Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.7s

Alternatives: 10

Speedup: 1.0×

• 35.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]

2. Final simplification 100.0%

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

Alternative 2: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := x + x \cdot z\\ t_3 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+168} \lor \neg \left(x \leq 4.8 \cdot 10^{+263}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (+ x (* x z))) (t_3 (+ x (* (- y z) t))))
   (if (<= x -1.6e+147)
     t_2
     (if (<= x -2e+51)
       t_3
       (if (<= x -5.4e-26)
         t_1
         (if (<= x 2.8e+52)
           t_3
           (if (or (<= x 4.6e+168) (not (<= x 4.8e+263))) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + (x * z);
	double t_3 = x + ((y - z) * t);
	double tmp;
	if (x <= -1.6e+147) {
		tmp = t_2;
	} else if (x <= -2e+51) {
		tmp = t_3;
	} else if (x <= -5.4e-26) {
		tmp = t_1;
	} else if (x <= 2.8e+52) {
		tmp = t_3;
	} else if ((x <= 4.6e+168) || !(x <= 4.8e+263)) {
		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) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = x + (x * z)
    t_3 = x + ((y - z) * t)
    if (x <= (-1.6d+147)) then
        tmp = t_2
    else if (x <= (-2d+51)) then
        tmp = t_3
    else if (x <= (-5.4d-26)) then
        tmp = t_1
    else if (x <= 2.8d+52) then
        tmp = t_3
    else if ((x <= 4.6d+168) .or. (.not. (x <= 4.8d+263))) 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 * (1.0 - y);
	double t_2 = x + (x * z);
	double t_3 = x + ((y - z) * t);
	double tmp;
	if (x <= -1.6e+147) {
		tmp = t_2;
	} else if (x <= -2e+51) {
		tmp = t_3;
	} else if (x <= -5.4e-26) {
		tmp = t_1;
	} else if (x <= 2.8e+52) {
		tmp = t_3;
	} else if ((x <= 4.6e+168) || !(x <= 4.8e+263)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = x + (x * z)
	t_3 = x + ((y - z) * t)
	tmp = 0
	if x <= -1.6e+147:
		tmp = t_2
	elif x <= -2e+51:
		tmp = t_3
	elif x <= -5.4e-26:
		tmp = t_1
	elif x <= 2.8e+52:
		tmp = t_3
	elif (x <= 4.6e+168) or not (x <= 4.8e+263):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(x + Float64(x * z))
	t_3 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (x <= -1.6e+147)
		tmp = t_2;
	elseif (x <= -2e+51)
		tmp = t_3;
	elseif (x <= -5.4e-26)
		tmp = t_1;
	elseif (x <= 2.8e+52)
		tmp = t_3;
	elseif ((x <= 4.6e+168) || !(x <= 4.8e+263))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = x + (x * z);
	t_3 = x + ((y - z) * t);
	tmp = 0.0;
	if (x <= -1.6e+147)
		tmp = t_2;
	elseif (x <= -2e+51)
		tmp = t_3;
	elseif (x <= -5.4e-26)
		tmp = t_1;
	elseif (x <= 2.8e+52)
		tmp = t_3;
	elseif ((x <= 4.6e+168) || ~((x <= 4.8e+263)))
		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[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+147], t$95$2, If[LessEqual[x, -2e+51], t$95$3, If[LessEqual[x, -5.4e-26], t$95$1, If[LessEqual[x, 2.8e+52], t$95$3, If[Or[LessEqual[x, 4.6e+168], N[Not[LessEqual[x, 4.8e+263]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.59999999999999989e147 or 2.8e52 < x < 4.5999999999999999e168 or 4.8000000000000001e263 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. distribute-lft-neg-out 73.8%

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

      3. *-commutative 73.8%

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

   4. Simplified 73.8%

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

   5. Taylor expanded in t around 0 63.7%

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

   if -1.59999999999999989e147 < x < -2e51 or -5.39999999999999963e-26 < x < 2.8e52

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 82.4%

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

   if -2e51 < x < -5.39999999999999963e-26 or 4.5999999999999999e168 < x < 4.8000000000000001e263

