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

Percentage Accurate: 95.1% → 98.0%

Time: 10.0s

Alternatives: 11

Speedup: 0.6×

• 22.2% 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: 95.1% 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: 98.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} + \frac{t}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;t\_1 \leq 10^{+284}:\\ \;\;\;\;t\_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ y z) (/ t (+ z -1.0)))))
   (if (<= t_1 (- INFINITY))
     (/ (* y x) z)
     (if (<= t_1 1e+284) (* t_1 x) (* y (/ x z))))))

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 if (t_1 <= 1e+284) {
		tmp = t_1 * x;
	} else {
		tmp = y * (x / z);
	}
	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 if (t_1 <= 1e+284) {
		tmp = t_1 * x;
	} else {
		tmp = y * (x / z);
	}
	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
	elif t_1 <= 1e+284:
		tmp = t_1 * x
	else:
		tmp = y * (x / z)
	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(Float64(y * x) / z);
	elseif (t_1 <= 1e+284)
		tmp = Float64(t_1 * x);
	else
		tmp = Float64(y * Float64(x / z));
	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;
	elseif (t_1 <= 1e+284)
		tmp = t_1 * x;
	else
		tmp = y * (x / z);
	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[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 1e+284], N[(t$95$1 * x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 68.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 68.7%

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

   5. Simplified 68.7%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
   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 100.0%

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

   7. Applied egg-rr 100.0%

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

   if -inf.0 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 1.00000000000000008e284

   1. Initial program 97.6%

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

   if 1.00000000000000008e284 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 73.3%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 68.1%

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

   5. Simplified 68.1%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. div-inv N/A

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

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

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

      6. /-lowering-/.f64 99.9%

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

   7. Applied egg-rr 99.9%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} + \frac{t}{z + -1} \leq -\infty:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} + \frac{t}{z + -1} \leq 10^{+284}:\\ \;\;\;\;\left(\frac{y}{z} + \frac{t}{z + -1}\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-248}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -6.5e+78)
     t_1
     (if (<= t -6e-248)
       (* (/ y z) x)
       (if (<= t 1.55e+159) (/ 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 <= -6.5e+78) {
		tmp = t_1;
	} else if (t <= -6e-248) {
		tmp = (y / z) * x;
	} else if (t <= 1.55e+159) {
		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 <= (-6.5d+78)) then
        tmp = t_1
    else if (t <= (-6d-248)) then
        tmp = (y / z) * x
    else if (t <= 1.55d+159) 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 <= -6.5e+78) {
		tmp = t_1;
	} else if (t <= -6e-248) {
		tmp = (y / z) * x;
	} else if (t <= 1.55e+159) {
		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 <= -6.5e+78:
		tmp = t_1
	elif t <= -6e-248:
		tmp = (y / z) * x
	elif t <= 1.55e+159:
		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 <= -6.5e+78)
		tmp = t_1;
	elseif (t <= -6e-248)
		tmp = Float64(Float64(y / z) * x);
	elseif (t <= 1.55e+159)
		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 * (t / z);
	tmp = 0.0;
	if (t <= -6.5e+78)
		tmp = t_1;
	elseif (t <= -6e-248)
		tmp = (y / z) * x;
	elseif (t <= 1.55e+159)
		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, -6.5e+78], t$95$1, If[LessEqual[t, -6e-248], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 1.55e+159], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.50000000000000036e78 or 1.5499999999999999e159 < t

