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

Percentage Accurate: 97.9% → 100.0%

Time: 6.5s

Alternatives: 7

Speedup: 1.3×

• 20.9% 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: 97.9% 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. distribute-lft-out-- 98.0%

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

   2. *-rgt-identity 98.0%

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

   3. cancel-sign-sub-inv 98.0%

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

   4. +-commutative 98.0%

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

   5. associate-+r+ 98.0%

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

   6. +-commutative 98.0%

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

   7. distribute-rgt-out 100.0%

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

   8. fma-def 100.0%

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

   9. +-commutative 100.0%

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

   10. 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. Final simplification 100.0%

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

Alternative 2: 60.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+196}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+118}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-73}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-110}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-7}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+52} \lor \neg \left(y \leq 1.25 \cdot 10^{+152}\right) \land y \leq 2.1 \cdot 10^{+235}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= y -1.2e+196)
     t_0
     (if (<= y -1.3e+118)
       (* y x)
       (if (<= y -2.2e+63)
         t_0
         (if (<= y -3.2e+43)
           (* y x)
           (if (<= y -1.0)
             t_0
             (if (<= y -8e-73)
               z
               (if (<= y -9.6e-110)
                 (* y x)
                 (if (<= y 9.5e-7)
                   z
                   (if (or (<= y 2.15e+52)
                           (and (not (<= y 1.25e+152)) (<= y 2.1e+235)))
                     (* y x)
                     t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (y <= -1.2e+196) {
		tmp = t_0;
	} else if (y <= -1.3e+118) {
		tmp = y * x;
	} else if (y <= -2.2e+63) {
		tmp = t_0;
	} else if (y <= -3.2e+43) {
		tmp = y * x;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -8e-73) {
		tmp = z;
	} else if (y <= -9.6e-110) {
		tmp = y * x;
	} else if (y <= 9.5e-7) {
		tmp = z;
	} else if ((y <= 2.15e+52) || (!(y <= 1.25e+152) && (y <= 2.1e+235))) {
		tmp = y * x;
	} 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 = y * -z
    if (y <= (-1.2d+196)) then
        tmp = t_0
    else if (y <= (-1.3d+118)) then
        tmp = y * x
    else if (y <= (-2.2d+63)) then
        tmp = t_0
    else if (y <= (-3.2d+43)) then
        tmp = y * x
    else if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= (-8d-73)) then
        tmp = z
    else if (y <= (-9.6d-110)) then
        tmp = y * x
    else if (y <= 9.5d-7) then
        tmp = z
    else if ((y <= 2.15d+52) .or. (.not. (y <= 1.25d+152)) .and. (y <= 2.1d+235)) then
        tmp = y * x
    else
        tmp = t_0
    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 <= -1.2e+196) {
		tmp = t_0;
	} else if (y <= -1.3e+118) {
		tmp = y * x;
	} else if (y <= -2.2e+63) {
		tmp = t_0;
	} else if (y <= -3.2e+43) {
		tmp = y * x;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -8e-73) {
		tmp = z;
	} else if (y <= -9.6e-110) {
		tmp = y * x;
	} else if (y <= 9.5e-7) {
		tmp = z;
	} else if ((y <= 2.15e+52) || (!(y <= 1.25e+152) && (y <= 2.1e+235))) {
		tmp = y * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if y <= -1.2e+196:
		tmp = t_0
	elif y <= -1.3e+118:
		tmp = y * x
	elif y <= -2.2e+63:
		tmp = t_0
	elif y <= -3.2e+43:
		tmp = y * x
	elif y <= -1.0:
		tmp = t_0
	elif y <= -8e-73:
		tmp = z
	elif y <= -9.6e-110:
		tmp = y * x
	elif y <= 9.5e-7:
		tmp = z
	elif (y <= 2.15e+52) or (not (y <= 1.25e+152) and (y <= 2.1e+235)):
		tmp = y * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	tmp = 0.0
	if (y <= -1.2e+196)
		tmp = t_0;
	elseif (y <= -1.3e+118)
		tmp = Float64(y * x);
	elseif (y <= -2.2e+63)
		tmp = t_0;
	elseif (y <= -3.2e+43)
		tmp = Float64(y * x);
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= -8e-73)
		tmp = z;
	elseif (y <= -9.6e-110)
		tmp = Float64(y * x);
	elseif (y <= 9.5e-7)
		tmp = z;
	elseif ((y <= 2.15e+52) || (!(y <= 1.25e+152) && (y <= 2.1e+235)))
		tmp = Float64(y * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	tmp = 0.0;
	if (y <= -1.2e+196)
		tmp = t_0;
	elseif (y <= -1.3e+118)
		tmp = y * x;
	elseif (y <= -2.2e+63)
		tmp = t_0;
	elseif (y <= -3.2e+43)
		tmp = y * x;
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= -8e-73)
		tmp = z;
	elseif (y <= -9.6e-110)
		tmp = y * x;
	elseif (y <= 9.5e-7)
		tmp = z;
	elseif ((y <= 2.15e+52) || (~((y <= 1.25e+152)) && (y <= 2.1e+235)))
		tmp = y * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[y, -1.2e+196], t$95$0, If[LessEqual[y, -1.3e+118], N[(y * x), $MachinePrecision], If[LessEqual[y, -2.2e+63], t$95$0, If[LessEqual[y, -3.2e+43], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, -8e-73], z, If[LessEqual[y, -9.6e-110], N[(y * x), $MachinePrecision], If[LessEqual[y, 9.5e-7], z, If[Or[LessEqual[y, 2.15e+52], And[N[Not[LessEqual[y, 1.25e+152]], $MachinePrecision], LessEqual[y, 2.1e+235]]], N[(y * x), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e196 or -1.30000000000000008e118 < y < -2.1999999999999999e63 or -3.20000000000000014e43 < y < -1 or 2.15e52 < y < 1.25e152 or 2.1000000000000001e235 < y

