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

Percentage Accurate: 99.9% → 99.9%

Time: 10.5s

Alternatives: 17

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + \cos y\right) - z \cdot \sin y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ 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)
    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]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \cos y\right) - z \cdot \sin y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ 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)
    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]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\sin y, -z, x + \cos y\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. *-commutative N/A

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

   4. distribute-rgt-neg-in N/A

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

   5. accelerator-lowering-fma.f64 N/A

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

   6. sin-lowering-sin.f64 N/A

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

   7. neg-lowering-neg.f64 N/A

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

   8. +-lowering-+.f64 N/A

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

   9. cos-lowering-cos.f64 99.9

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

4. Applied egg-rr 99.9%

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

Alternative 2: 74.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \cos y\right) - \sin y \cdot z\\ t_1 := x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{if}\;t\_0 \leq -1000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.9999999999999998:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;t\_0 \leq 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x (cos y)) (* (sin y) z))) (t_1 (- x (fma y z -1.0))))
   (if (<= t_0 -1000.0)
     t_1
     (if (<= t_0 0.9999999999999998)
       (cos y)
       (if (<= t_0 1e+202) t_1 (+ x 1.0))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + cos(y)) - (sin(y) * z);
	double t_1 = x - fma(y, z, -1.0);
	double tmp;
	if (t_0 <= -1000.0) {
		tmp = t_1;
	} else if (t_0 <= 0.9999999999999998) {
		tmp = cos(y);
	} else if (t_0 <= 1e+202) {
		tmp = t_1;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + cos(y)) - Float64(sin(y) * z))
	t_1 = Float64(x - fma(y, z, -1.0))
	tmp = 0.0
	if (t_0 <= -1000.0)
		tmp = t_1;
	elseif (t_0 <= 0.9999999999999998)
		tmp = cos(y);
	elseif (t_0 <= 1e+202)
		tmp = t_1;
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x - N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1000.0], t$95$1, If[LessEqual[t$95$0, 0.9999999999999998], N[Cos[y], $MachinePrecision], If[LessEqual[t$95$0, 1e+202], t$95$1, N[(x + 1.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -1e3 or 0.99999999999999978 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 9.999999999999999e201

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right)}\right) + 1 \]

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. --lowering--.f64 N/A

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

      6. sub-neg N/A

         \[\leadsto x - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(1\right)\right)\right)} \]

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 78.1

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(y, z, -1\right)} \]

   5. Simplified 78.1%

      \[\leadsto \color{blue}{x - \mathsf{fma}\left(y, z, -1\right)} \]

   if -1e3 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.99999999999999978

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

      2. cos-lowering-cos.f64 N/A

         \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \cos y - \color{blue}{z \cdot \sin y} \]

      4. sin-lowering-sin.f64 97.0

         \[\leadsto \cos y - z \cdot \color{blue}{\sin y} \]

   5. Simplified 97.0%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\cos y} \]
   7. Step-by-step derivation

      1. cos-lowering-cos.f64 94.9

         \[\leadsto \color{blue}{\cos y} \]

   8. Simplified 94.9%

      \[\leadsto \color{blue}{\cos y} \]

   if 9.999999999999999e201 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. +-lowering-+.f64 72.1

         \[\leadsto \color{blue}{x + 1} \]

   5. Simplified 72.1%

      \[\leadsto \color{blue}{x + 1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - \sin y \cdot z \leq -1000:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{elif}\;\left(x + \cos y\right) - \sin y \cdot z \leq 0.9999999999999998:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;\left(x + \cos y\right) - \sin y \cdot z \leq 10^{+202}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot z\\ t_1 := \left(x + \cos y\right) - t\_0\\ t_2 := \left(x + 1\right) - t\_0\\ \mathbf{if}\;t\_1 \leq -4000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.9999999999999998:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) z))
        (t_1 (- (+ x (cos y)) t_0))
        (t_2 (- (+ x 1.0) t_0)))
   (if (<= t_1 -4000000000000.0)
     t_2
     (if (<= t_1 0.9999999999999998) (fma (sin y) (- z) (cos y)) t_2))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * z;
	double t_1 = (x + cos(y)) - t_0;
	double t_2 = (x + 1.0) - t_0;
	double tmp;
	if (t_1 <= -4000000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.9999999999999998) {
		tmp = fma(sin(y), -z, cos(y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * z)
	t_1 = Float64(Float64(x + cos(y)) - t_0)
	t_2 = Float64(Float64(x + 1.0) - t_0)
	tmp = 0.0
	if (t_1 <= -4000000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.9999999999999998)
		tmp = fma(sin(y), Float64(-z), cos(y));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * z), $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, -4000000000000.0], t$95$2, If[LessEqual[t$95$1, 0.9999999999999998], N[(N[Sin[y], $MachinePrecision] * (-z) + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -4e12 or 0.99999999999999978 < (-.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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 99.9

