Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C

Percentage Accurate: 94.9% → 96.5%

Time: 10.0s

Alternatives: 12

Speedup: 0.5×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y / z) - (t / (1.0d0 - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 (- INFINITY)) (* y (/ x z)) (* t_1 x))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (x / z);
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) + (t / (z + -1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x / z);
	} else {
		tmp = t_1 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) + (t / (z + -1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (x / z)
	else:
		tmp = t_1 * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) + Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(t_1 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) + (t / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (x / z);
	else
		tmp = t_1 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] + N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < -inf.0

   1. Initial program 60.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]

      3. /-lowering-/.f64 60.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 60.4%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 99.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Applied egg-rr 99.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{z}\right)}\right) \]

      4. /-lowering-/.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 99.8%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 96.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.4%

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

Alternative 2: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+219}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -1.7e+141)
     t_1
     (if (<= t 1.6e-209)
       (/ (* y x) z)
       (if (<= t 1.02e+219) (/ y (/ z x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -1.7e+141) {
		tmp = t_1;
	} else if (t <= 1.6e-209) {
		tmp = (y * x) / z;
	} else if (t <= 1.02e+219) {
		tmp = y / (z / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / t)
    if (t <= (-1.7d+141)) then
        tmp = t_1
    else if (t <= 1.6d-209) then
        tmp = (y * x) / z
    else if (t <= 1.02d+219) then
        tmp = y / (z / x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -1.7e+141) {
		tmp = t_1;
	} else if (t <= 1.6e-209) {
		tmp = (y * x) / z;
	} else if (t <= 1.02e+219) {
		tmp = y / (z / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -1.7e+141:
		tmp = t_1
	elif t <= 1.6e-209:
		tmp = (y * x) / z
	elif t <= 1.02e+219:
		tmp = y / (z / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -1.7e+141)
		tmp = t_1;
	elseif (t <= 1.6e-209)
		tmp = Float64(Float64(y * x) / z);
	elseif (t <= 1.02e+219)
		tmp = Float64(y / Float64(z / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -1.7e+141)
		tmp = t_1;
	elseif (t <= 1.6e-209)
		tmp = (y * x) / z;
	elseif (t <= 1.02e+219)
		tmp = y / (z / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+141], t$95$1, If[LessEqual[t, 1.6e-209], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, 1.02e+219], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6999999999999999e141 or 1.02e219 < t

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - -1 \cdot t\right)\right), \color{blue}{z}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - -1 \cdot t\right)\right), z\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right)\right), z\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + 1 \cdot t\right)\right), z\right) \]

      5. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + t\right)\right), z\right) \]

      6. +-lowering-+.f64 61.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right), z\right) \]

   5. Simplified 61.9%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{t}\right), z\right) \]
   7. Step-by-step derivation

   8. Simplified 56.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{z}{t}\right)}\right) \]

      5. /-lowering-/.f64 63.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right) \]

   10. Applied egg-rr 63.6%

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

   if -1.6999999999999999e141 < t < 1.6000000000000001e-209

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]

      3. /-lowering-/.f64 71.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 71.8%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 75.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Applied egg-rr 75.3%

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

   if 1.6000000000000001e-209 < t < 1.02e219

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]

      3. /-lowering-/.f64 75.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 75.7%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 69.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Applied egg-rr 69.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{z}{x}\right)}\right) \]

      6. /-lowering-/.f64 79.0%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{x}\right)\right) \]

   9. Applied egg-rr 79.0%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+141}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+219}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-16}:\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -1.05) t_1 (if (<= z 9e-16) (/ (* x (- y (* z t))) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -1.05) {
		tmp = t_1;
	} else if (z <= 9e-16) {
		tmp = (x * (y - (z * t))) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y + t) / z)
    if (z <= (-1.05d0)) then
        tmp = t_1
    else if (z <= 9d-16) then
        tmp = (x * (y - (z * t))) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -1.05) {
		tmp = t_1;
	} else if (z <= 9e-16) {
		tmp = (x * (y - (z * t))) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + t) / z)
	tmp = 0
	if z <= -1.05:
		tmp = t_1
	elif z <= 9e-16:
		tmp = (x * (y - (z * t))) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -1.05)
		tmp = t_1;
	elseif (z <= 9e-16)
		tmp = Float64(Float64(x * Float64(y - Float64(z * t))) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + t) / z);
	tmp = 0.0;
	if (z <= -1.05)
		tmp = t_1;
	elseif (z <= 9e-16)
		tmp = (x * (y - (z * t))) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05], t$95$1, If[LessEqual[z, 9e-16], N[(N[(x * N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000004 or 9.0000000000000003e-16 < z

