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

Percentage Accurate: 99.9% → 99.9%

Time: 3.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\sin y + \mathsf{fma}\left(\cos y, z, x\right) \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Applied rewrites 99.9%

   \[\leadsto \sin y + \mathsf{fma}\left(\cos y, z, x\right) \]
4. Add Preprocessing

Alternative 2: 90.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_0 := \left(x + \sin y\right) + z\\ \mathbf{if}\;x \leq -1.2064225709139271 \cdot 10^{-51}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.3907246641268288 \cdot 10^{-133}:\\ \;\;\;\;\mathsf{fma}\left(z, \cos y, \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (+ (+ x (sin y)) z)))
  (if (<= x -1.2064225709139271e-51)
    t_0
    (if (<= x 1.3907246641268288e-133) (fma z (cos y) (sin y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + sin(y)) + z;
	double tmp;
	if (x <= -1.2064225709139271e-51) {
		tmp = t_0;
	} else if (x <= 1.3907246641268288e-133) {
		tmp = fma(z, cos(y), sin(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + sin(y)) + z)
	tmp = 0.0
	if (x <= -1.2064225709139271e-51)
		tmp = t_0;
	elseif (x <= 1.3907246641268288e-133)
		tmp = fma(z, cos(y), sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -1.2064225709139271e-51], t$95$0, If[LessEqual[x, 1.3907246641268288e-133], N[(z * N[Cos[y], $MachinePrecision] + N[Sin[y], $MachinePrecision]), $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 = ((x + (sin(y))) + z) IN
		LET tmp_1 = IF (x <= (13907246641268287719553288589367698732274009277678938853341083963550402305825730272558285284260707557226592286720658421468340914383077588215032524302117800378662076704866440675793204111827833749549383931163536547600078549247750976353053708772891633938598045310131695191357079148094045872458853184477607279647119117250357415993544663024295005016028881072998046875e-494)) THEN ((z * (cos(y))) + (sin(y))) ELSE t_0 ENDIF IN
		LET tmp = IF (x <= (-1206422570913927125523414655424086006973612323856849477897271803401450903142584014094535191051817179243784378392130538577803905582984389521783441523439250886440277099609375e-222)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -1.2064225709139271e-51 or 1.3907246641268288e-133 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.3%

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

   if -1.2064225709139271e-51 < x < 1.3907246641268288e-133

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \sin y + z \cdot \cos y \]
   3. Step-by-step derivation

   4. Applied rewrites 58.7%

      \[\leadsto \sin y + z \cdot \cos y \]
   5. Step-by-step derivation

   6. Applied rewrites 58.7%

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

Alternative 3: 89.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -5.28748223434074 \cdot 10^{+73}:\\ \;\;\;\;\left(x + y\right) + t\_0\\ \mathbf{elif}\;z \leq 9.798786776982002 \cdot 10^{+41}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{1}{t\_0}}\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* z (cos y))))
  (if (<= z -5.28748223434074e+73)
    (+ (+ x y) t_0)
    (if (<= z 9.798786776982002e+41)
      (+ (+ x (sin y)) z)
      (/ 1.0 (/ 1.0 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -5.28748223434074e+73) {
		tmp = (x + y) + t_0;
	} else if (z <= 9.798786776982002e+41) {
		tmp = (x + sin(y)) + z;
	} else {
		tmp = 1.0 / (1.0 / 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 = z * cos(y)
    if (z <= (-5.28748223434074d+73)) then
        tmp = (x + y) + t_0
    else if (z <= 9.798786776982002d+41) then
        tmp = (x + sin(y)) + z
    else
        tmp = 1.0d0 / (1.0d0 / t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -5.28748223434074e+73) {
		tmp = (x + y) + t_0;
	} else if (z <= 9.798786776982002e+41) {
		tmp = (x + Math.sin(y)) + z;
	} else {
		tmp = 1.0 / (1.0 / t_0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -5.28748223434074e+73:
		tmp = (x + y) + t_0
	elif z <= 9.798786776982002e+41:
		tmp = (x + math.sin(y)) + z
	else:
		tmp = 1.0 / (1.0 / t_0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -5.28748223434074e+73)
		tmp = Float64(Float64(x + y) + t_0);
	elseif (z <= 9.798786776982002e+41)
		tmp = Float64(Float64(x + sin(y)) + z);
	else
		tmp = Float64(1.0 / Float64(1.0 / t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -5.28748223434074e+73)
		tmp = (x + y) + t_0;
	elseif (z <= 9.798786776982002e+41)
		tmp = (x + sin(y)) + z;
	else
		tmp = 1.0 / (1.0 / t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.28748223434074e+73], N[(N[(x + y), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[z, 9.798786776982002e+41], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(1.0 / N[(1.0 / t$95$0), $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 =
	LET t_0 = (z * (cos(y))) IN
		LET tmp_1 = IF (z <= (979878677698200176404151365115154792448000)) THEN ((x + (sin(y))) + z) ELSE ((1) / ((1) / t_0)) ENDIF IN
		LET tmp = IF (z <= (-52874822343407397655864544993387752694108327141706237168610951579553497088)) THEN ((x + y) + t_0) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if z < -5.2874822343407398e73

