Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3

Percentage Accurate: 97.7% → 100.0%

Time: 4.8s

Alternatives: 8

Speedup: 1.3×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot y + z \cdot \left(1 - y\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - 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 * y) + (z * (1.0d0 - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y + z \cdot \left(1 - y\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - 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 * y) + (z * (1.0d0 - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (fma y (- x z) z))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. sub-neg 98.0%

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

   2. +-commutative 98.0%

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

   3. distribute-rgt-in 98.0%

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

   4. *-lft-identity 98.0%

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

   5. associate-+r+ 98.0%

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

   6. +-commutative 98.0%

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

   7. distribute-lft-neg-out 98.0%

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

   8. distribute-rgt-neg-out 98.0%

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

   9. *-commutative 98.0%

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

   10. distribute-lft-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. unsub-neg 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, x - z, z\right) \]
6. Add Preprocessing

Alternative 2: 61.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+194}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{+102}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-9} \lor \neg \left(y \leq 3.4 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= y -1.8e+194)
     t_0
     (if (<= y -9.8e+102)
       (* y x)
       (if (<= y -1.12e+63)
         t_0
         (if (or (<= y -8.5e-9) (not (<= y 3.4e-8))) (* y x) z))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (y <= -1.8e+194) {
		tmp = t_0;
	} else if (y <= -9.8e+102) {
		tmp = y * x;
	} else if (y <= -1.12e+63) {
		tmp = t_0;
	} else if ((y <= -8.5e-9) || !(y <= 3.4e-8)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	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 = y * -z
    if (y <= (-1.8d+194)) then
        tmp = t_0
    else if (y <= (-9.8d+102)) then
        tmp = y * x
    else if (y <= (-1.12d+63)) then
        tmp = t_0
    else if ((y <= (-8.5d-9)) .or. (.not. (y <= 3.4d-8))) then
        tmp = y * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (y <= -1.8e+194) {
		tmp = t_0;
	} else if (y <= -9.8e+102) {
		tmp = y * x;
	} else if (y <= -1.12e+63) {
		tmp = t_0;
	} else if ((y <= -8.5e-9) || !(y <= 3.4e-8)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if y <= -1.8e+194:
		tmp = t_0
	elif y <= -9.8e+102:
		tmp = y * x
	elif y <= -1.12e+63:
		tmp = t_0
	elif (y <= -8.5e-9) or not (y <= 3.4e-8):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -1.8e+194)
		tmp = t_0;
	elseif (y <= -9.8e+102)
		tmp = Float64(y * x);
	elseif (y <= -1.12e+63)
		tmp = t_0;
	elseif ((y <= -8.5e-9) || !(y <= 3.4e-8))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	tmp = 0.0;
	if (y <= -1.8e+194)
		tmp = t_0;
	elseif (y <= -9.8e+102)
		tmp = y * x;
	elseif (y <= -1.12e+63)
		tmp = t_0;
	elseif ((y <= -8.5e-9) || ~((y <= 3.4e-8)))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -1.8e+194], t$95$0, If[LessEqual[y, -9.8e+102], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.12e+63], t$95$0, If[Or[LessEqual[y, -8.5e-9], N[Not[LessEqual[y, 3.4e-8]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e194 or -9.80000000000000089e102 < y < -1.12000000000000006e63

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. sub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 69.2%

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

      1. associate-*r* 69.2%

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

      2. neg-mul-1 69.2%

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

      3. *-commutative 69.2%

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

   8. Simplified 69.2%

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

   if -1.8e194 < y < -9.80000000000000089e102 or -1.12000000000000006e63 < y < -8.5e-9 or 3.4e-8 < y

   1. Initial program 95.3%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.3%

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

      1. *-commutative 56.3%

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

   5. Simplified 56.3%

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

   if -8.5e-9 < y < 3.4e-8

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.5%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{+102}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-9} \lor \neg \left(y \leq 3.4 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-9} \lor \neg \left(y \leq -1.9 \cdot 10^{-62}\right) \land \left(y \leq -1.86 \cdot 10^{-202} \lor \neg \left(y \leq 4 \cdot 10^{-6}\right)\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1e-9)
         (and (not (<= y -1.9e-62)) (or (<= y -1.86e-202) (not (<= y 4e-6)))))
   (* y (- x z))
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e-9) || (!(y <= -1.9e-62) && ((y <= -1.86e-202) || !(y <= 4e-6)))) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	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 ((y <= (-3.1d-9)) .or. (.not. (y <= (-1.9d-62))) .and. (y <= (-1.86d-202)) .or. (.not. (y <= 4d-6))) then
        tmp = y * (x - z)
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e-9) || (!(y <= -1.9e-62) && ((y <= -1.86e-202) || !(y <= 4e-6)))) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.1e-9) or (not (y <= -1.9e-62) and ((y <= -1.86e-202) or not (y <= 4e-6))):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.1e-9) || (!(y <= -1.9e-62) && ((y <= -1.86e-202) || !(y <= 4e-6))))
		tmp = Float64(y * Float64(x - z));
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.1e-9) || (~((y <= -1.9e-62)) && ((y <= -1.86e-202) || ~((y <= 4e-6)))))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.1e-9], And[N[Not[LessEqual[y, -1.9e-62]], $MachinePrecision], Or[LessEqual[y, -1.86e-202], N[Not[LessEqual[y, 4e-6]], $MachinePrecision]]]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000005e-9 or -1.90000000000000003e-62 < y < -1.85999999999999998e-202 or 3.99999999999999982e-6 < y

