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

Percentage Accurate: 94.4% → 96.3%

Time: 7.8s

Alternatives: 10

Speedup: 0.9×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.4% 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: 96.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} - \frac{t}{1 - z}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;x \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ y z) (/ t (- 1.0 z)))))
   (if (<= t_1 2e+305) (* x t_1) (/ (* y x) z))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 2e+305) {
		tmp = x * t_1;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / z) - (t / (1.0d0 - z))
    if (t_1 <= 2d+305) then
        tmp = x * t_1
    else
        tmp = (y * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) - (t / (1.0 - z));
	double tmp;
	if (t_1 <= 2e+305) {
		tmp = x * t_1;
	} else {
		tmp = (y * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) - (t / (1.0 - z))
	tmp = 0
	if t_1 <= 2e+305:
		tmp = x * t_1
	else:
		tmp = (y * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) - Float64(t / Float64(1.0 - z)))
	tmp = 0.0
	if (t_1 <= 2e+305)
		tmp = Float64(x * t_1);
	else
		tmp = Float64(Float64(y * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) - (t / (1.0 - z));
	tmp = 0.0;
	if (t_1 <= 2e+305)
		tmp = x * t_1;
	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[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+305], N[(x * t$95$1), $MachinePrecision], N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z))) < 1.9999999999999999e305

   1. Initial program 96.8%

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

   if 1.9999999999999999e305 < (-.f64 (/.f64 y z) (/.f64 t (-.f64 #s(literal 1 binary64) z)))

   1. Initial program 57.6%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 57.6

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

   5. Applied rewrites 57.6%

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

   7. Applied rewrites 99.9%

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

Alternative 2: 64.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{z}\\ t_2 := x \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+279}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+155}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+247}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t z))) (t_2 (* x (- t))))
   (if (<= t -2.9e+279)
     t_1
     (if (<= t -8.6e+155)
       t_2
       (if (<= t 6.7e+168) (* y (/ x z)) (if (<= t 8e+247) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / z);
	double t_2 = x * -t;
	double tmp;
	if (t <= -2.9e+279) {
		tmp = t_1;
	} else if (t <= -8.6e+155) {
		tmp = t_2;
	} else if (t <= 6.7e+168) {
		tmp = y * (x / z);
	} else if (t <= 8e+247) {
		tmp = t_2;
	} 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 * (t / z)
    t_2 = x * -t
    if (t <= (-2.9d+279)) then
        tmp = t_1
    else if (t <= (-8.6d+155)) then
        tmp = t_2
    else if (t <= 6.7d+168) then
        tmp = y * (x / z)
    else if (t <= 8d+247) then
        tmp = t_2
    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 t_2 = x * -t;
	double tmp;
	if (t <= -2.9e+279) {
		tmp = t_1;
	} else if (t <= -8.6e+155) {
		tmp = t_2;
	} else if (t <= 6.7e+168) {
		tmp = y * (x / z);
	} else if (t <= 8e+247) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / z)
	t_2 = x * -t
	tmp = 0
	if t <= -2.9e+279:
		tmp = t_1
	elif t <= -8.6e+155:
		tmp = t_2
	elif t <= 6.7e+168:
		tmp = y * (x / z)
	elif t <= 8e+247:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / z))
	t_2 = Float64(x * Float64(-t))
	tmp = 0.0
	if (t <= -2.9e+279)
		tmp = t_1;
	elseif (t <= -8.6e+155)
		tmp = t_2;
	elseif (t <= 6.7e+168)
		tmp = Float64(y * Float64(x / z));
	elseif (t <= 8e+247)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / z);
	t_2 = x * -t;
	tmp = 0.0;
	if (t <= -2.9e+279)
		tmp = t_1;
	elseif (t <= -8.6e+155)
		tmp = t_2;
	elseif (t <= 6.7e+168)
		tmp = y * (x / z);
	elseif (t <= 8e+247)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x * (-t)), $MachinePrecision]}, If[LessEqual[t, -2.9e+279], t$95$1, If[LessEqual[t, -8.6e+155], t$95$2, If[LessEqual[t, 6.7e+168], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+247], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.89999999999999975e279 or 7.99999999999999962e247 < t

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 88.1

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

   5. Applied rewrites 88.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 88.1%

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

   if -2.89999999999999975e279 < t < -8.6000000000000005e155 or 6.7000000000000003e168 < t < 7.99999999999999962e247