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 71.5%

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

   if -5.2874822343407398e73 < z < 9.7987867769820018e41

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.3%

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

   if 9.7987867769820018e41 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto x + z \]
   3. Step-by-step derivation

   4. Applied rewrites 66.3%

      \[\leadsto x + z \]

   6. Applied rewrites 66.1%

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

   7. Taylor expanded in z around inf

      \[\leadsto \frac{1}{\frac{1}{z \cdot \cos y}} \]
   8. Step-by-step derivation

   9. Applied rewrites 42.6%

      \[\leadsto \frac{1}{\frac{1}{z \cdot \cos y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 88.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_0 := \left(x + y\right) + z \cdot \cos y\\ \mathbf{if}\;z \leq -5.28748223434074 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 6.994970959352771 \cdot 10^{+79}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (+ (+ x y) (* z (cos y)))))
  (if (<= z -5.28748223434074e+73)
    t_0
    (if (<= z 6.994970959352771e+79) (+ (+ x (sin y)) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + y) + (z * cos(y));
	double tmp;
	if (z <= -5.28748223434074e+73) {
		tmp = t_0;
	} else if (z <= 6.994970959352771e+79) {
		tmp = (x + sin(y)) + z;
	} 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 = (x + y) + (z * cos(y))
    if (z <= (-5.28748223434074d+73)) then
        tmp = t_0
    else if (z <= 6.994970959352771d+79) then
        tmp = (x + sin(y)) + z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + y) + (z * Math.cos(y));
	double tmp;
	if (z <= -5.28748223434074e+73) {
		tmp = t_0;
	} else if (z <= 6.994970959352771e+79) {
		tmp = (x + Math.sin(y)) + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + y) + (z * math.cos(y))
	tmp = 0
	if z <= -5.28748223434074e+73:
		tmp = t_0
	elif z <= 6.994970959352771e+79:
		tmp = (x + math.sin(y)) + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + y) + Float64(z * cos(y)))
	tmp = 0.0
	if (z <= -5.28748223434074e+73)
		tmp = t_0;
	elseif (z <= 6.994970959352771e+79)
		tmp = Float64(Float64(x + sin(y)) + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + y) + (z * cos(y));
	tmp = 0.0;
	if (z <= -5.28748223434074e+73)
		tmp = t_0;
	elseif (z <= 6.994970959352771e+79)
		tmp = (x + sin(y)) + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + y), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.28748223434074e+73], t$95$0, If[LessEqual[z, 6.994970959352771e+79], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $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 = ((x + y) + (z * (cos(y)))) IN
		LET tmp_1 = IF (z <= (69949709593527711519130508415402423261954380287341550860642068283017517170950144)) THEN ((x + (sin(y))) + z) ELSE t_0 ENDIF IN
		LET tmp = IF (z <= (-52874822343407397655864544993387752694108327141706237168610951579553497088)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -5.2874822343407398e73 or 6.9949709593527712e79 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 71.5%

