Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3

Percentage Accurate: 88.7% → 99.6%

Time: 7.9s

Alternatives: 14

Speedup: 0.6×

• 20.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-16} \lor \neg \left(z \leq 5 \cdot 10^{-75}\right):\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.2e-16) (not (<= z 5e-75)))
   (* x (+ (/ (+ y 1.0) z) -1.0))
   (/ (+ x (* x y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e-16) || !(z <= 5e-75)) {
		tmp = x * (((y + 1.0) / z) + -1.0);
	} else {
		tmp = (x + (x * y)) / 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 ((z <= (-2.2d-16)) .or. (.not. (z <= 5d-75))) then
        tmp = x * (((y + 1.0d0) / z) + (-1.0d0))
    else
        tmp = (x + (x * y)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e-16) || !(z <= 5e-75)) {
		tmp = x * (((y + 1.0) / z) + -1.0);
	} else {
		tmp = (x + (x * y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.2e-16) or not (z <= 5e-75):
		tmp = x * (((y + 1.0) / z) + -1.0)
	else:
		tmp = (x + (x * y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.2e-16) || !(z <= 5e-75))
		tmp = Float64(x * Float64(Float64(Float64(y + 1.0) / z) + -1.0));
	else
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.2e-16) || ~((z <= 5e-75)))
		tmp = x * (((y + 1.0) / z) + -1.0);
	else
		tmp = (x + (x * y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e-16], N[Not[LessEqual[z, 5e-75]], $MachinePrecision]], N[(x * N[(N[(N[(y + 1.0), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e-16 or 4.99999999999999979e-75 < z

   1. Initial program 71.3%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   if -2.2e-16 < z < 4.99999999999999979e-75

   1. Initial program 99.9%

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

      1. distribute-lft-in 100.0%

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

      2. fma-define 100.0%

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

      3. *-rgt-identity 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-16} \lor \neg \left(z \leq 5 \cdot 10^{-75}\right):\\ \;\;\;\;x \cdot \left(\frac{y + 1}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 60.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+117}:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq -47000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-264}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+21}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= z -1.05e+117)
     (- x)
     (if (<= z -47000000000000.0)
       t_0
       (if (<= z 1.35e-264) (/ x z) (if (<= z 1.8e+21) t_0 (- x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -1.05e+117) {
		tmp = -x;
	} else if (z <= -47000000000000.0) {
		tmp = t_0;
	} else if (z <= 1.35e-264) {
		tmp = x / z;
	} else if (z <= 1.8e+21) {
		tmp = t_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 * (y / z)
    if (z <= (-1.05d+117)) then
        tmp = -x
    else if (z <= (-47000000000000.0d0)) then
        tmp = t_0
    else if (z <= 1.35d-264) then
        tmp = x / z
    else if (z <= 1.8d+21) then
        tmp = t_0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (z <= -1.05e+117) {
		tmp = -x;
	} else if (z <= -47000000000000.0) {
		tmp = t_0;
	} else if (z <= 1.35e-264) {
		tmp = x / z;
	} else if (z <= 1.8e+21) {
		tmp = t_0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if z <= -1.05e+117:
		tmp = -x
	elif z <= -47000000000000.0:
		tmp = t_0
	elif z <= 1.35e-264:
		tmp = x / z
	elif z <= 1.8e+21:
		tmp = t_0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (z <= -1.05e+117)
		tmp = Float64(-x);
	elseif (z <= -47000000000000.0)
		tmp = t_0;
	elseif (z <= 1.35e-264)
		tmp = Float64(x / z);
	elseif (z <= 1.8e+21)
		tmp = t_0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	tmp = 0.0;
	if (z <= -1.05e+117)
		tmp = -x;
	elseif (z <= -47000000000000.0)
		tmp = t_0;
	elseif (z <= 1.35e-264)
		tmp = x / z;
	elseif (z <= 1.8e+21)
		tmp = t_0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+117], (-x), If[LessEqual[z, -47000000000000.0], t$95$0, If[LessEqual[z, 1.35e-264], N[(x / z), $MachinePrecision], If[LessEqual[z, 1.8e+21], t$95$0, (-x)]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0500000000000001e117 or 1.8e21 < z