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

   5. Simplified 99.9%

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

   if -4e12 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.99999999999999978

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

      2. cos-lowering-cos.f64 N/A

         \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \cos y - \color{blue}{z \cdot \sin y} \]

      4. sin-lowering-sin.f64 97.2

         \[\leadsto \cos y - z \cdot \color{blue}{\sin y} \]

   5. Simplified 97.2%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \color{blue}{\cos y + \left(\mathsf{neg}\left(z\right)\right) \cdot \sin y} \]

      2. *-commutative N/A

         \[\leadsto \cos y + \color{blue}{\sin y \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      3. +-commutative N/A

         \[\leadsto \color{blue}{\sin y \cdot \left(\mathsf{neg}\left(z\right)\right) + \cos y} \]

      4. accelerator-lowering-fma.f64 N/A

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

      5. sin-lowering-sin.f64 N/A

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

      6. neg-lowering-neg.f64 N/A

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

      7. cos-lowering-cos.f64 97.2

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

   7. Applied egg-rr 97.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - \sin y \cdot z \leq -4000000000000:\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \mathbf{elif}\;\left(x + \cos y\right) - \sin y \cdot z \leq 0.9999999999999998:\\ \;\;\;\;\mathsf{fma}\left(\sin y, -z, \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot z\\ t_1 := \left(x + \cos y\right) - t\_0\\ t_2 := \left(x + 1\right) - t\_0\\ \mathbf{if}\;t\_1 \leq -4000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.9999999999999998:\\ \;\;\;\;\cos y - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) z))
        (t_1 (- (+ x (cos y)) t_0))
        (t_2 (- (+ x 1.0) t_0)))
   (if (<= t_1 -4000000000000.0)
     t_2
     (if (<= t_1 0.9999999999999998) (- (cos y) t_0) t_2))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * z;
	double t_1 = (x + cos(y)) - t_0;
	double t_2 = (x + 1.0) - t_0;
	double tmp;
	if (t_1 <= -4000000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.9999999999999998) {
		tmp = cos(y) - t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    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 = sin(y) * z
    t_1 = (x + cos(y)) - t_0
    t_2 = (x + 1.0d0) - t_0
    if (t_1 <= (-4000000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.9999999999999998d0) then
        tmp = cos(y) - t_0
    else
        tmp = t_2
    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 t_1 = (x + Math.cos(y)) - t_0;
	double t_2 = (x + 1.0) - t_0;
	double tmp;
	if (t_1 <= -4000000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.9999999999999998) {
		tmp = Math.cos(y) - t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * z
	t_1 = (x + math.cos(y)) - t_0
	t_2 = (x + 1.0) - t_0
	tmp = 0
	if t_1 <= -4000000000000.0:
		tmp = t_2
	elif t_1 <= 0.9999999999999998:
		tmp = math.cos(y) - t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * z)
	t_1 = Float64(Float64(x + cos(y)) - t_0)
	t_2 = Float64(Float64(x + 1.0) - t_0)
	tmp = 0.0
	if (t_1 <= -4000000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.9999999999999998)
		tmp = Float64(cos(y) - t_0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * z;
	t_1 = (x + cos(y)) - t_0;
	t_2 = (x + 1.0) - t_0;
	tmp = 0.0;
	if (t_1 <= -4000000000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.9999999999999998)
		tmp = cos(y) - t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * z), $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, -4000000000000.0], t$95$2, If[LessEqual[t$95$1, 0.9999999999999998], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -4e12 or 0.99999999999999978 < (-.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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 99.9

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

   5. Simplified 99.9%

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

   if -4e12 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.99999999999999978

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

      2. cos-lowering-cos.f64 N/A

         \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \cos y - \color{blue}{z \cdot \sin y} \]