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

   if -5.2874822343407398e73 < z < 6.9949709593527712e79

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.3%

      \[\leadsto \left(x + \sin y\right) + z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 85.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} t_0 := \mathsf{fma}\left(z, \cos y, y\right)\\ \mathbf{if}\;z \leq -2.6050087589972047 \cdot 10^{+231}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.29415652404265 \cdot 10^{+104}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (fma z (cos y) y)))
  (if (<= z -2.6050087589972047e+231)
    t_0
    (if (<= z 3.29415652404265e+104) (+ (+ x (sin y)) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(z, cos(y), y);
	double tmp;
	if (z <= -2.6050087589972047e+231) {
		tmp = t_0;
	} else if (z <= 3.29415652404265e+104) {
		tmp = (x + sin(y)) + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = fma(z, cos(y), y)
	tmp = 0.0
	if (z <= -2.6050087589972047e+231)
		tmp = t_0;
	elseif (z <= 3.29415652404265e+104)
		tmp = Float64(Float64(x + sin(y)) + z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[z, -2.6050087589972047e+231], t$95$0, If[LessEqual[z, 3.29415652404265e+104], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $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 = ((z * (cos(y))) + y) IN
		LET tmp_1 = IF (z <= (329415652404265010418554586415017209981269810080201608232477072466112801212201144210986410850081598078976)) THEN ((x + (sin(y))) + z) ELSE t_0 ENDIF IN
		LET tmp = IF (z <= (-2605008758997204731862540525904623120202226198490563335109080502117871832311430881960948842708104076398331597073757562736175411220495072925082581483231614811605404858423706667269037393238998684482922839234465216156774559113321381888)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -2.6050087589972047e231 or 3.2941565240426501e104 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 71.5%

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

   5. Taylor expanded in x around 0

      \[\leadsto y + z \cdot \cos y \]
   6. Step-by-step derivation

   7. Applied rewrites 38.5%

      \[\leadsto y + z \cdot \cos y \]
   8. Step-by-step derivation

   9. Applied rewrites 38.5%

      \[\leadsto \mathsf{fma}\left(z, \cos y, y\right) \]

   if -2.6050087589972047e231 < z < 3.2941565240426501e104

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.3%

      \[\leadsto \left(x + \sin y\right) + z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 76.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3693315375584638 \cdot 10^{-23}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.8401859998667305 \cdot 10^{-111}:\\ \;\;\;\;\sin y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= x -1.3693315375584638e-23)
  (+ x z)
  (if (<= x 1.8401859998667305e-111) (+ (sin y) z) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3693315375584638e-23) {
		tmp = x + z;
	} else if (x <= 1.8401859998667305e-111) {
		tmp = sin(y) + z;
	} else {
		tmp = x + z;
	}
	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 (x <= (-1.3693315375584638d-23)) then
        tmp = x + z
    else if (x <= 1.8401859998667305d-111) then
        tmp = sin(y) + z
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3693315375584638e-23) {
		tmp = x + z;
	} else if (x <= 1.8401859998667305e-111) {
		tmp = Math.sin(y) + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3693315375584638e-23:
		tmp = x + z
	elif x <= 1.8401859998667305e-111:
		tmp = math.sin(y) + z
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3693315375584638e-23)
		tmp = Float64(x + z);
	elseif (x <= 1.8401859998667305e-111)
		tmp = Float64(sin(y) + z);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.3693315375584638e-23)
		tmp = x + z;
	elseif (x <= 1.8401859998667305e-111)
		tmp = sin(y) + z;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3693315375584638e-23], N[(x + z), $MachinePrecision], If[LessEqual[x, 1.8401859998667305e-111], N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision], N[(x + 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 =
	LET tmp_1 = IF (x <= (184018599986673049805691613416603898063221139119644273742008916997875723735219713640021868179631727986170486433482239334249893247915031318203120656150366966758516334389313631113526126602288921270947752277548694013337231896514795509136510648494433478015723861463863258135231770751261137775145471096038818359375e-419)) THEN ((sin(y)) + z) ELSE (x + z) ENDIF IN
	LET tmp = IF (x <= (-13693315375584637783697793251116340862481554836732444073609167058125368754417650052346289157867431640625e-126)) THEN (x + z) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -1.3693315375584638e-23 or 1.8401859998667305e-111 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto x + z \]
   3. Step-by-step derivation