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - -1 \cdot t}{z}\right)}\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y - -1 \cdot t\right), \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right), z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + 1 \cdot t\right), z\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + t\right), z\right)\right) \]

      5. +-lowering-+.f64 93.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), z\right)\right) \]

   5. Simplified 93.2%

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

   if -1.05000000000000004 < z < 9.0000000000000003e-16

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot \left(t \cdot \left(x \cdot z\right)\right) + x \cdot y\right), \color{blue}{z}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + -1 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right), z\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(t \cdot \left(x \cdot z\right)\right)\right)\right), z\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - t \cdot \left(x \cdot z\right)\right), z\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(t \cdot x\right) \cdot z\right), z\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(x \cdot t\right) \cdot z\right), z\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - x \cdot \left(t \cdot z\right)\right), z\right) \]

      8. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - t \cdot z\right)\right), z\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y + \left(\mathsf{neg}\left(t \cdot z\right)\right)\right)\right), z\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y + -1 \cdot \left(t \cdot z\right)\right)\right), z\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + -1 \cdot \left(t \cdot z\right)\right)\right), z\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(\mathsf{neg}\left(t \cdot z\right)\right)\right)\right), z\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - t \cdot z\right)\right), z\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \left(t \cdot z\right)\right)\right), z\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \left(z \cdot t\right)\right)\right), z\right) \]

      16. *-lowering-*.f64 97.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right)\right), z\right) \]

   5. Simplified 97.3%

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

Alternative 4: 93.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -1.0) t_1 (if (<= z 9e-16) (* x (- (/ y z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 9e-16) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y + t) / z)
    if (z <= (-1.0d0)) then
        tmp = t_1
    else if (z <= 9d-16) then
        tmp = x * ((y / z) - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y + t) / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 9e-16) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + t) / z)
	tmp = 0
	if z <= -1.0:
		tmp = t_1
	elif z <= 9e-16:
		tmp = x * ((y / z) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y + t) / z))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= 9e-16)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y + t) / z);
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= 9e-16)
		tmp = x * ((y / z) - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, 9e-16], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 9.0000000000000003e-16 < z

   1. Initial program 93.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y - -1 \cdot t}{z}\right)}\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y - -1 \cdot t\right), \color{blue}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right), z\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + 1 \cdot t\right), z\right)\right) \]

      4. *-lft-identity N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\left(y + t\right), z\right)\right) \]

      5. +-lowering-+.f64 93.2%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(y, t\right), z\right)\right) \]

   5. Simplified 93.2%

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

   if -1 < z < 9.0000000000000003e-16

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 93.0%

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

Alternative 5: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.42e+81)
   (* (/ y z) x)
   (if (<= z 9.6e-6) (* x (- (/ y z) t)) (* x (/ t (+ z -1.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.42e+81) {
		tmp = (y / z) * x;
	} else if (z <= 9.6e-6) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * (t / (z + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.42d+81)) then
        tmp = (y / z) * x
    else if (z <= 9.6d-6) then
        tmp = x * ((y / z) - t)
    else
        tmp = x * (t / (z + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.42e+81) {
		tmp = (y / z) * x;
	} else if (z <= 9.6e-6) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = x * (t / (z + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.42e+81:
		tmp = (y / z) * x
	elif z <= 9.6e-6:
		tmp = x * ((y / z) - t)
	else:
		tmp = x * (t / (z + -1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.42e+81)
		tmp = Float64(Float64(y / z) * x);
	elseif (z <= 9.6e-6)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(x * Float64(t / Float64(z + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.42e+81)
		tmp = (y / z) * x;
	elseif (z <= 9.6e-6)
		tmp = x * ((y / z) - t);
	else
		tmp = x * (t / (z + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.42e+81], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 9.6e-6], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.41999999999999998e81

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]

