Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.7s

Alternatives: 13

Speedup: 1.0×

• 34.7% 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. Add Preprocessing

Alternative 2: 37.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-20}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+205} \lor \neg \left(y \leq 1.2 \cdot 10^{+222}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.32e-20)
   (* y t)
   (if (<= y 1.45e-6)
     x
     (if (<= y 1.9e+63)
       (* z (- t))
       (if (or (<= y 2.55e+205) (not (<= y 1.2e+222))) (* y (- x)) (* y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.32e-20) {
		tmp = y * t;
	} else if (y <= 1.45e-6) {
		tmp = x;
	} else if (y <= 1.9e+63) {
		tmp = z * -t;
	} else if ((y <= 2.55e+205) || !(y <= 1.2e+222)) {
		tmp = y * -x;
	} 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 <= (-1.32d-20)) then
        tmp = y * t
    else if (y <= 1.45d-6) then
        tmp = x
    else if (y <= 1.9d+63) then
        tmp = z * -t
    else if ((y <= 2.55d+205) .or. (.not. (y <= 1.2d+222))) then
        tmp = y * -x
    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 <= -1.32e-20) {
		tmp = y * t;
	} else if (y <= 1.45e-6) {
		tmp = x;
	} else if (y <= 1.9e+63) {
		tmp = z * -t;
	} else if ((y <= 2.55e+205) || !(y <= 1.2e+222)) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.32e-20:
		tmp = y * t
	elif y <= 1.45e-6:
		tmp = x
	elif y <= 1.9e+63:
		tmp = z * -t
	elif (y <= 2.55e+205) or not (y <= 1.2e+222):
		tmp = y * -x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.32e-20)
		tmp = Float64(y * t);
	elseif (y <= 1.45e-6)
		tmp = x;
	elseif (y <= 1.9e+63)
		tmp = Float64(z * Float64(-t));
	elseif ((y <= 2.55e+205) || !(y <= 1.2e+222))
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.32e-20)
		tmp = y * t;
	elseif (y <= 1.45e-6)
		tmp = x;
	elseif (y <= 1.9e+63)
		tmp = z * -t;
	elseif ((y <= 2.55e+205) || ~((y <= 1.2e+222)))
		tmp = y * -x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.32e-20], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.45e-6], x, If[LessEqual[y, 1.9e+63], N[(z * (-t)), $MachinePrecision], If[Or[LessEqual[y, 2.55e+205], N[Not[LessEqual[y, 1.2e+222]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.32000000000000004e-20 or 2.55e205 < y < 1.2000000000000001e222

   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 60.7%

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

   4. Taylor expanded in y around inf 50.8%

      \[\leadsto x + \color{blue}{t \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 50.8%

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

   6. Simplified 50.8%

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

   7. Taylor expanded in x around 0 50.0%

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

   if -1.32000000000000004e-20 < y < 1.4500000000000001e-6

   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 71.0%

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

   4. Taylor expanded in x around inf 37.7%

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

   if 1.4500000000000001e-6 < y < 1.9000000000000001e63

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in t around inf 37.9%

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

   7. Taylor expanded in x around 0 37.8%

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

      1. associate-*r* 37.8%

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

      2. neg-mul-1 37.8%

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

      3. *-commutative 37.8%

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

   9. Simplified 37.8%

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

   if 1.9000000000000001e63 < y < 2.55e205 or 1.2000000000000001e222 < y

   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 84.0%

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

      1. *-commutative 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in x around inf 55.9%

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

      1. neg-mul-1 55.9%

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

      2. unsub-neg 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in y around inf 55.9%

