Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B

Percentage Accurate: 99.9% → 99.9%

Time: 3.1s

Alternatives: 10

Speedup: N/A×

Specification

Math

\[\left(x + \cos y\right) - z \cdot \sin y \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (- (+ x (cos y)) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(y));
}

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 + cos(y)) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.cos(y)) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + math.cos(y)) - (z * math.sin(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + cos(y)) - (z * sin(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $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 + (cos(y))) - (z * (sin(y)))
END code

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\left(x + \cos y\right) - z \cdot \sin y \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (- (+ x (cos y)) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(y));
}

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 + cos(y)) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.cos(y)) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + math.cos(y)) - (z * math.sin(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + cos(y)) - (z * sin(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $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 + (cos(y))) - (z * (sin(y)))
END code

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[x + \left(\cos y - \sin y \cdot z\right) \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (+ x (- (cos y) (* (sin y) z))))

C

double code(double x, double y, double z) {
	return x + (cos(y) - (sin(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 + (cos(y) - (sin(y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (Math.cos(y) - (Math.sin(y) * z));
}

Python

def code(x, y, z):
	return x + (math.cos(y) - (math.sin(y) * z))

Julia

function code(x, y, z)
	return Float64(x + Float64(cos(y) - Float64(sin(y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (cos(y) - (sin(y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[Cos[y], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $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 + ((cos(y)) - ((sin(y)) * z))
END code

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]
2. Step-by-step derivation

3. Applied rewrites 99.9%

   \[\leadsto x + \left(\cos y - \sin y \cdot z\right) \]
4. Add Preprocessing

Alternative 2: 98.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := x + \cos y\\ t_1 := z \cdot \sin y\\ t_2 := t\_0 - t\_1\\ t_3 := \left(x + 1\right) - t\_1\\ \mathbf{if}\;t\_2 \leq -500:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 50000000000000:\\ \;\;\;\;\frac{x \cdot t\_0}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (+ x (cos y)))
       (t_1 (* z (sin y)))
       (t_2 (- t_0 t_1))
       (t_3 (- (+ x 1.0) t_1)))
  (if (<= t_2 -500.0)
    t_3
    (if (<= t_2 50000000000000.0) (/ (* x t_0) x) t_3))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double t_1 = z * sin(y);
	double t_2 = t_0 - t_1;
	double t_3 = (x + 1.0) - t_1;
	double tmp;
	if (t_2 <= -500.0) {
		tmp = t_3;
	} else if (t_2 <= 50000000000000.0) {
		tmp = (x * t_0) / x;
	} else {
		tmp = t_3;
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x + cos(y)
    t_1 = z * sin(y)
    t_2 = t_0 - t_1
    t_3 = (x + 1.0d0) - t_1
    if (t_2 <= (-500.0d0)) then
        tmp = t_3
    else if (t_2 <= 50000000000000.0d0) then
        tmp = (x * t_0) / x
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + Math.cos(y);
	double t_1 = z * Math.sin(y);
	double t_2 = t_0 - t_1;
	double t_3 = (x + 1.0) - t_1;
	double tmp;
	if (t_2 <= -500.0) {
		tmp = t_3;
	} else if (t_2 <= 50000000000000.0) {
		tmp = (x * t_0) / x;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.cos(y)
	t_1 = z * math.sin(y)
	t_2 = t_0 - t_1
	t_3 = (x + 1.0) - t_1
	tmp = 0
	if t_2 <= -500.0:
		tmp = t_3
	elif t_2 <= 50000000000000.0:
		tmp = (x * t_0) / x
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	t_1 = Float64(z * sin(y))
	t_2 = Float64(t_0 - t_1)
	t_3 = Float64(Float64(x + 1.0) - t_1)
	tmp = 0.0
	if (t_2 <= -500.0)
		tmp = t_3;
	elseif (t_2 <= 50000000000000.0)
		tmp = Float64(Float64(x * t_0) / x);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + cos(y);
	t_1 = z * sin(y);
	t_2 = t_0 - t_1;
	t_3 = (x + 1.0) - t_1;
	tmp = 0.0;
	if (t_2 <= -500.0)
		tmp = t_3;
	elseif (t_2 <= 50000000000000.0)
		tmp = (x * t_0) / x;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + 1.0), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -500.0], t$95$3, If[LessEqual[t$95$2, 50000000000000.0], N[(N[(x * t$95$0), $MachinePrecision] / x), $MachinePrecision], t$95$3]]]]]]

