Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A

Percentage Accurate: 92.0% → 99.7%

Time: 4.2s

Alternatives: 3

Speedup: 0.2×

Specification

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (/ (* x y) z))

C

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

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * y) / z
END code

Initial Program: 92.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (/ (* x y) z))

C

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

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(x * y) / z
END code

Alternative 1: 99.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(\left|x\right|, \left|y\right|\right)\\ t_1 := \mathsf{min}\left(\left|x\right|, \left|y\right|\right)\\ \mathsf{copysign}\left(1, x\right) \cdot \left(\mathsf{copysign}\left(1, y\right) \cdot \left(\mathsf{copysign}\left(1, z\right) \cdot \begin{array}{l} \mathbf{if}\;\left|z\right| \leq 5.993716184525197 \cdot 10^{-31}:\\ \;\;\;\;t\_0 \cdot \frac{t\_1}{\left|z\right|}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{\frac{\left|z\right|}{t\_0}}\\ \end{array}\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (fmax (fabs x) (fabs y))) (t_1 (fmin (fabs x) (fabs y))))
  (*
   (copysign 1.0 x)
   (*
    (copysign 1.0 y)
    (*
     (copysign 1.0 z)
     (if (<= (fabs z) 5.993716184525197e-31)
       (* t_0 (/ t_1 (fabs z)))
       (/ t_1 (/ (fabs z) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = fmax(fabs(x), fabs(y));
	double t_1 = fmin(fabs(x), fabs(y));
	double tmp;
	if (fabs(z) <= 5.993716184525197e-31) {
		tmp = t_0 * (t_1 / fabs(z));
	} else {
		tmp = t_1 / (fabs(z) / t_0);
	}
	return copysign(1.0, x) * (copysign(1.0, y) * (copysign(1.0, z) * tmp));
}

Java

public static double code(double x, double y, double z) {
	double t_0 = fmax(Math.abs(x), Math.abs(y));
	double t_1 = fmin(Math.abs(x), Math.abs(y));
	double tmp;
	if (Math.abs(z) <= 5.993716184525197e-31) {
		tmp = t_0 * (t_1 / Math.abs(z));
	} else {
		tmp = t_1 / (Math.abs(z) / t_0);
	}
	return Math.copySign(1.0, x) * (Math.copySign(1.0, y) * (Math.copySign(1.0, z) * tmp));
}

Python

def code(x, y, z):
	t_0 = fmax(math.fabs(x), math.fabs(y))
	t_1 = fmin(math.fabs(x), math.fabs(y))
	tmp = 0
	if math.fabs(z) <= 5.993716184525197e-31:
		tmp = t_0 * (t_1 / math.fabs(z))
	else:
		tmp = t_1 / (math.fabs(z) / t_0)
	return math.copysign(1.0, x) * (math.copysign(1.0, y) * (math.copysign(1.0, z) * tmp))

Julia

function code(x, y, z)
	t_0 = fmax(abs(x), abs(y))
	t_1 = fmin(abs(x), abs(y))
	tmp = 0.0
	if (abs(z) <= 5.993716184525197e-31)
		tmp = Float64(t_0 * Float64(t_1 / abs(z)));
	else
		tmp = Float64(t_1 / Float64(abs(z) / t_0));
	end
	return Float64(copysign(1.0, x) * Float64(copysign(1.0, y) * Float64(copysign(1.0, z) * tmp)))
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = max(abs(x), abs(y));
	t_1 = min(abs(x), abs(y));
	tmp = 0.0;
	if (abs(z) <= 5.993716184525197e-31)
		tmp = t_0 * (t_1 / abs(z));
	else
		tmp = t_1 / (abs(z) / t_0);
	end
	tmp_2 = (sign(x) * abs(1.0)) * ((sign(y) * abs(1.0)) * ((sign(z) * abs(1.0)) * tmp));
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[Abs[x], $MachinePrecision], N[Abs[y], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Min[N[Abs[x], $MachinePrecision], N[Abs[y], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[z], $MachinePrecision], 5.993716184525197e-31], N[(t$95$0 * N[(t$95$1 / N[Abs[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(N[Abs[z], $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 5.9937161845251967e-31

