Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.3s

Alternatives: 13

Speedup: 1.0×

• 34.5% 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: 69.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x - z \cdot t\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-296}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-151}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-11} \lor \neg \left(y \leq 3 \cdot 10^{+56}\right) \land y \leq 3.3 \cdot 10^{+69}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (- x (* z t))))
   (if (<= y -7.2e-8)
     t_1
     (if (<= y -2.9e-296)
       t_2
       (if (<= y 1.35e-151)
         (+ x (* z x))
         (if (or (<= y 3.8e-11) (and (not (<= y 3e+56)) (<= y 3.3e+69)))
           t_2
           t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x - (z * t);
	double tmp;
	if (y <= -7.2e-8) {
		tmp = t_1;
	} else if (y <= -2.9e-296) {
		tmp = t_2;
	} else if (y <= 1.35e-151) {
		tmp = x + (z * x);
	} else if ((y <= 3.8e-11) || (!(y <= 3e+56) && (y <= 3.3e+69))) {
		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 = y * (t - x)
    t_2 = x - (z * t)
    if (y <= (-7.2d-8)) then
        tmp = t_1
    else if (y <= (-2.9d-296)) then
        tmp = t_2
    else if (y <= 1.35d-151) then
        tmp = x + (z * x)
    else if ((y <= 3.8d-11) .or. (.not. (y <= 3d+56)) .and. (y <= 3.3d+69)) 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 = y * (t - x);
	double t_2 = x - (z * t);
	double tmp;
	if (y <= -7.2e-8) {
		tmp = t_1;
	} else if (y <= -2.9e-296) {
		tmp = t_2;
	} else if (y <= 1.35e-151) {
		tmp = x + (z * x);
	} else if ((y <= 3.8e-11) || (!(y <= 3e+56) && (y <= 3.3e+69))) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x - (z * t)
	tmp = 0
	if y <= -7.2e-8:
		tmp = t_1
	elif y <= -2.9e-296:
		tmp = t_2
	elif y <= 1.35e-151:
		tmp = x + (z * x)
	elif (y <= 3.8e-11) or (not (y <= 3e+56) and (y <= 3.3e+69)):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (y <= -7.2e-8)
		tmp = t_1;
	elseif (y <= -2.9e-296)
		tmp = t_2;
	elseif (y <= 1.35e-151)
		tmp = Float64(x + Float64(z * x));
	elseif ((y <= 3.8e-11) || (!(y <= 3e+56) && (y <= 3.3e+69)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x - (z * t);
	tmp = 0.0;
	if (y <= -7.2e-8)
		tmp = t_1;
	elseif (y <= -2.9e-296)
		tmp = t_2;
	elseif (y <= 1.35e-151)
		tmp = x + (z * x);
	elseif ((y <= 3.8e-11) || (~((y <= 3e+56)) && (y <= 3.3e+69)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e-8], t$95$1, If[LessEqual[y, -2.9e-296], t$95$2, If[LessEqual[y, 1.35e-151], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.8e-11], And[N[Not[LessEqual[y, 3e+56]], $MachinePrecision], LessEqual[y, 3.3e+69]]], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.19999999999999962e-8 or 3.7999999999999998e-11 < y < 3.00000000000000006e56 or 3.2999999999999999e69 < 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 76.4%

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

      1. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in x around 0 74.9%

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

   7. Taylor expanded in y around inf 75.3%

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

      1. mul-1-neg 75.3%

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

      2. sub-neg 75.3%

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

   9. Simplified 75.3%

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

   if -7.19999999999999962e-8 < y < -2.89999999999999983e-296 or 1.35000000000000004e-151 < y < 3.7999999999999998e-11 or 3.00000000000000006e56 < y < 3.2999999999999999e69

   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 91.9%

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

      1. mul-1-neg 91.9%

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

      2. unsub-neg 91.9%

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

   5. Simplified 91.9%

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

   6. Taylor expanded in t around inf 69.8%

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

   if -2.89999999999999983e-296 < y < 1.35000000000000004e-151

   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 96.5%

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

      1. mul-1-neg 96.5%

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

      2. unsub-neg 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in t around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. *-commutative 82.6%

