Linear.Quaternion:$csin from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 2.5s

Alternatives: 9

Speedup: 1.0×

• 50.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\cos x \cdot \frac{\sinh y}{y} \]

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y) {
	return Math.cos(x) * (Math.sinh(y) / y);
}

Python

def code(x, y):
	return math.cos(x) * (math.sinh(y) / y)

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(cos(x)) * ((((1) / (2)) * ((exp(y)) + ((- (1)) / (exp(y))))) / y)
END code

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\cos x \cdot \frac{\sinh y}{y} \]

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y) {
	return Math.cos(x) * (Math.sinh(y) / y);
}

Python

def code(x, y):
	return math.cos(x) * (math.sinh(y) / y)

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(cos(x)) * ((((1) / (2)) * ((exp(y)) + ((- (1)) / (exp(y))))) / y)
END code

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\frac{\sinh y \cdot \cos x}{y} \]

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y) {
	return (Math.sinh(y) * Math.cos(x)) / y;
}

Python

def code(x, y):
	return (math.sinh(y) * math.cos(x)) / y

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	((((1) / (2)) * ((exp(y)) + ((- (1)) / (exp(y))))) * (cos(x))) / y
END code

Derivation

1. Initial program 100.0%

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

3. Applied rewrites 99.9%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

\[\sinh y \cdot \frac{\cos x}{y} \]

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y) {
	return Math.sinh(y) * (Math.cos(x) / y);
}

Python

def code(x, y):
	return math.sinh(y) * (math.cos(x) / y)

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(((1) / (2)) * ((exp(y)) + ((- (1)) / (exp(y))))) * ((cos(x)) / y)
END code

Derivation

1. Initial program 100.0%

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

3. Applied rewrites 99.9%

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

Alternative 3: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \frac{\sinh y}{y}\\ t_1 := \cos x \cdot t\_0\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot x, -0.5, 1\right) \cdot \sinh y}{y}\\ \mathbf{elif}\;t\_1 \leq 0.9999999999933117:\\ \;\;\;\;\frac{y \cdot \cos x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (/ (sinh y) y)) (t_1 (* (cos x) t_0)))
  (if (<= t_1 (- INFINITY))
    (/ (* (fma (* x x) -0.5 1.0) (sinh y)) y)
    (if (<= t_1 0.9999999999933117) (/ (* y (cos x)) y) t_0))))

C

double code(double x, double y) {
	double t_0 = sinh(y) / y;
	double t_1 = cos(x) * t_0;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (fma((x * x), -0.5, 1.0) * sinh(y)) / y;
	} else if (t_1 <= 0.9999999999933117) {
		tmp = (y * cos(x)) / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(sinh(y) / y)
	t_1 = Float64(cos(x) * t_0)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(fma(Float64(x * x), -0.5, 1.0) * sinh(y)) / y);
	elseif (t_1 <= 0.9999999999933117)
		tmp = Float64(Float64(y * cos(x)) / y);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$1 = N[(N[Cos[x], $MachinePrecision] * t$95$0), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(x * x), $MachinePrecision] * -0.5 + 1.0), $MachinePrecision] * N[Sinh[y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999999933117], N[(N[(y * N[Cos[x], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y)) < -inf.0

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(1 + \frac{-1}{2} \cdot {x}^{2}\right) \cdot \frac{\sinh y}{y} \]
   3. Step-by-step derivation

   4. Applied rewrites 63.3%

      \[\leadsto \left(1 + -0.5 \cdot {x}^{2}\right) \cdot \frac{\sinh y}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.3%

      \[\leadsto \frac{\mathsf{fma}\left(x \cdot x, -0.5, 1\right) \cdot \sinh y}{y} \]

   if -inf.0 < (*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y)) < 0.99999999999331168

   1. Initial program 100.0%

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

   3. Applied rewrites 99.9%

      \[\leadsto \frac{\sinh y \cdot \cos x}{y} \]

   4. Taylor expanded in y around 0

      \[\leadsto \frac{y \cdot \cos x}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 50.5%

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

   if 0.99999999999331168 < (*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]
   3. Step-by-step derivation

   4. Applied rewrites 40.1%

      \[\leadsto 0.5 \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 65.3%

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

Alternative 4: 77.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\cos x \leq -0.05:\\ \;\;\;\;\frac{\mathsf{fma}\left(x \cdot x, -0.5, 1\right) \cdot \sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (cos x) -0.05)
  (/ (* (fma (* x x) -0.5 1.0) (sinh y)) y)
  (/ (sinh y) y)))

