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

Percentage Accurate: 94.7% → 95.8%

Time: 10.1s

Alternatives: 10

Speedup: 0.6×

• 21.1% 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: 94.7% 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: 95.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+282}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 -5e+282) (* 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 <= -5e+282) {
		tmp = y * (x / z);
	} else {
		tmp = t_1 * x;
	}
	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 = (y / z) + (t / (z + (-1.0d0)))
    if (t_1 <= (-5d+282)) then
        tmp = y * (x / z)
    else
        tmp = t_1 * x
    end if
    code = tmp
end function

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 <= -5e+282) {
		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 <= -5e+282:
		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 <= -5e+282)
		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 <= -5e+282)
		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, -5e+282], 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))) < -4.99999999999999978e282

   1. Initial program 75.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 75.5%

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

   5. Simplified 75.5%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. /-lowering-/.f64 78.9%

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

   7. Applied egg-rr 78.9%

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

      1. associate-/r/ N/A

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

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

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

      3. /-lowering-/.f64 100.0%

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

   9. Applied egg-rr 100.0%

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

   if -4.99999999999999978e282 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 98.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -5 \cdot 10^{+282}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -0.95:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0036:\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -0.95) t_1 (if (<= z 0.0036) (/ (* 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 <= -0.95) {
		tmp = t_1;
	} else if (z <= 0.0036) {
		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 <= (-0.95d0)) then
        tmp = t_1
    else if (z <= 0.0036d0) 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 <= -0.95) {
		tmp = t_1;
	} else if (z <= 0.0036) {
		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 <= -0.95:
		tmp = t_1
	elif z <= 0.0036:
		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 <= -0.95)
		tmp = t_1;
	elseif (z <= 0.0036)
		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 <= -0.95)
		tmp = t_1;
	elseif (z <= 0.0036)
		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, -0.95], t$95$1, If[LessEqual[z, 0.0036], 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 < -0.94999999999999996 or 0.0035999999999999999 < z

   1. Initial program 99.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 98.4%

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

   5. Simplified 98.4%

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

   if -0.94999999999999996 < z < 0.0035999999999999999

   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 95.7%

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

   5. Simplified 95.7%

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

Alternative 3: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -1.0) t_1 (if (<= z 5.6e-5) (* 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 <= 5.6e-5) {
		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 <= 5.6d-5) 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 <= 5.6e-5) {
		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 <= 5.6e-5:
		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 <= 5.6e-5)
		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 <= 5.6e-5)
		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, 5.6e-5], 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 5.59999999999999992e-5 < z

   1. Initial program 99.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 98.4%

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

   5. Simplified 98.4%

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

   if -1 < z < 5.59999999999999992e-5

   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

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

   5. Simplified 92.7%

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

Alternative 4: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z + -1}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (+ z -1.0)))))
   (if (<= t -4.8e+152) t_1 (if (<= t 4.2e+81) (/ x (/ z y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / (z + -1.0));
	double tmp;
	if (t <= -4.8e+152) {
		tmp = t_1;
	} else if (t <= 4.2e+81) {
		tmp = x / (z / y);
	} 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 * (t / (z + (-1.0d0)))
    if (t <= (-4.8d+152)) then
        tmp = t_1
    else if (t <= 4.2d+81) then
        tmp = x / (z / y)
    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 * (t / (z + -1.0));
	double tmp;
	if (t <= -4.8e+152) {
		tmp = t_1;
	} else if (t <= 4.2e+81) {
		tmp = x / (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / (z + -1.0))
	tmp = 0
	if t <= -4.8e+152:
		tmp = t_1
	elif t <= 4.2e+81:
		tmp = x / (z / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(z + -1.0)))
	tmp = 0.0
	if (t <= -4.8e+152)
		tmp = t_1;
	elseif (t <= 4.2e+81)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / (z + -1.0));
	tmp = 0.0;
	if (t <= -4.8e+152)
		tmp = t_1;
	elseif (t <= 4.2e+81)
		tmp = x / (z / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e+152], t$95$1, If[LessEqual[t, 4.2e+81], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.7999999999999998e152 or 4.1999999999999997e81 < t

   1. Initial program 93.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 93.8%

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

   4. Applied egg-rr 93.8%

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

   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. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. +-lowering-+.f64 79.9%

