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

Percentage Accurate: 87.6% → 99.9%

Time: 7.1s

Alternatives: 15

Speedup: 0.8×

• 20.2% 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: 87.6% 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: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;z \leq 82000000000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e+26)
   (- (* x (/ y z)) x)
   (if (<= z 82000000000000.0)
     (* (/ x z) (+ 1.0 (- y z)))
     (- (/ x (/ z y)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+26) {
		tmp = (x * (y / z)) - x;
	} else if (z <= 82000000000000.0) {
		tmp = (x / z) * (1.0 + (y - 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 <= (-2d+26)) then
        tmp = (x * (y / z)) - x
    else if (z <= 82000000000000.0d0) then
        tmp = (x / z) * (1.0d0 + (y - 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 <= -2e+26) {
		tmp = (x * (y / z)) - x;
	} else if (z <= 82000000000000.0) {
		tmp = (x / z) * (1.0 + (y - z));
	} else {
		tmp = (x / (z / y)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e+26:
		tmp = (x * (y / z)) - x
	elif z <= 82000000000000.0:
		tmp = (x / z) * (1.0 + (y - z))
	else:
		tmp = (x / (z / y)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e+26)
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	elseif (z <= 82000000000000.0)
		tmp = Float64(Float64(x / z) * Float64(1.0 + Float64(y - 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 <= -2e+26)
		tmp = (x * (y / z)) - x;
	elseif (z <= 82000000000000.0)
		tmp = (x / z) * (1.0 + (y - z));
	else
		tmp = (x / (z / y)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e+26], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[z, 82000000000000.0], N[(N[(x / z), $MachinePrecision] * N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0000000000000001e26

   1. Initial program 69.2%

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

   2. Taylor expanded in x around 0 69.2%

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

      1. associate--l+ 69.2%

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

      2. +-commutative 69.2%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

      6. div-sub 99.9%

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

      7. sub-neg 99.9%

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

      8. *-inverses 99.9%

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

      9. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

      1. distribute-rgt-in 99.9%

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

      2. div-inv 99.9%

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

      3. associate-*l* 97.1%

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

      4. associate-/r/ 97.1%

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

      5. clear-num 97.1%

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

      6. neg-mul-1 97.1%

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

   6. Applied egg-rr 97.1%

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

   7. Taylor expanded in y around inf 85.1%

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

      1. associate-/l* 99.9%

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

   9. Simplified 99.9%

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

       1. unsub-neg 99.9%

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

       2. div-inv 99.9%

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

       3. clear-num 99.9%

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

   11. Applied egg-rr 99.9%

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

   if -2.0000000000000001e26 < z < 8.2e13

   1. Initial program 99.8%

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

      1. associate-/l* 93.8%

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

      2. associate-/r/ 99.8%

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

   3. Applied egg-rr 99.8%

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

   if 8.2e13 < z

   1. Initial program 72.5%

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

   2. Taylor expanded in x around 0 72.5%

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

      1. associate--l+ 72.5%

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

      2. +-commutative 72.5%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate--l+ 99.8%

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

      6. div-sub 99.8%

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

      7. sub-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

      1. distribute-rgt-in 99.8%

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

      2. div-inv 99.8%

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

      3. associate-*l* 92.8%

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

      4. associate-/r/ 92.9%

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

      5. clear-num 92.9%

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

      6. neg-mul-1 92.9%

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

   6. Applied egg-rr 92.9%

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

   7. Taylor expanded in y around inf 89.6%

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

      1. associate-/l* 99.9%

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

   9. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;z \leq 82000000000000:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + \left(y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \]