   1. Initial program 61.0%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 84.4%

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

      1. neg-mul-1 84.4%

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

   7. Simplified 84.4%

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

   if -1.0500000000000001e117 < z < -4.7e13 or 1.34999999999999997e-264 < z < 1.8e21

   1. Initial program 95.0%

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

      1. associate-/l* 93.0%

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

      2. +-commutative 93.0%

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

      3. associate-+r- 93.0%

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

      4. div-sub 93.0%

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

      5. *-inverses 93.0%

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

      6. sub-neg 93.0%

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

      7. +-commutative 93.0%

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

      8. metadata-eval 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in y around inf 61.4%

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

      1. associate-/l* 57.6%

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

   7. Simplified 57.6%

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

   if -4.7e13 < z < 1.34999999999999997e-264

   1. Initial program 100.0%

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

      1. associate-/l* 95.9%

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

      2. +-commutative 95.9%

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

      3. associate-+r- 95.9%

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

      4. div-sub 96.0%

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

      5. *-inverses 96.0%

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

      6. sub-neg 96.0%

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

      7. +-commutative 96.0%

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

      8. metadata-eval 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in y around 0 61.4%

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

      1. sub-neg 61.4%

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

      2. metadata-eval 61.4%

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

      3. distribute-rgt-in 61.4%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot x + -1 \cdot x} \]

      4. associate-*l/ 61.5%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{z}} + -1 \cdot x \]

      5. *-lft-identity 61.5%

         \[\leadsto \frac{\color{blue}{x}}{z} + -1 \cdot x \]

      6. neg-mul-1 61.5%

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

      7. unsub-neg 61.5%

         \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   7. Simplified 61.5%

      \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   8. Taylor expanded in z around 0 57.0%

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

Alternative 3: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.81 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + 1\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.81) (not (<= z 1.0)))
   (* x (+ -1.0 (/ y z)))
   (* (+ y 1.0) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.81) || !(z <= 1.0)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = (y + 1.0) * (x / 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 ((z <= (-0.81d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * ((-1.0d0) + (y / z))
    else
        tmp = (y + 1.0d0) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.81) || !(z <= 1.0)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = (y + 1.0) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.81) or not (z <= 1.0):
		tmp = x * (-1.0 + (y / z))
	else:
		tmp = (y + 1.0) * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.81) || !(z <= 1.0))
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	else
		tmp = Float64(Float64(y + 1.0) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.81) || ~((z <= 1.0)))
		tmp = x * (-1.0 + (y / z));
	else
		tmp = (y + 1.0) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.81], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + 1.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.81000000000000005 or 1 < z

   1. Initial program 68.0%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.2%

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

   if -0.81000000000000005 < z < 1

   1. Initial program 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. fma-define 99.9%

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

      3. *-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 98.4%

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

      1. *-un-lft-identity 98.4%

         \[\leadsto \frac{\color{blue}{1 \cdot x} + x \cdot y}{z} \]

      2. *-commutative 98.4%

         \[\leadsto \frac{1 \cdot x + \color{blue}{y \cdot x}}{z} \]

      3. distribute-rgt-out 98.4%

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

      4. +-commutative 98.4%

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

      5. associate-*l/ 98.3%

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

   7. Applied egg-rr 98.3%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.81 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + 1\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -23500000 \lor \neg \left(y \leq 0.0052\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -23500000.0) (not (<= y 0.0052)))
   (* x (+ -1.0 (/ y z)))
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -23500000.0) || !(y <= 0.0052)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = (x / z) - 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 <= (-23500000.0d0)) .or. (.not. (y <= 0.0052d0))) then
        tmp = x * ((-1.0d0) + (y / z))
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -23500000.0) || !(y <= 0.0052)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -23500000.0) or not (y <= 0.0052):
		tmp = x * (-1.0 + (y / z))
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -23500000.0) || !(y <= 0.0052))
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -23500000.0) || ~((y <= 0.0052)))
		tmp = x * (-1.0 + (y / z));
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -23500000.0], N[Not[LessEqual[y, 0.0052]], $MachinePrecision]], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.35e7 or 0.0051999999999999998 < y

