 = Float64(Float64(t_1 * c) * i)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(c * Float64(t_1 * i)))));
	elseif (t_2 <= 5e+299)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - t_2));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(c / Float64(1.0 / Float64(b * Float64(c * i)))))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
end

↓

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = a + (b * c);
	t_2 = (t_1 * c) * i;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (t_1 * i))));
	elseif (t_2 <= 5e+299)
		tmp = 2.0 * (((x * y) + (z * t)) - t_2);
	else
		tmp = 2.0 * ((x * y) + ((z * t) - (c / (1.0 / (b * (c * i))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 * c), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(c * N[(t$95$1 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+299], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(c / N[(1.0 / N[(b * N[(c * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	6.3
Target	1.8
Herbie	1.6

\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right) \]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < -inf.0

   1. Initial program 64.0

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Simplified 10.0

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\right)} \]
      Proof

      [Start] 64.0	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      rational.json-simplify-1 [=>] 64.0	\[ 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      rational.json-simplify-48 [=>] 64.0	\[ 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]
      rational.json-simplify-2 [=>] 64.0	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) \]
      rational.json-simplify-2 [=>] 64.0	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - i \cdot \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)}\right)\right) \]
      rational.json-simplify-43 [=>] 10.0	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right)\right) \]

   if -inf.0 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i) < 5.0000000000000003e299

   1. Initial program 0.3

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   if 5.0000000000000003e299 < (*.f64 (*.f64 (+.f64 a (*.f64 b c)) c) i)

   1. Initial program 59.4

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]

   2. Simplified 11.9

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\right)} \]
      Proof

      [Start] 59.4	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      rational.json-simplify-1 [=>] 59.4	\[ 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      rational.json-simplify-48 [=>] 59.4	\[ 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]
      rational.json-simplify-2 [=>] 59.4	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) \]
      rational.json-simplify-2 [=>] 59.4	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - i \cdot \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)}\right)\right) \]
      rational.json-simplify-43 [=>] 11.9	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right)\right) \]

   3. Taylor expanded in a around 0 20.9

      \[\leadsto 2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \color{blue}{\left(c \cdot \left(i \cdot b\right)\right)}\right)\right) \]

   4. Applied egg-rr 41.6

      \[\leadsto 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{\frac{i \cdot b}{\frac{1}{c \cdot c}}}\right)\right) \]

   5. Simplified 21.2

      \[\leadsto 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{c \cdot \frac{c}{\frac{\frac{1}{i}}{b}}}\right)\right) \]
      Proof

      [Start] 41.6	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \frac{i \cdot b}{\frac{1}{c \cdot c}}\right)\right) \]
      rational.json-simplify-61 [=>] 41.6	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{\frac{c \cdot c}{\frac{1}{i \cdot b}}}\right)\right) \]
      rational.json-simplify-49 [=>] 21.2	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{c \cdot \frac{c}{\frac{1}{i \cdot b}}}\right)\right) \]
      rational.json-simplify-46 [=>] 21.2	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \frac{c}{\color{blue}{\frac{\frac{1}{i}}{b}}}\right)\right) \]

   6. Applied egg-rr 20.9

      \[\leadsto 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{\frac{c}{\frac{1}{c \cdot \left(i \cdot b\right)}}}\right)\right) \]

   7. Applied egg-rr 20.9

      \[\leadsto 2 \cdot \left(x \cdot y + \left(z \cdot t - \frac{c}{\color{blue}{\frac{1}{c \cdot \left(i \cdot b\right)} + 0}}\right)\right) \]

   8. Simplified 18.2

      \[\leadsto 2 \cdot \left(x \cdot y + \left(z \cdot t - \frac{c}{\color{blue}{\frac{1}{b \cdot \left(c \cdot i\right)}}}\right)\right) \]
      Proof