      4. sin-lowering-sin.f64 97.2

         \[\leadsto \cos y - z \cdot \color{blue}{\sin y} \]

   5. Simplified 97.2%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - \sin y \cdot z \leq -4000000000000:\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \mathbf{elif}\;\left(x + \cos y\right) - \sin y \cdot z \leq 0.9999999999999998:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ t_1 := \sin y \cdot z\\ t_2 := t\_0 - t\_1\\ t_3 := \left(x + 1\right) - t\_1\\ \mathbf{if}\;t\_2 \leq -1000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0.9999999999999998:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y)))
        (t_1 (* (sin y) z))
        (t_2 (- t_0 t_1))
        (t_3 (- (+ x 1.0) t_1)))
   (if (<= t_2 -1000.0) t_3 (if (<= t_2 0.9999999999999998) t_0 t_3))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double t_1 = sin(y) * z;
	double t_2 = t_0 - t_1;
	double t_3 = (x + 1.0) - t_1;
	double tmp;
	if (t_2 <= -1000.0) {
		tmp = t_3;
	} else if (t_2 <= 0.9999999999999998) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    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 = sin(y) * z
    t_2 = t_0 - t_1
    t_3 = (x + 1.0d0) - t_1
    if (t_2 <= (-1000.0d0)) then
        tmp = t_3
    else if (t_2 <= 0.9999999999999998d0) then
        tmp = t_0
    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 = Math.sin(y) * z;
	double t_2 = t_0 - t_1;
	double t_3 = (x + 1.0) - t_1;
	double tmp;
	if (t_2 <= -1000.0) {
		tmp = t_3;
	} else if (t_2 <= 0.9999999999999998) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.cos(y)
	t_1 = math.sin(y) * z
	t_2 = t_0 - t_1
	t_3 = (x + 1.0) - t_1
	tmp = 0
	if t_2 <= -1000.0:
		tmp = t_3
	elif t_2 <= 0.9999999999999998:
		tmp = t_0
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	t_1 = Float64(sin(y) * z)
	t_2 = Float64(t_0 - t_1)
	t_3 = Float64(Float64(x + 1.0) - t_1)
	tmp = 0.0
	if (t_2 <= -1000.0)
		tmp = t_3;
	elseif (t_2 <= 0.9999999999999998)
		tmp = t_0;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + cos(y);
	t_1 = sin(y) * z;
	t_2 = t_0 - t_1;
	t_3 = (x + 1.0) - t_1;
	tmp = 0.0;
	if (t_2 <= -1000.0)
		tmp = t_3;
	elseif (t_2 <= 0.9999999999999998)
		tmp = t_0;
	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[(N[Sin[y], $MachinePrecision] * z), $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, -1000.0], t$95$3, If[LessEqual[t$95$2, 0.9999999999999998], t$95$0, t$95$3]]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -1e3 or 0.99999999999999978 < (-.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. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 99.5

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

   5. Simplified 99.5%

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

   if -1e3 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.99999999999999978

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      3. cos-lowering-cos.f64 97.8

         \[\leadsto \color{blue}{\cos y} + x \]