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

   7. Simplified 79.9%

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

   if -4.7999999999999998e152 < t < 4.1999999999999997e81

   1. Initial program 97.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 82.0%

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

   5. Simplified 82.0%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. /-lowering-/.f64 82.3%

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

   7. Applied egg-rr 82.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= z -3.1e+87) t_1 (if (<= z 1.05e+15) (* x (- (/ y z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -3.1e+87) {
		tmp = t_1;
	} else if (z <= 1.05e+15) {
		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 * (t / z)
    if (z <= (-3.1d+87)) then
        tmp = t_1
    else if (z <= 1.05d+15) 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 * (t / z);
	double tmp;
	if (z <= -3.1e+87) {
		tmp = t_1;
	} else if (z <= 1.05e+15) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if z <= -3.1e+87:
		tmp = t_1
	elif z <= 1.05e+15:
		tmp = x * ((y / z) - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (z <= -3.1e+87)
		tmp = t_1;
	elseif (z <= 1.05e+15)
		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 * (t / z);
	tmp = 0.0;
	if (z <= -3.1e+87)
		tmp = t_1;
	elseif (z <= 1.05e+15)
		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[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+87], t$95$1, If[LessEqual[z, 1.05e+15], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e87 or 1.05e15 < z

   1. Initial program 98.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 98.8%

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

   4. Applied egg-rr 98.8%

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

   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. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. +-lowering-+.f64 65.9%

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

   7. Simplified 65.9%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 65.8%

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

   if -3.1e87 < z < 1.05e15

   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 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 87.7%

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

Alternative 6: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+153}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.05e+153)
   (/ x (/ z t))
   (if (<= t 9.6e+80) (/ x (/ z y)) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e+153) {
		tmp = x / (z / t);
	} else if (t <= 9.6e+80) {
		tmp = x / (z / y);
	} else {
		tmp = x * (t / 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 (t <= (-1.05d+153)) then
        tmp = x / (z / t)
    else if (t <= 9.6d+80) then
        tmp = x / (z / y)
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e+153) {
		tmp = x / (z / t);
	} else if (t <= 9.6e+80) {
		tmp = x / (z / y);
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.05e+153:
		tmp = x / (z / t)
	elif t <= 9.6e+80:
		tmp = x / (z / y)
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.05e+153)
		tmp = Float64(x / Float64(z / t));
	elseif (t <= 9.6e+80)
		tmp = Float64(x / Float64(z / y));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.05e+153)
		tmp = x / (z / t);
	elseif (t <= 9.6e+80)
		tmp = x / (z / y);
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.05e+153], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.6e+80], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05000000000000008e153

   1. Initial program 94.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 94.1%

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

   4. Applied egg-rr 94.1%

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

   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. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. +-lowering-+.f64 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 57.9%

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

       1. clear-num N/A

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

       2. un-div-inv N/A

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

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

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

       4. /-lowering-/.f64 58.0%

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

   12. Applied egg-rr 58.0%

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

   if -1.05000000000000008e153 < t < 9.59999999999999916e80

   1. Initial program 97.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 82.0%

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

   5. Simplified 82.0%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. /-lowering-/.f64 82.3%

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

   7. Applied egg-rr 82.3%

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

   if 9.59999999999999916e80 < t

   1. Initial program 93.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 93.6%

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

   4. Applied egg-rr 93.6%

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

   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. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. +-lowering-+.f64 79.6%

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

   7. Simplified 79.6%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 59.3%

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

Alternative 7: 68.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.3e+152)
   (/ x (/ z t))
   (if (<= t 1.8e+82) (* (/ y z) x) (* x (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.3e+152) {
		tmp = x / (z / t);
	} else if (t <= 1.8e+82) {
		tmp = (y / z) * x;
	} else {
		tmp = x * (t / 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 (t <= (-2.3d+152)) then
        tmp = x / (z / t)
    else if (t <= 1.8d+82) then
        tmp = (y / z) * x
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.3e+152) {
		tmp = x / (z / t);
	} else if (t <= 1.8e+82) {
		tmp = (y / z) * x;
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.3e+152:
		tmp = x / (z / t)
	elif t <= 1.8e+82:
		tmp = (y / z) * x
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.3e+152)
		tmp = Float64(x / Float64(z / t));
	elseif (t <= 1.8e+82)
		tmp = Float64(Float64(y / z) * x);
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.3e+152)
		tmp = x / (z / t);
	elseif (t <= 1.8e+82)
		tmp = (y / z) * x;
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.3e+152], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e+82], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.29999999999999985e152