   1. Initial program 97.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 52.9%

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

   8. Simplified 52.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 62.5%

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

   10. Applied egg-rr 62.5%

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

   if -6.50000000000000036e78 < t < -6.00000000000000027e-248

   1. Initial program 95.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 84.6%

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

   5. Simplified 84.6%

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

   if -6.00000000000000027e-248 < t < 1.5499999999999999e159

   1. Initial program 89.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 70.4%

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

   5. Simplified 70.4%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. div-inv N/A

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

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

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

      6. /-lowering-/.f64 75.4%

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

   7. Applied egg-rr 75.4%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. /-lowering-/.f64 75.5%

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

   9. Applied egg-rr 75.5%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-248}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-248}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -2.7e+79)
     t_1
     (if (<= t -6.4e-248)
       (* (/ y z) x)
       (if (<= t 3.7e+157) (* y (/ x z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -2.7e+79) {
		tmp = t_1;
	} else if (t <= -6.4e-248) {
		tmp = (y / z) * x;
	} else if (t <= 3.7e+157) {
		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 * (t / z)
    if (t <= (-2.7d+79)) then
        tmp = t_1
    else if (t <= (-6.4d-248)) then
        tmp = (y / z) * x
    else if (t <= 3.7d+157) 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 * (t / z);
	double tmp;
	if (t <= -2.7e+79) {
		tmp = t_1;
	} else if (t <= -6.4e-248) {
		tmp = (y / z) * x;
	} else if (t <= 3.7e+157) {
		tmp = y * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -2.7e+79:
		tmp = t_1
	elif t <= -6.4e-248:
		tmp = (y / z) * x
	elif t <= 3.7e+157:
		tmp = y * (x / z)
	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 <= -2.7e+79)
		tmp = t_1;
	elseif (t <= -6.4e-248)
		tmp = Float64(Float64(y / z) * x);
	elseif (t <= 3.7e+157)
		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 * (t / z);
	tmp = 0.0;
	if (t <= -2.7e+79)
		tmp = t_1;
	elseif (t <= -6.4e-248)
		tmp = (y / z) * x;
	elseif (t <= 3.7e+157)
		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[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.7e+79], t$95$1, If[LessEqual[t, -6.4e-248], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t, 3.7e+157], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7e79 or 3.6999999999999999e157 < t

   1. Initial program 97.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 52.9%

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

   8. Simplified 52.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 62.5%

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

   10. Applied egg-rr 62.5%

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

   if -2.7e79 < t < -6.40000000000000035e-248

   1. Initial program 95.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 84.6%

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

   5. Simplified 84.6%

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

   if -6.40000000000000035e-248 < t < 3.6999999999999999e157

   1. Initial program 89.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 70.4%

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

   5. Simplified 70.4%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. div-inv N/A

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

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

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

      6. /-lowering-/.f64 75.4%

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

   7. Applied egg-rr 75.4%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-248}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -0.9:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x \cdot \left(y - z \cdot t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -0.9) t_1 (if (<= z 1.0) (/ (* 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 <= -0.9) {
		tmp = t_1;
	} else if (z <= 1.0) {
		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 <= (-0.9d0)) then
        tmp = t_1
    else if (z <= 1.0d0) 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 <= -0.9) {
		tmp = t_1;
	} else if (z <= 1.0) {
		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 <= -0.9:
		tmp = t_1
	elif z <= 1.0:
		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 <= -0.9)
		tmp = t_1;
	elseif (z <= 1.0)
		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 <= -0.9)
		tmp = t_1;
	elseif (z <= 1.0)
		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, -0.9], t$95$1, If[LessEqual[z, 1.0], 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 < -0.900000000000000022 or 1 < z

   1. Initial program 96.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 95.0%

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

   5. Simplified 95.0%

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

   if -0.900000000000000022 < z < 1

   1. Initial program 90.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 95.2%

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

   5. Simplified 95.2%

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

Alternative 5: 94.3% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -1.0) t_1 (if (<= z 1.0) (* 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 <= 1.0) {
		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 <= 1.0d0) 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 <= 1.0) {
		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 <= 1.0:
		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 <= 1.0)
		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 <= 1.0)
		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, 1.0], 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 1 < z

   1. Initial program 96.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 95.0%

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

   5. Simplified 95.0%

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

   if -1 < z < 1

   1. Initial program 90.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 90.0%

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

Alternative 6: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= z -3.7e+123) t_1 (if (<= z 7.2e+55) (* 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 <= -3.7e+123) {
		tmp = t_1;
	} else if (z <= 7.2e+55) {
		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 <= (-3.7d+123)) then
        tmp = t_1
    else if (z <= 7.2d+55) 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 <= -3.7e+123) {
		tmp = t_1;
	} else if (z <= 7.2e+55) {
		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 <= -3.7e+123:
		tmp = t_1
	elif z <= 7.2e+55:
		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 <= -3.7e+123)
		tmp = t_1;
	elseif (z <= 7.2e+55)
		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 <= -3.7e+123)
		tmp = t_1;
	elseif (z <= 7.2e+55)
		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, -3.7e+123], t$95$1, If[LessEqual[z, 7.2e+55], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.69999999999999996e123 or 7.19999999999999975e55 < 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 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 51.7%