C

double code(double x, double y) {
	double tmp;
	if (cos(x) <= -0.05) {
		tmp = (fma((x * x), -0.5, 1.0) * sinh(y)) / y;
	} else {
		tmp = sinh(y) / y;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (cos(x) <= -0.05)
		tmp = Float64(Float64(fma(Float64(x * x), -0.5, 1.0) * sinh(y)) / y);
	else
		tmp = Float64(sinh(y) / y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[Cos[x], $MachinePrecision], -0.05], N[(N[(N[(N[(x * x), $MachinePrecision] * -0.5 + 1.0), $MachinePrecision] * N[Sinh[y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF ((cos(x)) <= (-5000000000000000277555756156289135105907917022705078125e-56)) THEN (((((x * x) * (-5e-1)) + (1)) * (((1) / (2)) * ((exp(y)) + ((- (1)) / (exp(y)))))) / y) ELSE ((((1) / (2)) * ((exp(y)) + ((- (1)) / (exp(y))))) / y) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (cos.f64 x) < -0.050000000000000003

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(1 + \frac{-1}{2} \cdot {x}^{2}\right) \cdot \frac{\sinh y}{y} \]
   3. Step-by-step derivation

   4. Applied rewrites 63.3%

      \[\leadsto \left(1 + -0.5 \cdot {x}^{2}\right) \cdot \frac{\sinh y}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.3%

      \[\leadsto \frac{\mathsf{fma}\left(x \cdot x, -0.5, 1\right) \cdot \sinh y}{y} \]

   if -0.050000000000000003 < (cos.f64 x)

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]
   3. Step-by-step derivation

   4. Applied rewrites 40.1%

      \[\leadsto 0.5 \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 65.3%

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

Alternative 5: 74.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\cos x \leq -0.05:\\ \;\;\;\;\frac{\frac{1}{\frac{2}{\mathsf{fma}\left(x \cdot x, -0.5, 1\right) \cdot \left(2 \cdot y\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (cos x) -0.05)
  (/ (/ 1.0 (/ 2.0 (* (fma (* x x) -0.5 1.0) (* 2.0 y)))) y)
  (/ (sinh y) y)))

C

double code(double x, double y) {
	double tmp;
	if (cos(x) <= -0.05) {
		tmp = (1.0 / (2.0 / (fma((x * x), -0.5, 1.0) * (2.0 * y)))) / y;
	} else {
		tmp = sinh(y) / y;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (cos(x) <= -0.05)
		tmp = Float64(Float64(1.0 / Float64(2.0 / Float64(fma(Float64(x * x), -0.5, 1.0) * Float64(2.0 * y)))) / y);
	else
		tmp = Float64(sinh(y) / y);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[Cos[x], $MachinePrecision], -0.05], N[(N[(1.0 / N[(2.0 / N[(N[(N[(x * x), $MachinePrecision] * -0.5 + 1.0), $MachinePrecision] * N[(2.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF ((cos(x)) <= (-5000000000000000277555756156289135105907917022705078125e-56)) THEN (((1) / ((2) / ((((x * x) * (-5e-1)) + (1)) * ((2) * y)))) / y) ELSE ((((1) / (2)) * ((exp(y)) + ((- (1)) / (exp(y))))) / y) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (cos.f64 x) < -0.050000000000000003

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \left(1 + \frac{-1}{2} \cdot {x}^{2}\right) \cdot \frac{\sinh y}{y} \]
   3. Step-by-step derivation

   4. Applied rewrites 63.3%

      \[\leadsto \left(1 + -0.5 \cdot {x}^{2}\right) \cdot \frac{\sinh y}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 63.3%

      \[\leadsto \frac{\mathsf{fma}\left(x \cdot x, -0.5, 1\right) \cdot \sinh y}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 63.2%

      \[\leadsto \frac{\frac{1}{\frac{2}{\mathsf{fma}\left(x \cdot x, -0.5, 1\right) \cdot \left(2 \cdot \sinh y\right)}}}{y} \]

   9. Taylor expanded in y around 0

      \[\leadsto \frac{\frac{1}{\frac{2}{\mathsf{fma}\left(x \cdot x, -0.5, 1\right) \cdot \left(2 \cdot y\right)}}}{y} \]
   10. Step-by-step derivation

   11. Applied rewrites 35.6%

       \[\leadsto \frac{\frac{1}{\frac{2}{\mathsf{fma}\left(x \cdot x, -0.5, 1\right) \cdot \left(2 \cdot y\right)}}}{y} \]

   if -0.050000000000000003 < (cos.f64 x)

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]
   3. Step-by-step derivation

   4. Applied rewrites 40.1%

      \[\leadsto 0.5 \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 65.3%

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

Alternative 6: 71.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\cos x \leq -0.07735711983696969:\\ \;\;\;\;\frac{\left(\left|y\right| - -1\right) - \mathsf{fma}\left(\mathsf{fma}\left(0.5, \left|y\right|, -1\right), \left|y\right|, 1\right)}{\left|y\right|} \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{\sinh \left(\left|y\right|\right)}{\left|y\right|}\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (cos x) -0.07735711983696969)
  (*
   (/
    (- (- (fabs y) -1.0) (fma (fma 0.5 (fabs y) -1.0) (fabs y) 1.0))
    (fabs y))
   0.5)
  (/ (sinh (fabs y)) (fabs y))))