   1. Initial program 93.7%

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

   2. Taylor expanded in y around inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. sub-neg 99.6%

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

   4. Simplified 99.6%

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

   5. Taylor expanded in x around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. distribute-rgt-neg-out 74.0%

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

   7. Simplified 74.0%

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

   if -1.2e196 < y < -1.30000000000000008e118 or -2.1999999999999999e63 < y < -3.20000000000000014e43 or -7.99999999999999998e-73 < y < -9.60000000000000026e-110 or 9.5000000000000001e-7 < y < 2.15e52 or 1.25e152 < y < 2.1000000000000001e235

   1. Initial program 98.3%

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

   2. Taylor expanded in x around inf 78.4%

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

      1. *-commutative 78.4%

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

   4. Simplified 78.4%

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

   if -1 < y < -7.99999999999999998e-73 or -9.60000000000000026e-110 < y < 9.5000000000000001e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 70.1%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+196}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+118}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+43}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-73}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-110}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-7}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+52} \lor \neg \left(y \leq 1.25 \cdot 10^{+152}\right) \land y \leq 2.1 \cdot 10^{+235}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-11} \lor \neg \left(y \leq -7.4 \cdot 10^{-73}\right) \land \left(y \leq -1.16 \cdot 10^{-109} \lor \neg \left(y \leq 9 \cdot 10^{-7}\right)\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.4e-11)
         (and (not (<= y -7.4e-73)) (or (<= y -1.16e-109) (not (<= y 9e-7)))))
   (* y (- x z))
   z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.4e-11) || (!(y <= -7.4e-73) && ((y <= -1.16e-109) || !(y <= 9e-7)))) {
		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 <= (-8.4d-11)) .or. (.not. (y <= (-7.4d-73))) .and. (y <= (-1.16d-109)) .or. (.not. (y <= 9d-7))) 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 <= -8.4e-11) || (!(y <= -7.4e-73) && ((y <= -1.16e-109) || !(y <= 9e-7)))) {
		tmp = y * (x - z);
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.4e-11) or (not (y <= -7.4e-73) and ((y <= -1.16e-109) or not (y <= 9e-7))):
		tmp = y * (x - z)
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.4e-11) || (!(y <= -7.4e-73) && ((y <= -1.16e-109) || !(y <= 9e-7))))
		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 <= -8.4e-11) || (~((y <= -7.4e-73)) && ((y <= -1.16e-109) || ~((y <= 9e-7)))))
		tmp = y * (x - z);
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.4e-11], And[N[Not[LessEqual[y, -7.4e-73]], $MachinePrecision], Or[LessEqual[y, -1.16e-109], N[Not[LessEqual[y, 9e-7]], $MachinePrecision]]]], N[(y * N[(x - z), $MachinePrecision]), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if y < -8.3999999999999994e-11 or -7.4000000000000002e-73 < y < -1.1600000000000001e-109 or 8.99999999999999959e-7 < y