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 =
	LET t_0 = (x + (cos(y))) IN
		LET t_1 = (z * (sin(y))) IN
			LET t_2 = (t_0 - t_1) IN
				LET t_3 = ((x + (1)) - t_1) IN
					LET tmp_1 = IF (t_2 <= (5e13)) THEN ((x * t_0) / x) ELSE t_3 ENDIF IN
					LET tmp = IF (t_2 <= (-500)) THEN t_3 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -500 or 5e13 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(x + 1\right) - z \cdot \sin y \]
   3. Step-by-step derivation

   4. Applied rewrites 88.1%

      \[\leadsto \left(x + 1\right) - z \cdot \sin y \]

   if -500 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 5e13

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Step-by-step derivation

   3. Applied rewrites 99.9%

      \[\leadsto x + \left(\cos y - \sin y \cdot z\right) \]

   5. Applied rewrites 74.9%

      \[\leadsto \frac{x \cdot \left(x - \left(\sin y \cdot z - \cos y\right)\right)}{x} \]

   6. Taylor expanded in z around 0

      \[\leadsto \frac{x \cdot \left(x + \cos y\right)}{x} \]
   7. Step-by-step derivation

   8. Applied rewrites 51.6%

      \[\leadsto \frac{x \cdot \left(x + \cos y\right)}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := z \cdot \sin y\\ t_1 := \left(x + \cos y\right) - t\_0\\ t_2 := \left(x + 1\right) - t\_0\\ \mathbf{if}\;t\_1 \leq -500:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.9998:\\ \;\;\;\;\frac{x \cdot \cos y}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* z (sin y)))
       (t_1 (- (+ x (cos y)) t_0))
       (t_2 (- (+ x 1.0) t_0)))
  (if (<= t_1 -500.0)
    t_2
    (if (<= t_1 0.9998) (/ (* x (cos y)) x) t_2))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double t_1 = (x + cos(y)) - t_0;
	double t_2 = (x + 1.0) - t_0;
	double tmp;
	if (t_1 <= -500.0) {
		tmp = t_2;
	} else if (t_1 <= 0.9998) {
		tmp = (x * cos(y)) / x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = z * sin(y)
    t_1 = (x + cos(y)) - t_0
    t_2 = (x + 1.0d0) - t_0
    if (t_1 <= (-500.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.9998d0) then
        tmp = (x * cos(y)) / x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double t_1 = (x + Math.cos(y)) - t_0;
	double t_2 = (x + 1.0) - t_0;
	double tmp;
	if (t_1 <= -500.0) {
		tmp = t_2;
	} else if (t_1 <= 0.9998) {
		tmp = (x * Math.cos(y)) / x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	t_1 = (x + math.cos(y)) - t_0
	t_2 = (x + 1.0) - t_0
	tmp = 0
	if t_1 <= -500.0:
		tmp = t_2
	elif t_1 <= 0.9998:
		tmp = (x * math.cos(y)) / x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	t_1 = Float64(Float64(x + cos(y)) - t_0)
	t_2 = Float64(Float64(x + 1.0) - t_0)
	tmp = 0.0
	if (t_1 <= -500.0)
		tmp = t_2;
	elseif (t_1 <= 0.9998)
		tmp = Float64(Float64(x * cos(y)) / x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	t_1 = (x + cos(y)) - t_0;
	t_2 = (x + 1.0) - t_0;
	tmp = 0.0;
	if (t_1 <= -500.0)
		tmp = t_2;
	elseif (t_1 <= 0.9998)
		tmp = (x * cos(y)) / x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + 1.0), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[t$95$1, -500.0], t$95$2, If[LessEqual[t$95$1, 0.9998], N[(N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], t$95$2]]]]]

