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

Average Error: 6.1 → 0.5

Time: 48.1s

Precision: binary64

Cost: 1864

Math

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

↓

\[\begin{array}{l} t_1 := 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \mathbf{if}\;i \leq -5 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{+50}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot a + \frac{b \cdot \left(i \cdot \left(c + c\right)\right)}{2}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i)))))
   (if (<= i -5e+20)
     t_1
     (if (<= i 1.45e+50)
       (*
        2.0
        (+ (* x y) (- (* z t) (* c (+ (* i a) (/ (* b (* i (+ c c))) 2.0))))))
       t_1))))

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 = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
	double tmp;
	if (i <= -5e+20) {
		tmp = t_1;
	} else if (i <= 1.45e+50) {
		tmp = 2.0 * ((x * y) + ((z * t) - (c * ((i * a) + ((b * (i * (c + c))) / 2.0)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))
end function

↓

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))
    if (i <= (-5d+20)) then
        tmp = t_1
    else if (i <= 1.45d+50) then
        tmp = 2.0d0 * ((x * y) + ((z * t) - (c * ((i * a) + ((b * (i * (c + c))) / 2.0d0)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

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 = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
	double tmp;
	if (i <= -5e+20) {
		tmp = t_1;
	} else if (i <= 1.45e+50) {
		tmp = 2.0 * ((x * y) + ((z * t) - (c * ((i * a) + ((b * (i * (c + c))) / 2.0)))));
	} else {
		tmp = t_1;
	}
	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 = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i))
	tmp = 0
	if i <= -5e+20:
		tmp = t_1
	elif i <= 1.45e+50:
		tmp = 2.0 * ((x * y) + ((z * t) - (c * ((i * a) + ((b * (i * (c + c))) / 2.0)))))
	else:
		tmp = t_1
	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(2.0 * Float64(Float64(Float64(x * y) + Float64(z * t)) - Float64(Float64(Float64(a + Float64(b * c)) * c) * i)))
	tmp = 0.0
	if (i <= -5e+20)
		tmp = t_1;
	elseif (i <= 1.45e+50)
		tmp = Float64(2.0 * Float64(Float64(x * y) + Float64(Float64(z * t) - Float64(c * Float64(Float64(i * a) + Float64(Float64(b * Float64(i * Float64(c + c))) / 2.0))))));
	else
		tmp = t_1;
	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 = 2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i));
	tmp = 0.0;
	if (i <= -5e+20)
		tmp = t_1;
	elseif (i <= 1.45e+50)
		tmp = 2.0 * ((x * y) + ((z * t) - (c * ((i * a) + ((b * (i * (c + c))) / 2.0)))));
	else
		tmp = t_1;
	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[(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]}, If[LessEqual[i, -5e+20], t$95$1, If[LessEqual[i, 1.45e+50], N[(2.0 * N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(c * N[(N[(i * a), $MachinePrecision] + N[(N[(b * N[(i * N[(c + c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Target

Original	6.1
Target	1.8
Herbie	0.5

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

Derivation

1. Split input into 2 regimes

2. if i < -5e20 or 1.45e50 < i

   1. Initial program 0.8

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

   if -5e20 < i < 1.45e50

   1. Initial program 8.7

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

   2. Simplified 1.6

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

      [Start] 8.7	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      rational.json-simplify-1 [=>] 8.7	\[ 2 \cdot \left(\color{blue}{\left(z \cdot t + x \cdot y\right)} - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      rational.json-simplify-48 [=>] 8.7	\[ 2 \cdot \color{blue}{\left(x \cdot y + \left(z \cdot t - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\right)} \]
      rational.json-simplify-2 [=>] 8.7	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right)\right) \]
      rational.json-simplify-2 [=>] 8.7	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - i \cdot \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)}\right)\right) \]
      rational.json-simplify-43 [=>] 1.6	\[ 2 \cdot \left(x \cdot y + \left(z \cdot t - \color{blue}{c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)}\right)\right) \]

   3. Taylor expanded in a around 0 1.5

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

   4. Applied egg-rr 0.4

      \[\leadsto 2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot a + \color{blue}{\frac{b \cdot \left(i \cdot \left(c + c\right)\right)}{2}}\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{+50}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot a + \frac{b \cdot \left(i \cdot \left(c + c\right)\right)}{2}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.1
Cost	2376

\[\begin{array}{l} t_1 := c \cdot \left(i \cdot b\right)\\ t_2 := \left(a + b \cdot c\right) \cdot c\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+305}:\\ \;\;\;\;2 \cdot \left(t \cdot z - c \cdot \left(t_1 + a \cdot i\right)\right)\\ \mathbf{elif}\;t_2 \leq 10^{+305}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t_2 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(i \cdot a + t_1\right)\right)\right)\\ \end{array} \]

Alternative 2
Error	1.8
Cost	2248

\[\begin{array}{l} t_1 := c \cdot \left(i \cdot b\right)\\ t_2 := \left(a + b \cdot c\right) \cdot c\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+305}:\\ \;\;\;\;2 \cdot \left(t \cdot z - c \cdot \left(t_1 + a \cdot i\right)\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - t_2 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot t_1\right)\right)\\ \end{array} \]

