Average Error: 3.8 → 1.0
Time: 4.9s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
↓
\[\begin{array}{l} t_1 := \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+148}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + t_1\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-0.3333333333333333}{z}, y - \frac{t}{y}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + \frac{y}{3} \cdot \frac{-1}{z}\right)\\ \end{array} \]
(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 (* (* z 3.0) y))))
   (if (<= (* z 3.0) -4e+148)
     (+ (- x (/ (/ y z) 3.0)) t_1)
     (if (<= (* z 3.0) 5e-6)
       (fma (/ -0.3333333333333333 z) (- y (/ t y)) x)
       (+ t_1 (+ x (* (/ y 3.0) (/ -1.0 z))))))))
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 / ((z * 3.0) * y);
	double tmp;
	if ((z * 3.0) <= -4e+148) {
		tmp = (x - ((y / z) / 3.0)) + t_1;
	} else if ((z * 3.0) <= 5e-6) {
		tmp = fma((-0.3333333333333333 / z), (y - (t / y)), x);
	} else {
		tmp = t_1 + (x + ((y / 3.0) * (-1.0 / z)));
	}
	return tmp;
}

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(Float64(z * 3.0) * y))
	tmp = 0.0
	if (Float64(z * 3.0) <= -4e+148)
		tmp = Float64(Float64(x - Float64(Float64(y / z) / 3.0)) + t_1);
	elseif (Float64(z * 3.0) <= 5e-6)
		tmp = fma(Float64(-0.3333333333333333 / z), Float64(y - Float64(t / y)), x);
	else
		tmp = Float64(t_1 + Float64(x + Float64(Float64(y / 3.0) * Float64(-1.0 / z))));
	end
	return tmp
end

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[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * 3.0), $MachinePrecision], -4e+148], N[(N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 5e-6], N[(N[(-0.3333333333333333 / z), $MachinePrecision] * N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(t$95$1 + N[(x + N[(N[(y / 3.0), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
t_1 := \frac{t}{\left(z \cdot 3\right) \cdot y}\\
\mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+148}:\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + t_1\\

\mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-6}:\\
\;\;\;\;\mathsf{fma}\left(\frac{-0.3333333333333333}{z}, y - \frac{t}{y}, x\right)\\

\mathbf{else}:\\
\;\;\;\;t_1 + \left(x + \frac{y}{3} \cdot \frac{-1}{z}\right)\\


\end{array}

Error

Target

Original3.8
Target1.6
Herbie1.0
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 z 3) < -4.0000000000000002e148

    1. Initial program 0.6

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

    2. Applied egg-rr0.5

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

    if -4.0000000000000002e148 < (*.f64 z 3) < 5.00000000000000041e-6

    1. Initial program 7.3

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

    2. Simplified1.5

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-0.3333333333333333}{z}, y - \frac{t}{y}, x\right)} \]

    if 5.00000000000000041e-6 < (*.f64 z 3)

    1. Initial program 0.4

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

    2. Applied egg-rr0.4

      \[\leadsto \left(x - \color{blue}{\frac{1}{z} \cdot \frac{y}{3}}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+148}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(\frac{-0.3333333333333333}{z}, y - \frac{t}{y}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x + \frac{y}{3} \cdot \frac{-1}{z}\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2022186 
(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))))