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

      3. distribute-rgt-neg-in 82.6%

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

   8. Simplified 82.6%

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

      1. sub-neg 82.6%

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

      2. +-commutative 82.6%

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

      3. distribute-rgt-neg-out 82.6%

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

      4. remove-double-neg 82.6%

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

      5. *-commutative 82.6%

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

   10. Applied egg-rr 82.6%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-296}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-151}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-11} \lor \neg \left(y \leq 3 \cdot 10^{+56}\right) \land y \leq 3.3 \cdot 10^{+69}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+92}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-38}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-168}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+65}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.55e+92)
   (* z x)
   (if (<= z -4.2e-38)
     (* y t)
     (if (<= z -2.55e-139)
       x
       (if (<= z -2.9e-168)
         (* y t)
         (if (<= z 3.05e-55) x (if (<= z 1.7e+65) (* y t) (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.55e+92) {
		tmp = z * x;
	} else if (z <= -4.2e-38) {
		tmp = y * t;
	} else if (z <= -2.55e-139) {
		tmp = x;
	} else if (z <= -2.9e-168) {
		tmp = y * t;
	} else if (z <= 3.05e-55) {
		tmp = x;
	} else if (z <= 1.7e+65) {
		tmp = y * 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) :: tmp
    if (z <= (-2.55d+92)) then
        tmp = z * x
    else if (z <= (-4.2d-38)) then
        tmp = y * t
    else if (z <= (-2.55d-139)) then
        tmp = x
    else if (z <= (-2.9d-168)) then
        tmp = y * t
    else if (z <= 3.05d-55) then
        tmp = x
    else if (z <= 1.7d+65) then
        tmp = y * 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 tmp;
	if (z <= -2.55e+92) {
		tmp = z * x;
	} else if (z <= -4.2e-38) {
		tmp = y * t;
	} else if (z <= -2.55e-139) {
		tmp = x;
	} else if (z <= -2.9e-168) {
		tmp = y * t;
	} else if (z <= 3.05e-55) {
		tmp = x;
	} else if (z <= 1.7e+65) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.55e+92:
		tmp = z * x
	elif z <= -4.2e-38:
		tmp = y * t
	elif z <= -2.55e-139:
		tmp = x
	elif z <= -2.9e-168:
		tmp = y * t
	elif z <= 3.05e-55:
		tmp = x
	elif z <= 1.7e+65:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.55e+92)
		tmp = Float64(z * x);
	elseif (z <= -4.2e-38)
		tmp = Float64(y * t);
	elseif (z <= -2.55e-139)
		tmp = x;
	elseif (z <= -2.9e-168)
		tmp = Float64(y * t);
	elseif (z <= 3.05e-55)
		tmp = x;
	elseif (z <= 1.7e+65)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.55e+92)
		tmp = z * x;
	elseif (z <= -4.2e-38)
		tmp = y * t;
	elseif (z <= -2.55e-139)
		tmp = x;
	elseif (z <= -2.9e-168)
		tmp = y * t;
	elseif (z <= 3.05e-55)
		tmp = x;
	elseif (z <= 1.7e+65)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.55e+92], N[(z * x), $MachinePrecision], If[LessEqual[z, -4.2e-38], N[(y * t), $MachinePrecision], If[LessEqual[z, -2.55e-139], x, If[LessEqual[z, -2.9e-168], N[(y * t), $MachinePrecision], If[LessEqual[z, 3.05e-55], x, If[LessEqual[z, 1.7e+65], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5500000000000001e92 or 1.7e65 < 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 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

   5. Simplified 86.6%

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

   6. Taylor expanded in t around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. *-commutative 47.3%

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

      3. distribute-rgt-neg-in 47.3%

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

   8. Simplified 47.3%

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

   9. Taylor expanded in z around inf 47.3%

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

   if -2.5500000000000001e92 < z < -4.20000000000000026e-38 or -2.55000000000000018e-139 < z < -2.8999999999999998e-168 or 3.0500000000000001e-55 < z < 1.7e65

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 77.4%

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

      1. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in x around 0 75.5%

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

   7. Taylor expanded in t around inf 46.3%

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

      1. *-commutative 46.3%

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

   9. Simplified 46.3%

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

   if -4.20000000000000026e-38 < z < -2.55000000000000018e-139 or -2.8999999999999998e-168 < z < 3.0500000000000001e-55