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 =
	LET t_0 = (z * (sin(y))) IN
		LET t_1 = ((x + (cos(y))) - t_0) IN
			LET t_2 = ((x + (1)) - t_0) IN
				LET tmp_1 = IF (t_1 <= (999800000000000022026824808563105762004852294921875e-51)) THEN ((x * (cos(y))) / x) ELSE t_2 ENDIF IN
				LET tmp = IF (t_1 <= (-500)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -500 or 0.99980000000000002 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

      \[\leadsto \left(x + 1\right) - z \cdot \sin y \]
   3. Step-by-step derivation

   4. Applied rewrites 88.1%

      \[\leadsto \left(x + 1\right) - z \cdot \sin y \]

   if -500 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.99980000000000002

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Step-by-step derivation

   3. Applied rewrites 99.9%

      \[\leadsto x + \left(\cos y - \sin y \cdot z\right) \]

   5. Applied rewrites 74.9%

      \[\leadsto \frac{x \cdot \left(x - \left(\sin y \cdot z - \cos y\right)\right)}{x} \]

   6. Taylor expanded in z around 0

      \[\leadsto \frac{x \cdot \left(x + \cos y\right)}{x} \]
   7. Step-by-step derivation

   8. Applied rewrites 51.6%

      \[\leadsto \frac{x \cdot \left(x + \cos y\right)}{x} \]

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 32.5%

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

Alternative 4: 72.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_0 := \left(x + \cos y\right) - z \cdot \sin y\\ \mathbf{if}\;t\_0 \leq -500:\\ \;\;\;\;x - -1\\ \mathbf{elif}\;t\_0 \leq 0.9998:\\ \;\;\;\;\frac{x \cdot \cos y}{x}\\ \mathbf{else}:\\ \;\;\;\;x - -1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (- (+ x (cos y)) (* z (sin y)))))
  (if (<= t_0 -500.0)
    (- x -1.0)
    (if (<= t_0 0.9998) (/ (* x (cos y)) x) (- x -1.0)))))

C

double code(double x, double y, double z) {
	double t_0 = (x + cos(y)) - (z * sin(y));
	double tmp;
	if (t_0 <= -500.0) {
		tmp = x - -1.0;
	} else if (t_0 <= 0.9998) {
		tmp = (x * cos(y)) / x;
	} else {
		tmp = x - -1.0;
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + cos(y)) - (z * sin(y))
    if (t_0 <= (-500.0d0)) then
        tmp = x - (-1.0d0)
    else if (t_0 <= 0.9998d0) then
        tmp = (x * cos(y)) / x
    else
        tmp = x - (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + Math.cos(y)) - (z * Math.sin(y));
	double tmp;
	if (t_0 <= -500.0) {
		tmp = x - -1.0;
	} else if (t_0 <= 0.9998) {
		tmp = (x * Math.cos(y)) / x;
	} else {
		tmp = x - -1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + math.cos(y)) - (z * math.sin(y))
	tmp = 0
	if t_0 <= -500.0:
		tmp = x - -1.0
	elif t_0 <= 0.9998:
		tmp = (x * math.cos(y)) / x
	else:
		tmp = x - -1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
	tmp = 0.0
	if (t_0 <= -500.0)
		tmp = Float64(x - -1.0);
	elseif (t_0 <= 0.9998)
		tmp = Float64(Float64(x * cos(y)) / x);
	else
		tmp = Float64(x - -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + cos(y)) - (z * sin(y));
	tmp = 0.0;
	if (t_0 <= -500.0)
		tmp = x - -1.0;
	elseif (t_0 <= 0.9998)
		tmp = (x * cos(y)) / x;
	else
		tmp = x - -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -500.0], N[(x - -1.0), $MachinePrecision], If[LessEqual[t$95$0, 0.9998], N[(N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(x - -1.0), $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 =
	LET t_0 = ((x + (cos(y))) - (z * (sin(y)))) IN
		LET tmp_1 = IF (t_0 <= (999800000000000022026824808563105762004852294921875e-51)) THEN ((x * (cos(y))) / x) ELSE (x - (-1)) ENDIF IN
		LET tmp = IF (t_0 <= (-500)) THEN (x - (-1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -500 or 0.99980000000000002 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 92.3%

      \[\leadsto x \cdot \left(\left(1 + \frac{\cos y}{x}\right) - \frac{z \cdot \sin y}{x}\right) \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 61.8%

      \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]

   9. Applied rewrites 61.8%

      \[\leadsto x - -1 \]

   if -500 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.99980000000000002

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Step-by-step derivation

   3. Applied rewrites 99.9%

      \[\leadsto x + \left(\cos y - \sin y \cdot z\right) \]

