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

Average Error: 3.0 → 3.0

Time: 7.7s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

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

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	3.0
Target	1.9
Herbie	3.0

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

Derivation

1. Initial program 3.0

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

2. Final simplification 3.0

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

Alternatives

Alternative 1
Error	18.6
Cost	914

\[\begin{array}{l} \mathbf{if}\;y \leq -80000000000 \lor \neg \left(y \leq 10^{-108}\right) \land \left(y \leq 1.82 \cdot 10^{-66} \lor \neg \left(y \leq 1.05 \cdot 10^{+73}\right)\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]

Alternative 2
Error	18.7
Cost	912

\[\begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{t}}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+79}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 3
Error	30.3
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+190} \lor \neg \left(z \leq 1.05 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 4
Error	30.2
Cost	192

\[\frac{x}{y} \]

Reproduce

herbie shell --seed 2023045 
(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))))