   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 77.2%

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

   4. Taylor expanded in x around inf 46.8%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+92}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-38}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-168}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+65}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+197}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 13.8:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+119} \lor \neg \left(y \leq 4.3 \cdot 10^{+257}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -2.5e+197)
     t_1
     (if (<= y -3.15e+119)
       (* y t)
       (if (<= y 13.8)
         (* x (+ z 1.0))
         (if (or (<= y 1.9e+119) (not (<= y 4.3e+257))) t_1 (* y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -2.5e+197) {
		tmp = t_1;
	} else if (y <= -3.15e+119) {
		tmp = y * t;
	} else if (y <= 13.8) {
		tmp = x * (z + 1.0);
	} else if ((y <= 1.9e+119) || !(y <= 4.3e+257)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * -y
    if (y <= (-2.5d+197)) then
        tmp = t_1
    else if (y <= (-3.15d+119)) then
        tmp = y * t
    else if (y <= 13.8d0) then
        tmp = x * (z + 1.0d0)
    else if ((y <= 1.9d+119) .or. (.not. (y <= 4.3d+257))) then
        tmp = t_1
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -2.5e+197) {
		tmp = t_1;
	} else if (y <= -3.15e+119) {
		tmp = y * t;
	} else if (y <= 13.8) {
		tmp = x * (z + 1.0);
	} else if ((y <= 1.9e+119) || !(y <= 4.3e+257)) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -2.5e+197:
		tmp = t_1
	elif y <= -3.15e+119:
		tmp = y * t
	elif y <= 13.8:
		tmp = x * (z + 1.0)
	elif (y <= 1.9e+119) or not (y <= 4.3e+257):
		tmp = t_1
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -2.5e+197)
		tmp = t_1;
	elseif (y <= -3.15e+119)
		tmp = Float64(y * t);
	elseif (y <= 13.8)
		tmp = Float64(x * Float64(z + 1.0));
	elseif ((y <= 1.9e+119) || !(y <= 4.3e+257))
		tmp = t_1;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	tmp = 0.0;
	if (y <= -2.5e+197)
		tmp = t_1;
	elseif (y <= -3.15e+119)
		tmp = y * t;
	elseif (y <= 13.8)
		tmp = x * (z + 1.0);
	elseif ((y <= 1.9e+119) || ~((y <= 4.3e+257)))
		tmp = t_1;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -2.5e+197], t$95$1, If[LessEqual[y, -3.15e+119], N[(y * t), $MachinePrecision], If[LessEqual[y, 13.8], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.9e+119], N[Not[LessEqual[y, 4.3e+257]], $MachinePrecision]], t$95$1, N[(y * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000004e197 or 13.800000000000001 < y < 1.89999999999999995e119 or 4.2999999999999998e257 < y

   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 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in z around 0 58.3%

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

   7. Taylor expanded in y around inf 56.5%

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

      1. associate-*r* 56.5%

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

      2. neg-mul-1 56.5%

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

      3. *-commutative 56.5%

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

   9. Simplified 56.5%

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

   if -2.50000000000000004e197 < y < -3.1499999999999999e119 or 1.89999999999999995e119 < y < 4.2999999999999998e257

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 84.4%

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

      1. *-commutative 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in x around 0 79.9%

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

   7. Taylor expanded in t around inf 61.7%

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

      1. *-commutative 61.7%

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

   9. Simplified 61.7%

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

   if -3.1499999999999999e119 < y < 13.800000000000001

   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 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in y around 0 59.9%