   1. Initial program 92.0%

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

   3. Applied rewrites 92.0%

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

   if 5.9937161845251967e-31 < z

   1. Initial program 92.0%

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

   3. Applied rewrites 91.9%

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

   5. Applied rewrites 91.8%

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

Alternative 2: 98.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{max}\left(\left|x\right|, \left|y\right|\right)\\ t_1 := \mathsf{min}\left(\left|x\right|, \left|y\right|\right)\\ \mathsf{copysign}\left(1, x\right) \cdot \left(\mathsf{copysign}\left(1, y\right) \cdot \left(\mathsf{copysign}\left(1, z\right) \cdot \begin{array}{l} \mathbf{if}\;\left|z\right| \leq 1.8715037001475357 \cdot 10^{-84}:\\ \;\;\;\;t\_0 \cdot \frac{t\_1}{\left|z\right|}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \frac{t\_0}{\left|z\right|}\\ \end{array}\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (fmax (fabs x) (fabs y))) (t_1 (fmin (fabs x) (fabs y))))
  (*
   (copysign 1.0 x)
   (*
    (copysign 1.0 y)
    (*
     (copysign 1.0 z)
     (if (<= (fabs z) 1.8715037001475357e-84)
       (* t_0 (/ t_1 (fabs z)))
       (* t_1 (/ t_0 (fabs z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = fmax(fabs(x), fabs(y));
	double t_1 = fmin(fabs(x), fabs(y));
	double tmp;
	if (fabs(z) <= 1.8715037001475357e-84) {
		tmp = t_0 * (t_1 / fabs(z));
	} else {
		tmp = t_1 * (t_0 / fabs(z));
	}
	return copysign(1.0, x) * (copysign(1.0, y) * (copysign(1.0, z) * tmp));
}

Java

public static double code(double x, double y, double z) {
	double t_0 = fmax(Math.abs(x), Math.abs(y));
	double t_1 = fmin(Math.abs(x), Math.abs(y));
	double tmp;
	if (Math.abs(z) <= 1.8715037001475357e-84) {
		tmp = t_0 * (t_1 / Math.abs(z));
	} else {
		tmp = t_1 * (t_0 / Math.abs(z));
	}
	return Math.copySign(1.0, x) * (Math.copySign(1.0, y) * (Math.copySign(1.0, z) * tmp));
}

Python

def code(x, y, z):
	t_0 = fmax(math.fabs(x), math.fabs(y))
	t_1 = fmin(math.fabs(x), math.fabs(y))
	tmp = 0
	if math.fabs(z) <= 1.8715037001475357e-84:
		tmp = t_0 * (t_1 / math.fabs(z))
	else:
		tmp = t_1 * (t_0 / math.fabs(z))
	return math.copysign(1.0, x) * (math.copysign(1.0, y) * (math.copysign(1.0, z) * tmp))

Julia

function code(x, y, z)
	t_0 = fmax(abs(x), abs(y))
	t_1 = fmin(abs(x), abs(y))
	tmp = 0.0
	if (abs(z) <= 1.8715037001475357e-84)
		tmp = Float64(t_0 * Float64(t_1 / abs(z)));
	else
		tmp = Float64(t_1 * Float64(t_0 / abs(z)));
	end
	return Float64(copysign(1.0, x) * Float64(copysign(1.0, y) * Float64(copysign(1.0, z) * tmp)))
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = max(abs(x), abs(y));
	t_1 = min(abs(x), abs(y));
	tmp = 0.0;
	if (abs(z) <= 1.8715037001475357e-84)
		tmp = t_0 * (t_1 / abs(z));
	else
		tmp = t_1 * (t_0 / abs(z));
	end
	tmp_2 = (sign(x) * abs(1.0)) * ((sign(y) * abs(1.0)) * ((sign(z) * abs(1.0)) * tmp));
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Max[N[Abs[x], $MachinePrecision], N[Abs[y], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Min[N[Abs[x], $MachinePrecision], N[Abs[y], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[z]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[z], $MachinePrecision], 1.8715037001475357e-84], N[(t$95$0 * N[(t$95$1 / N[Abs[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(t$95$0 / N[Abs[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 1.8715037001475357e-84

   1. Initial program 92.0%

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

   3. Applied rewrites 92.0%

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

   if 1.8715037001475357e-84 < z

   1. Initial program 92.0%

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

   3. Applied rewrites 91.9%

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

Alternative 3: 91.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (* x (/ y z)))

C

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

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (y / z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	x * (y / z)
END code

Derivation

1. Initial program 92.0%

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

3. Applied rewrites 91.9%

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

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64
  (/ (* x y) z))