      3. /-lowering-/.f64 68.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 68.4%

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

   if -1.41999999999999998e81 < z < 9.5999999999999996e-6

   1. Initial program 94.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 89.6%

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

   if 9.5999999999999996e-6 < z

   1. Initial program 95.1%

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

      1. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \left(\frac{1}{\color{blue}{\frac{1 - z}{t}}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{1 - z}{t}\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(1 - z\right), \color{blue}{t}\right)\right)\right)\right) \]

      4. --lowering--.f64 95.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, z\right), t\right)\right)\right)\right) \]

   4. Applied egg-rr 95.1%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{t}{1 - z}\right)}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\mathsf{neg}\left(\frac{t}{1 - z}\right)\right)\right) \]

      2. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{t}{\color{blue}{\mathsf{neg}\left(\left(1 - z\right)\right)}}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(\mathsf{neg}\left(\left(1 - z\right)\right)\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(1 + -1 \cdot z\right)\right)\right)\right)\right) \]

      6. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\mathsf{neg}\left(\left(-1 \cdot z + 1\right)\right)\right)\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\left(\mathsf{neg}\left(-1 \cdot z\right)\right) + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      9. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(z + \left(\mathsf{neg}\left(\color{blue}{1}\right)\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \left(z + -1\right)\right)\right) \]

      11. +-lowering-+.f64 64.3%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{+.f64}\left(z, \color{blue}{-1}\right)\right)\right) \]

   7. Simplified 64.3%

      \[\leadsto x \cdot \color{blue}{\frac{t}{z + -1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 45000000000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.9e+80)
   (* (/ y z) x)
   (if (<= z 45000000000.0) (* x (- (/ y z) t)) (* t (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.9e+80) {
		tmp = (y / z) * x;
	} else if (z <= 45000000000.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.9d+80)) then
        tmp = (y / z) * x
    else if (z <= 45000000000.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = t * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.9e+80) {
		tmp = (y / z) * x;
	} else if (z <= 45000000000.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.9e+80:
		tmp = (y / z) * x
	elif z <= 45000000000.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.9e+80)
		tmp = Float64(Float64(y / z) * x);
	elseif (z <= 45000000000.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.9e+80)
		tmp = (y / z) * x;
	elseif (z <= 45000000000.0)
		tmp = x * ((y / z) - t);
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.9e+80], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 45000000000.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.89999999999999999e80

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]

      3. /-lowering-/.f64 68.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 68.4%

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

   if -3.89999999999999999e80 < z < 4.5e10

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, z\right), \color{blue}{t}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 89.2%

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

   if 4.5e10 < z

   1. Initial program 94.9%

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

   3. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - -1 \cdot t\right)\right), \color{blue}{z}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - -1 \cdot t\right)\right), z\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right)\right), z\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + 1 \cdot t\right)\right), z\right) \]

      5. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + t\right)\right), z\right) \]

      6. +-lowering-+.f64 88.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right), z\right) \]

   5. Simplified 88.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(y + t\right), \color{blue}{\left(\frac{x}{z}\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t + y\right), \left(\frac{\color{blue}{x}}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, y\right), \left(\frac{\color{blue}{x}}{z}\right)\right) \]

      6. /-lowering-/.f64 88.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, y\right), \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 88.4%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(x, z\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 64.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;z \leq 45000000000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+145}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+219}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -7.8e+145) t_1 (if (<= t 1.05e+219) (/ y (/ z x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -7.8e+145) {
		tmp = t_1;
	} else if (t <= 1.05e+219) {
		tmp = y / (z / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / t)
    if (t <= (-7.8d+145)) then
        tmp = t_1
    else if (t <= 1.05d+219) then
        tmp = y / (z / x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -7.8e+145) {
		tmp = t_1;
	} else if (t <= 1.05e+219) {
		tmp = y / (z / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -7.8e+145:
		tmp = t_1
	elif t <= 1.05e+219:
		tmp = y / (z / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -7.8e+145)
		tmp = t_1;
	elseif (t <= 1.05e+219)
		tmp = Float64(y / Float64(z / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -7.8e+145)
		tmp = t_1;
	elseif (t <= 1.05e+219)
		tmp = y / (z / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+145], t$95$1, If[LessEqual[t, 1.05e+219], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.7999999999999995e145 or 1.04999999999999994e219 < t