Alternative 2: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-15} \lor \neg \left(z \leq 1.1 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(\frac{1 + y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.1e-15) (not (<= z 1.1e-16)))
   (* x (+ (/ (+ 1.0 y) z) -1.0))
   (/ (+ x (* x y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.1e-15) || !(z <= 1.1e-16)) {
		tmp = x * (((1.0 + y) / 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 <= (-2.1d-15)) .or. (.not. (z <= 1.1d-16))) then
        tmp = x * (((1.0d0 + y) / 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 <= -2.1e-15) || !(z <= 1.1e-16)) {
		tmp = x * (((1.0 + y) / z) + -1.0);
	} else {
		tmp = (x + (x * y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.1e-15) or not (z <= 1.1e-16):
		tmp = x * (((1.0 + y) / z) + -1.0)
	else:
		tmp = (x + (x * y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.1e-15) || !(z <= 1.1e-16))
		tmp = Float64(x * Float64(Float64(Float64(1.0 + y) / 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 <= -2.1e-15) || ~((z <= 1.1e-16)))
		tmp = x * (((1.0 + y) / z) + -1.0);
	else
		tmp = (x + (x * y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.1e-15], N[Not[LessEqual[z, 1.1e-16]], $MachinePrecision]], N[(x * N[(N[(N[(1.0 + y), $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 < -2.09999999999999981e-15 or 1.1e-16 < z

   1. Initial program 75.1%

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

   2. Taylor expanded in x around 0 75.1%

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

      1. associate--l+ 75.1%

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

      2. +-commutative 75.1%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate--l+ 99.8%

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

      6. div-sub 99.8%

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

      7. sub-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   if -2.09999999999999981e-15 < z < 1.1e-16

   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-def 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. Taylor expanded in z around 0 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-15} \lor \neg \left(z \leq 1.1 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(\frac{1 + y}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \]

Alternative 3: 97.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{-199}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(1 + y\right)}} - x\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 7e-199)
   (- (/ 1.0 (/ z (* x (+ 1.0 y)))) x)
   (- (* (+ 1.0 y) (/ x z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 7e-199) {
		tmp = (1.0 / (z / (x * (1.0 + y)))) - x;
	} else {
		tmp = ((1.0 + y) * (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 (x <= 7d-199) then
        tmp = (1.0d0 / (z / (x * (1.0d0 + y)))) - x
    else
        tmp = ((1.0d0 + y) * (x / z)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 7e-199) {
		tmp = (1.0 / (z / (x * (1.0 + y)))) - x;
	} else {
		tmp = ((1.0 + y) * (x / z)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 7e-199:
		tmp = (1.0 / (z / (x * (1.0 + y)))) - x
	else:
		tmp = ((1.0 + y) * (x / z)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 7e-199)
		tmp = Float64(Float64(1.0 / Float64(z / Float64(x * Float64(1.0 + y)))) - x);
	else
		tmp = Float64(Float64(Float64(1.0 + y) * Float64(x / z)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 7e-199)
		tmp = (1.0 / (z / (x * (1.0 + y)))) - x;
	else
		tmp = ((1.0 + y) * (x / z)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 7e-199], N[(N[(1.0 / N[(z / N[(x * N[(1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], N[(N[(N[(1.0 + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.9999999999999998e-199

   1. Initial program 91.4%

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

   2. Taylor expanded in x around 0 91.4%

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

      1. associate--l+ 91.4%

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

      2. +-commutative 91.4%

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

      3. associate-*r/ 94.8%

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

      4. +-commutative 94.8%

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

      5. associate--l+ 94.8%

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

      6. div-sub 94.9%

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

      7. sub-neg 94.9%

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

      8. *-inverses 94.9%

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

      9. metadata-eval 94.9%

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

   4. Simplified 94.9%

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

      1. distribute-rgt-in 94.9%

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

      2. div-inv 94.9%

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

      3. associate-*l* 96.2%

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

      4. associate-/r/ 96.3%

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

      5. clear-num 96.4%

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

      6. neg-mul-1 96.4%

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

   6. Applied egg-rr 96.4%

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

      1. associate-*r/ 95.6%

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

      2. clear-num 95.5%

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

   8. Applied egg-rr 95.5%

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

   if 6.9999999999999998e-199 < x

   1. Initial program 80.0%

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

   2. Taylor expanded in x around 0 80.0%

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

      1. associate--l+ 80.0%

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

      2. +-commutative 80.0%

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

      3. associate-*r/ 98.0%

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

      4. +-commutative 98.0%

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

      5. associate--l+ 98.0%

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

      6. div-sub 98.0%

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

      7. sub-neg 98.0%

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

      8. *-inverses 98.0%

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

      9. metadata-eval 98.0%

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

   4. Simplified 98.0%

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

      1. distribute-rgt-in 98.0%

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

      2. div-inv 97.9%

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

      3. associate-*l* 99.8%

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

      4. associate-/r/ 99.8%

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

      5. clear-num 99.9%

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

      6. neg-mul-1 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7 \cdot 10^{-199}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot \left(1 + y\right)}} - x\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array} \]