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

       1. mul-1-neg 55.9%

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

       2. distribute-rgt-neg-out 55.9%

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

   11. Simplified 55.9%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-20}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+63}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+205} \lor \neg \left(y \leq 1.2 \cdot 10^{+222}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot x\\ t_2 := x + y \cdot t\\ \mathbf{if}\;x \leq -2 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-300}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-263}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;x \leq 620000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z x))) (t_2 (+ x (* y t))))
   (if (<= x -2e+51)
     t_1
     (if (<= x 6.2e-300)
       t_2
       (if (<= x 7e-263) (- x (* z t)) (if (<= x 620000000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = x + (y * t);
	double tmp;
	if (x <= -2e+51) {
		tmp = t_1;
	} else if (x <= 6.2e-300) {
		tmp = t_2;
	} else if (x <= 7e-263) {
		tmp = x - (z * t);
	} else if (x <= 620000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * x)
    t_2 = x + (y * t)
    if (x <= (-2d+51)) then
        tmp = t_1
    else if (x <= 6.2d-300) then
        tmp = t_2
    else if (x <= 7d-263) then
        tmp = x - (z * t)
    else if (x <= 620000000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = x + (y * t);
	double tmp;
	if (x <= -2e+51) {
		tmp = t_1;
	} else if (x <= 6.2e-300) {
		tmp = t_2;
	} else if (x <= 7e-263) {
		tmp = x - (z * t);
	} else if (x <= 620000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * x)
	t_2 = x + (y * t)
	tmp = 0
	if x <= -2e+51:
		tmp = t_1
	elif x <= 6.2e-300:
		tmp = t_2
	elif x <= 7e-263:
		tmp = x - (z * t)
	elif x <= 620000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * x))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (x <= -2e+51)
		tmp = t_1;
	elseif (x <= 6.2e-300)
		tmp = t_2;
	elseif (x <= 7e-263)
		tmp = Float64(x - Float64(z * t));
	elseif (x <= 620000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * x);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (x <= -2e+51)
		tmp = t_1;
	elseif (x <= 6.2e-300)
		tmp = t_2;
	elseif (x <= 7e-263)
		tmp = x - (z * t);
	elseif (x <= 620000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+51], t$95$1, If[LessEqual[x, 6.2e-300], t$95$2, If[LessEqual[x, 7e-263], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 620000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2e51 or 6.2e8 < 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 86.2%

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

      1. mul-1-neg 86.2%

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

      2. distribute-rgt-neg-in 86.2%

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

      3. neg-sub0 86.2%

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

      4. sub-neg 86.2%

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

      5. +-commutative 86.2%

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

      6. associate--r+ 86.2%

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

      7. neg-sub0 86.2%

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

      8. remove-double-neg 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in z around inf 61.5%

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

   if -2e51 < x < 6.2000000000000005e-300 or 6.99999999999999938e-263 < x < 6.2e8

   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 80.9%

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

   4. Taylor expanded in y around inf 61.7%

      \[\leadsto x + \color{blue}{t \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 61.7%

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

   6. Simplified 61.7%

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

   if 6.2000000000000005e-300 < x < 6.99999999999999938e-263

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.1%

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

      1. mul-1-neg 88.1%

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

      2. unsub-neg 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in t around inf 88.1%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+51}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-300}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-263}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;x \leq 620000000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot x\\ t_2 := x + y \cdot t\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-299}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-262}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 550000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z x))) (t_2 (+ x (* y t))))
   (if (<= x -1.95e+51)
     t_1
     (if (<= x 3.3e-299)
       t_2
       (if (<= x 1.25e-262) (* z (- t)) (if (<= x 550000000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = x + (y * t);
	double tmp;
	if (x <= -1.95e+51) {
		tmp = t_1;
	} else if (x <= 3.3e-299) {
		tmp = t_2;
	} else if (x <= 1.25e-262) {
		tmp = z * -t;
	} else if (x <= 550000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * x)
    t_2 = x + (y * t)
    if (x <= (-1.95d+51)) then
        tmp = t_1
    else if (x <= 3.3d-299) then
        tmp = t_2
    else if (x <= 1.25d-262) then
        tmp = z * -t
    else if (x <= 550000000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = x + (y * t);
	double tmp;
	if (x <= -1.95e+51) {
		tmp = t_1;
	} else if (x <= 3.3e-299) {
		tmp = t_2;
	} else if (x <= 1.25e-262) {
		tmp = z * -t;
	} else if (x <= 550000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * x)
	t_2 = x + (y * t)
	tmp = 0
	if x <= -1.95e+51:
		tmp = t_1
	elif x <= 3.3e-299:
		tmp = t_2
	elif x <= 1.25e-262:
		tmp = z * -t
	elif x <= 550000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * x))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (x <= -1.95e+51)
		tmp = t_1;
	elseif (x <= 3.3e-299)
		tmp = t_2;
	elseif (x <= 1.25e-262)
		tmp = Float64(z * Float64(-t));
	elseif (x <= 550000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * x);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (x <= -1.95e+51)
		tmp = t_1;
	elseif (x <= 3.3e-299)
		tmp = t_2;
	elseif (x <= 1.25e-262)
		tmp = z * -t;
	elseif (x <= 550000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.95e+51], t$95$1, If[LessEqual[x, 3.3e-299], t$95$2, If[LessEqual[x, 1.25e-262], N[(z * (-t)), $MachinePrecision], If[LessEqual[x, 550000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.94999999999999992e51 or 5.5e8 < 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 86.2%

