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

Average Error: 6.2 → 2.0

Time: 39.7s

Precision: binary64

Cost: 2632

Math

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

↓

\[\begin{array}{l} t_1 := a + b \cdot c\\ t_2 := t_1 \cdot c\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+129}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(0.5 \cdot \left(a + \left(a + c \cdot \left(b + b\right)\right)\right)\right) \cdot c\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(t_1 \cdot i\right)\right)\right)\\ \end{array} \]

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)))
   (if (<= t_2 (- INFINITY))
     (* 2.0 (+ (* x y) (- (* z t) (* c (* c (* i b))))))
     (if (<= t_2 5e+129)
       (*
        2.0
        (- (+ (* x y) (* z t)) (* (* (* 0.5 (+ a (+ a (* c (+ b b))))) c) i)))
       (* 2.0 (+ (* x y) (- (* z t) (* c (* t_1 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;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (c * (i * b)))));
	} else if (t_2 <= 5e+129) {
		tmp = 2.0 * (((x * y) + (z * t)) - (((0.5 * (a + (a + (c * (b + b))))) * c) * i));
	} else {
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (t_1 * 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;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (c * (i * b)))));
	} else if (t_2 <= 5e+129) {
		tmp = 2.0 * (((x * y) + (z * t)) - (((0.5 * (a + (a + (c * (b + b))))) * c) * i));
	} else {
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (t_1 * 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
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (c * (i * b)))))
	elif t_2 <= 5e+129:
		tmp = 2.0 * (((x * y) + (z * t)) - (((0.5 * (a + (a + (c * (b + b))))) * c) * i))
	else:
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (t_1 * 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(t_1 * c)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(c * Float64(c * Float64(i * b))))));
	elseif (t_2 <= 5e+129)
		tmp = Float64(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(0.5 * Float64(a + Float64(a + Float64(c * Float64(b + b))))) * c) * i)));
	else
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(c * Float64(t_1 * 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;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (c * (i * b)))));
	elseif (t_2 <= 5e+129)
		tmp = 2.0 * (((x * y) + (z * t)) - (((0.5 * (a + (a + (c * (b + b))))) * c) * i));
	else
		tmp = 2.0 * ((x * y) + ((z * t) - (c * (t_1 * 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[(t$95$1 * c), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(c * N[(c * N[(i * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+129], N[(2.0 * N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(0.5 * N[(a + N[(a + N[(c * N[(b + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]]]]

Target

Original	6.2
Target	1.8
Herbie	2.0

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 (+.f64 a (*.f64 b c)) c) < -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 10.4

      \[\leadsto \color{blue}{2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\right)} \]
      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 [=>] 10.4	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right)\right) \]

   3. Taylor expanded in a around 0 19.4

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

   if -inf.0 < (*.f64 (+.f64 a (*.f64 b c)) c) < 5.0000000000000003e129

   1. Initial program 0.4

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

   2. Applied egg-rr 0.4

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\color{blue}{\left(0.5 \cdot \left(c \cdot \left(b + b\right) + \left(a + a\right)\right)\right)} \cdot c\right) \cdot i\right) \]

   3. Simplified 0.4

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\color{blue}{\left(0.5 \cdot \left(a + \left(a + c \cdot \left(b + b\right)\right)\right)\right)} \cdot c\right) \cdot i\right) \]
      Proof

      [Start] 0.4	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(0.5 \cdot \left(c \cdot \left(b + b\right) + \left(a + a\right)\right)\right) \cdot c\right) \cdot i\right) \]
      rational.json-simplify-41 [=>] 0.4	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(0.5 \cdot \color{blue}{\left(a + \left(a + c \cdot \left(b + b\right)\right)\right)}\right) \cdot c\right) \cdot i\right) \]

   if 5.0000000000000003e129 < (*.f64 (+.f64 a (*.f64 b c)) c)

