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

Average Error: 3.5 → 0.5

Time: 11.5s

Precision: binary64

Cost: 1224

Math

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

↓

\[\begin{array}{l} t_1 := \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+94}:\\ \;\;\;\;\left(x + -0.3333333333333333 \cdot \frac{y}{z}\right) + t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + t_1\\ \end{array} \]

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
 (let* ((t_1 (/ t (* y (* z 3.0)))))
   (if (<= t -2.2e+94)
     (+ (+ x (* -0.3333333333333333 (/ y z))) t_1)
     (if (<= t 5e-41)
       (+ x (/ (- y (/ t y)) (* z -3.0)))
       (+ (- x (/ y (* z 3.0))) t_1)))))

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 t_1 = t / (y * (z * 3.0));
	double tmp;
	if (t <= -2.2e+94) {
		tmp = (x + (-0.3333333333333333 * (y / z))) + t_1;
	} else if (t <= 5e-41) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = (x - (y / (z * 3.0))) + t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = t / (y * (z * 3.0d0))
    if (t <= (-2.2d+94)) then
        tmp = (x + ((-0.3333333333333333d0) * (y / z))) + t_1
    else if (t <= 5d-41) then
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    else
        tmp = (x - (y / (z * 3.0d0))) + t_1
    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 t_1 = t / (y * (z * 3.0));
	double tmp;
	if (t <= -2.2e+94) {
		tmp = (x + (-0.3333333333333333 * (y / z))) + t_1;
	} else if (t <= 5e-41) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = (x - (y / (z * 3.0))) + t_1;
	}
	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):
	t_1 = t / (y * (z * 3.0))
	tmp = 0
	if t <= -2.2e+94:
		tmp = (x + (-0.3333333333333333 * (y / z))) + t_1
	elif t <= 5e-41:
		tmp = x + ((y - (t / y)) / (z * -3.0))
	else:
		tmp = (x - (y / (z * 3.0))) + t_1
	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)
	t_1 = Float64(t / Float64(y * Float64(z * 3.0)))
	tmp = 0.0
	if (t <= -2.2e+94)
		tmp = Float64(Float64(x + Float64(-0.3333333333333333 * Float64(y / z))) + t_1);
	elseif (t <= 5e-41)
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	else
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + t_1);
	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)
	t_1 = t / (y * (z * 3.0));
	tmp = 0.0;
	if (t <= -2.2e+94)
		tmp = (x + (-0.3333333333333333 * (y / z))) + t_1;
	elseif (t <= 5e-41)
		tmp = x + ((y - (t / y)) / (z * -3.0));
	else
		tmp = (x - (y / (z * 3.0))) + t_1;
	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_] := Block[{t$95$1 = N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+94], N[(N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 5e-41], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Target

Original	3.5
Target	1.8
Herbie	0.5

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

Derivation

1. Split input into 3 regimes

2. if t < -2.20000000000000012e94

   1. Initial program 0.8

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

   2. Simplified 0.8

      \[\leadsto \color{blue}{\left(x + -0.3333333333333333 \cdot \frac{y}{z}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}} \]
      Proof
      (+.f64 (+.f64 x (*.f64 -1/3 (/.f64 y z))) (/.f64 t (*.f64 y (*.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 x (*.f64 (Rewrite<= metadata-eval (/.f64 -1 3)) (/.f64 y z))) (/.f64 t (*.f64 y (*.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 x (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 y) (*.f64 3 z)))) (/.f64 t (*.f64 y (*.f64 z 3)))): 11 points increase in error, 21 points decrease in error
      (+.f64 (+.f64 x (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 y)) (*.f64 3 z))) (/.f64 t (*.f64 y (*.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 x (/.f64 (neg.f64 y) (Rewrite<= *-commutative_binary64 (*.f64 z 3)))) (/.f64 t (*.f64 y (*.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 x (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 y (*.f64 z 3))))) (/.f64 t (*.f64 y (*.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 x (/.f64 y (*.f64 z 3)))) (/.f64 t (*.f64 y (*.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 z 3) y)))): 0 points increase in error, 0 points decrease in error