Alternative 3
Error	21.2
Cost	1752

\[\begin{array}{l} t_1 := c \cdot \left(i \cdot b\right)\\ \mathbf{if}\;c \leq -1.3 \cdot 10^{+165}:\\ \;\;\;\;c \cdot \left(b \cdot \left(i \cdot \left(c \cdot -2\right)\right)\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{+132}:\\ \;\;\;\;2 \cdot \left(t \cdot z - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -240000000000:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot t_1\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot \left(x \cdot y + c \cdot \left(i \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-102}:\\ \;\;\;\;2 \cdot \left(t \cdot z - i \cdot \left(c \cdot \left(c \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+90}:\\ \;\;\;\;\left(y \cdot x + t \cdot \left(z + z\right)\right) + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(c \cdot \left(\left(a \cdot i + t_1\right) \cdot -1\right)\right)\\ \end{array} \]

Alternative 4
Error	21.3
Cost	1624

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{+173}:\\ \;\;\;\;c \cdot \left(b \cdot \left(i \cdot \left(c \cdot -2\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{+132}:\\ \;\;\;\;2 \cdot \left(t \cdot z - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot \left(x \cdot y + c \cdot \left(i \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-102}:\\ \;\;\;\;2 \cdot \left(t \cdot z - i \cdot \left(c \cdot \left(c \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+84}:\\ \;\;\;\;2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	21.3
Cost	1624

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\\ \mathbf{if}\;c \leq -6.1 \cdot 10^{+177}:\\ \;\;\;\;c \cdot \left(b \cdot \left(i \cdot \left(c \cdot -2\right)\right)\right)\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{+132}:\\ \;\;\;\;2 \cdot \left(t \cdot z - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot \left(x \cdot y + c \cdot \left(i \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-102}:\\ \;\;\;\;2 \cdot \left(t \cdot z - i \cdot \left(c \cdot \left(c \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+84}:\\ \;\;\;\;\left(y \cdot x + t \cdot \left(z + z\right)\right) + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	21.6
Cost	1496

\[\begin{array}{l} t_1 := -2 \cdot \left(c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{+181}:\\ \;\;\;\;c \cdot \left(b \cdot \left(i \cdot \left(c \cdot -2\right)\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{+132}:\\ \;\;\;\;2 \cdot \left(t \cdot z - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-59}:\\ \;\;\;\;2 \cdot \left(x \cdot y + c \cdot \left(i \cdot \left(-a\right)\right)\right)\\ \mathbf{elif}\;c \leq -1.6 \cdot 10^{-102}:\\ \;\;\;\;2 \cdot \left(t \cdot z - i \cdot \left(c \cdot \left(c \cdot b\right)\right)\right)\\ \mathbf{elif}\;c \leq 10^{+91}:\\ \;\;\;\;2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	14.3
Cost	1480

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;x \cdot y \leq -1.1 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+68}:\\ \;\;\;\;2 \cdot \left(t \cdot z - i \cdot \left(c \cdot \left(a + c \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	11.5
Cost	1480

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;x \cdot y \leq -1.1 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+41}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	3.1
Cost	1480

\[\begin{array}{l} t_1 := 2 \cdot \left(x \cdot y + \left(z \cdot t - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\right)\\ \mathbf{if}\;c \leq -3.5 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-94}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot a\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	9.0
Cost	1352

\[\begin{array}{l} \mathbf{if}\;c \leq -8 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+90}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot a\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t \cdot z - c \cdot \left(c \cdot \left(i \cdot b\right) + a \cdot i\right)\right)\\ \end{array} \]

Alternative 11
Error	8.7
Cost	1352

\[\begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot \left(t \cdot z - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+61}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot a\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - c \cdot \left(i \cdot a + c \cdot \left(i \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 12
Error	20.9
Cost	1232

\[\begin{array}{l} t_1 := -2 \cdot \left(c \cdot \left(i \cdot \left(c \cdot b + a\right)\right)\right)\\ t_2 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;c \leq -2.8 \cdot 10^{+174}:\\ \;\;\;\;c \cdot \left(b \cdot \left(i \cdot \left(c \cdot -2\right)\right)\right)\\ \mathbf{elif}\;c \leq -7 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	17.6
Cost	1224

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 0.002:\\ \;\;\;\;2 \cdot \left(t \cdot z - a \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	8.9
Cost	1224

\[\begin{array}{l} t_1 := a + c \cdot b\\ \mathbf{if}\;c \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot \left(t \cdot z - t_1 \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+80}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(c \cdot a\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(y \cdot x - t_1 \cdot \left(i \cdot c\right)\right)\\ \end{array} \]

Alternative 15
Error	21.6
Cost	1104

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ t_2 := c \cdot \left(b \cdot \left(i \cdot \left(c \cdot -2\right)\right)\right)\\ \mathbf{if}\;c \leq -1.55 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -27:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.35 \cdot 10^{-13}:\\ \;\;\;\;\left(c \cdot \left(i \cdot a\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	21.9
Cost	1104

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;c \leq -2.1 \cdot 10^{+185}:\\ \;\;\;\;c \cdot \left(b \cdot \left(i \cdot \left(c \cdot -2\right)\right)\right)\\ \mathbf{elif}\;c \leq -27:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.35 \cdot 10^{-13}:\\ \;\;\;\;\left(c \cdot \left(i \cdot a\right)\right) \cdot -2\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(\left(c \cdot \left(i \cdot b\right)\right) \cdot -2\right)\\ \end{array} \]

Alternative 17
Error	36.5
Cost	848

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ t_2 := 2 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	37.1
Cost	848

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ t_2 := 2 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 18000:\\ \;\;\;\;i \cdot \left(-2 \cdot \left(c \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	23.7
Cost	840

\[\begin{array}{l} t_1 := i \cdot \left(-2 \cdot \left(c \cdot a\right)\right)\\ \mathbf{if}\;i \leq -1.26 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+78}:\\ \;\;\;\;2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	42.3
Cost	320

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

Reproduce

herbie shell --seed 2023064 
(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))))