   4. Applied rewrites 66.3%

      \[\leadsto x + z \]

   if -1.3693315375584638e-23 < x < 1.8401859998667305e-111

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 82.3%

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

   5. Taylor expanded in x around 0

      \[\leadsto \sin y + z \]
   6. Step-by-step derivation

   7. Applied rewrites 41.6%

      \[\leadsto \sin y + z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 70.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4406378747069113:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 62203358.3813149:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.5, z, -0.16666666666666666 \cdot y\right), y, 1\right), y, z + x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= y -1.4406378747069113)
  (+ x z)
  (if (<= y 62203358.3813149)
    (fma
     (fma (fma -0.5 z (* -0.16666666666666666 y)) y 1.0)
     y
     (+ z x))
    (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4406378747069113) {
		tmp = x + z;
	} else if (y <= 62203358.3813149) {
		tmp = fma(fma(fma(-0.5, z, (-0.16666666666666666 * y)), y, 1.0), y, (z + x));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4406378747069113)
		tmp = Float64(x + z);
	elseif (y <= 62203358.3813149)
		tmp = fma(fma(fma(-0.5, z, Float64(-0.16666666666666666 * y)), y, 1.0), y, Float64(z + x));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4406378747069113], N[(x + z), $MachinePrecision], If[LessEqual[y, 62203358.3813149], N[(N[(N[(-0.5 * z + N[(-0.16666666666666666 * y), $MachinePrecision]), $MachinePrecision] * y + 1.0), $MachinePrecision] * y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(x + 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 =
	LET tmp_1 = IF (y <= (622033583813149034976959228515625e-25)) THEN (((((((-5e-1) * z) + ((-1666666666666666574148081281236954964697360992431640625e-55) * y)) * y) + (1)) * y) + (z + x)) ELSE (x + z) ENDIF IN
	LET tmp = IF (y <= (-14406378747069112922218891981174238026142120361328125e-52)) THEN (x + z) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -1.4406378747069113 or 62203358.381314903 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto x + z \]
   3. Step-by-step derivation

   4. Applied rewrites 66.3%

      \[\leadsto x + z \]

   if -1.4406378747069113 < y < 62203358.381314903

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 54.5%

      \[\leadsto x + \left(z + y \cdot \left(1 + y \cdot \mathsf{fma}\left(-0.5, z, -0.16666666666666666 \cdot y\right)\right)\right) \]

   6. Applied rewrites 54.5%

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

Alternative 8: 69.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -7.013759171231195 \cdot 10^{+82}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 0.0037464000066246743:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= y -7.013759171231195e+82)
  (+ x z)
  (if (<= y 0.0037464000066246743)
    (+ x (+ z (* y (+ 1.0 (* -0.5 (* y z))))))
    (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.013759171231195e+82) {
		tmp = x + z;
	} else if (y <= 0.0037464000066246743) {
		tmp = x + (z + (y * (1.0 + (-0.5 * (y * z)))));
	} else {
		tmp = x + z;
	}
	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 <= (-7.013759171231195d+82)) then
        tmp = x + z
    else if (y <= 0.0037464000066246743d0) then
        tmp = x + (z + (y * (1.0d0 + ((-0.5d0) * (y * z)))))
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.013759171231195e+82) {
		tmp = x + z;
	} else if (y <= 0.0037464000066246743) {
		tmp = x + (z + (y * (1.0 + (-0.5 * (y * z)))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.013759171231195e+82:
		tmp = x + z
	elif y <= 0.0037464000066246743:
		tmp = x + (z + (y * (1.0 + (-0.5 * (y * z)))))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.013759171231195e+82)
		tmp = Float64(x + z);
	elseif (y <= 0.0037464000066246743)
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(-0.5 * Float64(y * z))))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.013759171231195e+82)
		tmp = x + z;
	elseif (y <= 0.0037464000066246743)
		tmp = x + (z + (y * (1.0 + (-0.5 * (y * z)))));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.013759171231195e+82], N[(x + z), $MachinePrecision], If[LessEqual[y, 0.0037464000066246743], N[(x + N[(z + N[(y * N[(1.0 + N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 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 =
	LET tmp_1 = IF (y <= (3746400006624674323962853605962664005346596240997314453125e-60)) THEN (x + (z + (y * ((1) + ((-5e-1) * (y * z)))))) ELSE (x + z) ENDIF IN
	LET tmp = IF (y <= (-70137591712311951039236750982046534214821916744479065190814041306896360460198608896)) THEN (x + z) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -7.0137591712311951e82 or 0.0037464000066246743 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto x + z \]
   3. Step-by-step derivation