   5. Simplified 97.8%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - \sin y \cdot z \leq -1000:\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \mathbf{elif}\;\left(x + \cos y\right) - \sin y \cdot z \leq 0.9999999999999998:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ t_1 := \sin y \cdot z\\ t_2 := t\_0 - t\_1\\ t_3 := x - t\_1\\ \mathbf{if}\;t\_2 \leq -1000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 400000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y)))
        (t_1 (* (sin y) z))
        (t_2 (- t_0 t_1))
        (t_3 (- x t_1)))
   (if (<= t_2 -1000.0) t_3 (if (<= t_2 400000.0) t_0 t_3))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double t_1 = sin(y) * z;
	double t_2 = t_0 - t_1;
	double t_3 = x - t_1;
	double tmp;
	if (t_2 <= -1000.0) {
		tmp = t_3;
	} else if (t_2 <= 400000.0) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    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 = sin(y) * z
    t_2 = t_0 - t_1
    t_3 = x - t_1
    if (t_2 <= (-1000.0d0)) then
        tmp = t_3
    else if (t_2 <= 400000.0d0) then
        tmp = t_0
    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 = Math.sin(y) * z;
	double t_2 = t_0 - t_1;
	double t_3 = x - t_1;
	double tmp;
	if (t_2 <= -1000.0) {
		tmp = t_3;
	} else if (t_2 <= 400000.0) {
		tmp = t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.cos(y)
	t_1 = math.sin(y) * z
	t_2 = t_0 - t_1
	t_3 = x - t_1
	tmp = 0
	if t_2 <= -1000.0:
		tmp = t_3
	elif t_2 <= 400000.0:
		tmp = t_0
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	t_1 = Float64(sin(y) * z)
	t_2 = Float64(t_0 - t_1)
	t_3 = Float64(x - t_1)
	tmp = 0.0
	if (t_2 <= -1000.0)
		tmp = t_3;
	elseif (t_2 <= 400000.0)
		tmp = t_0;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + cos(y);
	t_1 = sin(y) * z;
	t_2 = t_0 - t_1;
	t_3 = x - t_1;
	tmp = 0.0;
	if (t_2 <= -1000.0)
		tmp = t_3;
	elseif (t_2 <= 400000.0)
		tmp = t_0;
	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[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -1000.0], t$95$3, If[LessEqual[t$95$2, 400000.0], t$95$0, t$95$3]]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -1e3 or 4e5 < (-.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. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 98.8%

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

   if -1e3 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 4e5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      3. cos-lowering-cos.f64 98.1

         \[\leadsto \color{blue}{\cos y} + x \]

   5. Simplified 98.1%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - \sin y \cdot z \leq -1000:\\ \;\;\;\;x - \sin y \cdot z\\ \mathbf{elif}\;\left(x + \cos y\right) - \sin y \cdot z \leq 400000:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x - \sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \cos y\right) - \sin y \cdot z\\ \mathbf{if}\;t\_0 \leq -0.01:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_0 \leq 1000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x (cos y)) (* (sin y) z))))
   (if (<= t_0 -0.01) x (if (<= t_0 1000.0) 1.0 x))))

C

double code(double x, double y, double z) {
	double t_0 = (x + cos(y)) - (sin(y) * z);
	double tmp;
	if (t_0 <= -0.01) {
		tmp = x;
	} else if (t_0 <= 1000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    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)) - (sin(y) * z)
    if (t_0 <= (-0.01d0)) then
        tmp = x
    else if (t_0 <= 1000.0d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + Math.cos(y)) - (Math.sin(y) * z);
	double tmp;
	if (t_0 <= -0.01) {
		tmp = x;
	} else if (t_0 <= 1000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + math.cos(y)) - (math.sin(y) * z)
	tmp = 0
	if t_0 <= -0.01:
		tmp = x
	elif t_0 <= 1000.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + cos(y)) - Float64(sin(y) * z))
	tmp = 0.0
	if (t_0 <= -0.01)
		tmp = x;
	elseif (t_0 <= 1000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + cos(y)) - (sin(y) * z);
	tmp = 0.0;
	if (t_0 <= -0.01)
		tmp = x;
	elseif (t_0 <= 1000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.01], x, If[LessEqual[t$95$0, 1000.0], 1.0, x]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -0.0100000000000000002 or 1e3 < (-.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. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 56.4%

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

   if -0.0100000000000000002 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 1e3

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

      2. cos-lowering-cos.f64 N/A

         \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \cos y - \color{blue}{z \cdot \sin y} \]

      4. sin-lowering-sin.f64 97.4

         \[\leadsto \cos y - z \cdot \color{blue}{\sin y} \]

