Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.1s

Alternatives: 13

Speedup: 1.0×

• 35.6% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - z, t - x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y - z, t - x, x\right) \]
6. Add Preprocessing

Alternative 2: 35.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+185}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+140}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+182} \lor \neg \left(x \leq 1.55 \cdot 10^{+222}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= x -3.7e+185)
     t_1
     (if (<= x -3.2e+140)
       (* z x)
       (if (<= x -4.7e+80)
         t_1
         (if (<= x -5.7e-18)
           x
           (if (<= x 1.05e+26)
             (* z (- t))
             (if (or (<= x 2.9e+182) (not (<= x 1.55e+222)))
               (* z x)
               t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (x <= -3.7e+185) {
		tmp = t_1;
	} else if (x <= -3.2e+140) {
		tmp = z * x;
	} else if (x <= -4.7e+80) {
		tmp = t_1;
	} else if (x <= -5.7e-18) {
		tmp = x;
	} else if (x <= 1.05e+26) {
		tmp = z * -t;
	} else if ((x <= 2.9e+182) || !(x <= 1.55e+222)) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -x
    if (x <= (-3.7d+185)) then
        tmp = t_1
    else if (x <= (-3.2d+140)) then
        tmp = z * x
    else if (x <= (-4.7d+80)) then
        tmp = t_1
    else if (x <= (-5.7d-18)) then
        tmp = x
    else if (x <= 1.05d+26) then
        tmp = z * -t
    else if ((x <= 2.9d+182) .or. (.not. (x <= 1.55d+222))) then
        tmp = z * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (x <= -3.7e+185) {
		tmp = t_1;
	} else if (x <= -3.2e+140) {
		tmp = z * x;
	} else if (x <= -4.7e+80) {
		tmp = t_1;
	} else if (x <= -5.7e-18) {
		tmp = x;
	} else if (x <= 1.05e+26) {
		tmp = z * -t;
	} else if ((x <= 2.9e+182) || !(x <= 1.55e+222)) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if x <= -3.7e+185:
		tmp = t_1
	elif x <= -3.2e+140:
		tmp = z * x
	elif x <= -4.7e+80:
		tmp = t_1
	elif x <= -5.7e-18:
		tmp = x
	elif x <= 1.05e+26:
		tmp = z * -t
	elif (x <= 2.9e+182) or not (x <= 1.55e+222):
		tmp = z * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (x <= -3.7e+185)
		tmp = t_1;
	elseif (x <= -3.2e+140)
		tmp = Float64(z * x);
	elseif (x <= -4.7e+80)
		tmp = t_1;
	elseif (x <= -5.7e-18)
		tmp = x;
	elseif (x <= 1.05e+26)
		tmp = Float64(z * Float64(-t));
	elseif ((x <= 2.9e+182) || !(x <= 1.55e+222))
		tmp = Float64(z * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (x <= -3.7e+185)
		tmp = t_1;
	elseif (x <= -3.2e+140)
		tmp = z * x;
	elseif (x <= -4.7e+80)
		tmp = t_1;
	elseif (x <= -5.7e-18)
		tmp = x;
	elseif (x <= 1.05e+26)
		tmp = z * -t;
	elseif ((x <= 2.9e+182) || ~((x <= 1.55e+222)))
		tmp = z * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[x, -3.7e+185], t$95$1, If[LessEqual[x, -3.2e+140], N[(z * x), $MachinePrecision], If[LessEqual[x, -4.7e+80], t$95$1, If[LessEqual[x, -5.7e-18], x, If[LessEqual[x, 1.05e+26], N[(z * (-t)), $MachinePrecision], If[Or[LessEqual[x, 2.9e+182], N[Not[LessEqual[x, 1.55e+222]], $MachinePrecision]], N[(z * x), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.6999999999999997e185 or -3.20000000000000011e140 < x < -4.70000000000000009e80 or 2.8999999999999998e182 < x < 1.5499999999999999e222

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.4%

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

      1. mul-1-neg 87.4%

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

      2. unsub-neg 87.4%

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

   5. Simplified 87.4%

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

   6. Taylor expanded in y around inf 63.0%

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

      1. mul-1-neg 63.0%

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

      2. distribute-rgt-neg-out 63.0%

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

   8. Simplified 63.0%

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

   if -3.6999999999999997e185 < x < -3.20000000000000011e140 or 1.05e26 < x < 2.8999999999999998e182 or 1.5499999999999999e222 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. unsub-neg 88.0%

