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

Average Error: 6.3 → 2.6

Time: 33.2s

Precision: binary64

Cost: 3780

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot y + z \cdot t\\ t_2 := a + b \cdot c\\ t_3 := t_1 - c \cdot \left(\left(a + c \cdot b\right) \cdot i\right)\\ \mathbf{if}\;c \leq -2.9 \cdot 10^{+65}:\\ \;\;\;\;2 \cdot \left(t_3 \cdot \left(t_3 \cdot \frac{1}{t_3}\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{-177}:\\ \;\;\;\;2 \cdot \left(t_1 - \left(t_2 \cdot c\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 - c \cdot \left(t_2 \cdot i\right)\right)\\ \end{array} \]

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 (+ (* x y) (* z t)))
        (t_2 (+ a (* b c)))
        (t_3 (- t_1 (* c (* (+ a (* c b)) i)))))
   (if (<= c -2.9e+65)
     (* 2.0 (* t_3 (* t_3 (/ 1.0 t_3))))
     (if (<= c 3.7e-177)
       (* 2.0 (- t_1 (* (* t_2 c) i)))
       (* 2.0 (- t_1 (* c (* t_2 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 = (x * y) + (z * t);
	double t_2 = a + (b * c);
	double t_3 = t_1 - (c * ((a + (c * b)) * i));
	double tmp;
	if (c <= -2.9e+65) {
		tmp = 2.0 * (t_3 * (t_3 * (1.0 / t_3)));
	} else if (c <= 3.7e-177) {
		tmp = 2.0 * (t_1 - ((t_2 * c) * i));
	} else {
		tmp = 2.0 * (t_1 - (c * (t_2 * i)));
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * y) + (z * t)
    t_2 = a + (b * c)
    t_3 = t_1 - (c * ((a + (c * b)) * i))
    if (c <= (-2.9d+65)) then
        tmp = 2.0d0 * (t_3 * (t_3 * (1.0d0 / t_3)))
    else if (c <= 3.7d-177) then
        tmp = 2.0d0 * (t_1 - ((t_2 * c) * i))
    else
        tmp = 2.0d0 * (t_1 - (c * (t_2 * i)))
    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 = (x * y) + (z * t);
	double t_2 = a + (b * c);
	double t_3 = t_1 - (c * ((a + (c * b)) * i));
	double tmp;
	if (c <= -2.9e+65) {
		tmp = 2.0 * (t_3 * (t_3 * (1.0 / t_3)));
	} else if (c <= 3.7e-177) {
		tmp = 2.0 * (t_1 - ((t_2 * c) * i));
	} else {
		tmp = 2.0 * (t_1 - (c * (t_2 * 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 = (x * y) + (z * t)
	t_2 = a + (b * c)
	t_3 = t_1 - (c * ((a + (c * b)) * i))
	tmp = 0
	if c <= -2.9e+65:
		tmp = 2.0 * (t_3 * (t_3 * (1.0 / t_3)))
	elif c <= 3.7e-177:
		tmp = 2.0 * (t_1 - ((t_2 * c) * i))
	else:
		tmp = 2.0 * (t_1 - (c * (t_2 * 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(Float64(x * y) + Float64(z * t))
	t_2 = Float64(a + Float64(b * c))
	t_3 = Float64(t_1 - Float64(c * Float64(Float64(a + Float64(c * b)) * i)))
	tmp = 0.0
	if (c <= -2.9e+65)
		tmp = Float64(2.0 * Float64(t_3 * Float64(t_3 * Float64(1.0 / t_3))));
	elseif (c <= 3.7e-177)
		tmp = Float64(2.0 * Float64(t_1 - Float64(Float64(t_2 * c) * i)));
	else
		tmp = Float64(2.0 * Float64(t_1 - Float64(c * Float64(t_2 * 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 = (x * y) + (z * t);
	t_2 = a + (b * c);
	t_3 = t_1 - (c * ((a + (c * b)) * i));
	tmp = 0.0;
	if (c <= -2.9e+65)
		tmp = 2.0 * (t_3 * (t_3 * (1.0 / t_3)));
	elseif (c <= 3.7e-177)
		tmp = 2.0 * (t_1 - ((t_2 * c) * i));
	else
		tmp = 2.0 * (t_1 - (c * (t_2 * 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[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 - N[(c * N[(N[(a + N[(c * b), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.9e+65], N[(2.0 * N[(t$95$3 * N[(t$95$3 * N[(1.0 / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.7e-177], N[(2.0 * N[(t$95$1 - N[(N[(t$95$2 * c), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 - N[(c * N[(t$95$2 * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	6.3
Target	1.8
Herbie	2.6

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

Derivation

1. Split input into 3 regimes

2. if c < -2.9e65

   1. Initial program 26.0

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

   2. Simplified 4.2

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

      [Start] 26.0	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      rational_best.json-simplify-2 [=>] 26.0	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right) \]
      rational_best.json-simplify-2 [=>] 26.0	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)}\right) \]
      rational_best.json-simplify-44 [=>] 4.2	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]
      rational_best.json-simplify-2 [=>] 4.2	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

