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

Average Error: 3.4 → 0.6

Time: 6.6s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_1 := x - \frac{\frac{y}{z}}{3}\\ \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{-96}:\\ \;\;\;\;\frac{t}{\left(z \cdot 3\right) \cdot y} + t_1\\ \mathbf{elif}\;z \cdot 3 \leq 4 \cdot 10^{+29}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z} \cdot \frac{t}{3 \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t_1 + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]

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 (- x (/ (/ y z) 3.0))))
   (if (<= (* z 3.0) -2e-96)
     (+ (/ t (* (* z 3.0) y)) t_1)
     (if (<= (* z 3.0) 4e+29)
       (+ (- x (/ y (* z 3.0))) (* (/ 1.0 z) (/ t (* 3.0 y))))
       (+ t_1 (* 0.3333333333333333 (/ t (* z y))))))))

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 = x - ((y / z) / 3.0);
	double tmp;
	if ((z * 3.0) <= -2e-96) {
		tmp = (t / ((z * 3.0) * y)) + t_1;
	} else if ((z * 3.0) <= 4e+29) {
		tmp = (x - (y / (z * 3.0))) + ((1.0 / z) * (t / (3.0 * y)));
	} else {
		tmp = t_1 + (0.3333333333333333 * (t / (z * y)));
	}
	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 = x - ((y / z) / 3.0d0)
    if ((z * 3.0d0) <= (-2d-96)) then
        tmp = (t / ((z * 3.0d0) * y)) + t_1
    else if ((z * 3.0d0) <= 4d+29) then
        tmp = (x - (y / (z * 3.0d0))) + ((1.0d0 / z) * (t / (3.0d0 * y)))
    else
        tmp = t_1 + (0.3333333333333333d0 * (t / (z * y)))
    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 = x - ((y / z) / 3.0);
	double tmp;
	if ((z * 3.0) <= -2e-96) {
		tmp = (t / ((z * 3.0) * y)) + t_1;
	} else if ((z * 3.0) <= 4e+29) {
		tmp = (x - (y / (z * 3.0))) + ((1.0 / z) * (t / (3.0 * y)));
	} else {
		tmp = t_1 + (0.3333333333333333 * (t / (z * y)));
	}
	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 = x - ((y / z) / 3.0)
	tmp = 0
	if (z * 3.0) <= -2e-96:
		tmp = (t / ((z * 3.0) * y)) + t_1
	elif (z * 3.0) <= 4e+29:
		tmp = (x - (y / (z * 3.0))) + ((1.0 / z) * (t / (3.0 * y)))
	else:
		tmp = t_1 + (0.3333333333333333 * (t / (z * y)))
	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(x - Float64(Float64(y / z) / 3.0))
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e-96)
		tmp = Float64(Float64(t / Float64(Float64(z * 3.0) * y)) + t_1);
	elseif (Float64(z * 3.0) <= 4e+29)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(1.0 / z) * Float64(t / Float64(3.0 * y))));
	else
		tmp = Float64(t_1 + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	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 = x - ((y / z) / 3.0);
	tmp = 0.0;
	if ((z * 3.0) <= -2e-96)
		tmp = (t / ((z * 3.0) * y)) + t_1;
	elseif ((z * 3.0) <= 4e+29)
		tmp = (x - (y / (z * 3.0))) + ((1.0 / z) * (t / (3.0 * y)));
	else
		tmp = t_1 + (0.3333333333333333 * (t / (z * y)));
	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[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e-96], N[(N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 4e+29], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / z), $MachinePrecision] * N[(t / N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	3.4
Target	1.7
Herbie	0.6

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -1.9999999999999998e-96

   1. Initial program 0.9

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

   2. Applied egg-rr 0.9

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

   if -1.9999999999999998e-96 < (*.f64 z 3) < 3.99999999999999966e29

   1. Initial program 10.2

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

   2. Applied egg-rr 0.4

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{1}{z} \cdot \frac{t}{3 \cdot y}} \]

   if 3.99999999999999966e29 < (*.f64 z 3)

   1. Initial program 0.3

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

   2. Taylor expanded in t around 0 0.4

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]

   3. Simplified 1.1

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}} \]

   4. Applied egg-rr 1.1

      \[\leadsto \color{blue}{\left(x + \frac{-\frac{y}{z}}{3}\right)} + \frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}} \]

   5. Taylor expanded in y around 0 0.4

      \[\leadsto \left(x + \frac{-\frac{y}{z}}{3}\right) + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{-96}:\\ \;\;\;\;\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{\frac{y}{z}}{3}\right)\\ \mathbf{elif}\;z \cdot 3 \leq 4 \cdot 10^{+29}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z} \cdot \frac{t}{3 \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]

Reproduce

herbie shell --seed 2022210 
(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))))