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

   5. Simplified 88.0%

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

   6. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

   8. Simplified 50.4%

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

   if -4.70000000000000009e80 < x < -5.69999999999999971e-18

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.1%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)} \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}} \]

      2. pow3 99.2%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   4. Applied egg-rr 99.2%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   5. Taylor expanded in x around inf 51.4%

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

   if -5.69999999999999971e-18 < x < 1.05e26

   1. Initial program 100.0%

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

      1. add-cube-cbrt 98.6%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)} \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}} \]

      2. pow3 98.6%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   4. Applied egg-rr 98.6%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around 0 55.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(t - x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 55.4%

         \[\leadsto x + \color{blue}{\left(-{1}^{0.3333333333333333} \cdot \left(z \cdot \left(t - x\right)\right)\right)} \]

      2. pow-base-1 55.4%

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

      3. *-lft-identity 55.4%

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

      4. unsub-neg 55.4%

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

   7. Simplified 55.4%

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

   8. Taylor expanded in x around 0 44.4%

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

      1. associate-*r* 44.4%

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

      2. mul-1-neg 44.4%

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

   10. Simplified 44.4%

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

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+185}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+140}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+182} \lor \neg \left(x \leq 1.55 \cdot 10^{+222}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ t_2 := x + y \cdot t\\ t_3 := x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{-64}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-299}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-212}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))) (t_2 (+ x (* y t))) (t_3 (* x (+ (- z y) 1.0))))
   (if (<= x -5.5e-64)
     t_3
     (if (<= x -6.5e-213)
       t_1
       (if (<= x -5e-299)
         t_2
         (if (<= x 3.9e-243)
           t_1
           (if (<= x 2.4e-212) t_2 (if (<= x 1.25e-5) t_1 t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double t_2 = x + (y * t);
	double t_3 = x * ((z - y) + 1.0);
	double tmp;
	if (x <= -5.5e-64) {
		tmp = t_3;
	} else if (x <= -6.5e-213) {
		tmp = t_1;
	} else if (x <= -5e-299) {
		tmp = t_2;
	} else if (x <= 3.9e-243) {
		tmp = t_1;
	} else if (x <= 2.4e-212) {
		tmp = t_2;
	} else if (x <= 1.25e-5) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x - (z * t)
    t_2 = x + (y * t)
    t_3 = x * ((z - y) + 1.0d0)
    if (x <= (-5.5d-64)) then
        tmp = t_3
    else if (x <= (-6.5d-213)) then
        tmp = t_1
    else if (x <= (-5d-299)) then
        tmp = t_2
    else if (x <= 3.9d-243) then
        tmp = t_1
    else if (x <= 2.4d-212) then
        tmp = t_2
    else if (x <= 1.25d-5) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double t_2 = x + (y * t);
	double t_3 = x * ((z - y) + 1.0);
	double tmp;
	if (x <= -5.5e-64) {
		tmp = t_3;
	} else if (x <= -6.5e-213) {
		tmp = t_1;
	} else if (x <= -5e-299) {
		tmp = t_2;
	} else if (x <= 3.9e-243) {
		tmp = t_1;
	} else if (x <= 2.4e-212) {
		tmp = t_2;
	} else if (x <= 1.25e-5) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	t_2 = x + (y * t)
	t_3 = x * ((z - y) + 1.0)
	tmp = 0
	if x <= -5.5e-64:
		tmp = t_3
	elif x <= -6.5e-213:
		tmp = t_1
	elif x <= -5e-299:
		tmp = t_2
	elif x <= 3.9e-243:
		tmp = t_1
	elif x <= 2.4e-212:
		tmp = t_2
	elif x <= 1.25e-5:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	t_2 = Float64(x + Float64(y * t))
	t_3 = Float64(x * Float64(Float64(z - y) + 1.0))
	tmp = 0.0
	if (x <= -5.5e-64)
		tmp = t_3;
	elseif (x <= -6.5e-213)
		tmp = t_1;
	elseif (x <= -5e-299)
		tmp = t_2;
	elseif (x <= 3.9e-243)
		tmp = t_1;
	elseif (x <= 2.4e-212)
		tmp = t_2;
	elseif (x <= 1.25e-5)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (z * t);
	t_2 = x + (y * t);
	t_3 = x * ((z - y) + 1.0);
	tmp = 0.0;
	if (x <= -5.5e-64)
		tmp = t_3;
	elseif (x <= -6.5e-213)
		tmp = t_1;
	elseif (x <= -5e-299)
		tmp = t_2;
	elseif (x <= 3.9e-243)
		tmp = t_1;
	elseif (x <= 2.4e-212)
		tmp = t_2;
	elseif (x <= 1.25e-5)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.5e-64], t$95$3, If[LessEqual[x, -6.5e-213], t$95$1, If[LessEqual[x, -5e-299], t$95$2, If[LessEqual[x, 3.9e-243], t$95$1, If[LessEqual[x, 2.4e-212], t$95$2, If[LessEqual[x, 1.25e-5], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.4999999999999999e-64 or 1.25000000000000006e-5 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.2%