   1. Initial program 96.0%

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

   2. Taylor expanded in y around inf 96.8%

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

      1. mul-1-neg 96.8%

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

      2. sub-neg 96.8%

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

   4. Simplified 96.8%

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

   if -8.3999999999999994e-11 < y < -7.4000000000000002e-73 or -1.1600000000000001e-109 < y < 8.99999999999999959e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 71.9%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-11} \lor \neg \left(y \leq -7.4 \cdot 10^{-73}\right) \land \left(y \leq -1.16 \cdot 10^{-109} \lor \neg \left(y \leq 9 \cdot 10^{-7}\right)\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 4: 61.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00055:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-73}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-111}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.00055)
   (* y x)
   (if (<= y -7.4e-73)
     z
     (if (<= y -4e-111) (* y x) (if (<= y 3e-8) z (* y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.00055) {
		tmp = y * x;
	} else if (y <= -7.4e-73) {
		tmp = z;
	} else if (y <= -4e-111) {
		tmp = y * x;
	} else if (y <= 3e-8) {
		tmp = z;
	} else {
		tmp = 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 <= (-0.00055d0)) then
        tmp = y * x
    else if (y <= (-7.4d-73)) then
        tmp = z
    else if (y <= (-4d-111)) then
        tmp = y * x
    else if (y <= 3d-8) then
        tmp = z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.00055) {
		tmp = y * x;
	} else if (y <= -7.4e-73) {
		tmp = z;
	} else if (y <= -4e-111) {
		tmp = y * x;
	} else if (y <= 3e-8) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.00055:
		tmp = y * x
	elif y <= -7.4e-73:
		tmp = z
	elif y <= -4e-111:
		tmp = y * x
	elif y <= 3e-8:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.00055)
		tmp = Float64(y * x);
	elseif (y <= -7.4e-73)
		tmp = z;
	elseif (y <= -4e-111)
		tmp = Float64(y * x);
	elseif (y <= 3e-8)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.00055)
		tmp = y * x;
	elseif (y <= -7.4e-73)
		tmp = z;
	elseif (y <= -4e-111)
		tmp = y * x;
	elseif (y <= 3e-8)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.00055], N[(y * x), $MachinePrecision], If[LessEqual[y, -7.4e-73], z, If[LessEqual[y, -4e-111], N[(y * x), $MachinePrecision], If[LessEqual[y, 3e-8], z, N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000033e-4 or -7.4000000000000002e-73 < y < -4.00000000000000035e-111 or 2.99999999999999973e-8 < y

   1. Initial program 95.9%

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

   2. Taylor expanded in x around inf 54.6%

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

      1. *-commutative 54.6%

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

   4. Simplified 54.6%

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

   if -5.50000000000000033e-4 < y < -7.4000000000000002e-73 or -4.00000000000000035e-111 < y < 2.99999999999999973e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 71.1%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00055:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-73}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-111}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 5: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.85 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 2.85e-5))) (* y (- x z)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2.85e-5)) {
		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 <= 2.85d-5))) 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 <= 2.85e-5)) {
		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 <= 2.85e-5):
		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 <= 2.85e-5))
		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 <= 2.85e-5)))
		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, 2.85e-5]], $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 2.8500000000000002e-5 < y

   1. Initial program 95.5%

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

   2. Taylor expanded in y around inf 98.9%

      \[\leadsto \color{blue}{y \cdot \left(x + -1 \cdot z\right)} \]
   3. 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%

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

   4. Simplified 98.9%

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

   if -1 < y < 2.8500000000000002e-5

   1. Initial program 100.0%

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

      1. distribute-lft-out-- 100.0%

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

      2. *-rgt-identity 100.0%

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

      3. cancel-sign-sub-inv 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-rgt-out 100.0%

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

      8. fma-def 100.0%

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

      9. +-commutative 100.0%

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

      10. 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. Step-by-step derivation

      1. fma-udef 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 98.6%

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

      1. *-commutative 98.6%

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

   8. Simplified 98.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.85 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

Alternative 6: 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. distribute-lft-out-- 98.0%

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

   2. *-rgt-identity 98.0%

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

   3. cancel-sign-sub-inv 98.0%

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

   4. +-commutative 98.0%

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

   5. associate-+r+ 98.0%

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

   6. +-commutative 98.0%

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

   7. distribute-rgt-out 100.0%

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

   8. fma-def 100.0%

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

   9. +-commutative 100.0%

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

   10. 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. Step-by-step derivation

   1. fma-udef 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 7: 36.8% 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. Taylor expanded in y around 0 38.8%

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

3. Final simplification 38.8%

   \[\leadsto z \]

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 2023271 
(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))))