Alternative 4: 64.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.49:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.49)
   (- x)
   (if (<= z 8.2e-169)
     (/ x z)
     (if (<= z 2.6e-123) (* y (/ x z)) (if (<= z 1.0) (/ x z) (- x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.49) {
		tmp = -x;
	} else if (z <= 8.2e-169) {
		tmp = x / z;
	} else if (z <= 2.6e-123) {
		tmp = y * (x / z);
	} else if (z <= 1.0) {
		tmp = x / z;
	} 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) :: tmp
    if (z <= (-0.49d0)) then
        tmp = -x
    else if (z <= 8.2d-169) then
        tmp = x / z
    else if (z <= 2.6d-123) then
        tmp = y * (x / z)
    else if (z <= 1.0d0) then
        tmp = x / z
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.49) {
		tmp = -x;
	} else if (z <= 8.2e-169) {
		tmp = x / z;
	} else if (z <= 2.6e-123) {
		tmp = y * (x / z);
	} else if (z <= 1.0) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.49:
		tmp = -x
	elif z <= 8.2e-169:
		tmp = x / z
	elif z <= 2.6e-123:
		tmp = y * (x / z)
	elif z <= 1.0:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.49)
		tmp = Float64(-x);
	elseif (z <= 8.2e-169)
		tmp = Float64(x / z);
	elseif (z <= 2.6e-123)
		tmp = Float64(y * Float64(x / z));
	elseif (z <= 1.0)
		tmp = Float64(x / z);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.49)
		tmp = -x;
	elseif (z <= 8.2e-169)
		tmp = x / z;
	elseif (z <= 2.6e-123)
		tmp = y * (x / z);
	elseif (z <= 1.0)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.49], (-x), If[LessEqual[z, 8.2e-169], N[(x / z), $MachinePrecision], If[LessEqual[z, 2.6e-123], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x / z), $MachinePrecision], (-x)]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.48999999999999999 or 1 < z

   1. Initial program 72.9%

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

   2. Taylor expanded in z around inf 72.0%

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

      1. mul-1-neg 72.0%

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

   4. Simplified 72.0%

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

   if -0.48999999999999999 < z < 8.1999999999999996e-169 or 2.59999999999999995e-123 < z < 1

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 66.5%

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

      1. associate-/l* 66.5%

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

   4. Simplified 66.5%

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

   5. Taylor expanded in z around 0 63.7%

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

   if 8.1999999999999996e-169 < z < 2.59999999999999995e-123

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 82.2%

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

      1. associate-/l* 82.1%

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

      2. associate-/r/ 90.7%

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

   4. Simplified 90.7%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.49:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 5: 94.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		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 <= -1.0) || ~((y <= 1.0)))
		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, -1.0], N[Not[LessEqual[y, 1.0]], $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 < -1 or 1 < y

   1. Initial program 84.1%

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

   2. Taylor expanded in x around 0 84.1%

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

      1. associate--l+ 84.1%

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

      2. +-commutative 84.1%

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

      3. associate-*r/ 91.4%

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

      4. +-commutative 91.4%

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

      5. associate--l+ 91.4%

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

      6. div-sub 91.4%

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

      7. sub-neg 91.4%

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

      8. *-inverses 91.4%

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

      9. metadata-eval 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in y around inf 90.1%

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

   if -1 < y < 1

   1. Initial program 89.4%

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

   2. Taylor expanded in x around 0 89.4%

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

      1. associate--l+ 89.4%

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

      2. +-commutative 89.4%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate--l+ 99.8%

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

      6. div-sub 99.8%

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

      7. sub-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around 0 98.9%

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

      1. sub-neg 98.9%

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

      2. metadata-eval 98.9%

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

      3. distribute-rgt-in 98.9%

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

      4. associate-*l/ 99.1%

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

      5. *-lft-identity 99.1%

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

      6. neg-mul-1 99.1%

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

      7. unsub-neg 99.1%

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

   7. Simplified 99.1%

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

4. Final simplification 95.1%

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

Alternative 6: 98.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 72.7%

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

   2. Taylor expanded in x around 0 72.7%

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

      1. associate--l+ 72.7%

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

      2. +-commutative 72.7%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate--l+ 99.8%