   3. Applied egg-rr 4.3

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

   if -2.9e65 < c < 3.69999999999999993e-177

   1. Initial program 0.9

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

   if 3.69999999999999993e-177 < c

   1. Initial program 9.1

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

   2. Simplified 4.8

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

      [Start] 9.1	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right) \]
      rational_best.json-simplify-2 [=>] 9.1	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{i \cdot \left(\left(a + b \cdot c\right) \cdot c\right)}\right) \]
      rational_best.json-simplify-2 [=>] 9.1	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - i \cdot \color{blue}{\left(c \cdot \left(a + b \cdot c\right)\right)}\right) \]
      rational_best.json-simplify-44 [=>] 4.8	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{c \cdot \left(i \cdot \left(a + b \cdot c\right)\right)}\right) \]
      rational_best.json-simplify-2 [=>] 4.8	\[ 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \color{blue}{\left(\left(a + b \cdot c\right) \cdot i\right)}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 2.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+65}:\\ \;\;\;\;2 \cdot \left(\left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(\left(a + c \cdot b\right) \cdot i\right)\right) \cdot \left(\left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(\left(a + c \cdot b\right) \cdot i\right)\right) \cdot \frac{1}{\left(x \cdot y + z \cdot t\right) - c \cdot \left(\left(a + c \cdot b\right) \cdot i\right)}\right)\right)\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{-177}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(\left(a + b \cdot c\right) \cdot i\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	28.5
Cost	2416

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ t_2 := 2 \cdot \left(y \cdot x - \left(c \cdot a\right) \cdot i\right)\\ t_3 := 2 \cdot \left(t \cdot z - c \cdot \left(i \cdot a\right)\right)\\ t_4 := 2 \cdot \left(t \cdot z - \left(c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{+212}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -9 \cdot 10^{+186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{+71}:\\ \;\;\;\;\left(a + c \cdot b\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.16 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{-285}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-73}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{+261}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	9.5
Cost	2376

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t_2 \leq -0.55:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{+17}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(c \cdot \left(i \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	9.7
Cost	2248

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - \left(a + c \cdot b\right) \cdot \left(c \cdot i\right)\right)\\ t_2 := \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{+17}:\\ \;\;\;\;2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	23.3
Cost	1892

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - c \cdot \left(i \cdot a\right)\right)\\ t_2 := 2 \cdot \left(y \cdot x - \left(c \cdot a\right) \cdot i\right)\\ t_3 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-142}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 34000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+74}:\\ \;\;\;\;b \cdot \left(c \cdot \left(c \cdot \left(-2 \cdot i\right)\right)\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+118}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+168}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	5.5
Cost	1860

\[\begin{array}{l} t_1 := a + b \cdot c\\ \mathbf{if}\;\left(t_1 \cdot c\right) \cdot i \leq -1 \cdot 10^{+164}:\\ \;\;\;\;\left(a + c \cdot b\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(t_1 \cdot i\right)\right)\\ \end{array} \]

Alternative 6
Error	23.4
Cost	1760

\[\begin{array}{l} t_1 := a + c \cdot b\\ t_2 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-190}:\\ \;\;\;\;2 \cdot \left(t \cdot z - c \cdot \left(i \cdot a\right)\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 11500000:\\ \;\;\;\;t_1 \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+73}:\\ \;\;\;\;2 \cdot \left(i \cdot \left(-c \cdot t_1\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+168}:\\ \;\;\;\;2 \cdot \left(y \cdot x - \left(c \cdot a\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	22.3
Cost	1628

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ t_2 := \left(a + c \cdot b\right) \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{if}\;c \leq -1.9 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -0.00162:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-86}:\\ \;\;\;\;2 \cdot \left(y \cdot x - \left(c \cdot a\right) \cdot i\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+205}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	2.6
Cost	1480

\[\begin{array}{l} t_1 := a + b \cdot c\\ t_2 := x \cdot y + z \cdot t\\ t_3 := 2 \cdot \left(t_2 - c \cdot \left(t_1 \cdot i\right)\right)\\ \mathbf{if}\;c \leq -2.9 \cdot 10^{+65}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-177}:\\ \;\;\;\;2 \cdot \left(t_2 - \left(t_1 \cdot c\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Error	22.9
Cost	1232

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z - c \cdot \left(i \cdot a\right)\right)\\ t_2 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{-142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 35000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	37.2
Cost	1112

\[\begin{array}{l} t_1 := 2 \cdot \left(t \cdot z\right)\\ t_2 := a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ t_3 := 2 \cdot \left(y \cdot x\right)\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.48 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Error	38.2
Cost	1112

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x\right)\\ t_2 := 2 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-78}:\\ \;\;\;\;c \cdot \left(\left(a \cdot i\right) \cdot -2\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-198}:\\ \;\;\;\;a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	25.2
Cost	1104

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x + t \cdot z\right)\\ t_2 := a \cdot \left(c \cdot \left(i \cdot -2\right)\right)\\ \mathbf{if}\;i \leq -4.8 \cdot 10^{+173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+145}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	38.6
Cost	848

\[\begin{array}{l} t_1 := 2 \cdot \left(y \cdot x\right)\\ t_2 := 2 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-239}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+212}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	43.0
Cost	320

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

Reproduce

herbie shell --seed 2023089 
(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))))