   1. Initial program 85.8%

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

      1. associate-/l* 93.2%

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

      2. +-commutative 93.2%

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

      3. associate-+r- 93.2%

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

      4. div-sub 93.2%

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

      5. *-inverses 93.2%

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

      6. sub-neg 93.2%

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

      7. +-commutative 93.2%

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

      8. metadata-eval 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in y around inf 93.2%

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

   if -2.35e7 < y < 0.0051999999999999998

   1. Initial program 83.7%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 98.6%

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

      1. sub-neg 98.6%

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

      2. metadata-eval 98.6%

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

      3. distribute-rgt-in 98.6%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot x + -1 \cdot x} \]

      4. associate-*l/ 98.8%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{z}} + -1 \cdot x \]

      5. *-lft-identity 98.8%

         \[\leadsto \frac{\color{blue}{x}}{z} + -1 \cdot x \]

      6. neg-mul-1 98.8%

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

      7. unsub-neg 98.8%

         \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   7. Simplified 98.8%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -23500000 \lor \neg \left(y \leq 0.0052\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.95:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.95)
   (* x (+ -1.0 (/ y z)))
   (if (<= z 1.0) (/ (* x (+ y 1.0)) z) (- (/ x (/ z y)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.95) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 1.0) {
		tmp = (x * (y + 1.0)) / z;
	} else {
		tmp = (x / (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 (z <= (-0.95d0)) then
        tmp = x * ((-1.0d0) + (y / z))
    else if (z <= 1.0d0) then
        tmp = (x * (y + 1.0d0)) / z
    else
        tmp = (x / (z / y)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.95) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 1.0) {
		tmp = (x * (y + 1.0)) / z;
	} else {
		tmp = (x / (z / y)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.95:
		tmp = x * (-1.0 + (y / z))
	elif z <= 1.0:
		tmp = (x * (y + 1.0)) / z
	else:
		tmp = (x / (z / y)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.95)
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	elseif (z <= 1.0)
		tmp = Float64(Float64(x * Float64(y + 1.0)) / z);
	else
		tmp = Float64(Float64(x / Float64(z / y)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.95)
		tmp = x * (-1.0 + (y / z));
	elseif (z <= 1.0)
		tmp = (x * (y + 1.0)) / z;
	else
		tmp = (x / (z / y)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.95], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.94999999999999996

   1. Initial program 66.4%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 97.5%

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

   if -0.94999999999999996 < z < 1

   1. Initial program 99.9%

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

      1. associate-/l* 93.0%

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

      2. +-commutative 93.0%

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

      3. associate-+r- 93.0%

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

      4. div-sub 92.9%

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

      5. *-inverses 92.9%

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

      6. sub-neg 92.9%

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

      7. +-commutative 92.9%

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

      8. metadata-eval 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in z around 0 98.4%