   5. Applied rewrites 74.9%

      \[\leadsto \frac{x \cdot \left(x - \left(\sin y \cdot z - \cos y\right)\right)}{x} \]

   6. Taylor expanded in z around 0

      \[\leadsto \frac{x \cdot \left(x + \cos y\right)}{x} \]
   7. Step-by-step derivation

   8. Applied rewrites 51.6%

      \[\leadsto \frac{x \cdot \left(x + \cos y\right)}{x} \]

   9. Taylor expanded in x around 0

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

   11. Applied rewrites 32.5%

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

Alternative 5: 69.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_0 := -\sin y \cdot z\\ \mathbf{if}\;z \leq -3.737729305523624 \cdot 10^{+231}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.7607919014336375 \cdot 10^{+58}:\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (- (* (sin y) z))))
  (if (<= z -3.737729305523624e+231)
    t_0
    (if (<= z 1.7607919014336375e+58) (- x -1.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -(sin(y) * z);
	double tmp;
	if (z <= -3.737729305523624e+231) {
		tmp = t_0;
	} else if (z <= 1.7607919014336375e+58) {
		tmp = x - -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -(sin(y) * z)
    if (z <= (-3.737729305523624d+231)) then
        tmp = t_0
    else if (z <= 1.7607919014336375d+58) then
        tmp = x - (-1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -(Math.sin(y) * z);
	double tmp;
	if (z <= -3.737729305523624e+231) {
		tmp = t_0;
	} else if (z <= 1.7607919014336375e+58) {
		tmp = x - -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -(math.sin(y) * z)
	tmp = 0
	if z <= -3.737729305523624e+231:
		tmp = t_0
	elif z <= 1.7607919014336375e+58:
		tmp = x - -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(sin(y) * z))
	tmp = 0.0
	if (z <= -3.737729305523624e+231)
		tmp = t_0;
	elseif (z <= 1.7607919014336375e+58)
		tmp = Float64(x - -1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -(sin(y) * z);
	tmp = 0.0;
	if (z <= -3.737729305523624e+231)
		tmp = t_0;
	elseif (z <= 1.7607919014336375e+58)
		tmp = x - -1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision])}, If[LessEqual[z, -3.737729305523624e+231], t$95$0, If[LessEqual[z, 1.7607919014336375e+58], N[(x - -1.0), $MachinePrecision], t$95$0]]]

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 =
	LET t_0 = (- ((sin(y)) * z)) IN
		LET tmp_1 = IF (z <= (17607919014336374748535380586874903373695221280381807362048)) THEN (x - (-1)) ELSE t_0 ENDIF IN
		LET tmp = IF (z <= (-3737729305523624032107527104040697113816461946576530999971219869223156379245005075091390095789724225462510454890464459924249846547795888638982488968222765902797659955335860345197956621663714593787998809591943458119245969122012430336)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -3.737729305523624e231 or 1.7607919014336375e58 < z

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \left(z \cdot \sin y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 28.3%

      \[\leadsto -1 \cdot \left(z \cdot \sin y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 28.3%

      \[\leadsto -\sin y \cdot z \]

   if -3.737729305523624e231 < z < 1.7607919014336375e58

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 92.3%

      \[\leadsto x \cdot \left(\left(1 + \frac{\cos y}{x}\right) - \frac{z \cdot \sin y}{x}\right) \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 61.8%

      \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]