   1. Initial program 94.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 94.1%

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

   4. Applied egg-rr 94.1%

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

   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. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. +-lowering-+.f64 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 57.9%

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

       1. clear-num N/A

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

       2. un-div-inv N/A

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

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

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

       4. /-lowering-/.f64 58.0%

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

   12. Applied egg-rr 58.0%

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

   if -2.29999999999999985e152 < t < 1.80000000000000007e82

   1. Initial program 97.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 82.0%

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

   5. Simplified 82.0%

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

   if 1.80000000000000007e82 < t

   1. Initial program 93.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 93.6%

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

   4. Applied egg-rr 93.6%

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

   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. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. +-lowering-+.f64 79.6%

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

   7. Simplified 79.6%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 59.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+152}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -1.3e+154) t_1 (if (<= t 2.6e+81) (* (/ y z) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -1.3e+154) {
		tmp = t_1;
	} else if (t <= 2.6e+81) {
		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 * (t / z)
    if (t <= (-1.3d+154)) then
        tmp = t_1
    else if (t <= 2.6d+81) 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 * (t / z);
	double tmp;
	if (t <= -1.3e+154) {
		tmp = t_1;
	} else if (t <= 2.6e+81) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -1.3e+154:
		tmp = t_1
	elif t <= 2.6e+81:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t <= -1.3e+154)
		tmp = t_1;
	elseif (t <= 2.6e+81)
		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 = x * (t / z);
	tmp = 0.0;
	if (t <= -1.3e+154)
		tmp = t_1;
	elseif (t <= 2.6e+81)
		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[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+154], t$95$1, If[LessEqual[t, 2.6e+81], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.29999999999999994e154 or 2.59999999999999992e81 < t

   1. Initial program 93.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 93.8%

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

   4. Applied egg-rr 93.8%

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

   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. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. +-lowering-+.f64 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 58.7%

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

   if -1.29999999999999994e154 < t < 2.59999999999999992e81

   1. Initial program 97.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 45.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t \cdot \left(0 - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= z -1.0) t_1 (if (<= z 1.0) (* t (- 0.0 x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		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 = x * (t / z)
    if (z <= (-1.0d0)) then
        tmp = t_1
    else if (z <= 1.0d0) 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 = x * (t / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = t * (0.0 - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if z <= -1.0:
		tmp = t_1
	elif z <= 1.0:
		tmp = t * (0.0 - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= 1.0)
		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 = x * (t / z);
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= 1.0)
		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[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, 1.0], N[(t * N[(0.0 - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 99.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 99.0%

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

   4. Applied egg-rr 99.0%

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

   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. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. +-lowering-+.f64 61.8%

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

   7. Simplified 61.8%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 61.1%

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

   if -1 < z < 1

   1. Initial program 93.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 93.6%

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

   4. Applied egg-rr 93.6%

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

   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. mul-1-neg N/A

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

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

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. mul-1-neg N/A

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

      8. distribute-neg-in N/A

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

      9. metadata-eval N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. +-lowering-+.f64 35.1%

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

   7. Simplified 35.1%

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

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot x\right)} \]
   9. 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. *-commutative N/A

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

      5. *-lowering-*.f64 34.3%

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

   10. Simplified 34.3%

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

       1. sub0-neg N/A

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

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

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

       3. *-commutative N/A

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

       4. *-lowering-*.f64 34.3%

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

   12. Applied egg-rr 34.3%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t \cdot \left(0 - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 23.6% 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 96.5%

   \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
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 96.4%

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

4. Applied egg-rr 96.4%

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

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. mul-1-neg N/A

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

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

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

   5. mul-1-neg N/A

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

   6. sub-neg N/A

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

   7. mul-1-neg N/A

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

   8. distribute-neg-in N/A

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

   9. metadata-eval N/A

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

   10. mul-1-neg N/A

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

   11. remove-double-neg N/A

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

   12. +-lowering-+.f64 49.2%

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

7. Simplified 49.2%

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

8. Taylor expanded in z around 0

   \[\leadsto \color{blue}{-1 \cdot \left(t \cdot x\right)} \]
9. 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. *-commutative N/A

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

   5. *-lowering-*.f64 25.4%

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

10. Simplified 25.4%

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

    1. sub0-neg N/A

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

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

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

    3. *-commutative N/A

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

    4. *-lowering-*.f64 25.4%

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

12. Applied egg-rr 25.4%

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

13. Final simplification 25.4%

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

Developer Target 1: 95.1% 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 2024160 
(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)))))