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

      1. mul-1-neg 79.2%

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

      2. unsub-neg 79.2%

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

   5. Simplified 79.2%

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

   if -5.4999999999999999e-64 < x < -6.5e-213 or -4.99999999999999956e-299 < x < 3.90000000000000015e-243 or 2.39999999999999989e-212 < x < 1.25000000000000006e-5

   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 79.8%

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

   4. Taylor expanded in y around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. unsub-neg 61.2%

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

      3. *-commutative 61.2%

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

   6. Simplified 61.2%

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

   if -6.5e-213 < x < -4.99999999999999956e-299 or 3.90000000000000015e-243 < x < 2.39999999999999989e-212

   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 94.8%

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

   4. Taylor expanded in y around inf 77.4%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-213}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-299}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-243}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-212}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-5}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+153}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -70000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+163}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -5.6e+186)
     t_1
     (if (<= z -1.15e+153)
       (* z x)
       (if (<= z -70000000000000.0)
         t_1
         (if (<= z 8.2e-20)
           (+ x (* y t))
           (if (<= z 3.2e+163) (- x (* z t)) (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -5.6e+186) {
		tmp = t_1;
	} else if (z <= -1.15e+153) {
		tmp = z * x;
	} else if (z <= -70000000000000.0) {
		tmp = t_1;
	} else if (z <= 8.2e-20) {
		tmp = x + (y * t);
	} else if (z <= 3.2e+163) {
		tmp = x - (z * t);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-5.6d+186)) then
        tmp = t_1
    else if (z <= (-1.15d+153)) then
        tmp = z * x
    else if (z <= (-70000000000000.0d0)) then
        tmp = t_1
    else if (z <= 8.2d-20) then
        tmp = x + (y * t)
    else if (z <= 3.2d+163) then
        tmp = x - (z * t)
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -5.6e+186) {
		tmp = t_1;
	} else if (z <= -1.15e+153) {
		tmp = z * x;
	} else if (z <= -70000000000000.0) {
		tmp = t_1;
	} else if (z <= 8.2e-20) {
		tmp = x + (y * t);
	} else if (z <= 3.2e+163) {
		tmp = x - (z * t);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -5.6e+186:
		tmp = t_1
	elif z <= -1.15e+153:
		tmp = z * x
	elif z <= -70000000000000.0:
		tmp = t_1
	elif z <= 8.2e-20:
		tmp = x + (y * t)
	elif z <= 3.2e+163:
		tmp = x - (z * t)
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -5.6e+186)
		tmp = t_1;
	elseif (z <= -1.15e+153)
		tmp = Float64(z * x);
	elseif (z <= -70000000000000.0)
		tmp = t_1;
	elseif (z <= 8.2e-20)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 3.2e+163)
		tmp = Float64(x - Float64(z * t));
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -5.6e+186)
		tmp = t_1;
	elseif (z <= -1.15e+153)
		tmp = z * x;
	elseif (z <= -70000000000000.0)
		tmp = t_1;
	elseif (z <= 8.2e-20)
		tmp = x + (y * t);
	elseif (z <= 3.2e+163)
		tmp = x - (z * t);
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -5.6e+186], t$95$1, If[LessEqual[z, -1.15e+153], N[(z * x), $MachinePrecision], If[LessEqual[z, -70000000000000.0], t$95$1, If[LessEqual[z, 8.2e-20], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+163], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.60000000000000037e186 or -1.1500000000000001e153 < z < -7e13