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

      1. mul-1-neg 86.2%

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

      2. distribute-rgt-neg-in 86.2%

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

      3. neg-sub0 86.2%

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

      4. sub-neg 86.2%

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

      5. +-commutative 86.2%

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

      6. associate--r+ 86.2%

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

      7. neg-sub0 86.2%

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

      8. remove-double-neg 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in z around inf 61.5%

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

   if -1.94999999999999992e51 < x < 3.3000000000000002e-299 or 1.24999999999999998e-262 < x < 5.5e8

   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 80.9%

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

   4. Taylor expanded in y around inf 61.7%

      \[\leadsto x + \color{blue}{t \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 61.7%

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

   6. Simplified 61.7%

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

   if 3.3000000000000002e-299 < x < 1.24999999999999998e-262

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.1%

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

      1. mul-1-neg 88.1%

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

      2. unsub-neg 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in t around inf 88.1%

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

   7. Taylor expanded in x around 0 88.1%

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

      1. associate-*r* 88.1%

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

      2. neg-mul-1 88.1%

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

      3. *-commutative 88.1%

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

   9. Simplified 88.1%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+51}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-299}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-262}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 550000000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot x\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-197}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-229}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z x))) (t_2 (* x (- 1.0 y))))
   (if (<= z -1.75e+79)
     t_1
     (if (<= z -8.2e-197)
       t_2
       (if (<= z -2.9e-229) (* y t) (if (<= z 4e+26) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -1.75e+79) {
		tmp = t_1;
	} else if (z <= -8.2e-197) {
		tmp = t_2;
	} else if (z <= -2.9e-229) {
		tmp = y * t;
	} else if (z <= 4e+26) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * x)
    t_2 = x * (1.0d0 - y)
    if (z <= (-1.75d+79)) then
        tmp = t_1
    else if (z <= (-8.2d-197)) then
        tmp = t_2
    else if (z <= (-2.9d-229)) then
        tmp = y * t
    else if (z <= 4d+26) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -1.75e+79) {
		tmp = t_1;
	} else if (z <= -8.2e-197) {
		tmp = t_2;
	} else if (z <= -2.9e-229) {
		tmp = y * t;
	} else if (z <= 4e+26) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * x)
	t_2 = x * (1.0 - y)
	tmp = 0
	if z <= -1.75e+79:
		tmp = t_1
	elif z <= -8.2e-197:
		tmp = t_2
	elif z <= -2.9e-229:
		tmp = y * t
	elif z <= 4e+26:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * x))
	t_2 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -1.75e+79)
		tmp = t_1;
	elseif (z <= -8.2e-197)
		tmp = t_2;
	elseif (z <= -2.9e-229)
		tmp = Float64(y * t);
	elseif (z <= 4e+26)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * x);
	t_2 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -1.75e+79)
		tmp = t_1;
	elseif (z <= -8.2e-197)
		tmp = t_2;
	elseif (z <= -2.9e-229)
		tmp = y * t;
	elseif (z <= 4e+26)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+79], t$95$1, If[LessEqual[z, -8.2e-197], t$95$2, If[LessEqual[z, -2.9e-229], N[(y * t), $MachinePrecision], If[LessEqual[z, 4e+26], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7499999999999999e79 or 4.00000000000000019e26 < z

   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 60.9%

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

      1. mul-1-neg 60.9%

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

      2. distribute-rgt-neg-in 60.9%

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

      3. neg-sub0 60.9%

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

      4. sub-neg 60.9%

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

      5. +-commutative 60.9%

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

      6. associate--r+ 60.9%

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

      7. neg-sub0 60.9%

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

      8. remove-double-neg 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in z around inf 55.7%

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

   if -1.7499999999999999e79 < z < -8.2e-197 or -2.9e-229 < z < 4.00000000000000019e26

