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

Average Error: 3.6 → 1.5

Time: 5.4s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;t \leq -1.3110050459942516 \cdot 10^{-113}:\\ \;\;\;\;\left(x + \frac{\frac{y}{z}}{-3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{elif}\;t \leq 6.568065307651204 \cdot 10^{+190}:\\ \;\;\;\;t_1 + \frac{1}{z} \cdot \frac{t}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \end{array} \]

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
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= t -1.3110050459942516e-113)
     (+ (+ x (/ (/ y z) -3.0)) (/ t (* y (* z 3.0))))
     (if (<= t 6.568065307651204e+190)
       (+ t_1 (* (/ 1.0 z) (/ t (* y 3.0))))
       (+ t_1 (/ t (* z (* y 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 t_1 = x - (y / (z * 3.0));
	double tmp;
	if (t <= -1.3110050459942516e-113) {
		tmp = (x + ((y / z) / -3.0)) + (t / (y * (z * 3.0)));
	} else if (t <= 6.568065307651204e+190) {
		tmp = t_1 + ((1.0 / z) * (t / (y * 3.0)));
	} else {
		tmp = t_1 + (t / (z * (y * 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (z * 3.0d0))
    if (t <= (-1.3110050459942516d-113)) then
        tmp = (x + ((y / z) / (-3.0d0))) + (t / (y * (z * 3.0d0)))
    else if (t <= 6.568065307651204d+190) then
        tmp = t_1 + ((1.0d0 / z) * (t / (y * 3.0d0)))
    else
        tmp = t_1 + (t / (z * (y * 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 t_1 = x - (y / (z * 3.0));
	double tmp;
	if (t <= -1.3110050459942516e-113) {
		tmp = (x + ((y / z) / -3.0)) + (t / (y * (z * 3.0)));
	} else if (t <= 6.568065307651204e+190) {
		tmp = t_1 + ((1.0 / z) * (t / (y * 3.0)));
	} else {
		tmp = t_1 + (t / (z * (y * 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):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if t <= -1.3110050459942516e-113:
		tmp = (x + ((y / z) / -3.0)) + (t / (y * (z * 3.0)))
	elif t <= 6.568065307651204e+190:
		tmp = t_1 + ((1.0 / z) * (t / (y * 3.0)))
	else:
		tmp = t_1 + (t / (z * (y * 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)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (t <= -1.3110050459942516e-113)
		tmp = Float64(Float64(x + Float64(Float64(y / z) / -3.0)) + Float64(t / Float64(y * Float64(z * 3.0))));
	elseif (t <= 6.568065307651204e+190)
		tmp = Float64(t_1 + Float64(Float64(1.0 / z) * Float64(t / Float64(y * 3.0))));
	else
		tmp = Float64(t_1 + Float64(t / Float64(z * Float64(y * 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)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if (t <= -1.3110050459942516e-113)
		tmp = (x + ((y / z) / -3.0)) + (t / (y * (z * 3.0)));
	elseif (t <= 6.568065307651204e+190)
		tmp = t_1 + ((1.0 / z) * (t / (y * 3.0)));
	else
		tmp = t_1 + (t / (z * (y * 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_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3110050459942516e-113], N[(N[(x + N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.568065307651204e+190], N[(t$95$1 + N[(N[(1.0 / z), $MachinePrecision] * N[(t / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	3.6
Target	1.7
Herbie	1.5

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

Derivation

1. Split input into 3 regimes

2. if t < -1.3110050459942516e-113

   1. Initial program 1.3

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

   2. Applied egg-rr 1.4

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

   3. Applied egg-rr 1.3

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

   if -1.3110050459942516e-113 < t < 6.5680653076512042e190

   1. Initial program 5.0

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

   2. Applied egg-rr 1.6

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

   if 6.5680653076512042e190 < t

   1. Initial program 1.3

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

   2. Applied egg-rr 1.3

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

4. Final simplification 1.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3110050459942516 \cdot 10^{-113}:\\ \;\;\;\;\left(x + \frac{\frac{y}{z}}{-3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{elif}\;t \leq 6.568065307651204 \cdot 10^{+190}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z} \cdot \frac{t}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \end{array} \]

Reproduce

herbie shell --seed 2022153 
(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))))