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

      6. div-sub 99.8%

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

      7. sub-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.1%

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

   if -1 < z < 1

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-*r/ 92.7%

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

      4. +-commutative 92.7%

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

      5. associate--l+ 92.7%

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

      6. div-sub 92.7%

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

      7. sub-neg 92.7%

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

      8. *-inverses 92.7%

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

      9. metadata-eval 92.7%

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

   4. Simplified 92.7%

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

   5. Taylor expanded in z around 0 97.3%

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

      1. *-commutative 97.3%

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

      2. associate-*r/ 97.3%

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

   7. Simplified 97.3%

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

4. Final simplification 98.1%

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

Alternative 7: 98.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if z < -0.94999999999999996

   1. Initial program 72.9%

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

   2. Taylor expanded in x around 0 72.9%

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

      1. associate--l+ 72.9%

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

      2. +-commutative 72.9%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate--l+ 99.8%

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

      6. div-sub 99.9%

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

      7. sub-neg 99.9%

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

      8. *-inverses 99.9%

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

      9. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

      1. distribute-rgt-in 99.9%

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

      2. div-inv 99.8%

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

      3. associate-*l* 97.4%

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

      4. associate-/r/ 97.4%

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

      5. clear-num 97.4%

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

      6. neg-mul-1 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in y around inf 85.5%

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

      1. associate-/l* 98.4%

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

   9. Simplified 98.4%

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

       1. unsub-neg 98.4%

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

       2. div-inv 98.5%

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

       3. clear-num 98.6%

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

   11. Applied egg-rr 98.6%

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

   if -0.94999999999999996 < z < 1

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.8%

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

      1. associate--l+ 99.8%

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

      2. +-commutative 99.8%

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

      3. associate-*r/ 92.7%

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

      4. +-commutative 92.7%

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

      5. associate--l+ 92.7%

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

      6. div-sub 92.7%

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

      7. sub-neg 92.7%

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

      8. *-inverses 92.7%

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

      9. metadata-eval 92.7%

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

   4. Simplified 92.7%

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

   5. Taylor expanded in z around 0 97.3%

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

      1. *-commutative 97.3%

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

      2. associate-*r/ 97.3%

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

   7. Simplified 97.3%

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

   if 1 < z

   1. Initial program 72.5%

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

   2. Taylor expanded in x around 0 72.5%

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

      1. associate--l+ 72.5%

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

      2. +-commutative 72.5%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate--l+ 99.8%

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

      6. div-sub 99.8%

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

      7. sub-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

4. Final simplification 98.1%

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

Alternative 8: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.98:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.98)
   (- (* x (/ y z)) x)
   (if (<= z 1.0) (/ (+ x (* x y)) z) (* x (+ -1.0 (/ y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.98) {
		tmp = (x * (y / z)) - x;
	} else if (z <= 1.0) {
		tmp = (x + (x * y)) / z;
	} else {
		tmp = x * (-1.0 + (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 <= (-0.98d0)) then
        tmp = (x * (y / z)) - x
    else if (z <= 1.0d0) then
        tmp = (x + (x * y)) / z
    else
        tmp = x * ((-1.0d0) + (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.98) {
		tmp = (x * (y / z)) - x;
	} else if (z <= 1.0) {
		tmp = (x + (x * y)) / z;
	} else {
		tmp = x * (-1.0 + (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.98:
		tmp = (x * (y / z)) - x
	elif z <= 1.0:
		tmp = (x + (x * y)) / z
	else:
		tmp = x * (-1.0 + (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.98)
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	elseif (z <= 1.0)
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	else
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.98)
		tmp = (x * (y / z)) - x;
	elseif (z <= 1.0)
		tmp = (x + (x * y)) / z;
	else
		tmp = x * (-1.0 + (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.98], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[z, 1.0], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.97999999999999998

   1. Initial program 72.9%

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

   2. Taylor expanded in x around 0 72.9%

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

      1. associate--l+ 72.9%

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

      2. +-commutative 72.9%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate--l+ 99.8%