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - -1 \cdot t\right)\right), \color{blue}{z}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - -1 \cdot t\right)\right), z\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right)\right), z\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + 1 \cdot t\right)\right), z\right) \]

      5. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + t\right)\right), z\right) \]

      6. +-lowering-+.f64 61.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right), z\right) \]

   5. Simplified 61.9%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{t}\right), z\right) \]
   7. Step-by-step derivation

   8. Simplified 56.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{z}{t}\right)}\right) \]

      5. /-lowering-/.f64 63.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right) \]

   10. Applied egg-rr 63.6%

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

   if -7.7999999999999995e145 < t < 1.04999999999999994e219

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]

      3. /-lowering-/.f64 73.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 73.4%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 72.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Applied egg-rr 72.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{z}{x}\right)}\right) \]

      6. /-lowering-/.f64 74.6%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{x}\right)\right) \]

   9. Applied egg-rr 74.6%

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

Alternative 8: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z}{t}}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+219}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ z t))))
   (if (<= t -6.2e+144) t_1 (if (<= t 4.2e+219) (* y (/ x z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -6.2e+144) {
		tmp = t_1;
	} else if (t <= 4.2e+219) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z / t)
    if (t <= (-6.2d+144)) then
        tmp = t_1
    else if (t <= 4.2d+219) then
        tmp = y * (x / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z / t);
	double tmp;
	if (t <= -6.2e+144) {
		tmp = t_1;
	} else if (t <= 4.2e+219) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (z / t)
	tmp = 0
	if t <= -6.2e+144:
		tmp = t_1
	elif t <= 4.2e+219:
		tmp = y * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(z / t))
	tmp = 0.0
	if (t <= -6.2e+144)
		tmp = t_1;
	elseif (t <= 4.2e+219)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (z / t);
	tmp = 0.0;
	if (t <= -6.2e+144)
		tmp = t_1;
	elseif (t <= 4.2e+219)
		tmp = y * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+144], t$95$1, If[LessEqual[t, 4.2e+219], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2000000000000003e144 or 4.19999999999999976e219 < t

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - -1 \cdot t\right)\right), \color{blue}{z}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - -1 \cdot t\right)\right), z\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right)\right), z\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + 1 \cdot t\right)\right), z\right) \]

      5. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + t\right)\right), z\right) \]

      6. +-lowering-+.f64 61.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right), z\right) \]

   5. Simplified 61.9%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \color{blue}{t}\right), z\right) \]
   7. Step-by-step derivation

   8. Simplified 56.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{z}{t}\right)}\right) \]

      5. /-lowering-/.f64 63.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(z, \color{blue}{t}\right)\right) \]

   10. Applied egg-rr 63.6%

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

   if -6.2000000000000003e144 < t < 4.19999999999999976e219

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]

      3. /-lowering-/.f64 73.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 73.4%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 72.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Applied egg-rr 72.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{z}\right)}\right) \]

      4. /-lowering-/.f64 74.5%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 74.5%

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

Alternative 9: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+218}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))))
   (if (<= t -1.65e+144) t_1 (if (<= t 9.2e+218) (* y (/ x z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (t <= -1.65e+144) {
		tmp = t_1;
	} else if (t <= 9.2e+218) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x / z)
    if (t <= (-1.65d+144)) then
        tmp = t_1
    else if (t <= 9.2d+218) then
        tmp = y * (x / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (t <= -1.65e+144) {
		tmp = t_1;
	} else if (t <= 9.2e+218) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / z)
	tmp = 0
	if t <= -1.65e+144:
		tmp = t_1
	elif t <= 9.2e+218:
		tmp = y * (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (t <= -1.65e+144)
		tmp = t_1;
	elseif (t <= 9.2e+218)
		tmp = Float64(y * Float64(x / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / z);
	tmp = 0.0;
	if (t <= -1.65e+144)
		tmp = t_1;
	elseif (t <= 9.2e+218)
		tmp = y * (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+144], t$95$1, If[LessEqual[t, 9.2e+218], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.65e144 or 9.2000000000000004e218 < t

