Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.7s

Alternatives: 11

Speedup: 1.0×

• 34.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - z) * (t - 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 = x + ((y - z) * (t - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - z) * (t - 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 = x + ((y - z) * (t - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - z) * (t - 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 = x + ((y - z) * (t - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + \left(y - z\right) \cdot \left(t - x\right) \]
4. Add Preprocessing

Alternative 2: 58.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* (- y z) t)))
   (if (<= z -6.2e+56)
     t_1
     (if (<= z -4.5e-184)
       t_2
       (if (<= z 2.1e-236)
         x
         (if (<= z 7.5e-142) t_2 (if (<= z 3.5e-13) x t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -6.2e+56) {
		tmp = t_1;
	} else if (z <= -4.5e-184) {
		tmp = t_2;
	} else if (z <= 2.1e-236) {
		tmp = x;
	} else if (z <= 7.5e-142) {
		tmp = t_2;
	} else if (z <= 3.5e-13) {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = (y - z) * t
    if (z <= (-6.2d+56)) then
        tmp = t_1
    else if (z <= (-4.5d-184)) then
        tmp = t_2
    else if (z <= 2.1d-236) then
        tmp = x
    else if (z <= 7.5d-142) then
        tmp = t_2
    else if (z <= 3.5d-13) then
        tmp = 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 = z * (x - t);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -6.2e+56) {
		tmp = t_1;
	} else if (z <= -4.5e-184) {
		tmp = t_2;
	} else if (z <= 2.1e-236) {
		tmp = x;
	} else if (z <= 7.5e-142) {
		tmp = t_2;
	} else if (z <= 3.5e-13) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = (y - z) * t
	tmp = 0
	if z <= -6.2e+56:
		tmp = t_1
	elif z <= -4.5e-184:
		tmp = t_2
	elif z <= 2.1e-236:
		tmp = x
	elif z <= 7.5e-142:
		tmp = t_2
	elif z <= 3.5e-13:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (z <= -6.2e+56)
		tmp = t_1;
	elseif (z <= -4.5e-184)
		tmp = t_2;
	elseif (z <= 2.1e-236)
		tmp = x;
	elseif (z <= 7.5e-142)
		tmp = t_2;
	elseif (z <= 3.5e-13)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = (y - z) * t;
	tmp = 0.0;
	if (z <= -6.2e+56)
		tmp = t_1;
	elseif (z <= -4.5e-184)
		tmp = t_2;
	elseif (z <= 2.1e-236)
		tmp = x;
	elseif (z <= 7.5e-142)
		tmp = t_2;
	elseif (z <= 3.5e-13)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -6.2e+56], t$95$1, If[LessEqual[z, -4.5e-184], t$95$2, If[LessEqual[z, 2.1e-236], x, If[LessEqual[z, 7.5e-142], t$95$2, If[LessEqual[z, 3.5e-13], x, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.20000000000000009e56 or 3.5000000000000002e-13 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 91.8%

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

      3. fma-define 95.1%

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

   4. Applied egg-rr 95.1%

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

   5. Taylor expanded in y around 0 91.8%

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

      1. *-commutative 91.8%

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

   7. Simplified 91.8%

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

   8. Taylor expanded in x around 0 89.4%

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

   9. Taylor expanded in z around inf 84.6%

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

       1. neg-mul-1 84.6%

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

       2. sub-neg 84.6%

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

   11. Simplified 84.6%

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

   if -6.20000000000000009e56 < z < -4.5000000000000001e-184 or 2.09999999999999979e-236 < z < 7.49999999999999958e-142

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 98.6%

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

      3. fma-define 98.6%

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

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in y around 0 82.0%

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

      1. *-commutative 82.0%

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

   7. Simplified 82.0%

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

   8. Taylor expanded in x around 0 82.0%

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

   9. Taylor expanded in t around inf 52.7%

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

   if -4.5000000000000001e-184 < z < 2.09999999999999979e-236 or 7.49999999999999958e-142 < z < 3.5000000000000002e-13

