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

Percentage Accurate: 94.5% → 96.6%

Time: 8.9s

Alternatives: 8

Speedup: 0.5×

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: 94.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 47.0%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 47.0%

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

   5. Simplified 47.0%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. /-lowering-/.f64 99.7%

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

   7. Applied egg-rr 99.7%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. /-lowering-/.f64 99.8%

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

   9. Applied egg-rr 99.8%

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

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

   1. Initial program 99.0%

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

4. Final simplification 99.1%

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

Alternative 2: 94.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.006:\\ \;\;\;\;\left(y - z \cdot t\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -5.5e-30) t_1 (if (<= z 0.006) (* (- y (* z t)) (/ x 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 <= -5.5e-30) {
		tmp = t_1;
	} else if (z <= 0.006) {
		tmp = (y - (z * t)) * (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 * ((y + t) / z)
    if (z <= (-5.5d-30)) then
        tmp = t_1
    else if (z <= 0.006d0) then
        tmp = (y - (z * t)) * (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 * ((y + t) / z);
	double tmp;
	if (z <= -5.5e-30) {
		tmp = t_1;
	} else if (z <= 0.006) {
		tmp = (y - (z * t)) * (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y + t) / z)
	tmp = 0
	if z <= -5.5e-30:
		tmp = t_1
	elif z <= 0.006:
		tmp = (y - (z * t)) * (x / 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 <= -5.5e-30)
		tmp = t_1;
	elseif (z <= 0.006)
		tmp = Float64(Float64(y - Float64(z * t)) * Float64(x / 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 <= -5.5e-30)
		tmp = t_1;
	elseif (z <= 0.006)
		tmp = (y - (z * t)) * (x / 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, -5.5e-30], t$95$1, If[LessEqual[z, 0.006], N[(N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.49999999999999976e-30 or 0.0060000000000000001 < 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 98.6%

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

   5. Simplified 98.6%

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

   if -5.49999999999999976e-30 < z < 0.0060000000000000001

   1. Initial program 92.0%

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

   3. Taylor expanded in z around 0

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

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

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

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

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

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

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

      15. *-commutative N/A

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

      16. *-lowering-*.f64 91.6%

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

   5. Simplified 91.6%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

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

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

      6. /-lowering-/.f64 93.4%

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

   7. Applied egg-rr 93.4%

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

Alternative 3: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y + t}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.006:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (+ y t) z))))
   (if (<= z -1.0) t_1 (if (<= z 0.006) (* 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 <= 0.006) {
		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 <= 0.006d0) 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 <= 0.006) {
		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 <= 0.006:
		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 <= 0.006)
		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 <= 0.006)
		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, 0.006], 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 0.0060000000000000001 < 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 98.6%

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

   5. Simplified 98.6%

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

   if -1 < z < 0.0060000000000000001

   1. Initial program 92.0%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 92.0%

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

Alternative 4: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 0.76:\\ \;\;\;\;t \cdot \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e-123)
   (* y (/ x z))
   (if (<= y 0.76) (* t (/ x (+ z -1.0))) (/ y (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e-123) {
		tmp = y * (x / z);
	} else if (y <= 0.76) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = y / (z / 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) :: tmp
    if (y <= (-1.8d-123)) then
        tmp = y * (x / z)
    else if (y <= 0.76d0) then
        tmp = t * (x / (z + (-1.0d0)))
    else
        tmp = y / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e-123) {
		tmp = y * (x / z);
	} else if (y <= 0.76) {
		tmp = t * (x / (z + -1.0));
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e-123:
		tmp = y * (x / z)
	elif y <= 0.76:
		tmp = t * (x / (z + -1.0))
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e-123)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 0.76)
		tmp = Float64(t * Float64(x / Float64(z + -1.0)));
	else
		tmp = Float64(y / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.8e-123)
		tmp = y * (x / z);
	elseif (y <= 0.76)
		tmp = t * (x / (z + -1.0));
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e-123], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.76], N[(t * N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7999999999999998e-123

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 77.1%

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

   5. Simplified 77.1%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. /-lowering-/.f64 79.3%

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

   7. Applied egg-rr 79.3%

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

   if -1.7999999999999998e-123 < y < 0.76000000000000001

   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. sub-neg N/A

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

      2. distribute-rgt-in N/A

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

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

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

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

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

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

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

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

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

      7. distribute-neg-frac2 N/A

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

      8. /-lowering-/.f64 N/A

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

      9. neg-sub0 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), x\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \left(0 - \left(1 - z\right)\right)\right), x\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), x\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(0, \left(1 - z\right)\right)\right), x\right)\right) \]

      11. --lowering--.f64 98.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), x\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(0, \mathsf{\_.f64}\left(1, z\right)\right)\right), x\right)\right) \]

   4. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x + \frac{t}{0 - \left(1 - z\right)} \cdot x} \]

   5. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 77.1%

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

   7. Simplified 77.1%

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

   if 0.76000000000000001 < y

   1. Initial program 94.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 79.8%

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

   5. Simplified 79.8%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. /-lowering-/.f64 80.6%

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

   7. Applied egg-rr 80.6%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. /-lowering-/.f64 80.8%

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

   9. Applied egg-rr 80.8%

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

Alternative 5: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 0.075:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e-123)
   (* y (/ x z))
   (if (<= y 0.075) (* x (/ t z)) (/ y (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e-123) {
		tmp = y * (x / z);
	} else if (y <= 0.075) {
		tmp = x * (t / z);
	} else {
		tmp = y / (z / 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) :: tmp
    if (y <= (-1.8d-123)) then
        tmp = y * (x / z)
    else if (y <= 0.075d0) then
        tmp = x * (t / z)
    else
        tmp = y / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e-123) {
		tmp = y * (x / z);
	} else if (y <= 0.075) {
		tmp = x * (t / z);
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e-123:
		tmp = y * (x / z)
	elif y <= 0.075:
		tmp = x * (t / z)
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e-123)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 0.075)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = Float64(y / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.8e-123)
		tmp = y * (x / z);
	elseif (y <= 0.075)
		tmp = x * (t / z);
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e-123], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.075], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7999999999999998e-123