   1. Initial program 100.0%

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

      1. add-cube-cbrt 99.0%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)} \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}} \]

      2. pow3 99.0%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   4. Applied egg-rr 99.0%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around 0 83.7%

      \[\leadsto \color{blue}{x + -1 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(t - x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 83.7%

         \[\leadsto x + \color{blue}{\left(-{1}^{0.3333333333333333} \cdot \left(z \cdot \left(t - x\right)\right)\right)} \]

      2. pow-base-1 83.7%

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

      3. *-lft-identity 83.7%

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

      4. unsub-neg 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in x around 0 53.8%

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

      1. associate-*r* 53.8%

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

      2. mul-1-neg 53.8%

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

   10. Simplified 53.8%

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

   if -5.60000000000000037e186 < z < -1.1500000000000001e153 or 3.1999999999999998e163 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. unsub-neg 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in z around inf 68.3%

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

      1. *-commutative 68.3%

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

   8. Simplified 68.3%

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

   if -7e13 < z < 8.2000000000000002e-20

   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 75.6%

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

   4. Taylor expanded in y around inf 66.9%

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

   if 8.2000000000000002e-20 < z < 3.1999999999999998e163

   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 56.2%

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

   4. Taylor expanded in y around 0 46.6%

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

      1. mul-1-neg 46.6%

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

      2. unsub-neg 46.6%

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

      3. *-commutative 46.6%

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

   6. Simplified 46.6%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+153}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -70000000000000:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-20}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+163}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+151}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -2.9e+186)
     t_1
     (if (<= z -7.5e+151)
       (* z x)
       (if (<= z -3.2e+42)
         t_1
         (if (<= z 7.2e+97)
           (* x (- 1.0 y))
           (if (<= z 1.85e+164) t_1 (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -2.9e+186) {
		tmp = t_1;
	} else if (z <= -7.5e+151) {
		tmp = z * x;
	} else if (z <= -3.2e+42) {
		tmp = t_1;
	} else if (z <= 7.2e+97) {
		tmp = x * (1.0 - y);
	} else if (z <= 1.85e+164) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-2.9d+186)) then
        tmp = t_1
    else if (z <= (-7.5d+151)) then
        tmp = z * x
    else if (z <= (-3.2d+42)) then
        tmp = t_1
    else if (z <= 7.2d+97) then
        tmp = x * (1.0d0 - y)
    else if (z <= 1.85d+164) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -2.9e+186) {
		tmp = t_1;
	} else if (z <= -7.5e+151) {
		tmp = z * x;
	} else if (z <= -3.2e+42) {
		tmp = t_1;
	} else if (z <= 7.2e+97) {
		tmp = x * (1.0 - y);
	} else if (z <= 1.85e+164) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -2.9e+186:
		tmp = t_1
	elif z <= -7.5e+151:
		tmp = z * x
	elif z <= -3.2e+42:
		tmp = t_1
	elif z <= 7.2e+97:
		tmp = x * (1.0 - y)
	elif z <= 1.85e+164:
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -2.9e+186)
		tmp = t_1;
	elseif (z <= -7.5e+151)
		tmp = Float64(z * x);
	elseif (z <= -3.2e+42)
		tmp = t_1;
	elseif (z <= 7.2e+97)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 1.85e+164)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -2.9e+186)
		tmp = t_1;
	elseif (z <= -7.5e+151)
		tmp = z * x;
	elseif (z <= -3.2e+42)
		tmp = t_1;
	elseif (z <= 7.2e+97)
		tmp = x * (1.0 - y);
	elseif (z <= 1.85e+164)
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -2.9e+186], t$95$1, If[LessEqual[z, -7.5e+151], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.2e+42], t$95$1, If[LessEqual[z, 7.2e+97], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+164], t$95$1, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e186 or -7.49999999999999977e151 < z < -3.20000000000000002e42 or 7.19999999999999932e97 < z < 1.85e164

   1. Initial program 100.0%

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

      1. add-cube-cbrt 99.0%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)} \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}} \]