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - -1 \cdot t\right)\right), \color{blue}{z}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - -1 \cdot t\right)\right), z\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right)\right), z\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + 1 \cdot t\right)\right), z\right) \]

      5. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + t\right)\right), z\right) \]

      6. +-lowering-+.f64 61.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right), z\right) \]

   5. Simplified 61.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(y + t\right), \color{blue}{\left(\frac{x}{z}\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t + y\right), \left(\frac{\color{blue}{x}}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, y\right), \left(\frac{\color{blue}{x}}{z}\right)\right) \]

      6. /-lowering-/.f64 58.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, y\right), \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 58.7%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(x, z\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 57.0%

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

   if -1.65e144 < t < 9.2000000000000004e218

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]

      3. /-lowering-/.f64 73.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 73.4%

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

      1. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{z}\right) \]

      3. *-lowering-*.f64 72.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), z\right) \]

   7. Applied egg-rr 72.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{z}\right)}\right) \]

      4. /-lowering-/.f64 74.5%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 74.5%

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

Alternative 10: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+220}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))))
   (if (<= t -1.9e+147) t_1 (if (<= t 1.9e+220) (* (/ y z) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (t <= -1.9e+147) {
		tmp = t_1;
	} else if (t <= 1.9e+220) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x / z)
    if (t <= (-1.9d+147)) then
        tmp = t_1
    else if (t <= 1.9d+220) then
        tmp = (y / z) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (t <= -1.9e+147) {
		tmp = t_1;
	} else if (t <= 1.9e+220) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / z)
	tmp = 0
	if t <= -1.9e+147:
		tmp = t_1
	elif t <= 1.9e+220:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (t <= -1.9e+147)
		tmp = t_1;
	elseif (t <= 1.9e+220)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / z);
	tmp = 0.0;
	if (t <= -1.9e+147)
		tmp = t_1;
	elseif (t <= 1.9e+220)
		tmp = (y / z) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+147], t$95$1, If[LessEqual[t, 1.9e+220], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.89999999999999985e147 or 1.89999999999999992e220 < t

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - -1 \cdot t\right)\right), \color{blue}{z}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - -1 \cdot t\right)\right), z\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right)\right), z\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + 1 \cdot t\right)\right), z\right) \]

      5. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + t\right)\right), z\right) \]

      6. +-lowering-+.f64 61.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right), z\right) \]

   5. Simplified 61.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(y + t\right), \color{blue}{\left(\frac{x}{z}\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t + y\right), \left(\frac{\color{blue}{x}}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, y\right), \left(\frac{\color{blue}{x}}{z}\right)\right) \]

      6. /-lowering-/.f64 58.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, y\right), \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 58.7%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(x, z\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 57.0%

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

   if -1.89999999999999985e147 < t < 1.89999999999999992e220

   1. Initial program 92.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{y}{z}\right)}\right) \]

      3. /-lowering-/.f64 73.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 73.4%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+147}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+220}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(0 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))))
   (if (<= z -1.45e-31) t_1 (if (<= z 2e-8) (* t (- 0.0 x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (z <= -1.45e-31) {
		tmp = t_1;
	} else if (z <= 2e-8) {
		tmp = t * (0.0 - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x / z)
    if (z <= (-1.45d-31)) then
        tmp = t_1
    else if (z <= 2d-8) then
        tmp = t * (0.0d0 - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (z <= -1.45e-31) {
		tmp = t_1;
	} else if (z <= 2e-8) {
		tmp = t * (0.0 - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / z)
	tmp = 0
	if z <= -1.45e-31:
		tmp = t_1
	elif z <= 2e-8:
		tmp = t * (0.0 - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (z <= -1.45e-31)
		tmp = t_1;
	elseif (z <= 2e-8)
		tmp = Float64(t * Float64(0.0 - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / z);
	tmp = 0.0;
	if (z <= -1.45e-31)
		tmp = t_1;
	elseif (z <= 2e-8)
		tmp = t * (0.0 - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e-31], t$95$1, If[LessEqual[z, 2e-8], N[(t * N[(0.0 - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45e-31 or 2e-8 < z

   1. Initial program 93.4%

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

   3. Taylor expanded in z around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - -1 \cdot t\right)\right), \color{blue}{z}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - -1 \cdot t\right)\right), z\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right)\right), z\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + 1 \cdot t\right)\right), z\right) \]