   4. Applied rewrites 66.3%

      \[\leadsto x + z \]

   if -7.0137591712311951e82 < y < 0.0037464000066246743

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 58.0%

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

Alternative 9: 69.6% accurate, 5.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -8.607816989253337 \cdot 10^{+45}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.8336408030534186 \cdot 10^{-26}:\\ \;\;\;\;x + \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= y -8.607816989253337e+45)
  (+ x z)
  (if (<= y 1.8336408030534186e-26) (+ x (+ y z)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.607816989253337e+45) {
		tmp = x + z;
	} else if (y <= 1.8336408030534186e-26) {
		tmp = x + (y + z);
	} else {
		tmp = x + z;
	}
	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 <= (-8.607816989253337d+45)) then
        tmp = x + z
    else if (y <= 1.8336408030534186d-26) then
        tmp = x + (y + z)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.607816989253337e+45) {
		tmp = x + z;
	} else if (y <= 1.8336408030534186e-26) {
		tmp = x + (y + z);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.607816989253337e+45:
		tmp = x + z
	elif y <= 1.8336408030534186e-26:
		tmp = x + (y + z)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.607816989253337e+45)
		tmp = Float64(x + z);
	elseif (y <= 1.8336408030534186e-26)
		tmp = Float64(x + Float64(y + z));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.607816989253337e+45)
		tmp = x + z;
	elseif (y <= 1.8336408030534186e-26)
		tmp = x + (y + z);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.607816989253337e+45], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.8336408030534186e-26], N[(x + N[(y + z), $MachinePrecision]), $MachinePrecision], N[(x + 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 =
	LET tmp_1 = IF (y <= (18336408030534185630147711339110589968349689998395717197550123900054680307902810199038867722265422344207763671875e-138)) THEN (x + (y + z)) ELSE (x + z) ENDIF IN
	LET tmp = IF (y <= (-8607816989253337160308850915516592192007176192)) THEN (x + z) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -8.6078169892533372e45 or 1.8336408030534186e-26 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto x + z \]
   3. Step-by-step derivation

   4. Applied rewrites 66.3%

      \[\leadsto x + z \]

   if -8.6078169892533372e45 < y < 1.8336408030534186e-26

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 62.1%

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

Alternative 10: 66.3% accurate, 21.2× speedup

Math

\[x + z \]

FPCore

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

C

double code(double x, double y, double z) {
	return x + 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 + z
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(x + z)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + 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 + z
END code

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0

   \[\leadsto x + z \]
3. Step-by-step derivation

4. Applied rewrites 66.3%

   \[\leadsto x + z \]
5. Add Preprocessing

Alternative 11: 29.4% accurate, 21.2× speedup

Math

\[y + z \]

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = y + z
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(y + z)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y + 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 =
	y + z
END code

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0

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

4. Applied rewrites 62.1%

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

5. Taylor expanded in x around 0

   \[\leadsto y + z \]
6. Step-by-step derivation

7. Applied rewrites 29.4%

   \[\leadsto y + z \]
8. Add Preprocessing

Alternative 12: 26.1% accurate, 76.4× speedup

Math

\[z \]

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

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 =
	z
END code

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0

   \[\leadsto x + z \]
3. Step-by-step derivation

4. Applied rewrites 66.3%

   \[\leadsto x + z \]

5. Taylor expanded in x around 0

   \[\leadsto z \]
6. Step-by-step derivation

7. Applied rewrites 26.1%

   \[\leadsto z \]
8. Add Preprocessing

Reproduce

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