      [Start] 20.9	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \frac{c}{\frac{1}{c \cdot \left(i \cdot b\right)} + 0}\right)\right) \]
      rational.json-simplify-4 [=>] 20.9	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \frac{c}{\color{blue}{\frac{1}{c \cdot \left(i \cdot b\right)}}}\right)\right) \]
      rational.json-simplify-43 [<=] 18.2	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \frac{c}{\frac{1}{\color{blue}{b \cdot \left(c \cdot i\right)}}}\right)\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\right)\\ \mathbf{elif}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \leq 5 \cdot 10^{+299}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - \frac{c}{\frac{1}{b \cdot \left(c \cdot i\right)}}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	4.2
Cost	3792

\[\begin{array}{l} t_1 := a + b \cdot c\\ t_2 := 2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(t_1 \cdot i\right)\right)\right)\\ t_3 := \left(t_1 \cdot c\right) \cdot i\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{+108}:\\ \;\;\;\;2 \cdot \left(y \cdot x - t_3\right)\\ \mathbf{elif}\;t_3 \leq 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;2 \cdot \left(t \cdot z - t_3\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - \frac{c}{\frac{1}{b \cdot \left(c \cdot i\right)}}\right)\right)\\ \end{array} \]

Alternative 2
Error	9.7
Cost	3536

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ t_3 := 2 \cdot \left(y \cdot x - t_2\right)\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{+25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 10^{-49}:\\ \;\;\;\;2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+33}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	4.3
Cost	3148

\[\begin{array}{l} t_1 := a + b \cdot c\\ t_2 := 2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(t_1 \cdot i\right)\right)\right)\\ t_3 := \left(t_1 \cdot c\right) \cdot i\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{+108}:\\ \;\;\;\;2 \cdot \left(y \cdot x - t_3\right)\\ \mathbf{elif}\;t_3 \leq 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \end{array} \]

Alternative 4
Error	11.9
Cost	2892

\[\begin{array}{l} t_1 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+115}:\\ \;\;\;\;2 \cdot \left(\left(a + c \cdot b\right) \cdot \left(-c \cdot i\right)\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;2 \cdot \left(t \cdot z - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot z - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 5
Error	20.6
Cost	2264

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - \left(c \cdot a\right) \cdot i\right)\\ t_2 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-125}:\\ \;\;\;\;2 \cdot \left(\left(a + c \cdot b\right) \cdot \left(-c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-29}:\\ \;\;\;\;2 \cdot \left(t \cdot z - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	20.7
Cost	2264

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - \left(c \cdot a\right) \cdot i\right)\\ t_2 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-125}:\\ \;\;\;\;2 \cdot \left(\left(a + c \cdot b\right) \cdot \left(-c \cdot i\right)\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-29}:\\ \;\;\;\;2 \cdot \left(t \cdot z - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	23.1
Cost	2220

\[\begin{array}{l} t_1 := 2 \cdot \left(\left(a + c \cdot b\right) \cdot \left(-c \cdot i\right)\right)\\ t_2 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;x \leq -1.62 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-268}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-231}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(c \cdot a\right) \cdot i\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-49}:\\ \;\;\;\;2 \cdot \left(t \cdot z - b \cdot \left(c \cdot \left(c \cdot i\right)\right)\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+47}:\\ \;\;\;\;2 \cdot \left(x \cdot y + c \cdot \left(i \cdot \left(-a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	12.0
Cost	1480

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+91}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	20.6
Cost	1232

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ t_2 := \left(i \cdot \left(a + c \cdot b\right)\right) \cdot \left(c \cdot -2\right)\\ \mathbf{if}\;c \leq -3.3 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{-170}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(c \cdot a\right) \cdot i\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	36.7
Cost	1112

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x\right)\\ t_2 := 2 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-309}:\\ \;\;\;\;-2 \cdot \left(i \cdot \left(c \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	36.8
Cost	1112

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x\right)\\ t_2 := 2 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.0022:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-301}:\\ \;\;\;\;a \cdot \left(i \cdot \left(c \cdot -2\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	24.9
Cost	1104

\[\begin{array}{l} t_1 := a \cdot \left(i \cdot \left(c \cdot -2\right)\right)\\ t_2 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;b \leq -2.35 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	22.3
Cost	1104

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ t_2 := \left(b \cdot \left(c \cdot i\right)\right) \cdot \left(c \cdot -2\right)\\ \mathbf{if}\;c \leq -3.4 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-170}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(c \cdot a\right) \cdot i\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	36.0
Cost	848

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x\right)\\ t_2 := 2 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.0048:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	21.5
Cost	840

\[\begin{array}{l} t_1 := \left(b \cdot \left(c \cdot i\right)\right) \cdot \left(c \cdot -2\right)\\ \mathbf{if}\;c \leq -1.05 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	42.5
Cost	320

\[2 \cdot \left(t \cdot z\right) \]

Reproduce

herbie shell --seed 2023075 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))