   1. Initial program 97.5%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 97.5

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

   4. Applied rewrites 97.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 69.8

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

   7. Applied rewrites 69.8%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 65.3%

       \[\leadsto x \cdot \left(-t\right) \]

   if -8.6000000000000005e155 < t < 6.7000000000000003e168

   1. Initial program 92.8%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 76.1

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

   5. Applied rewrites 76.1%

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

   7. Applied rewrites 79.1%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+279}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+168}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+247}:\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 880000\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot z\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.95) (not (<= z 880000.0)))
   (* x (/ (+ t y) z))
   (/ (* x (- y (* t z))) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.95) || !(z <= 880000.0)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = (x * (y - (t * z))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-0.95d0)) .or. (.not. (z <= 880000.0d0))) then
        tmp = x * ((t + y) / z)
    else
        tmp = (x * (y - (t * z))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.95) || !(z <= 880000.0)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = (x * (y - (t * z))) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.95) or not (z <= 880000.0):
		tmp = x * ((t + y) / z)
	else:
		tmp = (x * (y - (t * z))) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.95) || !(z <= 880000.0))
		tmp = Float64(x * Float64(Float64(t + y) / z));
	else
		tmp = Float64(Float64(x * Float64(y - Float64(t * z))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.95) || ~((z <= 880000.0)))
		tmp = x * ((t + y) / z);
	else
		tmp = (x * (y - (t * z))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.95], N[Not[LessEqual[z, 880000.0]], $MachinePrecision]], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.94999999999999996 or 8.8e5 < z

   1. Initial program 96.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 94.1

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

   5. Applied rewrites 94.1%

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

   if -0.94999999999999996 < z < 8.8e5

   1. Initial program 91.1%

      \[x \cdot \left(\frac{y}{z} - \frac{t}{1 - z}\right) \]
   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. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. mul-1-neg N/A

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

      4. unsub-neg N/A

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

      5. associate-*r* N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

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

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. lower-*.f64 N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

      14. lower--.f64 N/A

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

      15. lower-*.f64 91.9

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

   5. Applied rewrites 91.9%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 880000\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - t \cdot z\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.54\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.54)))
   (* x (/ (+ t y) z))
   (* x (- (/ y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.54)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 0.54d0))) then
        tmp = x * ((t + y) / z)
    else
        tmp = x * ((y / z) - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.54)) {
		tmp = x * ((t + y) / z);
	} else {
		tmp = x * ((y / z) - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.54):
		tmp = x * ((t + y) / z)
	else:
		tmp = x * ((y / z) - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.54))
		tmp = Float64(x * Float64(Float64(t + y) / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 0.54)))
		tmp = x * ((t + y) / z);
	else
		tmp = x * ((y / z) - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.54]], $MachinePrecision]], N[(x * N[(N[(t + y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.54000000000000004 < z

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

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

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 94.2

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

   5. Applied rewrites 94.2%

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

   if -1 < z < 0.54000000000000004

   1. Initial program 91.0%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 90.9

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

   4. Applied rewrites 90.9%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 90.1

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

   7. Applied rewrites 90.1%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 90.1%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.54\right):\\ \;\;\;\;x \cdot \frac{t + y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-148} \lor \neg \left(y \leq 7 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.9e-148) (not (<= y 7e-89)))
   (/ (* x (+ y t)) z)
   (/ (* t x) (- z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.9e-148) || !(y <= 7e-89)) {
		tmp = (x * (y + t)) / z;
	} else {
		tmp = (t * x) / (z - 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.9d-148)) .or. (.not. (y <= 7d-89))) then
        tmp = (x * (y + t)) / z
    else
        tmp = (t * x) / (z - 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.9e-148) || !(y <= 7e-89)) {
		tmp = (x * (y + t)) / z;
	} else {
		tmp = (t * x) / (z - 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.9e-148) or not (y <= 7e-89):
		tmp = (x * (y + t)) / z
	else:
		tmp = (t * x) / (z - 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.9e-148) || !(y <= 7e-89))
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	else
		tmp = Float64(Float64(t * x) / Float64(z - 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.9e-148) || ~((y <= 7e-89)))
		tmp = (x * (y + t)) / z;
	else
		tmp = (t * x) / (z - 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.9e-148], N[Not[LessEqual[y, 7e-89]], $MachinePrecision]], N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / N[(z - 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9e-148 or 6.9999999999999994e-89 < y

