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

Average Error: 3.6 → 0.7

Time: 5.9s

Precision: binary64

Math

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

↓

\[\begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;t \leq -3.368747839604316 \cdot 10^{-141}:\\ \;\;\;\;t_1 + \frac{t}{3 \cdot \left(y \cdot z\right)}\\ \mathbf{elif}\;t \leq 10^{+32}:\\ \;\;\;\;t_1 + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{y}{3} \cdot \frac{-1}{z}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

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
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= t -3.368747839604316e-141)
     (+ t_1 (/ t (* 3.0 (* y z))))
     (if (<= t 1e+32)
       (+ t_1 (/ (/ t y) (* z 3.0)))
       (+ (+ x (* (/ y 3.0) (/ -1.0 z))) (/ 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 t_1 = x - (y / (z * 3.0));
	double tmp;
	if (t <= -3.368747839604316e-141) {
		tmp = t_1 + (t / (3.0 * (y * z)));
	} else if (t <= 1e+32) {
		tmp = t_1 + ((t / y) / (z * 3.0));
	} else {
		tmp = (x + ((y / 3.0) * (-1.0 / z))) + (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) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (z * 3.0d0))
    if (t <= (-3.368747839604316d-141)) then
        tmp = t_1 + (t / (3.0d0 * (y * z)))
    else if (t <= 1d+32) then
        tmp = t_1 + ((t / y) / (z * 3.0d0))
    else
        tmp = (x + ((y / 3.0d0) * ((-1.0d0) / z))) + (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 t_1 = x - (y / (z * 3.0));
	double tmp;
	if (t <= -3.368747839604316e-141) {
		tmp = t_1 + (t / (3.0 * (y * z)));
	} else if (t <= 1e+32) {
		tmp = t_1 + ((t / y) / (z * 3.0));
	} else {
		tmp = (x + ((y / 3.0) * (-1.0 / z))) + (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):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if t <= -3.368747839604316e-141:
		tmp = t_1 + (t / (3.0 * (y * z)))
	elif t <= 1e+32:
		tmp = t_1 + ((t / y) / (z * 3.0))
	else:
		tmp = (x + ((y / 3.0) * (-1.0 / z))) + (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)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (t <= -3.368747839604316e-141)
		tmp = Float64(t_1 + Float64(t / Float64(3.0 * Float64(y * z))));
	elseif (t <= 1e+32)
		tmp = Float64(t_1 + Float64(Float64(t / y) / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(x + Float64(Float64(y / 3.0) * Float64(-1.0 / z))) + 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)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if (t <= -3.368747839604316e-141)
		tmp = t_1 + (t / (3.0 * (y * z)));
	elseif (t <= 1e+32)
		tmp = t_1 + ((t / y) / (z * 3.0));
	else
		tmp = (x + ((y / 3.0) * (-1.0 / z))) + (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_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.368747839604316e-141], N[(t$95$1 + N[(t / N[(3.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+32], N[(t$95$1 + N[(N[(t / y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y / 3.0), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	3.6
Target	1.6
Herbie	0.7

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

Derivation

1. Split input into 3 regimes

2. if t < -3.36874783960431615e-141

   1. Initial program 1.3

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

   2. Taylor expanded in z around 0 1.3

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

   if -3.36874783960431615e-141 < t < 1.00000000000000005e32

   1. Initial program 6.3

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

   2. Applied egg-rr 1.1

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{1}{y} \cdot \left(t \cdot \frac{0.3333333333333333}{z}\right)} \]

   3. Applied egg-rr 1.1

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

   4. Applied egg-rr 0.2

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

   if 1.00000000000000005e32 < t

   1. Initial program 0.7

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

   2. Applied egg-rr 0.8

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

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.368747839604316 \cdot 10^{-141}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{3 \cdot \left(y \cdot z\right)}\\ \mathbf{elif}\;t \leq 10^{+32}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{y}{3} \cdot \frac{-1}{z}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

Reproduce

herbie shell --seed 2022211 
(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))))