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 81.7%

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

   4. Taylor expanded in x around inf 56.7%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+56}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-184}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-142}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{+79}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4800000000:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-180}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -7.5e+79)
     (* y t)
     (if (<= y -2.7e+36)
       t_1
       (if (<= y -4800000000.0)
         (* y t)
         (if (<= y 2.5e-180) x (if (<= y 1.25e+106) (* z (- t)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -7.5e+79) {
		tmp = y * t;
	} else if (y <= -2.7e+36) {
		tmp = t_1;
	} else if (y <= -4800000000.0) {
		tmp = y * t;
	} else if (y <= 2.5e-180) {
		tmp = x;
	} else if (y <= 1.25e+106) {
		tmp = 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
    if (y <= (-7.5d+79)) then
        tmp = y * t
    else if (y <= (-2.7d+36)) then
        tmp = t_1
    else if (y <= (-4800000000.0d0)) then
        tmp = y * t
    else if (y <= 2.5d-180) then
        tmp = x
    else if (y <= 1.25d+106) then
        tmp = 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;
	double tmp;
	if (y <= -7.5e+79) {
		tmp = y * t;
	} else if (y <= -2.7e+36) {
		tmp = t_1;
	} else if (y <= -4800000000.0) {
		tmp = y * t;
	} else if (y <= 2.5e-180) {
		tmp = x;
	} else if (y <= 1.25e+106) {
		tmp = z * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -7.5e+79:
		tmp = y * t
	elif y <= -2.7e+36:
		tmp = t_1
	elif y <= -4800000000.0:
		tmp = y * t
	elif y <= 2.5e-180:
		tmp = x
	elif y <= 1.25e+106:
		tmp = z * -t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -7.5e+79)
		tmp = Float64(y * t);
	elseif (y <= -2.7e+36)
		tmp = t_1;
	elseif (y <= -4800000000.0)
		tmp = Float64(y * t);
	elseif (y <= 2.5e-180)
		tmp = x;
	elseif (y <= 1.25e+106)
		tmp = Float64(z * Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	tmp = 0.0;
	if (y <= -7.5e+79)
		tmp = y * t;
	elseif (y <= -2.7e+36)
		tmp = t_1;
	elseif (y <= -4800000000.0)
		tmp = y * t;
	elseif (y <= 2.5e-180)
		tmp = x;
	elseif (y <= 1.25e+106)
		tmp = z * -t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -7.5e+79], N[(y * t), $MachinePrecision], If[LessEqual[y, -2.7e+36], t$95$1, If[LessEqual[y, -4800000000.0], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.5e-180], x, If[LessEqual[y, 1.25e+106], N[(z * (-t)), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.49999999999999967e79 or -2.7000000000000001e36 < y < -4.8e9

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 93.0%

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

      3. fma-define 95.3%

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in y around 0 78.8%

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

      1. *-commutative 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in x around 0 76.5%

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

   9. Taylor expanded in y around inf 56.2%

      \[\leadsto \color{blue}{t \cdot y} \]

   if -7.49999999999999967e79 < y < -2.7000000000000001e36 or 1.25e106 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 65.8%

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

      1. mul-1-neg 65.8%

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

      2. distribute-lft-neg-out 65.8%

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

      3. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in y around inf 50.7%

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

      1. associate-*r* 50.7%

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

      2. mul-1-neg 50.7%

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

   8. Simplified 50.7%

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

   if -4.8e9 < y < 2.5000000000000001e-180

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 69.3%

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

   4. Taylor expanded in x around inf 43.0%

      \[\leadsto \color{blue}{x} \]

   if 2.5000000000000001e-180 < y < 1.25e106

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 80.1%

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

   4. Taylor expanded in y around 0 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in x around 0 47.1%

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

      1. associate-*r* 47.1%

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

      2. neg-mul-1 47.1%

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

   9. Simplified 47.1%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+79}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -4800000000:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-180}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2250000000:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.96 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2250000000.0)
   (* y t)
   (if (<= y 3.2e-183) x (if (<= y 1.96e+87) (* z (- t)) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2250000000.0) {
		tmp = y * t;
	} else if (y <= 3.2e-183) {
		tmp = x;
	} else if (y <= 1.96e+87) {
		tmp = z * -t;
	} else {
		tmp = y * 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 (y <= (-2250000000.0d0)) then
        tmp = y * t
    else if (y <= 3.2d-183) then
        tmp = x
    else if (y <= 1.96d+87) then
        tmp = z * -t
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2250000000.0) {
		tmp = y * t;
	} else if (y <= 3.2e-183) {
		tmp = x;
	} else if (y <= 1.96e+87) {
		tmp = z * -t;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2250000000.0:
		tmp = y * t
	elif y <= 3.2e-183:
		tmp = x
	elif y <= 1.96e+87:
		tmp = z * -t
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2250000000.0)
		tmp = Float64(y * t);
	elseif (y <= 3.2e-183)
		tmp = x;
	elseif (y <= 1.96e+87)
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2250000000.0)
		tmp = y * t;
	elseif (y <= 3.2e-183)
		tmp = x;
	elseif (y <= 1.96e+87)
		tmp = z * -t;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2250000000.0], N[(y * t), $MachinePrecision], If[LessEqual[y, 3.2e-183], x, If[LessEqual[y, 1.96e+87], N[(z * (-t)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25e9 or 1.96e87 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 93.8%