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

      6. div-sub 99.9%

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

      7. sub-neg 99.9%

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

      8. *-inverses 99.9%

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

      9. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

      1. distribute-rgt-in 99.9%

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

      2. div-inv 99.8%

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

      3. associate-*l* 97.4%

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

      4. associate-/r/ 97.4%

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

      5. clear-num 97.4%

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

      6. neg-mul-1 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in y around inf 85.5%

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

      1. associate-/l* 98.4%

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

   9. Simplified 98.4%

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

       1. unsub-neg 98.4%

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

       2. div-inv 98.5%

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

       3. clear-num 98.6%

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

   11. Applied egg-rr 98.6%

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

   if -0.97999999999999998 < z < 1

   1. Initial program 99.8%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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-def 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. Taylor expanded in z around 0 97.3%

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

   if 1 < z

   1. Initial program 72.5%

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

   2. Taylor expanded in x around 0 72.5%

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

      1. associate--l+ 72.5%

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

      2. +-commutative 72.5%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate--l+ 99.8%

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

      6. div-sub 99.8%

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

      7. sub-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.98:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \end{array} \]

Alternative 9: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05)
   (- (* x (/ y z)) x)
   (if (<= z 1.0) (/ (+ x (* x y)) z) (- (/ x (/ z y)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05) {
		tmp = (x * (y / z)) - x;
	} else if (z <= 1.0) {
		tmp = (x + (x * y)) / 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 <= (-1.05d0)) then
        tmp = (x * (y / z)) - x
    else if (z <= 1.0d0) then
        tmp = (x + (x * y)) / 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 <= -1.05) {
		tmp = (x * (y / z)) - x;
	} else if (z <= 1.0) {
		tmp = (x + (x * y)) / z;
	} else {
		tmp = (x / (z / y)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05:
		tmp = (x * (y / z)) - x
	elif z <= 1.0:
		tmp = (x + (x * y)) / z
	else:
		tmp = (x / (z / y)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05)
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	elseif (z <= 1.0)
		tmp = Float64(Float64(x + Float64(x * y)) / 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 <= -1.05)
		tmp = (x * (y / z)) - x;
	elseif (z <= 1.0)
		tmp = (x + (x * y)) / z;
	else
		tmp = (x / (z / y)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[z, 1.0], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000004

   1. Initial program 72.9%

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

   2. Taylor expanded in x around 0 72.9%

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

      1. associate--l+ 72.9%

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

      2. +-commutative 72.9%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate--l+ 99.8%

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

      6. div-sub 99.9%

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

      7. sub-neg 99.9%

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

      8. *-inverses 99.9%

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

      9. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

      1. distribute-rgt-in 99.9%

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

      2. div-inv 99.8%

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

      3. associate-*l* 97.4%

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

      4. associate-/r/ 97.4%

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

      5. clear-num 97.4%

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

      6. neg-mul-1 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in y around inf 85.5%

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

      1. associate-/l* 98.4%

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

   9. Simplified 98.4%

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

       1. unsub-neg 98.4%

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

       2. div-inv 98.5%

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

       3. clear-num 98.6%

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

   11. Applied egg-rr 98.6%

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

   if -1.05000000000000004 < z < 1

   1. Initial program 99.8%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   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-def 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. Taylor expanded in z around 0 97.3%

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

   if 1 < z

   1. Initial program 72.5%

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

   2. Taylor expanded in x around 0 72.5%

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

      1. associate--l+ 72.5%

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

      2. +-commutative 72.5%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate--l+ 99.8%