      2. pow3 98.9%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   4. Applied egg-rr 98.9%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around 0 83.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(t - x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 83.4%

         \[\leadsto x + \color{blue}{\left(-{1}^{0.3333333333333333} \cdot \left(z \cdot \left(t - x\right)\right)\right)} \]

      2. pow-base-1 83.4%

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

      3. *-lft-identity 83.4%

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

      4. unsub-neg 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in x around 0 57.2%

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

      1. associate-*r* 57.2%

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

      2. mul-1-neg 57.2%

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

   10. Simplified 57.2%

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

   if -2.9e186 < z < -7.49999999999999977e151 or 1.85e164 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. unsub-neg 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in z around inf 68.3%

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

      1. *-commutative 68.3%

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

   8. Simplified 68.3%

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

   if -3.20000000000000002e42 < z < 7.19999999999999932e97

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.2%

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

      1. mul-1-neg 56.2%

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

      2. unsub-neg 56.2%

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

   5. Simplified 56.2%

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

   6. Taylor expanded in z around 0 52.2%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+151}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+164}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+186}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+152}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-14}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -1.55e+186)
     t_1
     (if (<= z -2.6e+152)
       (* z x)
       (if (<= z -3.4e+14)
         t_1
         (if (<= z 5.2e-14)
           (+ x (* y t))
           (if (<= z 1.85e+164) t_1 (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1.55e+186) {
		tmp = t_1;
	} else if (z <= -2.6e+152) {
		tmp = z * x;
	} else if (z <= -3.4e+14) {
		tmp = t_1;
	} else if (z <= 5.2e-14) {
		tmp = x + (y * t);
	} else if (z <= 1.85e+164) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-1.55d+186)) then
        tmp = t_1
    else if (z <= (-2.6d+152)) then
        tmp = z * x
    else if (z <= (-3.4d+14)) then
        tmp = t_1
    else if (z <= 5.2d-14) then
        tmp = x + (y * t)
    else if (z <= 1.85d+164) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1.55e+186) {
		tmp = t_1;
	} else if (z <= -2.6e+152) {
		tmp = z * x;
	} else if (z <= -3.4e+14) {
		tmp = t_1;
	} else if (z <= 5.2e-14) {
		tmp = x + (y * t);
	} else if (z <= 1.85e+164) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -1.55e+186:
		tmp = t_1
	elif z <= -2.6e+152:
		tmp = z * x
	elif z <= -3.4e+14:
		tmp = t_1
	elif z <= 5.2e-14:
		tmp = x + (y * t)
	elif z <= 1.85e+164:
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -1.55e+186)
		tmp = t_1;
	elseif (z <= -2.6e+152)
		tmp = Float64(z * x);
	elseif (z <= -3.4e+14)
		tmp = t_1;
	elseif (z <= 5.2e-14)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 1.85e+164)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -1.55e+186)
		tmp = t_1;
	elseif (z <= -2.6e+152)
		tmp = z * x;
	elseif (z <= -3.4e+14)
		tmp = t_1;
	elseif (z <= 5.2e-14)
		tmp = x + (y * t);
	elseif (z <= 1.85e+164)
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -1.55e+186], t$95$1, If[LessEqual[z, -2.6e+152], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.4e+14], t$95$1, If[LessEqual[z, 5.2e-14], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+164], t$95$1, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5500000000000001e186 or -2.6000000000000001e152 < z < -3.4e14 or 5.19999999999999993e-14 < z < 1.85e164

   1. Initial program 100.0%

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

      1. add-cube-cbrt 98.8%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)} \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}} \]

      2. pow3 98.8%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   4. Applied egg-rr 98.8%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around 0 75.0%

      \[\leadsto \color{blue}{x + -1 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(t - x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 75.0%

         \[\leadsto x + \color{blue}{\left(-{1}^{0.3333333333333333} \cdot \left(z \cdot \left(t - x\right)\right)\right)} \]

      2. pow-base-1 75.0%

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

      3. *-lft-identity 75.0%

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

      4. unsub-neg 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in x around 0 49.5%

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

      1. associate-*r* 49.5%

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

      2. mul-1-neg 49.5%

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

   10. Simplified 49.5%

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

   if -1.5500000000000001e186 < z < -2.6000000000000001e152 or 1.85e164 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. unsub-neg 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in z around inf 68.3%