   1. Initial program 97.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 92.8%

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

      1. mul-1-neg 92.8%

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

      2. sub-neg 92.8%

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

   5. Simplified 92.8%

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

   if -3.10000000000000005e-9 < y < -1.90000000000000003e-62 or -1.85999999999999998e-202 < y < 3.99999999999999982e-6

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 87.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-9} \lor \neg \left(y \leq -1.9 \cdot 10^{-62}\right) \land \left(y \leq -1.86 \cdot 10^{-202} \lor \neg \left(y \leq 4 \cdot 10^{-6}\right)\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-6} \lor \neg \left(y \leq -7.2 \cdot 10^{-65}\right) \land \left(y \leq -1.86 \cdot 10^{-202} \lor \neg \left(y \leq 0.78\right)\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e-6)
         (and (not (<= y -7.2e-65)) (or (<= y -1.86e-202) (not (<= y 0.78)))))
   (* y (- x z))
   (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e-6) || (!(y <= -7.2e-65) && ((y <= -1.86e-202) || !(y <= 0.78)))) {
		tmp = y * (x - z);
	} else {
		tmp = z * (1.0 - y);
	}
	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 ((y <= (-6.5d-6)) .or. (.not. (y <= (-7.2d-65))) .and. (y <= (-1.86d-202)) .or. (.not. (y <= 0.78d0))) then
        tmp = y * (x - z)
    else
        tmp = z * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e-6) || (!(y <= -7.2e-65) && ((y <= -1.86e-202) || !(y <= 0.78)))) {
		tmp = y * (x - z);
	} else {
		tmp = z * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e-6) or (not (y <= -7.2e-65) and ((y <= -1.86e-202) or not (y <= 0.78))):
		tmp = y * (x - z)
	else:
		tmp = z * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e-6) || (!(y <= -7.2e-65) && ((y <= -1.86e-202) || !(y <= 0.78))))
		tmp = Float64(y * Float64(x - z));
	else
		tmp = Float64(z * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e-6) || (~((y <= -7.2e-65)) && ((y <= -1.86e-202) || ~((y <= 0.78)))))
		tmp = y * (x - z);
	else
		tmp = z * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e-6], And[N[Not[LessEqual[y, -7.2e-65]], $MachinePrecision], Or[LessEqual[y, -1.86e-202], N[Not[LessEqual[y, 0.78]], $MachinePrecision]]]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999996e-6 or -7.1999999999999996e-65 < y < -1.85999999999999998e-202 or 0.78000000000000003 < y

   1. Initial program 97.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 92.8%

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

      1. mul-1-neg 92.8%

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

      2. sub-neg 92.8%

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

   5. Simplified 92.8%

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

   if -6.4999999999999996e-6 < y < -7.1999999999999996e-65 or -1.85999999999999998e-202 < y < 0.78000000000000003

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-6} \lor \neg \left(y \leq -7.2 \cdot 10^{-65}\right) \land \left(y \leq -1.86 \cdot 10^{-202} \lor \neg \left(y \leq 0.78\right)\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = y * (x - z);
	} else {
		tmp = z + (y * 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) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * (x - z)
    else
        tmp = z + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = y * (x - z);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.0):
		tmp = y * (x - z)
	else:
		tmp = z + (y * x)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 96.4%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.9%

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

      1. mul-1-neg 98.9%

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

      2. sub-neg 98.9%

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

   5. Simplified 98.9%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-out-- 100.0%

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

      3. *-rgt-identity 100.0%

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

      4. associate-+l- 100.0%

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

      5. distribute-rgt-out-- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{z - y \cdot \left(z - x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.0%

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

      1. mul-1-neg 99.0%

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

      2. distribute-lft-neg-out 99.0%

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

      3. *-commutative 99.0%

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

   7. Simplified 99.0%

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

      1. sub-neg 99.0%

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

      2. +-commutative 99.0%

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

      3. distribute-rgt-neg-out 99.0%

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

      4. remove-double-neg 99.0%

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

   9. Applied egg-rr 99.0%

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

4. Final simplification 98.9%

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

Alternative 6: 61.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-7} \lor \neg \left(y \leq 0.00045\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.5e-7) (not (<= y 0.00045))) (* y x) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e-7) || !(y <= 0.00045)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	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 ((y <= (-7.5d-7)) .or. (.not. (y <= 0.00045d0))) then
        tmp = y * x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.5e-7) || !(y <= 0.00045)) {
		tmp = y * x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.5e-7) or not (y <= 0.00045):
		tmp = y * x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.5e-7) || !(y <= 0.00045))
		tmp = Float64(y * x);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.5e-7) || ~((y <= 0.00045)))
		tmp = y * x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.5e-7], N[Not[LessEqual[y, 0.00045]], $MachinePrecision]], N[(y * x), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -7.5000000000000002e-7 or 4.4999999999999999e-4 < y

   1. Initial program 96.4%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 51.0%

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

      1. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   if -7.5000000000000002e-7 < y < 4.4999999999999999e-4

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.5%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-7} \lor \neg \left(y \leq 0.00045\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. +-commutative 98.0%

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

   2. distribute-lft-out-- 98.0%

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

   3. *-rgt-identity 98.0%

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

   4. associate-+l- 98.0%

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

   5. distribute-rgt-out-- 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{z - y \cdot \left(z - x\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 8: 35.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Derivation

1. Initial program 98.0%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0 36.8%

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

4. Final simplification 36.8%

   \[\leadsto z \]
5. Add Preprocessing

Developer target: 100.0% accurate, 1.3× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- z (* (- z x) y)))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (- z (* (- z x) y))

  (+ (* x y) (* z (- 1.0 y))))