   9. Applied rewrites 61.8%

      \[\leadsto x - -1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 69.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -2.77957140983966 \cdot 10^{+34}:\\ \;\;\;\;x - -1\\ \mathbf{elif}\;y \leq 0.0037464000066246743:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - -1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= y -2.77957140983966e+34)
  (- x -1.0)
  (if (<= y 0.0037464000066246743)
    (+
     1.0
     (+ x (* y (- (* y (- (* 0.16666666666666666 (* y z)) 0.5)) z))))
    (- x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.77957140983966e+34) {
		tmp = x - -1.0;
	} else if (y <= 0.0037464000066246743) {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	} else {
		tmp = x - -1.0;
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= (-2.77957140983966d+34)) then
        tmp = x - (-1.0d0)
    else if (y <= 0.0037464000066246743d0) then
        tmp = 1.0d0 + (x + (y * ((y * ((0.16666666666666666d0 * (y * z)) - 0.5d0)) - z)))
    else
        tmp = x - (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.77957140983966e+34) {
		tmp = x - -1.0;
	} else if (y <= 0.0037464000066246743) {
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	} else {
		tmp = x - -1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.77957140983966e+34:
		tmp = x - -1.0
	elif y <= 0.0037464000066246743:
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)))
	else:
		tmp = x - -1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.77957140983966e+34)
		tmp = Float64(x - -1.0);
	elseif (y <= 0.0037464000066246743)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(0.16666666666666666 * Float64(y * z)) - 0.5)) - z))));
	else
		tmp = Float64(x - -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.77957140983966e+34)
		tmp = x - -1.0;
	elseif (y <= 0.0037464000066246743)
		tmp = 1.0 + (x + (y * ((y * ((0.16666666666666666 * (y * z)) - 0.5)) - z)));
	else
		tmp = x - -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.77957140983966e+34], N[(x - -1.0), $MachinePrecision], If[LessEqual[y, 0.0037464000066246743], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(0.16666666666666666 * N[(y * z), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - -1.0), $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 =
	LET tmp_1 = IF (y <= (3746400006624674323962853605962664005346596240997314453125e-60)) THEN ((1) + (x + (y * ((y * (((1666666666666666574148081281236954964697360992431640625e-55) * (y * z)) - (5e-1))) - z)))) ELSE (x - (-1)) ENDIF IN
	LET tmp = IF (y <= (-27795714098396601956655166650318848)) THEN (x - (-1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -2.7795714098396602e34 or 0.0037464000066246743 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 92.3%

      \[\leadsto x \cdot \left(\left(1 + \frac{\cos y}{x}\right) - \frac{z \cdot \sin y}{x}\right) \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 61.8%

      \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]

   9. Applied rewrites 61.8%

      \[\leadsto x - -1 \]

   if -2.7795714098396602e34 < y < 0.0037464000066246743

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

      \[\leadsto 1 + \left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 55.3%

      \[\leadsto 1 + \left(x + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \left(y \cdot z\right) - 0.5\right) - z\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 69.1% accurate, 4.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -7.202250336853939 \cdot 10^{+61}:\\ \;\;\;\;x - -1\\ \mathbf{elif}\;y \leq 3.7534046655014413 \cdot 10^{+58}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - -1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= y -7.202250336853939e+61)
  (- x -1.0)
  (if (<= y 3.7534046655014413e+58) (- x (fma z y -1.0)) (- x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.202250336853939e+61) {
		tmp = x - -1.0;
	} else if (y <= 3.7534046655014413e+58) {
		tmp = x - fma(z, y, -1.0);
	} else {
		tmp = x - -1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.202250336853939e+61)
		tmp = Float64(x - -1.0);
	elseif (y <= 3.7534046655014413e+58)
		tmp = Float64(x - fma(z, y, -1.0));
	else
		tmp = Float64(x - -1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.202250336853939e+61], N[(x - -1.0), $MachinePrecision], If[LessEqual[y, 3.7534046655014413e+58], N[(x - N[(z * y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x - -1.0), $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 =
	LET tmp_1 = IF (y <= (37534046655014413318163465982650524569175125961626804551680)) THEN (x - ((z * y) + (-1))) ELSE (x - (-1)) ENDIF IN
	LET tmp = IF (y <= (-72022503368539393057692374051802676984285611840510104690491392)) THEN (x - (-1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -7.2022503368539393e61 or 3.7534046655014413e58 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 92.3%

      \[\leadsto x \cdot \left(\left(1 + \frac{\cos y}{x}\right) - \frac{z \cdot \sin y}{x}\right) \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 61.8%

      \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]

   9. Applied rewrites 61.8%

      \[\leadsto x - -1 \]

   if -7.2022503368539393e61 < y < 3.7534046655014413e58

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

      \[\leadsto 1 + \left(x + -1 \cdot \left(y \cdot z\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 63.7%

      \[\leadsto 1 + \left(x + -1 \cdot \left(y \cdot z\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 63.7%

      \[\leadsto x - \mathsf{fma}\left(z, y, -1\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 61.8% accurate, 21.2× speedup

Math

\[x - -1 \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (- x -1.0))

C

double code(double x, double y, double z) {
	return x - -1.0;
}

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 - (-1.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x - -1.0;
}