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 77.1%

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

   5. Simplified 77.1%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. /-lowering-/.f64 79.3%

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

   7. Applied egg-rr 79.3%

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

   if -1.7999999999999998e-123 < y < 0.0749999999999999972

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. +-lowering-+.f64 61.1%

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

   5. Simplified 61.1%

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

   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 56.5%

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

   8. Simplified 56.5%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

      6. associate-*l/ N/A

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

      7. *-lft-identity N/A

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

      8. /-lowering-/.f64 58.2%

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

   10. Applied egg-rr 58.2%

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

   if 0.0749999999999999972 < y

   1. Initial program 94.5%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 79.8%

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

   5. Simplified 79.8%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. /-lowering-/.f64 80.6%

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

   7. Applied egg-rr 80.6%

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

      1. clear-num N/A

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

      2. un-div-inv N/A

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

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

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

      4. /-lowering-/.f64 80.8%

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

   9. Applied egg-rr 80.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 0.075:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.075:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x z))))
   (if (<= y -1.9e-123) t_1 (if (<= y 0.075) (* x (/ t z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / z);
	double tmp;
	if (y <= -1.9e-123) {
		tmp = t_1;
	} else if (y <= 0.075) {
		tmp = x * (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 = y * (x / z)
    if (y <= (-1.9d-123)) then
        tmp = t_1
    else if (y <= 0.075d0) then
        tmp = x * (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 = y * (x / z);
	double tmp;
	if (y <= -1.9e-123) {
		tmp = t_1;
	} else if (y <= 0.075) {
		tmp = x * (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / z)
	tmp = 0
	if y <= -1.9e-123:
		tmp = t_1
	elif y <= 0.075:
		tmp = x * (t / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -1.9e-123)
		tmp = t_1;
	elseif (y <= 0.075)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / z);
	tmp = 0.0;
	if (y <= -1.9e-123)
		tmp = t_1;
	elseif (y <= 0.075)
		tmp = x * (t / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e-123], t$95$1, If[LessEqual[y, 0.075], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.89999999999999998e-123 or 0.0749999999999999972 < y

   1. Initial program 93.9%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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 78.3%

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

   5. Simplified 78.3%

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. /-lowering-/.f64 79.9%

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

   7. Applied egg-rr 79.9%

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

   if -1.89999999999999998e-123 < y < 0.0749999999999999972

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. +-lowering-+.f64 61.1%

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

   5. Simplified 61.1%

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

   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 56.5%

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

   8. Simplified 56.5%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

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

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

      6. associate-*l/ N/A

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

      7. *-lft-identity N/A

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

      8. /-lowering-/.f64 58.2%

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

   10. Applied egg-rr 58.2%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-123}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 0.075:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(0 - x\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+252}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 0.0 x))))
   (if (<= t -1.7e+155) t_1 (if (<= t 9.2e+252) (* (/ y z) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (0.0 - x);
	double tmp;
	if (t <= -1.7e+155) {
		tmp = t_1;
	} else if (t <= 9.2e+252) {
		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 * (0.0d0 - x)
    if (t <= (-1.7d+155)) then
        tmp = t_1
    else if (t <= 9.2d+252) 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 * (0.0 - x);
	double tmp;
	if (t <= -1.7e+155) {
		tmp = t_1;
	} else if (t <= 9.2e+252) {
		tmp = (y / z) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (0.0 - x)
	tmp = 0
	if t <= -1.7e+155:
		tmp = t_1
	elif t <= 9.2e+252:
		tmp = (y / z) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(0.0 - x))
	tmp = 0.0
	if (t <= -1.7e+155)
		tmp = t_1;
	elseif (t <= 9.2e+252)
		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 * (0.0 - x);
	tmp = 0.0;
	if (t <= -1.7e+155)
		tmp = t_1;
	elseif (t <= 9.2e+252)
		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[(0.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+155], t$95$1, If[LessEqual[t, 9.2e+252], N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7e155 or 9.1999999999999999e252 < t

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 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 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 46.3%

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

   8. Simplified 46.3%

      \[\leadsto \color{blue}{0 - x \cdot t} \]
   9. 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 46.3%

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

   10. Applied egg-rr 46.3%

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

   if -1.7e155 < t < 9.1999999999999999e252

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

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

      3. /-lowering-/.f64 74.3%

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

   5. Simplified 74.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \left(0 - x\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+252}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(0 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 23.3% 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 95.8%

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

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

5. Simplified 59.1%

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

6. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

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

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

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

   4. *-commutative N/A

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

   5. *-lowering-*.f64 22.9%

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

8. Simplified 22.9%

   \[\leadsto \color{blue}{0 - x \cdot t} \]
9. 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 22.9%

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

10. Applied egg-rr 22.9%

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

11. Final simplification 22.9%

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

Developer Target 1: 94.9% 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 2024152 
(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)))))