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 96.2%

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

   3. Applied egg-rr 96.2%

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

   4. Taylor expanded in t around 0 93.6%

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

      1. mul-1-neg 93.6%

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

      2. distribute-rgt-neg-in 93.6%

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

      3. mul-1-neg 93.6%

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

      4. distribute-lft-in 93.6%

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

      5. +-commutative 93.6%

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

      6. mul-1-neg 93.6%

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

      7. unsub-neg 93.6%

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

   6. Simplified 93.6%

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

   7. Taylor expanded in z around 0 71.8%

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

      1. *-rgt-identity 71.8%

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

      2. mul-1-neg 71.8%

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

      3. distribute-rgt-neg-out 71.8%

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

      4. distribute-lft-in 71.8%

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

      5. unsub-neg 71.8%

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

   9. Simplified 71.8%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+147}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;x \leq -2 \cdot 10^{+51}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+52}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+168} \lor \neg \left(x \leq 4.8 \cdot 10^{+263}\right):\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 3: 52.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := x + x \cdot z\\ t_3 := x + y \cdot t\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+75}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (+ x (* x z))) (t_3 (+ x (* y t))))
   (if (<= z -3.1e+187)
     t_2
     (if (<= z -7.6e+110)
       t_1
       (if (<= z -2.4e-6)
         t_2
         (if (<= z -7e-111)
           t_3
           (if (<= z -1.35e-202) t_1 (if (<= z 1.36e+75) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + (x * z);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -3.1e+187) {
		tmp = t_2;
	} else if (z <= -7.6e+110) {
		tmp = t_1;
	} else if (z <= -2.4e-6) {
		tmp = t_2;
	} else if (z <= -7e-111) {
		tmp = t_3;
	} else if (z <= -1.35e-202) {
		tmp = t_1;
	} else if (z <= 1.36e+75) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = x + (x * z)
    t_3 = x + (y * t)
    if (z <= (-3.1d+187)) then
        tmp = t_2
    else if (z <= (-7.6d+110)) then
        tmp = t_1
    else if (z <= (-2.4d-6)) then
        tmp = t_2
    else if (z <= (-7d-111)) then
        tmp = t_3
    else if (z <= (-1.35d-202)) then
        tmp = t_1
    else if (z <= 1.36d+75) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + (x * z);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -3.1e+187) {
		tmp = t_2;
	} else if (z <= -7.6e+110) {
		tmp = t_1;
	} else if (z <= -2.4e-6) {
		tmp = t_2;
	} else if (z <= -7e-111) {
		tmp = t_3;
	} else if (z <= -1.35e-202) {
		tmp = t_1;
	} else if (z <= 1.36e+75) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = x + (x * z)
	t_3 = x + (y * t)
	tmp = 0
	if z <= -3.1e+187:
		tmp = t_2
	elif z <= -7.6e+110:
		tmp = t_1
	elif z <= -2.4e-6:
		tmp = t_2
	elif z <= -7e-111:
		tmp = t_3
	elif z <= -1.35e-202:
		tmp = t_1
	elif z <= 1.36e+75:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(x + Float64(x * z))
	t_3 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -3.1e+187)
		tmp = t_2;
	elseif (z <= -7.6e+110)
		tmp = t_1;
	elseif (z <= -2.4e-6)
		tmp = t_2;
	elseif (z <= -7e-111)
		tmp = t_3;
	elseif (z <= -1.35e-202)
		tmp = t_1;
	elseif (z <= 1.36e+75)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = x + (x * z);
	t_3 = x + (y * t);
	tmp = 0.0;
	if (z <= -3.1e+187)
		tmp = t_2;
	elseif (z <= -7.6e+110)
		tmp = t_1;
	elseif (z <= -2.4e-6)
		tmp = t_2;
	elseif (z <= -7e-111)
		tmp = t_3;
	elseif (z <= -1.35e-202)
		tmp = t_1;
	elseif (z <= 1.36e+75)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+187], t$95$2, If[LessEqual[z, -7.6e+110], t$95$1, If[LessEqual[z, -2.4e-6], t$95$2, If[LessEqual[z, -7e-111], t$95$3, If[LessEqual[z, -1.35e-202], t$95$1, If[LessEqual[z, 1.36e+75], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.10000000000000012e187 or -7.59999999999999978e110 < z < -2.3999999999999999e-6 or 1.36e75 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 87.6%

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

      1. mul-1-neg 87.6%

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

      2. distribute-lft-neg-out 87.6%

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

      3. *-commutative 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in t around 0 53.4%

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

   if -3.10000000000000012e187 < z < -7.59999999999999978e110 or -7.0000000000000001e-111 < z < -1.3499999999999999e-202