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

   if 1 < z

   1. Initial program 69.6%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.7%

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

      1. distribute-rgt-in 98.8%

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

      2. neg-mul-1 98.8%

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

      3. unsub-neg 98.8%

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

      4. *-commutative 98.8%

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

   7. Applied egg-rr 98.8%

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

      1. clear-num 98.7%

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

      2. un-div-inv 98.8%

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

   9. Applied egg-rr 98.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.95:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.96:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(y + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.96)
   (* x (+ -1.0 (/ y z)))
   (if (<= z 1.0) (* (+ y 1.0) (/ x z)) (- (/ x (/ z y)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.96) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 1.0) {
		tmp = (y + 1.0) * (x / z);
	} else {
		tmp = (x / (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 (z <= (-0.96d0)) then
        tmp = x * ((-1.0d0) + (y / z))
    else if (z <= 1.0d0) then
        tmp = (y + 1.0d0) * (x / z)
    else
        tmp = (x / (z / y)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.96) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 1.0) {
		tmp = (y + 1.0) * (x / z);
	} else {
		tmp = (x / (z / y)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.96:
		tmp = x * (-1.0 + (y / z))
	elif z <= 1.0:
		tmp = (y + 1.0) * (x / z)
	else:
		tmp = (x / (z / y)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.96)
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	elseif (z <= 1.0)
		tmp = Float64(Float64(y + 1.0) * Float64(x / z));
	else
		tmp = Float64(Float64(x / Float64(z / y)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.96)
		tmp = x * (-1.0 + (y / z));
	elseif (z <= 1.0)
		tmp = (y + 1.0) * (x / z);
	else
		tmp = (x / (z / y)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.96], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(N[(y + 1.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.95999999999999996

   1. Initial program 66.4%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 97.5%

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

   if -0.95999999999999996 < z < 1

   1. Initial program 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. fma-define 99.9%

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

      3. *-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 98.4%

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

      1. *-un-lft-identity 98.4%

         \[\leadsto \frac{\color{blue}{1 \cdot x} + x \cdot y}{z} \]

      2. *-commutative 98.4%

         \[\leadsto \frac{1 \cdot x + \color{blue}{y \cdot x}}{z} \]

      3. distribute-rgt-out 98.4%

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

      4. +-commutative 98.4%

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

      5. associate-*l/ 98.3%

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

   7. Applied egg-rr 98.3%

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

   if 1 < z

   1. Initial program 69.6%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.7%

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

      1. distribute-rgt-in 98.8%

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

      2. neg-mul-1 98.8%

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

      3. unsub-neg 98.8%

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

      4. *-commutative 98.8%

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

   7. Applied egg-rr 98.8%

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

      1. clear-num 98.7%

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

      2. un-div-inv 98.8%

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

   9. Applied egg-rr 98.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.96:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(y + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.88:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(y + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.88)
   (* x (+ -1.0 (/ y z)))
   (if (<= z 1.0) (* (+ y 1.0) (/ x z)) (- (* x (/ y z)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.88) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 1.0) {
		tmp = (y + 1.0) * (x / z);
	} else {
		tmp = (x * (y / z)) - 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 (z <= (-0.88d0)) then
        tmp = x * ((-1.0d0) + (y / z))
    else if (z <= 1.0d0) then
        tmp = (y + 1.0d0) * (x / z)
    else
        tmp = (x * (y / z)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.88) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 1.0) {
		tmp = (y + 1.0) * (x / z);
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.88:
		tmp = x * (-1.0 + (y / z))
	elif z <= 1.0:
		tmp = (y + 1.0) * (x / z)
	else:
		tmp = (x * (y / z)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.88)
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	elseif (z <= 1.0)
		tmp = Float64(Float64(y + 1.0) * Float64(x / z));
	else
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.88)
		tmp = x * (-1.0 + (y / z));
	elseif (z <= 1.0)
		tmp = (y + 1.0) * (x / z);
	else
		tmp = (x * (y / z)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.88], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(N[(y + 1.0), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.880000000000000004

   1. Initial program 66.4%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 97.5%

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

   if -0.880000000000000004 < z < 1

   1. Initial program 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. fma-define 99.9%

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

      3. *-rgt-identity 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 98.4%

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

      1. *-un-lft-identity 98.4%

         \[\leadsto \frac{\color{blue}{1 \cdot x} + x \cdot y}{z} \]

      2. *-commutative 98.4%

         \[\leadsto \frac{1 \cdot x + \color{blue}{y \cdot x}}{z} \]