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf

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

      1. *-lft-identity N/A

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

      2. metadata-eval N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. remove-double-neg N/A

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

      8. mul-1-neg N/A

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

      9. distribute-neg-in N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. lower-/.f64 N/A

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 81.3%

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

   if -4.9e-148 < y < 6.9999999999999994e-89

   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 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 81.3

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

   5. Applied rewrites 81.3%

      \[\leadsto \color{blue}{\frac{t \cdot x}{z - 1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{-148} \lor \neg \left(y \leq 7 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -45000000000 \lor \neg \left(t \leq 1.35 \cdot 10^{+168}\right):\\ \;\;\;\;\frac{t \cdot x}{z - 1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -45000000000.0) (not (<= t 1.35e+168)))
   (/ (* t x) (- z 1.0))
   (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -45000000000.0) || !(t <= 1.35e+168)) {
		tmp = (t * x) / (z - 1.0);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-45000000000.0d0)) .or. (.not. (t <= 1.35d+168))) then
        tmp = (t * x) / (z - 1.0d0)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -45000000000.0) || !(t <= 1.35e+168)) {
		tmp = (t * x) / (z - 1.0);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -45000000000.0) or not (t <= 1.35e+168):
		tmp = (t * x) / (z - 1.0)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -45000000000.0) || !(t <= 1.35e+168))
		tmp = Float64(Float64(t * x) / Float64(z - 1.0));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -45000000000.0) || ~((t <= 1.35e+168)))
		tmp = (t * x) / (z - 1.0);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -45000000000.0], N[Not[LessEqual[t, 1.35e+168]], $MachinePrecision]], N[(N[(t * x), $MachinePrecision] / N[(z - 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5e10 or 1.35000000000000008e168 < t

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. mul-1-neg N/A

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

      10. remove-double-neg N/A

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

      11. sub-neg N/A

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

      12. lower--.f64 74.2

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

   5. Applied rewrites 74.2%

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

   if -4.5e10 < t < 1.35000000000000008e168

   1. Initial program 92.2%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 81.5

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

   5. Applied rewrites 81.5%

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

   7. Applied rewrites 84.5%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -45000000000 \lor \neg \left(t \leq 1.35 \cdot 10^{+168}\right):\\ \;\;\;\;\frac{t \cdot x}{z - 1}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-12} \lor \neg \left(z \leq 880000\right):\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.8e-12) (not (<= z 880000.0)))
   (* (+ t y) (/ x z))
   (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.8e-12) || !(z <= 880000.0)) {
		tmp = (t + y) * (x / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9.8d-12)) .or. (.not. (z <= 880000.0d0))) then
        tmp = (t + y) * (x / z)
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.8e-12) || !(z <= 880000.0)) {
		tmp = (t + y) * (x / z);
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.8e-12) or not (z <= 880000.0):
		tmp = (t + y) * (x / z)
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.8e-12) || !(z <= 880000.0))
		tmp = Float64(Float64(t + y) * Float64(x / z));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.8e-12) || ~((z <= 880000.0)))
		tmp = (t + y) * (x / z);
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.8e-12], N[Not[LessEqual[z, 880000.0]], $MachinePrecision]], N[(N[(t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.79999999999999944e-12 or 8.8e5 < z

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf

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

      1. *-lft-identity N/A

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

      2. metadata-eval N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. remove-double-neg N/A

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

      8. mul-1-neg N/A

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

      9. distribute-neg-in N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. lower-/.f64 N/A