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

      1. +-commutative 59.9%

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

   8. Simplified 59.9%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 13.8:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+119} \lor \neg \left(y \leq 4.3 \cdot 10^{+257}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 6.8:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+263}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -9.5e+196)
     t_1
     (if (<= y -3.15e+119)
       (* y t)
       (if (<= y 6.8)
         (* x (+ z 1.0))
         (if (<= y 4.5e+118)
           (* x (- 1.0 y))
           (if (<= y 1.2e+263) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -9.5e+196) {
		tmp = t_1;
	} else if (y <= -3.15e+119) {
		tmp = y * t;
	} else if (y <= 6.8) {
		tmp = x * (z + 1.0);
	} else if (y <= 4.5e+118) {
		tmp = x * (1.0 - y);
	} else if (y <= 1.2e+263) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * -y
    if (y <= (-9.5d+196)) then
        tmp = t_1
    else if (y <= (-3.15d+119)) then
        tmp = y * t
    else if (y <= 6.8d0) then
        tmp = x * (z + 1.0d0)
    else if (y <= 4.5d+118) then
        tmp = x * (1.0d0 - y)
    else if (y <= 1.2d+263) then
        tmp = y * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -9.5e+196) {
		tmp = t_1;
	} else if (y <= -3.15e+119) {
		tmp = y * t;
	} else if (y <= 6.8) {
		tmp = x * (z + 1.0);
	} else if (y <= 4.5e+118) {
		tmp = x * (1.0 - y);
	} else if (y <= 1.2e+263) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -9.5e+196:
		tmp = t_1
	elif y <= -3.15e+119:
		tmp = y * t
	elif y <= 6.8:
		tmp = x * (z + 1.0)
	elif y <= 4.5e+118:
		tmp = x * (1.0 - y)
	elif y <= 1.2e+263:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -9.5e+196)
		tmp = t_1;
	elseif (y <= -3.15e+119)
		tmp = Float64(y * t);
	elseif (y <= 6.8)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 4.5e+118)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (y <= 1.2e+263)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	tmp = 0.0;
	if (y <= -9.5e+196)
		tmp = t_1;
	elseif (y <= -3.15e+119)
		tmp = y * t;
	elseif (y <= 6.8)
		tmp = x * (z + 1.0);
	elseif (y <= 4.5e+118)
		tmp = x * (1.0 - y);
	elseif (y <= 1.2e+263)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -9.5e+196], t$95$1, If[LessEqual[y, -3.15e+119], N[(y * t), $MachinePrecision], If[LessEqual[y, 6.8], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e+118], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+263], N[(y * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.5000000000000004e196 or 1.2e263 < 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 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

   5. Simplified 67.9%

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

   6. Taylor expanded in z around 0 63.8%

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

   7. Taylor expanded in y around inf 63.8%

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

      1. associate-*r* 63.8%

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

      2. neg-mul-1 63.8%

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

      3. *-commutative 63.8%

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

   9. Simplified 63.8%

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

   if -9.5000000000000004e196 < y < -3.1499999999999999e119 or 4.50000000000000002e118 < y < 1.2e263

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 84.4%

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

      1. *-commutative 84.4%

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

   5. Simplified 84.4%

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

   6. Taylor expanded in x around 0 79.9%

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

   7. Taylor expanded in t around inf 61.7%

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

      1. *-commutative 61.7%

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

   9. Simplified 61.7%

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

   if -3.1499999999999999e119 < y < 6.79999999999999982

   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 64.2%

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

      1. mul-1-neg 64.2%

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

      2. unsub-neg 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in y around 0 59.9%

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

      1. +-commutative 59.9%

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

   8. Simplified 59.9%

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

   if 6.79999999999999982 < y < 4.50000000000000002e118

   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 66.8%

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

      1. mul-1-neg 66.8%

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

      2. unsub-neg 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in z around 0 49.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 6.8:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+263}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{if}\;y \leq -3.15 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.16:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-305}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* x (+ (- z y) 1.0))))
   (if (<= y -3.15e+119)
     t_1
     (if (<= y -0.16)
       t_2
       (if (<= y -1.42e-305) (- x (* z t)) (if (<= y 2.8e+95) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * ((z - y) + 1.0);
	double tmp;
	if (y <= -3.15e+119) {
		tmp = t_1;
	} else if (y <= -0.16) {
		tmp = t_2;
	} else if (y <= -1.42e-305) {
		tmp = x - (z * t);
	} else if (y <= 2.8e+95) {
		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 = y * (t - x)
    t_2 = x * ((z - y) + 1.0d0)
    if (y <= (-3.15d+119)) then
        tmp = t_1
    else if (y <= (-0.16d0)) then
        tmp = t_2
    else if (y <= (-1.42d-305)) then
        tmp = x - (z * t)
    else if (y <= 2.8d+95) 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 = y * (t - x);
	double t_2 = x * ((z - y) + 1.0);
	double tmp;
	if (y <= -3.15e+119) {
		tmp = t_1;
	} else if (y <= -0.16) {
		tmp = t_2;
	} else if (y <= -1.42e-305) {
		tmp = x - (z * t);
	} else if (y <= 2.8e+95) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x * ((z - y) + 1.0)
	tmp = 0
	if y <= -3.15e+119:
		tmp = t_1
	elif y <= -0.16:
		tmp = t_2
	elif y <= -1.42e-305:
		tmp = x - (z * t)
	elif y <= 2.8e+95:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x * Float64(Float64(z - y) + 1.0))
	tmp = 0.0
	if (y <= -3.15e+119)
		tmp = t_1;
	elseif (y <= -0.16)
		tmp = t_2;
	elseif (y <= -1.42e-305)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 2.8e+95)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x * ((z - y) + 1.0);
	tmp = 0.0;
	if (y <= -3.15e+119)
		tmp = t_1;
	elseif (y <= -0.16)
		tmp = t_2;
	elseif (y <= -1.42e-305)
		tmp = x - (z * t);
	elseif (y <= 2.8e+95)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.15e+119], t$95$1, If[LessEqual[y, -0.16], t$95$2, If[LessEqual[y, -1.42e-305], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+95], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1499999999999999e119 or 2.7999999999999998e95 < 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 87.7%

