Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B

Average Error: 2.7 → 2.8

Time: 5.7s

Precision: binary64

\[ \begin{array}{c}[z, t] = \mathsf{sort}([z, t])\\ \end{array} \]

Math

\[\frac{x}{y - z \cdot t} \]

↓

\[\begin{array}{l} \mathbf{if}\;t \leq 3.869325967662644 \cdot 10^{+236}:\\ \;\;\;\;\frac{x}{y - t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{\frac{x}{z}}}\\ \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x (- y (* z t))))

↓

(FPCore (x y z t)
 :precision binary64
 (if (<= t 3.869325967662644e+236)
   (/ x (- y (* t z)))
   (/ 1.0 (- (/ y x) (/ t (/ x z))))))

C

double code(double x, double y, double z, double t) {
	return x / (y - (z * t));
}

↓

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.869325967662644e+236) {
		tmp = x / (y - (t * z));
	} else {
		tmp = 1.0 / ((y / x) - (t / (x / z)));
	}
	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 * t))
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) :: tmp
    if (t <= 3.869325967662644d+236) then
        tmp = x / (y - (t * z))
    else
        tmp = 1.0d0 / ((y / x) - (t / (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	return x / (y - (z * t));
}

↓

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 3.869325967662644e+236) {
		tmp = x / (y - (t * z));
	} else {
		tmp = 1.0 / ((y / x) - (t / (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	return x / (y - (z * t))

↓

def code(x, y, z, t):
	tmp = 0
	if t <= 3.869325967662644e+236:
		tmp = x / (y - (t * z))
	else:
		tmp = 1.0 / ((y / x) - (t / (x / z)))
	return tmp

Julia

function code(x, y, z, t)
	return Float64(x / Float64(y - Float64(z * t)))
end

↓

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 3.869325967662644e+236)
		tmp = Float64(x / Float64(y - Float64(t * z)));
	else
		tmp = Float64(1.0 / Float64(Float64(y / x) - Float64(t / Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / (y - (z * t));
end

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 3.869325967662644e+236)
		tmp = x / (y - (t * z));
	else
		tmp = 1.0 / ((y / x) - (t / (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := If[LessEqual[t, 3.869325967662644e+236], N[(x / N[(y - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(y / x), $MachinePrecision] - N[(t / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	2.7
Target	1.8
Herbie	2.8

\[\begin{array}{l} \mathbf{if}\;x < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{elif}\;x < 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if t < 3.8693259676626439e236

   1. Initial program 2.0

      \[\frac{x}{y - z \cdot t} \]

   if 3.8693259676626439e236 < t

   1. Initial program 7.9

      \[\frac{x}{y - z \cdot t} \]

   2. Applied egg-rr 8.0

      \[\leadsto \color{blue}{\frac{1}{y - z \cdot t} \cdot x} \]

   3. Applied egg-rr 8.2

      \[\leadsto \color{blue}{\frac{1}{\frac{y - z \cdot t}{x}}} \]

   4. Applied egg-rr 8.9

      \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} - \frac{t}{\frac{x}{z}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 2.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.869325967662644 \cdot 10^{+236}:\\ \;\;\;\;\frac{x}{y - t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x} - \frac{t}{\frac{x}{z}}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022211 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< x -1.618195973607049e+50) (/ 1.0 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1.0 (- (/ y x) (* (/ z x) t)))))

  (/ x (- y (* z t))))