   5. Simplified 97.4%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1} \]
   7. Step-by-step derivation

   8. Simplified 75.9%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - \sin y \cdot z \leq -0.01:\\ \;\;\;\;x\\ \mathbf{elif}\;\left(x + \cos y\right) - \sin y \cdot z \leq 1000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + \cos y\right) - \sin y \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ 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)
    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(Float64(x + 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[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 9: 83.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot z\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+87}:\\ \;\;\;\;1 - t\_0\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+193}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;-t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) z)))
   (if (<= z -2.9e+87)
     (- 1.0 t_0)
     (if (<= z 1.6e+193) (+ x (cos y)) (- t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * z;
	double tmp;
	if (z <= -2.9e+87) {
		tmp = 1.0 - t_0;
	} else if (z <= 1.6e+193) {
		tmp = x + cos(y);
	} else {
		tmp = -t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    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 <= (-2.9d+87)) then
        tmp = 1.0d0 - t_0
    else if (z <= 1.6d+193) then
        tmp = x + cos(y)
    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 <= -2.9e+87) {
		tmp = 1.0 - t_0;
	} else if (z <= 1.6e+193) {
		tmp = x + Math.cos(y);
	} else {
		tmp = -t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * z
	tmp = 0
	if z <= -2.9e+87:
		tmp = 1.0 - t_0
	elif z <= 1.6e+193:
		tmp = x + math.cos(y)
	else:
		tmp = -t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * z)
	tmp = 0.0
	if (z <= -2.9e+87)
		tmp = Float64(1.0 - t_0);
	elseif (z <= 1.6e+193)
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(-t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * z;
	tmp = 0.0;
	if (z <= -2.9e+87)
		tmp = 1.0 - t_0;
	elseif (z <= 1.6e+193)
		tmp = x + cos(y);
	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, -2.9e+87], N[(1.0 - t$95$0), $MachinePrecision], If[LessEqual[z, 1.6e+193], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], (-t$95$0)]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999998e87

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

      2. cos-lowering-cos.f64 N/A

         \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \cos y - \color{blue}{z \cdot \sin y} \]

      4. sin-lowering-sin.f64 86.3

         \[\leadsto \cos y - z \cdot \color{blue}{\sin y} \]

   5. Simplified 86.3%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1} - z \cdot \sin y \]
   7. Step-by-step derivation

   8. Simplified 86.3%

      \[\leadsto \color{blue}{1} - z \cdot \sin y \]

   if -2.8999999999999998e87 < z < 1.60000000000000007e193

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      3. cos-lowering-cos.f64 92.9

         \[\leadsto \color{blue}{\cos y} + x \]

   5. Simplified 92.9%

      \[\leadsto \color{blue}{\cos y + x} \]

   if 1.60000000000000007e193 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \sin y\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\sin y \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\sin y \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\sin y \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      5. sin-lowering-sin.f64 N/A

         \[\leadsto \color{blue}{\sin y} \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      6. neg-lowering-neg.f64 69.7

         \[\leadsto \sin y \cdot \color{blue}{\left(-z\right)} \]

   5. Simplified 69.7%

      \[\leadsto \color{blue}{\sin y \cdot \left(-z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+87}:\\ \;\;\;\;1 - \sin y \cdot z\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+193}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;-\sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -\sin y \cdot z\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+193}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (sin y) z))))
   (if (<= z -6.2e+93) t_0 (if (<= z 2.1e+193) (+ x (cos y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -(sin(y) * z);
	double tmp;
	if (z <= -6.2e+93) {
		tmp = t_0;
	} else if (z <= 2.1e+193) {
		tmp = x + cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    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 <= (-6.2d+93)) then
        tmp = t_0
    else if (z <= 2.1d+193) then
        tmp = x + cos(y)
    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 <= -6.2e+93) {
		tmp = t_0;
	} else if (z <= 2.1e+193) {
		tmp = x + Math.cos(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -(math.sin(y) * z)
	tmp = 0
	if z <= -6.2e+93:
		tmp = t_0
	elif z <= 2.1e+193:
		tmp = x + math.cos(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(sin(y) * z))
	tmp = 0.0
	if (z <= -6.2e+93)
		tmp = t_0;
	elseif (z <= 2.1e+193)
		tmp = Float64(x + cos(y));
	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 <= -6.2e+93)
		tmp = t_0;
	elseif (z <= 2.1e+193)
		tmp = x + cos(y);
	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, -6.2e+93], t$95$0, If[LessEqual[z, 2.1e+193], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.20000000000000038e93 or 2.1e193 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \sin y\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\sin y \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\sin y \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\sin y \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      5. sin-lowering-sin.f64 N/A

         \[\leadsto \color{blue}{\sin y} \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      6. neg-lowering-neg.f64 75.8

         \[\leadsto \sin y \cdot \color{blue}{\left(-z\right)} \]