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

      3. fma-define 95.9%

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

   4. Applied egg-rr 95.9%

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

   5. Taylor expanded in y around 0 70.3%

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

      1. *-commutative 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in x around 0 69.2%

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

   9. Taylor expanded in y around inf 44.3%

      \[\leadsto \color{blue}{t \cdot y} \]

   if -2.25e9 < y < 3.2000000000000002e-183

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 69.3%

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

   4. Taylor expanded in x around inf 43.0%

      \[\leadsto \color{blue}{x} \]

   if 3.2000000000000002e-183 < y < 1.96e87

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 80.4%

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

   4. Taylor expanded in y around 0 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in x around 0 48.6%

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

      1. associate-*r* 48.6%

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

      2. neg-mul-1 48.6%

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

   9. Simplified 48.6%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2250000000:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.96 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y - z \leq -5 \cdot 10^{-7} \lor \neg \left(y - z \leq 1.3 \cdot 10^{-23}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (- y z) -5e-7) (not (<= (- y z) 1.3e-23))) (* (- y z) t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -5e-7) || !((y - z) <= 1.3e-23)) {
		tmp = (y - z) * t;
	} else {
		tmp = 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 - z) <= (-5d-7)) .or. (.not. ((y - z) <= 1.3d-23))) then
        tmp = (y - z) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -5e-7) || !((y - z) <= 1.3e-23)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y - z) <= -5e-7) or not ((y - z) <= 1.3e-23):
		tmp = (y - z) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y - z) <= -5e-7) || !(Float64(y - z) <= 1.3e-23))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y - z) <= -5e-7) || ~(((y - z) <= 1.3e-23)))
		tmp = (y - z) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y - z), $MachinePrecision], -5e-7], N[Not[LessEqual[N[(y - z), $MachinePrecision], 1.3e-23]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -4.99999999999999977e-7 or 1.3e-23 < (-.f64 y z)

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 94.0%

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

      3. fma-define 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in y around 0 81.6%

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

      1. *-commutative 81.6%

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

   7. Simplified 81.6%

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

   8. Taylor expanded in x around 0 80.0%

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

   9. Taylor expanded in t around inf 51.5%

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

   if -4.99999999999999977e-7 < (-.f64 y z) < 1.3e-23

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 99.8%

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

   4. Taylor expanded in x around inf 72.5%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -5 \cdot 10^{-7} \lor \neg \left(y - z \leq 1.3 \cdot 10^{-23}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+56} \lor \neg \left(z \leq 1.05 \cdot 10^{+24}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e+56) (not (<= z 1.05e+24)))
   (* z (- x t))
   (- x (* t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e+56) || !(z <= 1.05e+24)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (t * (z - y));
	}
	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 <= (-1.65d+56)) .or. (.not. (z <= 1.05d+24))) then
        tmp = z * (x - t)
    else
        tmp = x - (t * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e+56) || !(z <= 1.05e+24)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.65e+56) or not (z <= 1.05e+24):
		tmp = z * (x - t)
	else:
		tmp = x - (t * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e+56) || !(z <= 1.05e+24))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x - Float64(t * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.65e+56) || ~((z <= 1.05e+24)))
		tmp = z * (x - t);
	else
		tmp = x - (t * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e+56], N[Not[LessEqual[z, 1.05e+24]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65000000000000001e56 or 1.0500000000000001e24 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 93.0%

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

      3. fma-define 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in y around 0 92.1%

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

      1. *-commutative 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in x around 0 89.5%

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

   9. Taylor expanded in z around inf 89.0%

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

       1. neg-mul-1 89.0%

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

       2. sub-neg 89.0%

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

   11. Simplified 89.0%

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

   if -1.65000000000000001e56 < z < 1.0500000000000001e24

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 79.7%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+56} \lor \neg \left(z \leq 1.05 \cdot 10^{+24}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+51} \lor \neg \left(z \leq 9 \cdot 10^{+23}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.8e+51) (not (<= z 9e+23)))
   (* z (- x t))
   (- x (* y (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e+51) || !(z <= 9e+23)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (x - 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 <= (-5.8d+51)) .or. (.not. (z <= 9d+23))) then
        tmp = z * (x - t)
    else
        tmp = x - (y * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e+51) || !(z <= 9e+23)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.8e+51) or not (z <= 9e+23):
		tmp = z * (x - t)
	else:
		tmp = x - (y * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.8e+51) || !(z <= 9e+23))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x - Float64(y * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.8e+51) || ~((z <= 9e+23)))
		tmp = z * (x - t);
	else
		tmp = x - (y * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.8e+51], N[Not[LessEqual[z, 9e+23]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999997e51 or 8.99999999999999958e23 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 93.1%

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

      3. fma-define 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in y around 0 92.2%

