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

Percentage Accurate: 95.9% → 97.2%

Time: 6.3s

Alternatives: 7

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: 97.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y - z \cdot t \leq -1 \cdot 10^{+296}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, t, y\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (- y (* z t)) -1e+296) (/ (/ (- x) t) z) (/ x (fma (- z) t y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y - (z * t)) <= -1e+296) {
		tmp = (-x / t) / z;
	} else {
		tmp = x / fma(-z, t, y);
	}
	return tmp;
}

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y - Float64(z * t)) <= -1e+296)
		tmp = Float64(Float64(Float64(-x) / t) / z);
	else
		tmp = Float64(x / fma(Float64(-z), t, y));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision], -1e+296], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision], N[(x / N[((-z) * t + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y (*.f64 z t)) < -9.99999999999999981e295

   1. Initial program 73.4%

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

   3. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. times-frac N/A

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

      3. associate-*l/ N/A

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

      4. lower-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 99.9

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

   5. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t}} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.9%

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

   if -9.99999999999999981e295 < (-.f64 y (*.f64 z t))

   1. Initial program 99.5%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 99.5

         \[\leadsto \frac{x}{\mathsf{fma}\left(\color{blue}{-z}, t, y\right)} \]

   4. Applied rewrites 99.5%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(-z, t, y\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 63.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+116} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+141}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -5e+116) (not (<= (* z t) 2e+141)))
   (/ x (* t z))
   (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e+116) || !((z * t) <= 2e+141)) {
		tmp = x / (t * z);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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 (((z * t) <= (-5d+116)) .or. (.not. ((z * t) <= 2d+141))) then
        tmp = x / (t * z)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e+116) || !((z * t) <= 2e+141)) {
		tmp = x / (t * z);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -5e+116) or not ((z * t) <= 2e+141):
		tmp = x / (t * z)
	else:
		tmp = x / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -5e+116) || !(Float64(z * t) <= 2e+141))
		tmp = Float64(x / Float64(t * z));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -5e+116) || ~(((z * t) <= 2e+141)))
		tmp = x / (t * z);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -5e+116], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e+141]], $MachinePrecision]], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5.00000000000000025e116 or 2.00000000000000003e141 < (*.f64 z t)

   1. Initial program 89.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 89.9

         \[\leadsto \frac{x}{\mathsf{fma}\left(\color{blue}{-z}, t, y\right)} \]

   4. Applied rewrites 89.9%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(-z, t, y\right)}} \]

   6. Applied rewrites 61.0%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(z, t, y\right)}} \]

   7. Taylor expanded in y around 0

      \[\leadsto \frac{x}{\color{blue}{t \cdot z}} \]
   8. Step-by-step derivation

      1. lower-*.f64 61.0

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

   9. Applied rewrites 61.0%

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

   if -5.00000000000000025e116 < (*.f64 z t) < 2.00000000000000003e141

   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 65.5

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

   5. Applied rewrites 65.5%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+116} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+141}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-84} \lor \neg \left(y \leq 2.15 \cdot 10^{-66}\right):\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(-t\right) \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.4e-84) (not (<= y 2.15e-66)))
   (/ x (fma z t y))
   (/ x (* (- t) z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4e-84) || !(y <= 2.15e-66)) {
		tmp = x / fma(z, t, y);
	} else {
		tmp = x / (-t * z);
	}
	return tmp;
}

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.4e-84) || !(y <= 2.15e-66))
		tmp = Float64(x / fma(z, t, y));
	else
		tmp = Float64(x / Float64(Float64(-t) * z));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.4e-84], N[Not[LessEqual[y, 2.15e-66]], $MachinePrecision]], N[(x / N[(z * t + y), $MachinePrecision]), $MachinePrecision], N[(x / N[((-t) * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000021e-84 or 2.15000000000000007e-66 < y

   1. Initial program 96.4%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 96.5

         \[\leadsto \frac{x}{\mathsf{fma}\left(\color{blue}{-z}, t, y\right)} \]

   4. Applied rewrites 96.5%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(-z, t, y\right)}} \]

   6. Applied rewrites 81.9%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(z, t, y\right)}} \]

   if -3.40000000000000021e-84 < y < 2.15000000000000007e-66

   1. Initial program 97.7%

      \[\frac{x}{y - z \cdot t} \]
   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. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 81.3

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

   5. Applied rewrites 81.3%

      \[\leadsto \frac{x}{\color{blue}{\left(-t\right) \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-84} \lor \neg \left(y \leq 2.15 \cdot 10^{-66}\right):\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(-t\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 6.8 \cdot 10^{+168}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= x 6.8e+168) (/ x (fma z t y)) (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 6.8e+168) {
		tmp = x / fma(z, t, y);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (x <= 6.8e+168)
		tmp = Float64(x / fma(z, t, y));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[x, 6.8e+168], N[(x / N[(z * t + y), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.80000000000000005e168

   1. Initial program 97.9%

      \[\frac{x}{y - z \cdot t} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. fp-cancel-sub-sign-inv N/A

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

      4. +-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 97.9

         \[\leadsto \frac{x}{\mathsf{fma}\left(\color{blue}{-z}, t, y\right)} \]

   4. Applied rewrites 97.9%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(-z, t, y\right)}} \]

   6. Applied rewrites 64.5%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(z, t, y\right)}} \]

   if 6.80000000000000005e168 < x

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 62.9

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

   5. Applied rewrites 62.9%

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

Alternative 5: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{\mathsf{fma}\left(-z, t, y\right)} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (fma (- z) t y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return x / fma(-z, t, y);
}

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / fma(Float64(-z), t, y))
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[((-z) * t + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.0%

   \[\frac{x}{y - z \cdot t} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. fp-cancel-sub-sign-inv N/A

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

   4. +-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. lower-neg.f64 97.0

      \[\leadsto \frac{x}{\mathsf{fma}\left(\color{blue}{-z}, t, y\right)} \]

4. Applied rewrites 97.0%

   \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(-z, t, y\right)}} \]
5. Add Preprocessing

Alternative 6: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{y - z \cdot t} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (- y (* z t))))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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

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

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return x / (y - (z * t))

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / Float64(y - Float64(z * t)))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / (y - (z * t));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.0%

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

Alternative 7: 54.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{y} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x y))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this 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
end function

Java

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

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return x / y

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / y)
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / y;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 97.0%

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

3. Taylor expanded in y around inf

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

   1. lower-/.f64 50.4

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

5. Applied rewrites 50.4%

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

Developer Target 1: 96.4% 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 2024339 
(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))))