      3. distribute-rgt-out 98.4%

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

      4. +-commutative 98.4%

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

      5. associate-*l/ 98.3%

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

   7. Applied egg-rr 98.3%

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

   if 1 < z

   1. Initial program 69.6%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 98.7%

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

      1. distribute-rgt-in 98.8%

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

      2. neg-mul-1 98.8%

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

      3. unsub-neg 98.8%

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

      4. *-commutative 98.8%

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

   7. Applied egg-rr 98.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.88:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\left(y + 1\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+38} \lor \neg \left(y \leq 1.6 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7e+38) (not (<= y 1.6e+17))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e+38) || !(y <= 1.6e+17)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - 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 <= (-7d+38)) .or. (.not. (y <= 1.6d+17))) then
        tmp = y * (x / z)
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e+38) || !(y <= 1.6e+17)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7e+38) or not (y <= 1.6e+17):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7e+38) || !(y <= 1.6e+17))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7e+38) || ~((y <= 1.6e+17)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7e+38], N[Not[LessEqual[y, 1.6e+17]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.00000000000000003e38 or 1.6e17 < y

   1. Initial program 87.6%

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

      1. distribute-lft-in 87.6%

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

      2. fma-define 87.6%

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

      3. *-rgt-identity 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in z around 0 74.3%

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

      1. *-un-lft-identity 74.3%

         \[\leadsto \frac{\color{blue}{1 \cdot x} + x \cdot y}{z} \]

      2. *-commutative 74.3%

         \[\leadsto \frac{1 \cdot x + \color{blue}{y \cdot x}}{z} \]

      3. distribute-rgt-out 74.3%

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

      4. +-commutative 74.3%

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

      5. associate-*l/ 78.5%

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

   7. Applied egg-rr 78.5%

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

   8. Taylor expanded in y around inf 78.5%

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

   if -7.00000000000000003e38 < y < 1.6e17

   1. Initial program 82.0%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 97.2%

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

      1. sub-neg 97.2%

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

      2. metadata-eval 97.2%

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

      3. distribute-rgt-in 97.2%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot x + -1 \cdot x} \]

      4. associate-*l/ 97.3%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{z}} + -1 \cdot x \]

      5. *-lft-identity 97.3%

         \[\leadsto \frac{\color{blue}{x}}{z} + -1 \cdot x \]

      6. neg-mul-1 97.3%

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

      7. unsub-neg 97.3%

         \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   7. Simplified 97.3%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+38} \lor \neg \left(y \leq 1.6 \cdot 10^{+17}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+117} \lor \neg \left(z \leq 1.1 \cdot 10^{+20}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.05e+117) (not (<= z 1.1e+20))) (- x) (* y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e+117) || !(z <= 1.1e+20)) {
		tmp = -x;
	} else {
		tmp = y * (x / 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 ((z <= (-1.05d+117)) .or. (.not. (z <= 1.1d+20))) then
        tmp = -x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e+117) || !(z <= 1.1e+20)) {
		tmp = -x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.05e+117) or not (z <= 1.1e+20):
		tmp = -x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.05e+117) || !(z <= 1.1e+20))
		tmp = Float64(-x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.05e+117) || ~((z <= 1.1e+20)))
		tmp = -x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.05e+117], N[Not[LessEqual[z, 1.1e+20]], $MachinePrecision]], (-x), N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e117 or 1.1e20 < z

   1. Initial program 61.0%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-+r- 99.9%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 84.4%

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

      1. neg-mul-1 84.4%

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

   7. Simplified 84.4%

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

   if -1.0500000000000001e117 < z < 1.1e20

   1. Initial program 97.1%

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

      1. distribute-lft-in 97.1%

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

      2. fma-define 97.1%

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

      3. *-rgt-identity 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around 0 90.2%

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

      1. *-un-lft-identity 90.2%

         \[\leadsto \frac{\color{blue}{1 \cdot x} + x \cdot y}{z} \]

      2. *-commutative 90.2%

         \[\leadsto \frac{1 \cdot x + \color{blue}{y \cdot x}}{z} \]