      5. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + t\right)\right), z\right) \]

      6. +-lowering-+.f64 88.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, t\right)\right), z\right) \]

   5. Simplified 88.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(y + t\right), \color{blue}{\left(\frac{x}{z}\right)}\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(t + y\right), \left(\frac{\color{blue}{x}}{z}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, y\right), \left(\frac{\color{blue}{x}}{z}\right)\right) \]

      6. /-lowering-/.f64 88.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(t, y\right), \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 88.8%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{t}, \mathsf{/.f64}\left(x, z\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 54.2%

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

   if -1.45e-31 < z < 2e-8

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot \left(t \cdot \left(x \cdot z\right)\right) + x \cdot y\right), \color{blue}{z}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + -1 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right), z\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(t \cdot \left(x \cdot z\right)\right)\right)\right), z\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - t \cdot \left(x \cdot z\right)\right), z\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(t \cdot x\right) \cdot z\right), z\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(x \cdot t\right) \cdot z\right), z\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - x \cdot \left(t \cdot z\right)\right), z\right) \]

      8. distribute-lft-out-- N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - t \cdot z\right)\right), z\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y + \left(\mathsf{neg}\left(t \cdot z\right)\right)\right)\right), z\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y + -1 \cdot \left(t \cdot z\right)\right)\right), z\right) \]

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

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + -1 \cdot \left(t \cdot z\right)\right)\right), z\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(\mathsf{neg}\left(t \cdot z\right)\right)\right)\right), z\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - t \cdot z\right)\right), z\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \left(t \cdot z\right)\right)\right), z\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \left(z \cdot t\right)\right)\right), z\right) \]

      16. *-lowering-*.f64 97.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right)\right), z\right) \]

   5. Simplified 97.2%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(t \cdot x\right) \]

      2. neg-sub0 N/A

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

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

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot x\right)}\right) \]

      4. *-lowering-*.f64 30.4%

         \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right) \]

   8. Simplified 30.4%

      \[\leadsto \color{blue}{0 - t \cdot x} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(t \cdot x\right) \]

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

         \[\leadsto \mathsf{neg.f64}\left(\left(t \cdot x\right)\right) \]

      3. *-lowering-*.f64 30.4%

         \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(t, x\right)\right) \]

   10. Applied egg-rr 30.4%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(0 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 23.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(0 - x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t (- 0.0 x)))

C

double code(double x, double y, double z, double t) {
	return t * (0.0 - x);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t * (0.0d0 - x)
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * (0.0 - x);
}

Python

def code(x, y, z, t):
	return t * (0.0 - x)

Julia

function code(x, y, z, t)
	return Float64(t * Float64(0.0 - x))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * (0.0 - x);
end

Wolfram

code[x_, y_, z_, t_] := N[(t * N[(0.0 - x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.5%

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

3. Taylor expanded in z around 0

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

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

      \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot \left(t \cdot \left(x \cdot z\right)\right) + x \cdot y\right), \color{blue}{z}\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + -1 \cdot \left(t \cdot \left(x \cdot z\right)\right)\right), z\right) \]

   3. mul-1-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y + \left(\mathsf{neg}\left(t \cdot \left(x \cdot z\right)\right)\right)\right), z\right) \]

   4. unsub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - t \cdot \left(x \cdot z\right)\right), z\right) \]

   5. associate-*r* N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(t \cdot x\right) \cdot z\right), z\right) \]

   6. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - \left(x \cdot t\right) \cdot z\right), z\right) \]

   7. associate-*l* N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y - x \cdot \left(t \cdot z\right)\right), z\right) \]

   8. distribute-lft-out-- N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - t \cdot z\right)\right), z\right) \]

   9. unsub-neg N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y + \left(\mathsf{neg}\left(t \cdot z\right)\right)\right)\right), z\right) \]

   10. mul-1-neg N/A

       \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y + -1 \cdot \left(t \cdot z\right)\right)\right), z\right) \]

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

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + -1 \cdot \left(t \cdot z\right)\right)\right), z\right) \]

   12. mul-1-neg N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(\mathsf{neg}\left(t \cdot z\right)\right)\right)\right), z\right) \]