   5. Simplified 75.8%

      \[\leadsto \color{blue}{\sin y \cdot \left(-z\right)} \]

   if -6.20000000000000038e93 < z < 2.1e193

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      3. cos-lowering-cos.f64 92.9

         \[\leadsto \color{blue}{\cos y} + x \]

   5. Simplified 92.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+93}:\\ \;\;\;\;-\sin y \cdot z\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+193}:\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;-\sin y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-8}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-21}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))))
   (if (<= y -2.2e-8) t_0 (if (<= y 3.4e-21) (- x (fma y z -1.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double tmp;
	if (y <= -2.2e-8) {
		tmp = t_0;
	} else if (y <= 3.4e-21) {
		tmp = x - fma(y, z, -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	tmp = 0.0
	if (y <= -2.2e-8)
		tmp = t_0;
	elseif (y <= 3.4e-21)
		tmp = Float64(x - fma(y, z, -1.0));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e-8], t$95$0, If[LessEqual[y, 3.4e-21], N[(x - N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1999999999999998e-8 or 3.4e-21 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \color{blue}{\cos y + x} \]

      3. cos-lowering-cos.f64 69.0

         \[\leadsto \color{blue}{\cos y} + x \]

   5. Simplified 69.0%

      \[\leadsto \color{blue}{\cos y + x} \]

   if -2.1999999999999998e-8 < y < 3.4e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right)}\right) + 1 \]

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. --lowering--.f64 N/A

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

      6. sub-neg N/A

         \[\leadsto x - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(1\right)\right)\right)} \]

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 100.0

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(y, z, -1\right)} \]

   5. Simplified 100.0%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-8}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-21}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.8% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{+32}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(y, y \cdot -0.5 - z, x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.56e+32)
   (+ x 1.0)
   (if (<= y 1.02e+32) (fma y (- (* y -0.5) z) (+ x 1.0)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.56e+32) {
		tmp = x + 1.0;
	} else if (y <= 1.02e+32) {
		tmp = fma(y, ((y * -0.5) - z), (x + 1.0));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.56e+32)
		tmp = Float64(x + 1.0);
	elseif (y <= 1.02e+32)
		tmp = fma(y, Float64(Float64(y * -0.5) - z), Float64(x + 1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.56e+32], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 1.02e+32], N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision] + N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.56e32 or 1.0199999999999999e32 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. +-lowering-+.f64 40.5

         \[\leadsto \color{blue}{x + 1} \]

   5. Simplified 40.5%

      \[\leadsto \color{blue}{x + 1} \]

   if -1.56e32 < y < 1.0199999999999999e32

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(1 + x\right) + y \cdot \left(\frac{-1}{2} \cdot y - z\right)} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{y \cdot \left(\frac{-1}{2} \cdot y - z\right) + \left(1 + x\right)} \]

      3. accelerator-lowering-fma.f64 N/A

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

      4. --lowering--.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. +-commutative N/A

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

      8. +-lowering-+.f64 92.9

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

   5. Simplified 92.9%

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

Alternative 13: 69.8% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+55}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+55}:\\ \;\;\;\;x - \mathsf{fma}\left(y, z, -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.8e+55)
   (+ x 1.0)
   (if (<= y 4.4e+55) (- x (fma y z -1.0)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e+55) {
		tmp = x + 1.0;
	} else if (y <= 4.4e+55) {
		tmp = x - fma(y, z, -1.0);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.8e+55)
		tmp = Float64(x + 1.0);
	elseif (y <= 4.4e+55)
		tmp = Float64(x - fma(y, z, -1.0));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.8e+55], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 4.4e+55], N[(x - N[(y * z + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.7999999999999996e55 or 4.40000000000000021e55 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. +-lowering-+.f64 38.0

         \[\leadsto \color{blue}{x + 1} \]

   5. Simplified 38.0%

      \[\leadsto \color{blue}{x + 1} \]

   if -6.7999999999999996e55 < y < 4.40000000000000021e55

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

         \[\leadsto \left(x + \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right)}\right) + 1 \]

      3. unsub-neg N/A

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

      4. associate-+l- N/A

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

      5. --lowering--.f64 N/A

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

      6. sub-neg N/A

         \[\leadsto x - \color{blue}{\left(y \cdot z + \left(\mathsf{neg}\left(1\right)\right)\right)} \]