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

   8. Simplified 51.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 60.2%

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

   10. Applied egg-rr 60.2%

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

   if -3.69999999999999996e123 < z < 7.19999999999999975e55

   1. Initial program 92.7%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 83.0%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+156}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -3.5e+79) t_1 (if (<= t 5.6e+156) (/ (* y x) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double tmp;
	if (t <= -3.5e+79) {
		tmp = t_1;
	} else if (t <= 5.6e+156) {
		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 * (t / z)
    if (t <= (-3.5d+79)) then
        tmp = t_1
    else if (t <= 5.6d+156) 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 * (t / z);
	double tmp;
	if (t <= -3.5e+79) {
		tmp = t_1;
	} else if (t <= 5.6e+156) {
		tmp = (y * x) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	tmp = 0
	if t <= -3.5e+79:
		tmp = t_1
	elif t <= 5.6e+156:
		tmp = (y * x) / z
	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 <= -3.5e+79)
		tmp = t_1;
	elseif (t <= 5.6e+156)
		tmp = Float64(Float64(y * x) / z);
	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 <= -3.5e+79)
		tmp = t_1;
	elseif (t <= 5.6e+156)
		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[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+79], t$95$1, If[LessEqual[t, 5.6e+156], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4999999999999998e79 or 5.59999999999999975e156 < t

   1. Initial program 97.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 52.9%

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

   8. Simplified 52.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 62.5%

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

   10. Applied egg-rr 62.5%

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

   if -3.4999999999999998e79 < t < 5.59999999999999975e156

   1. Initial program 91.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 75.9%

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

   5. Simplified 75.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]
   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 77.6%

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

   7. Applied egg-rr 77.6%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+156}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+160}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))))
   (if (<= t -3.5e+79) t_1 (if (<= t 1.16e+160) (* (/ 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 <= -3.5e+79) {
		tmp = t_1;
	} else if (t <= 1.16e+160) {
		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 <= (-3.5d+79)) then
        tmp = t_1
    else if (t <= 1.16d+160) 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 <= -3.5e+79) {
		tmp = t_1;
	} else if (t <= 1.16e+160) {
		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 <= -3.5e+79:
		tmp = t_1
	elif t <= 1.16e+160:
		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 <= -3.5e+79)
		tmp = t_1;
	elseif (t <= 1.16e+160)
		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 <= -3.5e+79)
		tmp = t_1;
	elseif (t <= 1.16e+160)
		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, -3.5e+79], t$95$1, If[LessEqual[t, 1.16e+160], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4999999999999998e79 or 1.16000000000000006e160 < t

   1. Initial program 97.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 52.9%

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

   8. Simplified 52.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 62.5%

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

   10. Applied egg-rr 62.5%

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

   if -3.4999999999999998e79 < t < 1.16000000000000006e160

   1. Initial program 91.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+160}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))))
   (if (<= t -3.5e+79) t_1 (if (<= t 1.15e+159) (* (/ 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 <= -3.5e+79) {
		tmp = t_1;
	} else if (t <= 1.15e+159) {
		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 <= (-3.5d+79)) then
        tmp = t_1
    else if (t <= 1.15d+159) 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 <= -3.5e+79) {
		tmp = t_1;
	} else if (t <= 1.15e+159) {
		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 <= -3.5e+79:
		tmp = t_1
	elif t <= 1.15e+159:
		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 <= -3.5e+79)
		tmp = t_1;
	elseif (t <= 1.15e+159)
		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 <= -3.5e+79)
		tmp = t_1;
	elseif (t <= 1.15e+159)
		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, -3.5e+79], t$95$1, If[LessEqual[t, 1.15e+159], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4999999999999998e79 or 1.14999999999999998e159 < t

   1. Initial program 97.4%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 52.9%

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

   8. Simplified 52.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 50.5%

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

   10. Applied egg-rr 50.5%

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

   if -3.4999999999999998e79 < t < 1.14999999999999998e159

   1. Initial program 91.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+159}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.2% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x 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 = t * (x / 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 = t * (x / 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 = t * (x / 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 = t * (x / 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(t * Float64(x / 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 = t * (x / 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[(t * N[(x / 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 96.2%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 84.7%

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

   5. Simplified 84.7%

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

   6. Taylor expanded in y around 0

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 48.1%

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

   8. Simplified 48.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 47.6%

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

   10. Applied egg-rr 47.6%

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

   if -1 < z < 1

   1. Initial program 90.8%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 90.0%

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

   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 30.5%

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

   8. Simplified 30.5%

      \[\leadsto \color{blue}{0 - t \cdot x} \]
   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 30.5%

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

   10. Applied egg-rr 30.5%

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

4. Final simplification 39.2%

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

Alternative 11: 23.0% 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

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

5. Simplified 61.8%

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

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 19.1%

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

8. Simplified 19.1%

   \[\leadsto \color{blue}{0 - t \cdot x} \]
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 19.1%

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

10. Applied egg-rr 19.1%

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

11. Final simplification 19.1%

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

Developer Target 1: 95.4% 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 2024158 
(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)))))