      3. distribute-rgt-out 90.2%

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

      4. +-commutative 90.2%

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

      5. associate-*l/ 91.5%

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

   7. Applied egg-rr 91.5%

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

   8. Taylor expanded in y around inf 61.5%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+117} \lor \neg \left(z \leq 1.1 \cdot 10^{+20}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 9.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 9.2e-36) (/ (* x (+ (- y z) 1.0)) z) (- (/ x (/ z (+ y 1.0))) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 9.2e-36) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = (x / (z / (y + 1.0))) - 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 (x <= 9.2d-36) then
        tmp = (x * ((y - z) + 1.0d0)) / z
    else
        tmp = (x / (z / (y + 1.0d0))) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 9.2e-36) {
		tmp = (x * ((y - z) + 1.0)) / z;
	} else {
		tmp = (x / (z / (y + 1.0))) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 9.2e-36:
		tmp = (x * ((y - z) + 1.0)) / z
	else:
		tmp = (x / (z / (y + 1.0))) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 9.2e-36)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z);
	else
		tmp = Float64(Float64(x / Float64(z / Float64(y + 1.0))) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 9.2e-36)
		tmp = (x * ((y - z) + 1.0)) / z;
	else
		tmp = (x / (z / (y + 1.0))) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 9.2e-36], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / N[(z / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 9.19999999999999986e-36

   1. Initial program 91.0%

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

   if 9.19999999999999986e-36 < x

   1. Initial program 72.6%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.9%

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

      5. *-inverses 99.9%

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

      6. sub-neg 99.9%

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

      7. +-commutative 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 100.0%

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

      4. *-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 9.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + 1}} - x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 94.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y - z\right) + 1\\ \mathbf{if}\;x \leq 4.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot t\_0}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (- y z) 1.0)))
   (if (<= x 4.6e+36) (/ (* x t_0) z) (* t_0 (/ x z)))))

C

double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (x <= 4.6e+36) {
		tmp = (x * t_0) / z;
	} else {
		tmp = t_0 * (x / 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) + 1.0d0
    if (x <= 4.6d+36) then
        tmp = (x * t_0) / z
    else
        tmp = t_0 * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y - z) + 1.0;
	double tmp;
	if (x <= 4.6e+36) {
		tmp = (x * t_0) / z;
	} else {
		tmp = t_0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y - z) + 1.0
	tmp = 0
	if x <= 4.6e+36:
		tmp = (x * t_0) / z
	else:
		tmp = t_0 * (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y - z) + 1.0)
	tmp = 0.0
	if (x <= 4.6e+36)
		tmp = Float64(Float64(x * t_0) / z);
	else
		tmp = Float64(t_0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y - z) + 1.0;
	tmp = 0.0;
	if (x <= 4.6e+36)
		tmp = (x * t_0) / z;
	else
		tmp = t_0 * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x, 4.6e+36], N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], N[(t$95$0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < 4.59999999999999993e36

   1. Initial program 91.8%

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

   if 4.59999999999999993e36 < x

   1. Initial program 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 15.2\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 15.2))) (- x) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 15.2)) {
		tmp = -x;
	} else {
		tmp = x / 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 ((z <= (-1.0d0)) .or. (.not. (z <= 15.2d0))) then
        tmp = -x
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 15.2)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 15.2):
		tmp = -x
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 15.2))
		tmp = Float64(-x);
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 15.2)))
		tmp = -x;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 15.2]], $MachinePrecision]], (-x), N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 15.199999999999999 < z

   1. Initial program 67.8%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-+r- 99.8%

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

      4. div-sub 99.8%

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

      5. *-inverses 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 70.2%

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

      1. neg-mul-1 70.2%

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

   7. Simplified 70.2%

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

   if -1 < z < 15.199999999999999

   1. Initial program 99.9%

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

      1. associate-/l* 93.0%

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

      2. +-commutative 93.0%

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

      3. associate-+r- 93.0%

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

      4. div-sub 93.0%

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

      5. *-inverses 93.0%

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

      6. sub-neg 93.0%

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

      7. +-commutative 93.0%

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

      8. metadata-eval 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in y around 0 53.5%