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

      1. *-commutative 92.2%

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

   7. Simplified 92.2%

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

   8. Taylor expanded in x around 0 89.7%

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

   9. Taylor expanded in z around inf 88.4%

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

       1. neg-mul-1 88.4%

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

       2. sub-neg 88.4%

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

   11. Simplified 88.4%

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

   if -5.7999999999999997e51 < z < 8.99999999999999958e23

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+51} \lor \neg \left(z \leq 9 \cdot 10^{+23}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+23}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -9.8e+51) t_1 (if (<= z 9e+23) (- x (* y (- x t))) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -9.8e+51) {
		tmp = t_1;
	} else if (z <= 9e+23) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x + 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 = z * (x - t)
    if (z <= (-9.8d+51)) then
        tmp = t_1
    else if (z <= 9d+23) then
        tmp = x - (y * (x - t))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -9.8e+51) {
		tmp = t_1;
	} else if (z <= 9e+23) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -9.8e+51:
		tmp = t_1
	elif z <= 9e+23:
		tmp = x - (y * (x - t))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -9.8e+51)
		tmp = t_1;
	elseif (z <= 9e+23)
		tmp = Float64(x - Float64(y * Float64(x - t)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -9.8e+51)
		tmp = t_1;
	elseif (z <= 9e+23)
		tmp = x - (y * (x - t));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+51], t$95$1, If[LessEqual[z, 9e+23], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.79999999999999967e51

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 92.5%

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

      3. fma-define 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in y around 0 92.6%

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

      1. *-commutative 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in x around 0 88.8%

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

   9. Taylor expanded in z around inf 90.9%

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

       1. neg-mul-1 90.9%

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

       2. sub-neg 90.9%

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

   11. Simplified 90.9%

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

   if -9.79999999999999967e51 < z < 8.99999999999999958e23

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

   5. Simplified 88.1%

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

   if 8.99999999999999958e23 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 86.3%

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

      1. mul-1-neg 86.3%

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

      2. distribute-lft-neg-out 86.3%

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

      3. *-commutative 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in z around 0 86.3%

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

      1. mul-1-neg 86.3%

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

      2. unsub-neg 86.3%

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

   8. Simplified 86.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+23}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-16} \lor \neg \left(z \leq 9 \cdot 10^{+23}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e-16) (not (<= z 9e+23))) (* z (- x t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e-16) || !(z <= 9e+23)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * 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 <= (-6.2d-16)) .or. (.not. (z <= 9d+23))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e-16) || !(z <= 9e+23)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e-16) or not (z <= 9e+23):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e-16) || !(z <= 9e+23))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2e-16) || ~((z <= 9e+23)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e-16], N[Not[LessEqual[z, 9e+23]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000002e-16 or 8.99999999999999958e23 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 93.1%

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

      3. fma-define 96.1%

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

   4. Applied egg-rr 96.1%

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

   5. Taylor expanded in y around 0 89.4%

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

      1. *-commutative 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in x around 0 87.1%

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

   9. Taylor expanded in z around inf 83.1%

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

       1. neg-mul-1 83.1%

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

       2. sub-neg 83.1%

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

   11. Simplified 83.1%

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

   if -6.2000000000000002e-16 < z < 8.99999999999999958e23

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 82.3%

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

   4. Taylor expanded in y around inf 74.6%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-16} \lor \neg \left(z \leq 9 \cdot 10^{+23}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2250000000 \lor \neg \left(y \leq 1.3 \cdot 10^{-23}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2250000000.0) (not (<= y 1.3e-23))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2250000000.0) || !(y <= 1.3e-23)) {
		tmp = y * t;
	} else {
		tmp = 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 <= (-2250000000.0d0)) .or. (.not. (y <= 1.3d-23))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2250000000.0) || !(y <= 1.3e-23)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2250000000.0) or not (y <= 1.3e-23):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2250000000.0) || !(y <= 1.3e-23))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2250000000.0) || ~((y <= 1.3e-23)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2250000000.0], N[Not[LessEqual[y, 1.3e-23]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.25e9 or 1.3e-23 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 94.6%

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

      3. fma-define 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in y around 0 73.1%

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

      1. *-commutative 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in x around 0 72.2%

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

   9. Taylor expanded in y around inf 42.8%

      \[\leadsto \color{blue}{t \cdot y} \]

   if -2.25e9 < y < 1.3e-23

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 73.4%

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

   4. Taylor expanded in x around inf 38.2%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2250000000 \lor \neg \left(y \leq 1.3 \cdot 10^{-23}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 18.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = x
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing

3. Taylor expanded in t around inf 65.7%

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

4. Taylor expanded in x around inf 22.8%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 22.8%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((t * (y - z)) + (-x * (y - 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 + ((t * (y - z)) + (-x * (y - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

  (+ x (* (- y z) (- t x))))