Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, H

Average Error: 5.49% → 2.74%

Time: 18.3s

Precision: binary64

Cost: 1224

Math

\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

↓

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-119}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

↓

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.2e-119)
   (+ x (/ (- y (/ t y)) (* z -3.0)))
   (if (<= y 2.4e-142)
     (+ x (/ (* (/ t z) 0.3333333333333333) y))
     (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0)))))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

↓

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.2e-119) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else if (y <= 2.4e-142) {
		tmp = x + (((t / z) * 0.3333333333333333) / y);
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.2d-119)) then
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    else if (y <= 2.4d-142) then
        tmp = x + (((t / z) * 0.3333333333333333d0) / y)
    else
        tmp = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

↓

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.2e-119) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else if (y <= 2.4e-142) {
		tmp = x + (((t / z) * 0.3333333333333333) / y);
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

↓

def code(x, y, z, t):
	tmp = 0
	if y <= -2.2e-119:
		tmp = x + ((y - (t / y)) / (z * -3.0))
	elif y <= 2.4e-142:
		tmp = x + (((t / z) * 0.3333333333333333) / y)
	else:
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

↓

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.2e-119)
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	elseif (y <= 2.4e-142)
		tmp = Float64(x + Float64(Float64(Float64(t / z) * 0.3333333333333333) / y));
	else
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.2e-119)
		tmp = x + ((y - (t / y)) / (z * -3.0));
	elseif (y <= 2.4e-142)
		tmp = x + (((t / z) * 0.3333333333333333) / y);
	else
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := If[LessEqual[y, -2.2e-119], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-142], N[(x + N[(N[(N[(t / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	5.49%
Target	2.78%
Herbie	2.74%

\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \]

Derivation

1. Split input into 3 regimes

2. if y < -2.2000000000000001e-119

   1. Initial program 1.24

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Simplified 1.97

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
      Proof

      [Start] 1.24	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-+l- [=>] 1.24	\[ \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      sub-neg [=>] 1.24	\[ \color{blue}{x + \left(-\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} \]
      neg-mul-1 [=>] 1.24	\[ x + \color{blue}{-1 \cdot \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      distribute-lft-out-- [<=] 1.24	\[ x + \color{blue}{\left(-1 \cdot \frac{y}{z \cdot 3} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]
      associate-*r/ [=>] 1.24	\[ x + \left(\color{blue}{\frac{-1 \cdot y}{z \cdot 3}} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*l/ [<=] 1.32	\[ x + \left(\color{blue}{\frac{-1}{z \cdot 3} \cdot y} - -1 \cdot \frac{t}{\left(z \cdot 3\right) \cdot y}\right) \]
      associate-*r/ [=>] 1.32	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1 \cdot t}{\left(z \cdot 3\right) \cdot y}}\right) \]
      times-frac [=>] 1.96	\[ x + \left(\frac{-1}{z \cdot 3} \cdot y - \color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}}\right) \]
      distribute-lft-out-- [=>] 1.97	\[ x + \color{blue}{\frac{-1}{z \cdot 3} \cdot \left(y - \frac{t}{y}\right)} \]
      *-commutative [=>] 1.97	\[ x + \frac{-1}{\color{blue}{3 \cdot z}} \cdot \left(y - \frac{t}{y}\right) \]
      associate-/r* [=>] 1.97	\[ x + \color{blue}{\frac{\frac{-1}{3}}{z}} \cdot \left(y - \frac{t}{y}\right) \]
      metadata-eval [=>] 1.97	\[ x + \frac{\color{blue}{-0.3333333333333333}}{z} \cdot \left(y - \frac{t}{y}\right) \]

   3. Applied egg-rr 1.87

      \[\leadsto x + \color{blue}{\frac{y - \frac{t}{y}}{z \cdot -3}} \]

   if -2.2000000000000001e-119 < y < 2.39999999999999988e-142

   1. Initial program 16.02

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Simplified 4.03

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}} \]
      Proof

      [Start] 16.02	\[ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
      associate-/r* [=>] 4.03	\[ \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

   3. Taylor expanded in x around inf 4.28

      \[\leadsto \color{blue}{x} + \frac{\frac{t}{z \cdot 3}}{y} \]

   4. Applied egg-rr 4.35

      \[\leadsto x + \frac{\color{blue}{\frac{t}{z} \cdot 0.3333333333333333}}{y} \]

   if 2.39999999999999988e-142 < y

   1. Initial program 2.48

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 2.74

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-119}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	46.72%
Cost	1376

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{if}\;x \leq -4.7 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -6.8:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-109}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-163}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-67}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	47.08%
Cost	1376

\[\begin{array}{l} t_1 := -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{if}\;x \leq -7 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.5:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-108}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-259}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-92}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	47.26%
Cost	1376

\[\begin{array}{l} t_1 := -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{if}\;x \leq -2 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -10.2:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-256}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-90}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	25.18%
Cost	978

\[\begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-114} \lor \neg \left(y \leq 4.1 \cdot 10^{-203}\right) \land \left(y \leq 1.55 \cdot 10^{-145} \lor \neg \left(y \leq 2.9 \cdot 10^{-86}\right)\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \]

Alternative 5
Error	25.11%
Cost	977

\[\begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-114}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-203} \lor \neg \left(y \leq 3.8 \cdot 10^{-143}\right) \land y \leq 7.8 \cdot 10^{-86}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 6
Error	25.12%
Cost	976

\[\begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{if}\;y \leq -5 \cdot 10^{-114}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-145}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]

Alternative 7
Error	24.88%
Cost	976

\[\begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-114}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-181}:\\ \;\;\;\;\frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-142}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-86}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]

Alternative 8
Error	25.13%
Cost	976

\[\begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-114}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 10^{-204}:\\ \;\;\;\;\frac{\frac{t}{z}}{\frac{y}{0.3333333333333333}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-143}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-86}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]

Alternative 9
Error	2.41%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-107} \lor \neg \left(y \leq 1.9 \cdot 10^{-82}\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array} \]

Alternative 10
Error	2.41%
Cost	968

\[\begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -2 \cdot 10^{-107}:\\ \;\;\;\;x + t_1 \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-82}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{t_1}}\\ \end{array} \]

Alternative 11
Error	2.43%
Cost	968

\[\begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{t_1}{z \cdot -3}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{t_1}}\\ \end{array} \]

Alternative 12
Error	2.43%
Cost	968

\[\begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-111}:\\ \;\;\;\;x + \frac{t_1}{z \cdot -3}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t_1}{z}}{-3}\\ \end{array} \]

Alternative 13
Error	2.78%
Cost	960

\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \]

Alternative 14
Error	44.61%
Cost	849

\[\begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.3 \lor \neg \left(x \leq -8.5 \cdot 10^{-92}\right) \land x \leq 2.1 \cdot 10^{-67}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Error	44.56%
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -10.2:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-93}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-67}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16
Error	18.62%
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-68}:\\ \;\;\;\;\frac{y - \frac{t}{y}}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 17
Error	13.01%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]

Alternative 18
Error	9.33%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-27}:\\ \;\;\;\;x + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]

Alternative 19
Error	9.3%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-28}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]

Alternative 20
Error	58.48%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))