   if -2.20000000000000012e94 < t < 4.9999999999999996e-41

   1. Initial program 5.2

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

   2. Simplified 0.5

      \[\leadsto \color{blue}{x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)} \]
      Proof
      (+.f64 x (*.f64 (/.f64 -1/3 z) (-.f64 y (/.f64 t y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (*.f64 (/.f64 (Rewrite<= metadata-eval (/.f64 -1 3)) z) (-.f64 y (/.f64 t y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (*.f64 (Rewrite<= associate-/r*_binary64 (/.f64 -1 (*.f64 3 z))) (-.f64 y (/.f64 t y)))): 20 points increase in error, 26 points decrease in error
      (+.f64 x (*.f64 (/.f64 -1 (Rewrite<= *-commutative_binary64 (*.f64 z 3))) (-.f64 y (/.f64 t y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 (/.f64 -1 (*.f64 z 3)) y) (*.f64 (/.f64 -1 (*.f64 z 3)) (/.f64 t y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 -1 y) (*.f64 z 3))) (*.f64 (/.f64 -1 (*.f64 z 3)) (/.f64 t y)))): 8 points increase in error, 23 points decrease in error
      (+.f64 x (-.f64 (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 y)) (*.f64 z 3)) (*.f64 (/.f64 -1 (*.f64 z 3)) (/.f64 t y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 y (*.f64 z 3)))) (*.f64 (/.f64 -1 (*.f64 z 3)) (/.f64 t y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (neg.f64 (/.f64 y (*.f64 z 3))) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 t) (*.f64 (*.f64 z 3) y))))): 24 points increase in error, 27 points decrease in error
      (+.f64 x (-.f64 (neg.f64 (/.f64 y (*.f64 z 3))) (/.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 t)) (*.f64 (*.f64 z 3) y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (neg.f64 (/.f64 y (*.f64 z 3))) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 t (*.f64 (*.f64 z 3) y)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite<= unsub-neg_binary64 (+.f64 (neg.f64 (/.f64 y (*.f64 z 3))) (neg.f64 (neg.f64 (/.f64 t (*.f64 (*.f64 z 3) y))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 (/.f64 y (*.f64 z 3)) (neg.f64 (/.f64 t (*.f64 (*.f64 z 3) y))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 (/.f64 y (*.f64 z 3)) (/.f64 t (*.f64 (*.f64 z 3) y)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= sub-neg_binary64 (-.f64 x (-.f64 (/.f64 y (*.f64 z 3)) (/.f64 t (*.f64 (*.f64 z 3) y))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))): 0 points increase in error, 0 points decrease in error

   3. Applied egg-rr 0.5

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

   if 4.9999999999999996e-41 < t

   1. Initial program 0.6

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

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+94}:\\ \;\;\;\;\left(x + -0.3333333333333333 \cdot \frac{y}{z}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	29.2
Cost	1376

\[\begin{array}{l} t_1 := -0.3333333333333333 \cdot \frac{y}{z}\\ t_2 := \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-46}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-199}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	0.5
Cost	1224

\[\begin{array}{l} t_1 := \left(x + -0.3333333333333333 \cdot \frac{y}{z}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{if}\;t \leq -2.85 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	28.7
Cost	1112

\[\begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-84}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-53}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+45}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	16.1
Cost	976

\[\begin{array}{l} t_1 := \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ t_2 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{-279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	16.1
Cost	976

\[\begin{array}{l} t_1 := \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ t_2 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -5 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-279}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	16.1
Cost	976

\[\begin{array}{l} t_1 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{-297}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-274}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-89}:\\ \;\;\;\;\frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	2.0
Cost	968

\[\begin{array}{l} t_1 := x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	2.0
Cost	968

\[\begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-29}:\\ \;\;\;\;x + t_1 \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-89}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{t_1}}\\ \end{array} \]

Alternative 9
Error	2.0
Cost	968

\[\begin{array}{l} t_1 := x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-87}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	1.8
Cost	960

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

Alternative 11
Error	28.6
Cost	848

\[\begin{array}{l} t_1 := -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	28.5
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+45}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	28.8
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-47}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+46}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	12.8
Cost	840

\[\begin{array}{l} t_1 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+46}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	9.1
Cost	840

\[\begin{array}{l} t_1 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	8.5
Cost	840

\[\begin{array}{l} t_1 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	6.1
Cost	840

\[\begin{array}{l} t_1 := x + \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	37.3
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022338 
(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))))