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

      1. *-commutative 68.3%

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

   8. Simplified 68.3%

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

   if -3.4e14 < z < 5.19999999999999993e-14

   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 75.9%

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

   4. Taylor expanded in y around inf 67.4%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+152}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-14}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+164}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -660000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-185}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 19:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= y -660000000000.0)
     t_1
     (if (<= y 1.26e-185) (* z x) (if (<= y 19.0) x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -660000000000.0) {
		tmp = t_1;
	} else if (y <= 1.26e-185) {
		tmp = z * x;
	} else if (y <= 19.0) {
		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) :: tmp
    t_1 = y * -x
    if (y <= (-660000000000.0d0)) then
        tmp = t_1
    else if (y <= 1.26d-185) then
        tmp = z * x
    else if (y <= 19.0d0) 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 = y * -x;
	double tmp;
	if (y <= -660000000000.0) {
		tmp = t_1;
	} else if (y <= 1.26e-185) {
		tmp = z * x;
	} else if (y <= 19.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if y <= -660000000000.0:
		tmp = t_1
	elif y <= 1.26e-185:
		tmp = z * x
	elif y <= 19.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -660000000000.0)
		tmp = t_1;
	elseif (y <= 1.26e-185)
		tmp = Float64(z * x);
	elseif (y <= 19.0)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (y <= -660000000000.0)
		tmp = t_1;
	elseif (y <= 1.26e-185)
		tmp = z * x;
	elseif (y <= 19.0)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -660000000000.0], t$95$1, If[LessEqual[y, 1.26e-185], N[(z * x), $MachinePrecision], If[LessEqual[y, 19.0], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.6e11 or 19 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 49.8%

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

      1. mul-1-neg 49.8%

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

      2. unsub-neg 49.8%

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

   5. Simplified 49.8%

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

   6. Taylor expanded in y around inf 43.2%

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

      1. mul-1-neg 43.2%

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

      2. distribute-rgt-neg-out 43.2%

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

   8. Simplified 43.2%

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

   if -6.6e11 < y < 1.2599999999999999e-185

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. unsub-neg 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in z around inf 37.5%

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

      1. *-commutative 37.5%

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

   8. Simplified 37.5%

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

   if 1.2599999999999999e-185 < y < 19

   1. Initial program 100.0%

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

      1. add-cube-cbrt 99.4%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)} \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}} \]

      2. pow3 99.3%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   4. Applied egg-rr 99.3%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   5. Taylor expanded in x around inf 39.0%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -660000000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-185}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 19:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+29} \lor \neg \left(x \leq 1.05 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9.5e+29) (not (<= x 1.05e+28)))
   (* x (+ (- z y) 1.0))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.5e+29) || !(x <= 1.05e+28)) {
		tmp = x * ((z - y) + 1.0);
	} 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 ((x <= (-9.5d+29)) .or. (.not. (x <= 1.05d+28))) then
        tmp = x * ((z - y) + 1.0d0)
    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 ((x <= -9.5e+29) || !(x <= 1.05e+28)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9.5e+29) or not (x <= 1.05e+28):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9.5e+29) || !(x <= 1.05e+28))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	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 ((x <= -9.5e+29) || ~((x <= 1.05e+28)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9.5e+29], N[Not[LessEqual[x, 1.05e+28]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000003e29 or 1.04999999999999995e28 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. unsub-neg 87.5%

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

   5. Simplified 87.5%

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

   if -9.5000000000000003e29 < x < 1.04999999999999995e28

   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 82.0%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+29} \lor \neg \left(x \leq 1.05 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -64000000000000 \lor \neg \left(z \leq 2.2 \cdot 10^{+82}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -64000000000000.0) (not (<= z 2.2e+82)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -64000000000000.0) || !(z <= 2.2e+82)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - 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 ((z <= (-64000000000000.0d0)) .or. (.not. (z <= 2.2d+82))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -64000000000000.0) || !(z <= 2.2e+82)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -64000000000000.0) or not (z <= 2.2e+82):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -64000000000000.0) || !(z <= 2.2e+82))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -64000000000000.0) || ~((z <= 2.2e+82)))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -64000000000000.0], N[Not[LessEqual[z, 2.2e+82]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4e13 or 2.2000000000000001e82 < 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. add-cube-cbrt 99.0%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)} \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}} \]