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

   5. Applied rewrites 85.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 86.1%

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

   10. Applied rewrites 87.9%

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

   if -9.79999999999999944e-12 < z < 8.8e5

   1. Initial program 90.8%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 62.0

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

   5. Applied rewrites 62.0%

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

   7. Applied rewrites 70.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{-12} \lor \neg \left(z \leq 880000\right):\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00135:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;z \leq 880000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.00135)
   (/ (* x (+ y t)) z)
   (if (<= z 880000.0) (* x (- (/ y z) t)) (* (+ t y) (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.00135) {
		tmp = (x * (y + t)) / z;
	} else if (z <= 880000.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (t + y) * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-0.00135d0)) then
        tmp = (x * (y + t)) / z
    else if (z <= 880000.0d0) then
        tmp = x * ((y / z) - t)
    else
        tmp = (t + y) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.00135) {
		tmp = (x * (y + t)) / z;
	} else if (z <= 880000.0) {
		tmp = x * ((y / z) - t);
	} else {
		tmp = (t + y) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.00135:
		tmp = (x * (y + t)) / z
	elif z <= 880000.0:
		tmp = x * ((y / z) - t)
	else:
		tmp = (t + y) * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.00135)
		tmp = Float64(Float64(x * Float64(y + t)) / z);
	elseif (z <= 880000.0)
		tmp = Float64(x * Float64(Float64(y / z) - t));
	else
		tmp = Float64(Float64(t + y) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.00135)
		tmp = (x * (y + t)) / z;
	elseif (z <= 880000.0)
		tmp = x * ((y / z) - t);
	else
		tmp = (t + y) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.00135], N[(N[(x * N[(y + t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 880000.0], N[(x * N[(N[(y / z), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], N[(N[(t + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0013500000000000001

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf

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

      1. *-lft-identity N/A

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

      2. metadata-eval N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. remove-double-neg N/A

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

      8. mul-1-neg N/A

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

      9. distribute-neg-in N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. lower-/.f64 N/A

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

   5. Applied rewrites 89.2%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 88.3%

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

   if -0.0013500000000000001 < z < 8.8e5

   1. Initial program 91.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 91.0

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

   4. Applied rewrites 91.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 90.2

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

   7. Applied rewrites 90.2%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 90.2%

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

   if 8.8e5 < 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

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

      1. *-lft-identity N/A

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

      2. metadata-eval N/A

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

      3. associate-*r* N/A

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

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

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. remove-double-neg N/A

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

      8. mul-1-neg N/A

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

      9. distribute-neg-in N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. lower-/.f64 N/A

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

   5. Applied rewrites 85.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 84.9%

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

   10. Applied rewrites 91.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00135:\\ \;\;\;\;\frac{x \cdot \left(y + t\right)}{z}\\ \mathbf{elif}\;z \leq 880000:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t + y\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+155} \lor \neg \left(t \leq 6.7 \cdot 10^{+168}\right):\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.6e+155) (not (<= t 6.7e+168))) (* x (- t)) (* y (/ x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.6e+155) || !(t <= 6.7e+168)) {
		tmp = x * -t;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-8.6d+155)) .or. (.not. (t <= 6.7d+168))) then
        tmp = x * -t
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.6e+155) || !(t <= 6.7e+168)) {
		tmp = x * -t;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.6e+155) or not (t <= 6.7e+168):
		tmp = x * -t
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.6e+155) || !(t <= 6.7e+168))
		tmp = Float64(x * Float64(-t));
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.6e+155) || ~((t <= 6.7e+168)))
		tmp = x * -t;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.6e+155], N[Not[LessEqual[t, 6.7e+168]], $MachinePrecision]], N[(x * (-t)), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.6000000000000005e155 or 6.7000000000000003e168 < t

   1. Initial program 96.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 96.7

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

   4. Applied rewrites 96.7%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 53.7

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

   7. Applied rewrites 53.7%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 47.7%

       \[\leadsto x \cdot \left(-t\right) \]

   if -8.6000000000000005e155 < t < 6.7000000000000003e168

   1. Initial program 92.8%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 76.1

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

   5. Applied rewrites 76.1%

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

   7. Applied rewrites 79.1%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+155} \lor \neg \left(t \leq 6.7 \cdot 10^{+168}\right):\\ \;\;\;\;x \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 22.9% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

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 * -t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

   1. lift-/.f64 N/A

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

   2. clear-num N/A

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

   3. lower-/.f64 N/A

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

   4. lower-/.f64 93.7

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

4. Applied rewrites 93.7%

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

5. Taylor expanded in z around 0

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

   1. lower-/.f64 N/A

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

   2. +-commutative N/A

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

   3. associate-*r* N/A

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

   4. lower-fma.f64 N/A

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

   5. mul-1-neg N/A

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

   6. lower-neg.f64 65.7

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

7. Applied rewrites 65.7%

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

8. Taylor expanded in y around 0

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

10. Applied rewrites 26.0%

    \[\leadsto x \cdot \left(-t\right) \]

11. Final simplification 26.0%

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

Developer Target 1: 94.9% accurate, 0.3× 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 2024321 
(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)))))