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

      1. sub-neg 53.5%

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

      2. metadata-eval 53.5%

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

      3. distribute-rgt-in 53.5%

         \[\leadsto \color{blue}{\frac{1}{z} \cdot x + -1 \cdot x} \]

      4. associate-*l/ 53.6%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{z}} + -1 \cdot x \]

      5. *-lft-identity 53.6%

         \[\leadsto \frac{\color{blue}{x}}{z} + -1 \cdot x \]

      6. neg-mul-1 53.6%

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

      7. unsub-neg 53.6%

         \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   7. Simplified 53.6%

      \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   8. Taylor expanded in z around 0 52.1%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 15.2\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.5% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-x)

Derivation

1. Initial program 84.9%

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

   1. associate-/l* 96.2%

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

   2. +-commutative 96.2%

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

   3. associate-+r- 96.2%

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

   4. div-sub 96.2%

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

   5. *-inverses 96.2%

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

   6. sub-neg 96.2%

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

   7. +-commutative 96.2%

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

   8. metadata-eval 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in z around inf 34.6%

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

   1. neg-mul-1 34.6%

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

7. Simplified 34.6%

   \[\leadsto \color{blue}{-x} \]
8. Add Preprocessing

Alternative 14: 3.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 84.9%

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

   1. associate-/l* 96.2%

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

   2. +-commutative 96.2%

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

   3. associate-+r- 96.2%

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

   4. div-sub 96.2%

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

   5. *-inverses 96.2%

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

   6. sub-neg 96.2%

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

   7. +-commutative 96.2%

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

   8. metadata-eval 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in z around inf 34.6%

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

   1. neg-mul-1 34.6%

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

7. Simplified 34.6%

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

   1. neg-sub0 34.6%

      \[\leadsto \color{blue}{0 - x} \]

   2. sub-neg 34.6%

      \[\leadsto \color{blue}{0 + \left(-x\right)} \]

   3. add-sqr-sqrt 15.7%

      \[\leadsto 0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

   4. sqrt-unprod 16.3%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

   5. sqr-neg 16.3%

      \[\leadsto 0 + \sqrt{\color{blue}{x \cdot x}} \]

   6. sqrt-unprod 1.5%

      \[\leadsto 0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

   7. add-sqr-sqrt 2.9%

      \[\leadsto 0 + \color{blue}{x} \]

9. Applied egg-rr 2.9%

   \[\leadsto \color{blue}{0 + x} \]

10. Taylor expanded in x around 0 2.9%

    \[\leadsto \color{blue}{x} \]
11. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (+ 1.0 y) (/ x z)) x)))
   (if (< x -2.71483106713436e-162)
     t_0
     (if (< x 3.874108816439546e-197)
       (* (* x (+ (- y z) 1.0)) (/ 1.0 z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} 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 = ((1.0d0 + y) * (x / z)) - x
    if (x < (-2.71483106713436d-162)) then
        tmp = t_0
    else if (x < 3.874108816439546d-197) then
        tmp = (x * ((y - z) + 1.0d0)) * (1.0d0 / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((1.0 + y) * (x / z)) - x
	tmp = 0
	if x < -2.71483106713436e-162:
		tmp = t_0
	elif x < 3.874108816439546e-197:
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(1.0 + y) * Float64(x / z)) - x)
	tmp = 0.0
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) * Float64(1.0 / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((1.0 + y) * (x / z)) - x;
	tmp = 0.0;
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(1.0 + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[Less[x, -2.71483106713436e-162], t$95$0, If[Less[x, 3.874108816439546e-197], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024123 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -67870776678359/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (+ 1 y) (/ x z)) x) (if (< x 1937054408219773/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x))))

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