      7. metadata-eval N/A

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

      8. accelerator-lowering-fma.f64 90.8

         \[\leadsto x - \color{blue}{\mathsf{fma}\left(y, z, -1\right)} \]

   5. Simplified 90.8%

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

Alternative 14: 65.3% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-38}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.2e+36) x (if (<= x 1.75e-38) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.2e+36) {
		tmp = x;
	} else if (x <= 1.75e-38) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.2d+36)) then
        tmp = x
    else if (x <= 1.75d-38) then
        tmp = 1.0d0 - (y * 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 (x <= -5.2e+36) {
		tmp = x;
	} else if (x <= 1.75e-38) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.2e+36:
		tmp = x
	elif x <= 1.75e-38:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.2e+36)
		tmp = x;
	elseif (x <= 1.75e-38)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.2e+36)
		tmp = x;
	elseif (x <= 1.75e-38)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.2e+36], x, If[LessEqual[x, 1.75e-38], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.2000000000000003e36

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 91.6%

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

   if -5.2000000000000003e36 < x < 1.7500000000000001e-38

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

      2. cos-lowering-cos.f64 N/A

         \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \cos y - \color{blue}{z \cdot \sin y} \]

      4. sin-lowering-sin.f64 98.5

         \[\leadsto \cos y - z \cdot \color{blue}{\sin y} \]

   5. Simplified 98.5%

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + -1 \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(y \cdot z\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - y \cdot z} \]

      3. --lowering--.f64 N/A

         \[\leadsto \color{blue}{1 - y \cdot z} \]

      4. *-lowering-*.f64 51.6

         \[\leadsto 1 - \color{blue}{y \cdot z} \]

   8. Simplified 51.6%

      \[\leadsto \color{blue}{1 - y \cdot z} \]

   if 1.7500000000000001e-38 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. +-lowering-+.f64 81.9

         \[\leadsto \color{blue}{x + 1} \]

   5. Simplified 81.9%

      \[\leadsto \color{blue}{x + 1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 61.0% accurate, 15.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z -2e+135) (* y (- z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+135) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2d+135)) then
        tmp = y * -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 (z <= -2e+135) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e+135:
		tmp = y * -z
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e+135)
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2e+135)
		tmp = y * -z;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e+135], N[(y * (-z)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.99999999999999992e135

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z \cdot \sin y\right)} \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\color{blue}{\sin y \cdot z}\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \color{blue}{\sin y \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \color{blue}{\sin y \cdot \left(\mathsf{neg}\left(z\right)\right)} \]

      5. sin-lowering-sin.f64 N/A

         \[\leadsto \color{blue}{\sin y} \cdot \left(\mathsf{neg}\left(z\right)\right) \]

      6. neg-lowering-neg.f64 85.7

         \[\leadsto \sin y \cdot \color{blue}{\left(-z\right)} \]

   5. Simplified 85.7%

      \[\leadsto \color{blue}{\sin y \cdot \left(-z\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{y} \cdot \left(\mathsf{neg}\left(z\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 33.8%

      \[\leadsto \color{blue}{y} \cdot \left(-z\right) \]

   if -1.99999999999999992e135 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{x + 1} \]

      2. +-lowering-+.f64 69.3

         \[\leadsto \color{blue}{x + 1} \]

   5. Simplified 69.3%

      \[\leadsto \color{blue}{x + 1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 61.7% accurate, 53.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

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

Fortran

real(8) function code(x, y, z)
    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]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1 + x} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{x + 1} \]

   2. +-lowering-+.f64 62.4

      \[\leadsto \color{blue}{x + 1} \]

5. Simplified 62.4%

   \[\leadsto \color{blue}{x + 1} \]
6. Add Preprocessing

Alternative 17: 21.6% accurate, 212.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]
4. Step-by-step derivation

   1. --lowering--.f64 N/A

      \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

   2. cos-lowering-cos.f64 N/A

      \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \cos y - \color{blue}{z \cdot \sin y} \]

   4. sin-lowering-sin.f64 60.5

      \[\leadsto \cos y - z \cdot \color{blue}{\sin y} \]

5. Simplified 60.5%

   \[\leadsto \color{blue}{\cos y - z \cdot \sin y} \]

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1} \]
7. Step-by-step derivation

8. Simplified 23.8%

   \[\leadsto \color{blue}{1} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024204 
(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))))