C

double code(double x, double y) {
	double tmp;
	if (cos(x) <= -0.07735711983696969) {
		tmp = (((fabs(y) - -1.0) - fma(fma(0.5, fabs(y), -1.0), fabs(y), 1.0)) / fabs(y)) * 0.5;
	} else {
		tmp = sinh(fabs(y)) / fabs(y);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (cos(x) <= -0.07735711983696969)
		tmp = Float64(Float64(Float64(Float64(abs(y) - -1.0) - fma(fma(0.5, abs(y), -1.0), abs(y), 1.0)) / abs(y)) * 0.5);
	else
		tmp = Float64(sinh(abs(y)) / abs(y));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[N[Cos[x], $MachinePrecision], -0.07735711983696969], N[(N[(N[(N[(N[Abs[y], $MachinePrecision] - -1.0), $MachinePrecision] - N[(N[(0.5 * N[Abs[y], $MachinePrecision] + -1.0), $MachinePrecision] * N[Abs[y], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / N[Abs[y], $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision], N[(N[Sinh[N[Abs[y], $MachinePrecision]], $MachinePrecision] / N[Abs[y], $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF ((cos(x)) <= (-7735711983696968996326859269174747169017791748046875e-53)) THEN (((((abs(y)) - (-1)) - (((((5e-1) * (abs(y))) + (-1)) * (abs(y))) + (1))) / (abs(y))) * (5e-1)) ELSE ((((1) / (2)) * ((exp((abs(y)))) + ((- (1)) / (exp((abs(y))))))) / (abs(y))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (cos.f64 x) < -0.07735711983696969

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]
   3. Step-by-step derivation

   4. Applied rewrites 40.1%

      \[\leadsto 0.5 \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]

   5. Taylor expanded in y around 0

      \[\leadsto 0.5 \cdot \frac{\left(1 + y\right) - \frac{1}{1 + y}}{y} \]
   6. Step-by-step derivation

   7. Applied rewrites 3.4%

      \[\leadsto 0.5 \cdot \frac{\left(1 + y\right) - \frac{1}{1 + y}}{y} \]

   8. Taylor expanded in y around 0

      \[\leadsto 0.5 \cdot \frac{\left(1 + y\right) - \left(1 + y \cdot \left(\frac{1}{2} \cdot y - 1\right)\right)}{y} \]
   9. Step-by-step derivation

   10. Applied rewrites 15.4%

       \[\leadsto 0.5 \cdot \frac{\left(1 + y\right) - \left(1 + y \cdot \left(0.5 \cdot y - 1\right)\right)}{y} \]
   11. Step-by-step derivation

   12. Applied rewrites 15.4%

       \[\leadsto \frac{\left(y - -1\right) - \mathsf{fma}\left(\mathsf{fma}\left(0.5, y, -1\right), y, 1\right)}{y} \cdot 0.5 \]

   if -0.07735711983696969 < (cos.f64 x)

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{2} \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]
   3. Step-by-step derivation

   4. Applied rewrites 40.1%

      \[\leadsto 0.5 \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 65.3%

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

Alternative 7: 65.3% accurate, 2.9× speedup

Math

\[\frac{\sinh y}{y} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (/ (sinh y) y))

C

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

Fortran

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

Java

public static double code(double x, double y) {
	return Math.sinh(y) / y;
}

Python

def code(x, y):
	return math.sinh(y) / y

Julia

function code(x, y)
	return Float64(sinh(y) / y)
end

MATLAB

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

Wolfram

code[x_, y_] := N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(((1) / (2)) * ((exp(y)) + ((- (1)) / (exp(y))))) / y
END code

Derivation

1. Initial program 100.0%

   \[\cos x \cdot \frac{\sinh y}{y} \]

2. Taylor expanded in x around 0

   \[\leadsto \frac{1}{2} \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]
3. Step-by-step derivation

4. Applied rewrites 40.1%

   \[\leadsto 0.5 \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]
5. Step-by-step derivation

6. Applied rewrites 65.3%

   \[\leadsto \frac{\sinh y}{y} \]
7. Add Preprocessing

Alternative 8: 28.6% accurate, 13.9× speedup

Math

\[0.5 \cdot 2 \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (* 0.5 2.0))

C

double code(double x, double y) {
	return 0.5 * 2.0;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * 2.0d0
end function

Java

public static double code(double x, double y) {
	return 0.5 * 2.0;
}

Python

def code(x, y):
	return 0.5 * 2.0

Julia

function code(x, y)
	return Float64(0.5 * 2.0)
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * 2.0;
end

Wolfram

code[x_, y_] := N[(0.5 * 2.0), $MachinePrecision]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	(5e-1) * (2)
END code

Derivation

1. Initial program 100.0%

   \[\cos x \cdot \frac{\sinh y}{y} \]

2. Taylor expanded in x around 0

   \[\leadsto \frac{1}{2} \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]
3. Step-by-step derivation

4. Applied rewrites 40.1%

   \[\leadsto 0.5 \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y} \]

5. Taylor expanded in y around 0

   \[\leadsto 0.5 \cdot 2 \]
6. Step-by-step derivation

7. Applied rewrites 28.6%

   \[\leadsto 0.5 \cdot 2 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))