   13. unsub-neg N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - t \cdot z\right)\right), z\right) \]

   14. --lowering--.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \left(t \cdot z\right)\right)\right), z\right) \]

   15. *-commutative N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \left(z \cdot t\right)\right)\right), z\right) \]

   16. *-lowering-*.f64 65.1%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right)\right), z\right) \]

5. Simplified 65.1%

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

6. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(t \cdot x\right) \]

   2. neg-sub0 N/A

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

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

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{\left(t \cdot x\right)}\right) \]

   4. *-lowering-*.f64 21.3%

      \[\leadsto \mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(t, \color{blue}{x}\right)\right) \]

8. Simplified 21.3%

   \[\leadsto \color{blue}{0 - t \cdot x} \]
9. Step-by-step derivation

   1. sub0-neg N/A

      \[\leadsto \mathsf{neg}\left(t \cdot x\right) \]

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

      \[\leadsto \mathsf{neg.f64}\left(\left(t \cdot x\right)\right) \]

   3. *-lowering-*.f64 21.3%

      \[\leadsto \mathsf{neg.f64}\left(\mathsf{*.f64}\left(t, x\right)\right) \]

10. Applied egg-rr 21.3%

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

11. Final simplification 21.3%

    \[\leadsto t \cdot \left(0 - x\right) \]
12. Add Preprocessing

Developer Target 1: 95.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\frac{y}{z} - t \cdot \frac{1}{1 - z}\right)\\ t_2 := x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right)\\ \mathbf{if}\;t\_2 < -7.623226303312042 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4133944927702302 \cdot 10^{-211}:\\ \;\;\;\;\frac{y \cdot x}{z} + \left(-\frac{t \cdot x}{1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ y z) (* t (/ 1.0 (- 1.0 z))))))
        (t_2 (* x (- (/ y z) (/ t (- 1.0 z))))))
   (if (< t_2 -7.623226303312042e-196)
     t_1
     (if (< t_2 1.4133944927702302e-211)
       (+ (/ (* y x) z) (- (/ (* t x) (- 1.0 z))))
       t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y / z) - (t * (1.0d0 / (1.0d0 - z))))
    t_2 = x * ((y / z) - (t / (1.0d0 - z)))
    if (t_2 < (-7.623226303312042d-196)) then
        tmp = t_1
    else if (t_2 < 1.4133944927702302d-211) then
        tmp = ((y * x) / z) + -((t * x) / (1.0d0 - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	double t_2 = x * ((y / z) - (t / (1.0 - z)));
	double tmp;
	if (t_2 < -7.623226303312042e-196) {
		tmp = t_1;
	} else if (t_2 < 1.4133944927702302e-211) {
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))))
	t_2 = x * ((y / z) - (t / (1.0 - z)))
	tmp = 0
	if t_2 < -7.623226303312042e-196:
		tmp = t_1
	elif t_2 < 1.4133944927702302e-211:
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y / z) - Float64(t * Float64(1.0 / Float64(1.0 - z)))))
	t_2 = Float64(x * Float64(Float64(y / z) - Float64(t / Float64(1.0 - z))))
	tmp = 0.0
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = Float64(Float64(Float64(y * x) / z) + Float64(-Float64(Float64(t * x) / Float64(1.0 - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y / z) - (t * (1.0 / (1.0 - z))));
	t_2 = x * ((y / z) - (t / (1.0 - z)));
	tmp = 0.0;
	if (t_2 < -7.623226303312042e-196)
		tmp = t_1;
	elseif (t_2 < 1.4133944927702302e-211)
		tmp = ((y * x) / z) + -((t * x) / (1.0 - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t * N[(1.0 / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y / z), $MachinePrecision] - N[(t / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -7.623226303312042e-196], t$95$1, If[Less[t$95$2, 1.4133944927702302e-211], N[(N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision] + (-N[(N[(t * x), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024161 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- (/ y z) (/ t (- 1 z)))) -3811613151656021/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* x (- (/ y z) (* t (/ 1 (- 1 z))))) (if (< (* x (- (/ y z) (/ t (- 1 z)))) 7066972463851151/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (/ (* y x) z) (- (/ (* t x) (- 1 z)))) (* x (- (/ y z) (* t (/ 1 (- 1 z))))))))

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