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

      6. div-sub 99.8%

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

      7. sub-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

      1. distribute-rgt-in 99.8%

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

      2. div-inv 99.8%

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

      3. associate-*l* 92.8%

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

      4. associate-/r/ 92.9%

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

      5. clear-num 92.9%

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

      6. neg-mul-1 92.9%

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

   6. Applied egg-rr 92.9%

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

   7. Taylor expanded in y around inf 89.6%

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

      1. associate-/l* 99.9%

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

   9. Simplified 99.9%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}} - x\\ \end{array} \]

Alternative 10: 93.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{1 + y}{z} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.45e-77)
   (/ (* x (+ 1.0 (- y z))) z)
   (* x (+ (/ (+ 1.0 y) z) -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.45e-77) {
		tmp = (x * (1.0 + (y - z))) / z;
	} else {
		tmp = x * (((1.0 + y) / z) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.45d-77) then
        tmp = (x * (1.0d0 + (y - z))) / z
    else
        tmp = x * (((1.0d0 + y) / z) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.45e-77) {
		tmp = (x * (1.0 + (y - z))) / z;
	} else {
		tmp = x * (((1.0 + y) / z) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.45e-77:
		tmp = (x * (1.0 + (y - z))) / z
	else:
		tmp = x * (((1.0 + y) / z) + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.45e-77)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(y - z))) / z);
	else
		tmp = Float64(x * Float64(Float64(Float64(1.0 + y) / z) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.45e-77)
		tmp = (x * (1.0 + (y - z))) / z;
	else
		tmp = x * (((1.0 + y) / z) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.45e-77], N[(N[(x * N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x * N[(N[(N[(1.0 + y), $MachinePrecision] / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.4499999999999999e-77

   1. Initial program 92.5%

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

   if 1.4499999999999999e-77 < x

   1. Initial program 74.0%

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

   2. Taylor expanded in x around 0 74.0%

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

      1. associate--l+ 74.0%

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

      2. +-commutative 74.0%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

      6. div-sub 99.8%

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

      7. sub-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.45 \cdot 10^{-77}:\\ \;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{1 + y}{z} + -1\right)\\ \end{array} \]

Alternative 11: 93.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6 \cdot 10^{-43}:\\ \;\;\;\;\frac{x + x \cdot \left(y - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 6e-43) (/ (+ x (* x (- y z))) z) (- (* (+ 1.0 y) (/ x z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 6e-43) {
		tmp = (x + (x * (y - z))) / z;
	} else {
		tmp = ((1.0 + y) * (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 (x <= 6d-43) then
        tmp = (x + (x * (y - z))) / z
    else
        tmp = ((1.0d0 + y) * (x / z)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 6e-43) {
		tmp = (x + (x * (y - z))) / z;
	} else {
		tmp = ((1.0 + y) * (x / z)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 6e-43:
		tmp = (x + (x * (y - z))) / z
	else:
		tmp = ((1.0 + y) * (x / z)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 6e-43)
		tmp = Float64(Float64(x + Float64(x * Float64(y - z))) / z);
	else
		tmp = Float64(Float64(Float64(1.0 + y) * Float64(x / z)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 6e-43)
		tmp = (x + (x * (y - z))) / z;
	else
		tmp = ((1.0 + y) * (x / z)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 6e-43], N[(N[(x + N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(1.0 + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.00000000000000007e-43

   1. Initial program 92.7%

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

      1. distribute-lft-in 92.8%

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

      2. *-rgt-identity 92.8%

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

   3. Applied egg-rr 92.8%

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

   if 6.00000000000000007e-43 < x

   1. Initial program 71.8%

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

   2. Taylor expanded in x around 0 71.8%

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

      1. associate--l+ 71.8%

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

      2. +-commutative 71.8%

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

      3. associate-*r/ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate--l+ 99.9%

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

      6. div-sub 99.8%

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

      7. sub-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

      1. distribute-rgt-in 99.9%

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

      2. div-inv 99.8%

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

      3. associate-*l* 99.8%

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

      4. associate-/r/ 99.9%

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

      5. clear-num 99.9%

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

      6. neg-mul-1 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6 \cdot 10^{-43}:\\ \;\;\;\;\frac{x + x \cdot \left(y - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array} \]

Alternative 12: 85.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+20} \lor \neg \left(y \leq 2.3 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.15e+20) (not (<= y 2.3e+14))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e+20) || !(y <= 2.3e+14)) {
		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 <= (-1.15d+20)) .or. (.not. (y <= 2.3d+14))) 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 <= -1.15e+20) || !(y <= 2.3e+14)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.15e+20) or not (y <= 2.3e+14):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.15e+20) || !(y <= 2.3e+14))
		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 <= -1.15e+20) || ~((y <= 2.3e+14)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.15e+20], N[Not[LessEqual[y, 2.3e+14]], $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 < -1.15e20 or 2.3e14 < y