Python

def code(x, y, z):
	return x - -1.0

Julia

function code(x, y, z)
	return Float64(x - -1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - -1.0;
end

Wolfram

code[x_, y_, z_] := N[(x - -1.0), $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 - (-1)
END code

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]

2. Taylor expanded in x around inf

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

4. Applied rewrites 92.3%

   \[\leadsto x \cdot \left(\left(1 + \frac{\cos y}{x}\right) - \frac{z \cdot \sin y}{x}\right) \]

5. Taylor expanded in y around 0

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

7. Applied rewrites 61.8%

   \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]

9. Applied rewrites 61.8%

   \[\leadsto x - -1 \]
10. Add Preprocessing

Alternative 9: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_0 := \left(x + \cos y\right) - z \cdot \sin y\\ t_1 := -\left(-x\right)\\ \mathbf{if}\;t\_0 \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (- (+ x (cos y)) (* z (sin y)))) (t_1 (- (- x))))
  (if (<= t_0 -0.05) t_1 (if (<= t_0 2.0) 1.0 t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (x + cos(y)) - (z * sin(y));
	double t_1 = -(-x);
	double tmp;
	if (t_0 <= -0.05) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x + cos(y)) - (z * sin(y))
    t_1 = -(-x)
    if (t_0 <= (-0.05d0)) then
        tmp = t_1
    else if (t_0 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + Math.cos(y)) - (z * Math.sin(y));
	double t_1 = -(-x);
	double tmp;
	if (t_0 <= -0.05) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + math.cos(y)) - (z * math.sin(y))
	t_1 = -(-x)
	tmp = 0
	if t_0 <= -0.05:
		tmp = t_1
	elif t_0 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
	t_1 = Float64(-Float64(-x))
	tmp = 0.0
	if (t_0 <= -0.05)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + cos(y)) - (z * sin(y));
	t_1 = -(-x);
	tmp = 0.0;
	if (t_0 <= -0.05)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = (-(-x))}, If[LessEqual[t$95$0, -0.05], t$95$1, If[LessEqual[t$95$0, 2.0], 1.0, t$95$1]]]]

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 =
	LET t_0 = ((x + (cos(y))) - (z * (sin(y)))) IN
		LET t_1 = (- (- x)) IN
			LET tmp_1 = IF (t_0 <= (2)) THEN (1) ELSE t_1 ENDIF IN
			LET tmp = IF (t_0 <= (-5000000000000000277555756156289135105907917022705078125e-56)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -0.050000000000000003 or 2 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

      \[\leadsto 1 + \left(x + -1 \cdot \left(y \cdot z\right)\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 63.7%

      \[\leadsto 1 + \left(x + -1 \cdot \left(y \cdot z\right)\right) \]

   5. Taylor expanded in y around -inf

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

   7. Applied rewrites 51.8%

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

   8. Taylor expanded in x around inf

      \[\leadsto -1 \cdot \left(-1 \cdot x\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 42.4%

       \[\leadsto -1 \cdot \left(-1 \cdot x\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 42.4%

       \[\leadsto -\left(-x\right) \]

   if -0.050000000000000003 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 2

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 92.3%

      \[\leadsto x \cdot \left(\left(1 + \frac{\cos y}{x}\right) - \frac{z \cdot \sin y}{x}\right) \]

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 61.8%

      \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]

   9. Applied rewrites 61.8%

      \[\leadsto x - -1 \]

   10. Taylor expanded in x around 0

       \[\leadsto 1 \]
   11. Step-by-step derivation

   12. Applied rewrites 21.8%

       \[\leadsto 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 21.8% accurate, 76.4× speedup

Math

\[1 \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

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 = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

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 =
	1
END code

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]

2. Taylor expanded in x around inf

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

4. Applied rewrites 92.3%

   \[\leadsto x \cdot \left(\left(1 + \frac{\cos y}{x}\right) - \frac{z \cdot \sin y}{x}\right) \]

5. Taylor expanded in y around 0

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

7. Applied rewrites 61.8%

   \[\leadsto x \cdot \left(1 + \frac{1}{x}\right) \]

9. Applied rewrites 61.8%

   \[\leadsto x - -1 \]

10. Taylor expanded in x around 0

    \[\leadsto 1 \]
11. Step-by-step derivation

12. Applied rewrites 21.8%

    \[\leadsto 1 \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))