   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 85.7%

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

      1. *-commutative 85.7%

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

   5. Simplified 85.7%

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

   6. Taylor expanded in x around inf 59.3%

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

      1. neg-mul-1 59.3%

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

      2. unsub-neg 59.3%

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

   8. Simplified 59.3%

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

   if -8.2e-197 < z < -2.9e-229

   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 100.0%

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

   4. Taylor expanded in y around inf 100.0%

      \[\leadsto x + \color{blue}{t \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 78.4%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+79}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-197}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-229}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 44.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+174}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+184}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.8e+174)
   (* y t)
   (if (<= t 2.15e-43)
     (* x (- 1.0 y))
     (if (<= t 4e+184) (* y t) (* z (- t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.8e+174) {
		tmp = y * t;
	} else if (t <= 2.15e-43) {
		tmp = x * (1.0 - y);
	} else if (t <= 4e+184) {
		tmp = y * t;
	} else {
		tmp = 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 (t <= (-5.8d+174)) then
        tmp = y * t
    else if (t <= 2.15d-43) then
        tmp = x * (1.0d0 - y)
    else if (t <= 4d+184) then
        tmp = y * t
    else
        tmp = z * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.8e+174) {
		tmp = y * t;
	} else if (t <= 2.15e-43) {
		tmp = x * (1.0 - y);
	} else if (t <= 4e+184) {
		tmp = y * t;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.8e+174:
		tmp = y * t
	elif t <= 2.15e-43:
		tmp = x * (1.0 - y)
	elif t <= 4e+184:
		tmp = y * t
	else:
		tmp = z * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.8e+174)
		tmp = Float64(y * t);
	elseif (t <= 2.15e-43)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (t <= 4e+184)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.8e+174)
		tmp = y * t;
	elseif (t <= 2.15e-43)
		tmp = x * (1.0 - y);
	elseif (t <= 4e+184)
		tmp = y * t;
	else
		tmp = z * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.8e+174], N[(y * t), $MachinePrecision], If[LessEqual[t, 2.15e-43], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+184], N[(y * t), $MachinePrecision], N[(z * (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.7999999999999999e174 or 2.14999999999999982e-43 < t < 4.00000000000000007e184

   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 81.6%

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

   4. Taylor expanded in y around inf 55.2%

      \[\leadsto x + \color{blue}{t \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 55.2%

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

   6. Simplified 55.2%

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

   7. Taylor expanded in x around 0 49.7%

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

   if -5.7999999999999999e174 < t < 2.14999999999999982e-43

   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 60.1%

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

      1. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in x around inf 48.2%

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

      1. neg-mul-1 48.2%

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

      2. unsub-neg 48.2%

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

   8. Simplified 48.2%

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

   if 4.00000000000000007e184 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. unsub-neg 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in t around inf 76.0%

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

   7. Taylor expanded in x around 0 70.0%

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

      1. associate-*r* 70.0%

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

      2. neg-mul-1 70.0%

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

      3. *-commutative 70.0%

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

   9. Simplified 70.0%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+174}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+184}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+24} \lor \neg \left(z \leq 3300000000000\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.35e+24) (not (<= z 3300000000000.0)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.35e+24) || !(z <= 3300000000000.0)) {
		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 <= (-1.35d+24)) .or. (.not. (z <= 3300000000000.0d0))) 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 <= -1.35e+24) || !(z <= 3300000000000.0)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.35e+24) or not (z <= 3300000000000.0):
		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 <= -1.35e+24) || !(z <= 3300000000000.0))
		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 <= -1.35e+24) || ~((z <= 3300000000000.0)))
		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, -1.35e+24], N[Not[LessEqual[z, 3300000000000.0]], $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 < -1.35e24 or 3.3e12 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.4%

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

      1. mul-1-neg 82.4%

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

      2. unsub-neg 82.4%

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

   5. Simplified 82.4%

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

   if -1.35e24 < z < 3.3e12

   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 90.6%

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

      1. *-commutative 90.6%

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

   5. Simplified 90.6%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+24} \lor \neg \left(z \leq 3300000000000\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+95} \lor \neg \left(x \leq 7 \cdot 10^{-24}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.85e+95) (not (<= x 7e-24)))
   (+ x (* x (- z y)))
   (+ x (* t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.85e+95) || !(x <= 7e-24)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.85d+95)) .or. (.not. (x <= 7d-24))) then
        tmp = x + (x * (z - y))
    else
        tmp = x + (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.85e+95) || !(x <= 7e-24)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.85e+95) or not (x <= 7e-24):
		tmp = x + (x * (z - y))
	else:
		tmp = x + (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.85e+95) || !(x <= 7e-24))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.85e+95) || ~((x <= 7e-24)))
		tmp = x + (x * (z - y));
	else
		tmp = x + (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.85e+95], N[Not[LessEqual[x, 7e-24]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8500000000000001e95 or 6.9999999999999993e-24 < 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 86.3%