   1. Initial program 84.1%

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

   2. Taylor expanded in y around inf 75.2%

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

      1. associate-/l* 74.2%

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

      2. associate-/r/ 77.8%

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

   4. Simplified 77.8%

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

   if -1.15e20 < y < 2.3e14

   1. Initial program 89.2%

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

   2. Taylor expanded in x around 0 89.2%

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

      1. associate--l+ 89.2%

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

      2. +-commutative 89.2%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate--l+ 99.8%

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

      6. div-sub 99.8%

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

      7. sub-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around 0 97.7%

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

      1. sub-neg 97.7%

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

      2. metadata-eval 97.7%

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

      3. distribute-rgt-in 97.7%

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

      4. associate-*l/ 97.9%

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

      5. *-lft-identity 97.9%

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

      6. neg-mul-1 97.9%

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

      7. unsub-neg 97.9%

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

   7. Simplified 97.9%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+20} \lor \neg \left(y \leq 2.3 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 13: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 42000000000000:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.2e+16)
   (* y (/ x z))
   (if (<= y 42000000000000.0) (- (/ x z) x) (/ (* x y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+16) {
		tmp = y * (x / z);
	} else if (y <= 42000000000000.0) {
		tmp = (x / z) - x;
	} else {
		tmp = (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 (y <= (-1.2d+16)) then
        tmp = y * (x / z)
    else if (y <= 42000000000000.0d0) then
        tmp = (x / z) - x
    else
        tmp = (x * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+16) {
		tmp = y * (x / z);
	} else if (y <= 42000000000000.0) {
		tmp = (x / z) - x;
	} else {
		tmp = (x * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.2e+16:
		tmp = y * (x / z)
	elif y <= 42000000000000.0:
		tmp = (x / z) - x
	else:
		tmp = (x * y) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.2e+16)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 42000000000000.0)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(Float64(x * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.2e+16)
		tmp = y * (x / z);
	elseif (y <= 42000000000000.0)
		tmp = (x / z) - x;
	else
		tmp = (x * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.2e+16], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 42000000000000.0], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e16

   1. Initial program 82.7%

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

   2. Taylor expanded in y around inf 70.6%

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

      1. associate-/l* 70.8%

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

      2. associate-/r/ 77.5%

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

   4. Simplified 77.5%

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

   if -1.2e16 < y < 4.2e13

   1. Initial program 89.2%

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

   2. Taylor expanded in x around 0 89.2%

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

      1. associate--l+ 89.2%

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

      2. +-commutative 89.2%

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

      3. associate-*r/ 99.8%

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

      4. +-commutative 99.8%

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

      5. associate--l+ 99.8%

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

      6. div-sub 99.8%

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

      7. sub-neg 99.8%

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

      8. *-inverses 99.8%

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

      9. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in y around 0 97.7%

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

      1. sub-neg 97.7%

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

      2. metadata-eval 97.7%

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

      3. distribute-rgt-in 97.7%

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

      4. associate-*l/ 97.9%

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

      5. *-lft-identity 97.9%

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

      6. neg-mul-1 97.9%

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

      7. unsub-neg 97.9%

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

   7. Simplified 97.9%

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

   if 4.2e13 < y

   1. Initial program 85.5%

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

   2. Taylor expanded in y around inf 80.0%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 42000000000000:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 14: 64.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.49 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.49) (not (<= z 1.0))) (- x) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.49) || !(z <= 1.0)) {
		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 <= (-0.49d0)) .or. (.not. (z <= 1.0d0))) 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 <= -0.49) || !(z <= 1.0)) {
		tmp = -x;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.49) or not (z <= 1.0):
		tmp = -x
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.49) || !(z <= 1.0))
		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 <= -0.49) || ~((z <= 1.0)))
		tmp = -x;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.49], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], (-x), N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.48999999999999999 or 1 < z

   1. Initial program 72.9%

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

   2. Taylor expanded in z around inf 72.0%

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

      1. mul-1-neg 72.0%

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

   4. Simplified 72.0%

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

   if -0.48999999999999999 < z < 1

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 63.5%

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

      1. associate-/l* 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in z around 0 60.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.49 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 15: 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 87.0%

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

2. Taylor expanded in z around inf 36.1%

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

   1. mul-1-neg 36.1%

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

4. Simplified 36.1%

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

5. Final simplification 36.1%

   \[\leadsto -x \]

Developer target: 99.4% accurate, 0.6× 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 2023316 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

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