   1. Initial program 21.2

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

   2. Simplified 5.5

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

      [Start] 21.2	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      rational.json-simplify-1 [=>] 21.2	\[ 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      rational.json-simplify-48 [=>] 21.2	\[ 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]
      rational.json-simplify-2 [=>] 21.2	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) \]
      rational.json-simplify-2 [=>] 21.2	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - i \cdot \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)}\right)\right) \]
      rational.json-simplify-43 [=>] 5.5	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right)\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 2.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\right)\\ \mathbf{elif}\;\left(a + b \cdot c\right) \cdot c \leq 5 \cdot 10^{+129}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(0.5 \cdot \left(a + \left(a + c \cdot \left(b + b\right)\right)\right)\right) \cdot c\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.9
Cost	2248

\[\begin{array}{l} t_1 := a + b \cdot c\\ t_2 := t_1 \cdot c\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+129}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t_2 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(t_1 \cdot i\right)\right)\right)\\ \end{array} \]

Alternative 2
Error	13.1
Cost	2000

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+38}:\\ \;\;\;\;2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{elif}\;x \cdot y \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-19}:\\ \;\;\;\;2 \cdot \left(x \cdot y + c \cdot \left(-i \cdot a\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 3
Error	11.9
Cost	2000

\[\begin{array}{l} t_1 := \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\\ t_2 := 2 \cdot \left(y \cdot x - t_1\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+32}:\\ \;\;\;\;2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-143}:\\ \;\;\;\;2 \cdot \left(t \cdot z - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+24}:\\ \;\;\;\;2 \cdot \left(t \cdot z - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	10.9
Cost	2000

\[\begin{array}{l} t_1 := \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\\ t_2 := 2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\right)\\ t_3 := 2 \cdot \left(y \cdot x - t_1\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+24}:\\ \;\;\;\;2 \cdot \left(t \cdot z - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	21.6
Cost	1888

\[\begin{array}{l} t_1 := c \cdot \left(\left(i \cdot \left(a + c \cdot b\right)\right) \cdot -2\right)\\ t_2 := c \cdot \left(c \cdot \left(i \cdot b\right)\right)\\ t_3 := 2 \cdot \left(t \cdot z - t_2\right)\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -620000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.38 \cdot 10^{-33}:\\ \;\;\;\;2 \cdot \left(x \cdot y + c \cdot \left(-i \cdot a\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-65}:\\ \;\;\;\;2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+165}:\\ \;\;\;\;2 \cdot \left(y \cdot x - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+208}:\\ \;\;\;\;2 \cdot \left(y \cdot x - t_2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b + a\right) \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \]

Alternative 6
Error	21.5
Cost	1756

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\\ t_2 := c \cdot \left(\left(i \cdot \left(a + c \cdot b\right)\right) \cdot -2\right)\\ \mathbf{if}\;c \leq -3.4 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -14000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-65}:\\ \;\;\;\;2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{+165}:\\ \;\;\;\;2 \cdot \left(y \cdot x - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b + a\right) \cdot \left(c \cdot i\right)\right) \cdot -2\\ \end{array} \]

Alternative 7
Error	5.4
Cost	1736

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	20.1
Cost	1232

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ t_2 := 2 \cdot \left(y \cdot x - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	21.9
Cost	1232

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ t_2 := c \cdot \left(\left(i \cdot \left(a + c \cdot b\right)\right) \cdot -2\right)\\ \mathbf{if}\;c \leq -1650000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	38.0
Cost	1112

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ t_2 := a \cdot \left(\left(c \cdot i\right) \cdot -2\right)\\ t_3 := 2 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{-123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.0085:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+32}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Error	38.0
Cost	1112

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ t_2 := 2 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.0085:\\ \;\;\;\;a \cdot \left(\left(c \cdot i\right) \cdot -2\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+55}:\\ \;\;\;\;\left(c \cdot \left(i \cdot a\right)\right) \cdot -2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	24.8
Cost	1104

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ t_2 := \left(\left(c \cdot b\right) \cdot \left(c \cdot i\right)\right) \cdot -2\\ \mathbf{if}\;c \leq -14000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.32 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	23.9
Cost	840

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;y \leq 2.1 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-79}:\\ \;\;\;\;\left(c \cdot \left(i \cdot a\right)\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	36.3
Cost	584

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	43.1
Cost	320

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

Reproduce

herbie shell --seed 2023068 
(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))))