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

Percentage Accurate: 95.9% → 95.9%

Time: 5.0s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y - z \cdot t} \end{array} \]

FPCore

(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));
}

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

Java

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))

Julia

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y - z \cdot t} \end{array} \]

FPCore

(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));
}

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

Java

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))

Julia

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

Wolfram

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

Alternative 1: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y - t \cdot z} \end{array} \]

FPCore

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

C

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

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 - (t * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

   \[\frac{x}{y - z \cdot t} \]
2. Add Preprocessing

3. Final simplification 97.8%

   \[\leadsto \frac{x}{y - t \cdot z} \]
4. Add Preprocessing

Alternative 2: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(-z\right) \cdot t}\\ \mathbf{if}\;t \cdot z \leq -1 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \cdot z \leq 2 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- z) t))))
   (if (<= (* t z) -1e+89) t_1 (if (<= (* t z) 2e-47) (/ x y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (-z * t);
	double tmp;
	if ((t * z) <= -1e+89) {
		tmp = t_1;
	} else if ((t * z) <= 2e-47) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (-z * t)
    if ((t * z) <= (-1d+89)) then
        tmp = t_1
    else if ((t * z) <= 2d-47) then
        tmp = x / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (-z * t);
	double tmp;
	if ((t * z) <= -1e+89) {
		tmp = t_1;
	} else if ((t * z) <= 2e-47) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (-z * t)
	tmp = 0
	if (t * z) <= -1e+89:
		tmp = t_1
	elif (t * z) <= 2e-47:
		tmp = x / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(-z) * t))
	tmp = 0.0
	if (Float64(t * z) <= -1e+89)
		tmp = t_1;
	elseif (Float64(t * z) <= 2e-47)
		tmp = Float64(x / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (-z * t);
	tmp = 0.0;
	if ((t * z) <= -1e+89)
		tmp = t_1;
	elseif ((t * z) <= 2e-47)
		tmp = x / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[((-z) * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t * z), $MachinePrecision], -1e+89], t$95$1, If[LessEqual[N[(t * z), $MachinePrecision], 2e-47], N[(x / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -9.99999999999999995e88 or 1.9999999999999999e-47 < (*.f64 z t)

   1. Initial program 95.7%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(t \cdot z\right)}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

         \[\leadsto \frac{x}{\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot t} \]

      5. lower-neg.f64 81.8

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

   5. Applied rewrites 81.8%

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

   if -9.99999999999999995e88 < (*.f64 z t) < 1.9999999999999999e-47

   1. Initial program 100.0%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 79.7

         \[\leadsto \color{blue}{\frac{x}{y}} \]

   5. Applied rewrites 79.7%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -1 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot t}\\ \mathbf{elif}\;t \cdot z \leq 2 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t \cdot z}\\ \mathbf{if}\;t \cdot z \leq -1.2 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \cdot z \leq 2.2 \cdot 10^{+168}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* t z))))
   (if (<= (* t z) -1.2e+125) t_1 (if (<= (* t z) 2.2e+168) (/ x y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t * z);
	double tmp;
	if ((t * z) <= -1.2e+125) {
		tmp = t_1;
	} else if ((t * z) <= 2.2e+168) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t * z)
    if ((t * z) <= (-1.2d+125)) then
        tmp = t_1
    else if ((t * z) <= 2.2d+168) then
        tmp = x / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t * z);
	double tmp;
	if ((t * z) <= -1.2e+125) {
		tmp = t_1;
	} else if ((t * z) <= 2.2e+168) {
		tmp = x / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t * z)
	tmp = 0
	if (t * z) <= -1.2e+125:
		tmp = t_1
	elif (t * z) <= 2.2e+168:
		tmp = x / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t * z))
	tmp = 0.0
	if (Float64(t * z) <= -1.2e+125)
		tmp = t_1;
	elseif (Float64(t * z) <= 2.2e+168)
		tmp = Float64(x / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t * z);
	tmp = 0.0;
	if ((t * z) <= -1.2e+125)
		tmp = t_1;
	elseif ((t * z) <= 2.2e+168)
		tmp = x / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t * z), $MachinePrecision], -1.2e+125], t$95$1, If[LessEqual[N[(t * z), $MachinePrecision], 2.2e+168], N[(x / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.2e125 or 2.2000000000000002e168 < (*.f64 z t)

   1. Initial program 92.6%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(t \cdot z\right)}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

         \[\leadsto \frac{x}{\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot t} \]

      5. lower-neg.f64 88.9

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

   5. Applied rewrites 88.9%

      \[\leadsto \frac{x}{\color{blue}{\left(-z\right) \cdot t}} \]
   6. Step-by-step derivation

   7. Applied rewrites 53.8%

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

   if -1.2e125 < (*.f64 z t) < 2.2000000000000002e168

   1. Initial program 99.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 64.7

         \[\leadsto \color{blue}{\frac{x}{y}} \]

   5. Applied rewrites 64.7%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -1.2 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{elif}\;t \cdot z \leq 2.2 \cdot 10^{+168}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.8%

   \[\frac{x}{y - z \cdot t} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{\frac{x}{y}} \]
4. Step-by-step derivation

   1. lower-/.f64 50.7

      \[\leadsto \color{blue}{\frac{x}{y}} \]

5. Applied rewrites 50.7%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
6. Add Preprocessing

Developer Target 1: 96.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{if}\;x < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x < 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (- (/ y x) (* (/ z x) t)))))
   (if (< x -1.618195973607049e+50)
     t_1
     (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / ((y / x) - ((z / x) * t))
    if (x < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (x < 2.1378306434876444d+131) then
        tmp = x / (y - (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 / ((y / x) - ((z / x) * t))
	tmp = 0
	if x < -1.618195973607049e+50:
		tmp = t_1
	elif x < 2.1378306434876444e+131:
		tmp = x / (y - (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(Float64(y / x) - Float64(Float64(z / x) * t)))
	tmp = 0.0
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / ((y / x) - ((z / x) * t));
	tmp = 0.0;
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = x / (y - (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(N[(y / x), $MachinePrecision] - N[(N[(z / x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[x, -1.618195973607049e+50], t$95$1, If[Less[x, 2.1378306434876444e+131], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024331 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -161819597360704900000000000000000000000000000000000) (/ 1 (- (/ y x) (* (/ z x) t))) (if (< x 213783064348764440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t))))))

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