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

      1. *-commutative 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in x around 0 85.4%

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

   7. Taylor expanded in y around inf 87.7%

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

      1. mul-1-neg 87.7%

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

      2. sub-neg 87.7%

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

   9. Simplified 87.7%

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

   if -3.1499999999999999e119 < y < -0.160000000000000003 or -1.42000000000000002e-305 < y < 2.7999999999999998e95

   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 66.1%

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

      1. mul-1-neg 66.1%

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

      2. unsub-neg 66.1%

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

   5. Simplified 66.1%

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

   if -0.160000000000000003 < y < -1.42000000000000002e-305

   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 89.3%

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

      1. mul-1-neg 89.3%

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

      2. unsub-neg 89.3%

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

   5. Simplified 89.3%

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

   6. Taylor expanded in t around inf 70.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -0.16:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-305}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -95 \lor \neg \left(z \leq 3.4 \cdot 10^{+62}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -95.0) (not (<= z 3.4e+62)))
   (- x (* z (- t x)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -95.0) || !(z <= 3.4e+62)) {
		tmp = x - (z * (t - x));
	} 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 <= (-95.0d0)) .or. (.not. (z <= 3.4d+62))) then
        tmp = x - (z * (t - x))
    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 <= -95.0) || !(z <= 3.4e+62)) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -95.0) or not (z <= 3.4e+62):
		tmp = x - (z * (t - x))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -95.0) || !(z <= 3.4e+62))
		tmp = Float64(x - Float64(z * Float64(t - x)));
	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 <= -95.0) || ~((z <= 3.4e+62)))
		tmp = x - (z * (t - x));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -95.0], N[Not[LessEqual[z, 3.4e+62]], $MachinePrecision]], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -95 or 3.40000000000000014e62 < 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 83.2%

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

      1. mul-1-neg 83.2%

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

      2. unsub-neg 83.2%

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

   5. Simplified 83.2%

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

   if -95 < z < 3.40000000000000014e62

   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 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -95 \lor \neg \left(z \leq 3.4 \cdot 10^{+62}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+33} \lor \neg \left(t \leq 2.9 \cdot 10^{+78}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.05e+33) (not (<= t 2.9e+78)))
   (- x (* t (- z y)))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.05e+33) || !(t <= 2.9e+78)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.05d+33)) .or. (.not. (t <= 2.9d+78))) then
        tmp = x - (t * (z - y))
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.05e+33) || !(t <= 2.9e+78)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.05e+33) or not (t <= 2.9e+78):
		tmp = x - (t * (z - y))
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.05e+33) || !(t <= 2.9e+78))
		tmp = Float64(x - Float64(t * Float64(z - y)));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.05e+33) || ~((t <= 2.9e+78)))
		tmp = x - (t * (z - y));
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.05e+33], N[Not[LessEqual[t, 2.9e+78]], $MachinePrecision]], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e33 or 2.90000000000000017e78 < t

   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 88.1%

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

   if -1.05e33 < t < 2.90000000000000017e78

   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 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