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

      1. mul-1-neg 86.3%

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

      2. distribute-rgt-neg-in 86.3%

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

      3. neg-sub0 86.3%

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

      4. sub-neg 86.3%

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

      5. +-commutative 86.3%

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

      6. associate--r+ 86.3%

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

      7. neg-sub0 86.3%

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

      8. remove-double-neg 86.3%

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

   5. Simplified 86.3%

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

   if -1.8500000000000001e95 < x < 6.9999999999999993e-24

   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 85.0%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+95} \lor \neg \left(x \leq 7 \cdot 10^{-24}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+143} \lor \neg \left(x \leq 660000000\right):\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.2e+143) (not (<= x 660000000.0)))
   (+ x (* z x))
   (+ x (* t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e+143) || !(x <= 660000000.0)) {
		tmp = x + (z * x);
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.2d+143)) .or. (.not. (x <= 660000000.0d0))) then
        tmp = x + (z * x)
    else
        tmp = x + (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e+143) || !(x <= 660000000.0)) {
		tmp = x + (z * x);
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.2e+143) or not (x <= 660000000.0):
		tmp = x + (z * x)
	else:
		tmp = x + (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.2e+143) || !(x <= 660000000.0))
		tmp = Float64(x + Float64(z * x));
	else
		tmp = Float64(x + Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.2e+143) || ~((x <= 660000000.0)))
		tmp = x + (z * x);
	else
		tmp = x + (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.2e+143], N[Not[LessEqual[x, 660000000.0]], $MachinePrecision]], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.1999999999999998e143 or 6.6e8 < 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%

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

   6. Taylor expanded in z around inf 63.9%

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

   if -7.1999999999999998e143 < x < 6.6e8

   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 80.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+143} \lor \neg \left(x \leq 660000000\right):\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-20}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 750:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.32e-20) (* y t) (if (<= y 750.0) x (* y (- x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.32e-20) {
		tmp = y * t;
	} else if (y <= 750.0) {
		tmp = x;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.32d-20)) then
        tmp = y * t
    else if (y <= 750.0d0) then
        tmp = x
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.32e-20) {
		tmp = y * t;
	} else if (y <= 750.0) {
		tmp = x;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.32e-20:
		tmp = y * t
	elif y <= 750.0:
		tmp = x
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.32e-20)
		tmp = Float64(y * t);
	elseif (y <= 750.0)
		tmp = x;
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.32e-20)
		tmp = y * t;
	elseif (y <= 750.0)
		tmp = x;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.32e-20], N[(y * t), $MachinePrecision], If[LessEqual[y, 750.0], x, N[(y * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.32000000000000004e-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 58.9%

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

   4. Taylor expanded in y around inf 48.3%

      \[\leadsto x + \color{blue}{t \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 48.3%

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

   6. Simplified 48.3%

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

   7. Taylor expanded in x around 0 47.5%

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

   if -1.32000000000000004e-20 < y < 750

   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 71.1%

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

   4. Taylor expanded in x around inf 36.6%

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

   if 750 < y

   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 72.4%

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

      1. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in x around inf 41.7%

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

      1. neg-mul-1 41.7%

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

      2. unsub-neg 41.7%

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

   8. Simplified 41.7%

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

   9. Taylor expanded in y around inf 40.5%

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

       1. mul-1-neg 40.5%

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

       2. distribute-rgt-neg-out 40.5%

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

   11. Simplified 40.5%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{-20}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 750:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-20} \lor \neg \left(y \leq 2.1 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.02e-20) (not (<= y 2.1e-16))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e-20) || !(y <= 2.1e-16)) {
		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 <= (-1.02d-20)) .or. (.not. (y <= 2.1d-16))) 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 <= -1.02e-20) || !(y <= 2.1e-16)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.02e-20) or not (y <= 2.1e-16):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.02e-20) || !(y <= 2.1e-16))
		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 <= -1.02e-20) || ~((y <= 2.1e-16)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.02e-20], N[Not[LessEqual[y, 2.1e-16]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.02000000000000001e-20 or 2.1000000000000001e-16 < 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 inf 54.1%

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

   4. Taylor expanded in y around inf 41.9%

      \[\leadsto x + \color{blue}{t \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 41.9%

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

   6. Simplified 41.9%

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

   7. Taylor expanded in x around 0 41.1%

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

   if -1.02000000000000001e-20 < y < 2.1000000000000001e-16

   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 70.6%

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

   4. Taylor expanded in x around inf 38.1%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-20} \lor \neg \left(y \leq 2.1 \cdot 10^{-16}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 13: 17.6% 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 61.7%

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

4. Taylor expanded in x around inf 19.5%

   \[\leadsto \color{blue}{x} \]
5. 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 2024106 
(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))))