      2. pow3 98.9%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   4. Applied egg-rr 98.9%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   5. Taylor expanded in y around 0 86.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(t - x\right)\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 86.4%

         \[\leadsto x + \color{blue}{\left(-{1}^{0.3333333333333333} \cdot \left(z \cdot \left(t - x\right)\right)\right)} \]

      2. pow-base-1 86.4%

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

      3. *-lft-identity 86.4%

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

      4. unsub-neg 86.4%

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

   7. Simplified 86.4%

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

   if -6.4e13 < z < 2.2000000000000001e82

   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 87.1%

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

      1. *-commutative 87.1%

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

   5. Simplified 87.1%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -64000000000000 \lor \neg \left(z \leq 2.2 \cdot 10^{+82}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+27}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.7e+30)
   (* x (+ (- z y) 1.0))
   (if (<= x 4.5e+27) (+ x (* (- y z) t)) (+ x (* x (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.7e+30) {
		tmp = x * ((z - y) + 1.0);
	} else if (x <= 4.5e+27) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (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 (x <= (-2.7d+30)) then
        tmp = x * ((z - y) + 1.0d0)
    else if (x <= 4.5d+27) then
        tmp = x + ((y - z) * t)
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.7e+30) {
		tmp = x * ((z - y) + 1.0);
	} else if (x <= 4.5e+27) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.7e+30:
		tmp = x * ((z - y) + 1.0)
	elif x <= 4.5e+27:
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.7e+30)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	elseif (x <= 4.5e+27)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.7e+30)
		tmp = x * ((z - y) + 1.0);
	elseif (x <= 4.5e+27)
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.7e+30], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+27], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6999999999999999e30

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 86.4%

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

      1. mul-1-neg 86.4%

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

      2. unsub-neg 86.4%

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

   5. Simplified 86.4%

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

   if -2.6999999999999999e30 < x < 4.4999999999999999e27

   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 82.0%

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

   if 4.4999999999999999e27 < x

   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 88.6%

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

      1. mul-1-neg 88.6%

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

      2. distribute-rgt-neg-in 88.6%

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

      3. neg-sub0 88.6%

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

      4. sub-neg 88.6%

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

      5. +-commutative 88.6%

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

      6. associate--r+ 88.6%

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

      7. neg-sub0 88.6%

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

      8. remove-double-neg 88.6%

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

   5. Simplified 88.6%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+27}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -14500 \lor \neg \left(z \leq 2.7 \cdot 10^{-12}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -14500.0) (not (<= z 2.7e-12))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -14500.0) || !(z <= 2.7e-12)) {
		tmp = z * x;
	} 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 ((z <= (-14500.0d0)) .or. (.not. (z <= 2.7d-12))) then
        tmp = z * x
    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 ((z <= -14500.0) || !(z <= 2.7e-12)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -14500.0) or not (z <= 2.7e-12):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -14500.0) || !(z <= 2.7e-12))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -14500.0) || ~((z <= 2.7e-12)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -14500.0], N[Not[LessEqual[z, 2.7e-12]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -14500 or 2.6999999999999998e-12 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in z around inf 39.2%

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

      1. *-commutative 39.2%

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

   8. Simplified 39.2%

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

   if -14500 < z < 2.6999999999999998e-12

   1. Initial program 100.0%

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

      1. add-cube-cbrt 99.0%

         \[\leadsto x + \color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)} \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}} \]

      2. pow3 99.0%

         \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   4. Applied egg-rr 99.0%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

   5. Taylor expanded in x around inf 28.8%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -14500 \lor \neg \left(z \leq 2.7 \cdot 10^{-12}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 13: 17.4% 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. Step-by-step derivation

   1. add-cube-cbrt 99.0%

      \[\leadsto x + \color{blue}{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)} \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right) \cdot \sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}} \]

   2. pow3 98.9%

      \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

4. Applied egg-rr 98.9%

   \[\leadsto x + \color{blue}{{\left(\sqrt[3]{\left(y - z\right) \cdot \left(t - x\right)}\right)}^{3}} \]

5. Taylor expanded in x around inf 15.8%

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

6. Final simplification 15.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.1% 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 2024043 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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