   5. Simplified 81.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \left(y - z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+33} \lor \neg \left(t \leq 2.9 \cdot 10^{+78}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-11} \lor \neg \left(y \leq 1.46\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.2e-11) (not (<= y 1.46))) (* y (- t x)) (+ x (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e-11) || !(y <= 1.46)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.2d-11)) .or. (.not. (y <= 1.46d0))) then
        tmp = y * (t - x)
    else
        tmp = x + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e-11) || !(y <= 1.46)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.2e-11) or not (y <= 1.46):
		tmp = y * (t - x)
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.2e-11) || !(y <= 1.46))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.2e-11) || ~((y <= 1.46)))
		tmp = y * (t - x);
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.2e-11], N[Not[LessEqual[y, 1.46]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2000000000000001e-11 or 1.46 < 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 73.0%

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

      1. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in x around 0 71.6%

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

   7. Taylor expanded in y around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. sub-neg 72.0%

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

   9. Simplified 72.0%

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

   if -1.2000000000000001e-11 < y < 1.46

   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 92.6%

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

      1. mul-1-neg 92.6%

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

      2. unsub-neg 92.6%

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

   5. Simplified 92.6%

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

   6. Taylor expanded in t around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. *-commutative 66.7%

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

      3. distribute-rgt-neg-in 66.7%

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

   8. Simplified 66.7%

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

      1. sub-neg 66.7%

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

      2. +-commutative 66.7%

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

      3. distribute-rgt-neg-out 66.7%

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

      4. remove-double-neg 66.7%

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

      5. *-commutative 66.7%

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

   10. Applied egg-rr 66.7%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-11} \lor \neg \left(y \leq 1.46\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-11} \lor \neg \left(y \leq 7.4\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.2e-11) (not (<= y 7.4))) (* y (- t x)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e-11) || !(y <= 7.4)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.2d-11)) .or. (.not. (y <= 7.4d0))) then
        tmp = y * (t - x)
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e-11) || !(y <= 7.4)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.2e-11) or not (y <= 7.4):
		tmp = y * (t - x)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.2e-11) || !(y <= 7.4))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.2e-11) || ~((y <= 7.4)))
		tmp = y * (t - x);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.2e-11], N[Not[LessEqual[y, 7.4]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2000000000000001e-11 or 7.4000000000000004 < 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 73.0%

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

      1. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in x around 0 71.6%

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

   7. Taylor expanded in y around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. sub-neg 72.0%

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

   9. Simplified 72.0%

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

   if -1.2000000000000001e-11 < y < 7.4000000000000004

   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 66.8%

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

      1. mul-1-neg 66.8%

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

      2. unsub-neg 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in y around 0 66.7%

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

      1. +-commutative 66.7%

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

   8. Simplified 66.7%

      \[\leadsto \color{blue}{x \cdot \left(z + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-11} \lor \neg \left(y \leq 7.4\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -118000000000 \lor \neg \left(z \leq 86000000000000\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -118000000000.0) (not (<= z 86000000000000.0))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -118000000000.0) || !(z <= 86000000000000.0)) {
		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 <= (-118000000000.0d0)) .or. (.not. (z <= 86000000000000.0d0))) 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 <= -118000000000.0) || !(z <= 86000000000000.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -118000000000.0) or not (z <= 86000000000000.0):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -118000000000.0) || !(z <= 86000000000000.0))
		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 <= -118000000000.0) || ~((z <= 86000000000000.0)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -118000000000.0], N[Not[LessEqual[z, 86000000000000.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.18e11 or 8.6e13 < 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 80.6%

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

      1. mul-1-neg 80.6%

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

      2. unsub-neg 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in t around 0 44.1%

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

      1. mul-1-neg 44.1%

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

      2. *-commutative 44.1%

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

      3. distribute-rgt-neg-in 44.1%

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

   8. Simplified 44.1%

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

   9. Taylor expanded in z around inf 44.1%

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

   if -1.18e11 < z < 8.6e13

   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 74.9%

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

   4. Taylor expanded in x around inf 38.7%

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

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -118000000000 \lor \neg \left(z \leq 86000000000000\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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. Add Preprocessing

Alternative 13: 17.7% 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 63.0%

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

4. Taylor expanded in x around inf 21.9%

   \[\leadsto \color{blue}{x} \]
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 2024101 
(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))))