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 90.2%

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

   3. Applied egg-rr 90.2%

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

   4. Taylor expanded in t around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. distribute-rgt-neg-in 58.3%

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

      3. mul-1-neg 58.3%

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

      4. distribute-lft-in 63.2%

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

      5. +-commutative 63.2%

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

      6. mul-1-neg 63.2%

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

      7. unsub-neg 63.2%

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

   6. Simplified 63.2%

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

   7. Taylor expanded in z around 0 58.3%

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

      1. *-rgt-identity 58.3%

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

      2. mul-1-neg 58.3%

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

      3. distribute-rgt-neg-out 58.3%

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

      4. distribute-lft-in 58.3%

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

      5. unsub-neg 58.3%

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

   9. Simplified 58.3%

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

   if -2.3999999999999999e-6 < z < -7.0000000000000001e-111 or -1.3499999999999999e-202 < z < 1.36e75

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 86.3%

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

      1. *-commutative 86.3%

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

   4. Simplified 86.3%

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

   5. Taylor expanded in t around inf 68.5%

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

      1. *-commutative 68.5%

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

   7. Simplified 68.5%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+187}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-6}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-111}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-202}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+75}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot z\\ \end{array} \]

Alternative 4: 50.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ t_2 := x + y \cdot t\\ t_3 := x - z \cdot t\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-170}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x z))) (t_2 (+ x (* y t))) (t_3 (- x (* z t))))
   (if (<= y -5.2e+73)
     t_2
     (if (<= y -5e-114)
       t_3
       (if (<= y 4.8e-255)
         t_1
         (if (<= y 3.25e-170)
           t_3
           (if (<= y 4e-96) t_1 (if (<= y 3.8e+153) t_2 (* x (- 1.0 y))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x + (y * t);
	double t_3 = x - (z * t);
	double tmp;
	if (y <= -5.2e+73) {
		tmp = t_2;
	} else if (y <= -5e-114) {
		tmp = t_3;
	} else if (y <= 4.8e-255) {
		tmp = t_1;
	} else if (y <= 3.25e-170) {
		tmp = t_3;
	} else if (y <= 4e-96) {
		tmp = t_1;
	} else if (y <= 3.8e+153) {
		tmp = t_2;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (x * z)
    t_2 = x + (y * t)
    t_3 = x - (z * t)
    if (y <= (-5.2d+73)) then
        tmp = t_2
    else if (y <= (-5d-114)) then
        tmp = t_3
    else if (y <= 4.8d-255) then
        tmp = t_1
    else if (y <= 3.25d-170) then
        tmp = t_3
    else if (y <= 4d-96) then
        tmp = t_1
    else if (y <= 3.8d+153) then
        tmp = t_2
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x + (y * t);
	double t_3 = x - (z * t);
	double tmp;
	if (y <= -5.2e+73) {
		tmp = t_2;
	} else if (y <= -5e-114) {
		tmp = t_3;
	} else if (y <= 4.8e-255) {
		tmp = t_1;
	} else if (y <= 3.25e-170) {
		tmp = t_3;
	} else if (y <= 4e-96) {
		tmp = t_1;
	} else if (y <= 3.8e+153) {
		tmp = t_2;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * z)
	t_2 = x + (y * t)
	t_3 = x - (z * t)
	tmp = 0
	if y <= -5.2e+73:
		tmp = t_2
	elif y <= -5e-114:
		tmp = t_3
	elif y <= 4.8e-255:
		tmp = t_1
	elif y <= 3.25e-170:
		tmp = t_3
	elif y <= 4e-96:
		tmp = t_1
	elif y <= 3.8e+153:
		tmp = t_2
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * z))
	t_2 = Float64(x + Float64(y * t))
	t_3 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (y <= -5.2e+73)
		tmp = t_2;
	elseif (y <= -5e-114)
		tmp = t_3;
	elseif (y <= 4.8e-255)
		tmp = t_1;
	elseif (y <= 3.25e-170)
		tmp = t_3;
	elseif (y <= 4e-96)
		tmp = t_1;
	elseif (y <= 3.8e+153)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * z);
	t_2 = x + (y * t);
	t_3 = x - (z * t);
	tmp = 0.0;
	if (y <= -5.2e+73)
		tmp = t_2;
	elseif (y <= -5e-114)
		tmp = t_3;
	elseif (y <= 4.8e-255)
		tmp = t_1;
	elseif (y <= 3.25e-170)
		tmp = t_3;
	elseif (y <= 4e-96)
		tmp = t_1;
	elseif (y <= 3.8e+153)
		tmp = t_2;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+73], t$95$2, If[LessEqual[y, -5e-114], t$95$3, If[LessEqual[y, 4.8e-255], t$95$1, If[LessEqual[y, 3.25e-170], t$95$3, If[LessEqual[y, 4e-96], t$95$1, If[LessEqual[y, 3.8e+153], t$95$2, N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.2000000000000001e73 or 3.9999999999999996e-96 < y < 3.79999999999999966e153

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 80.9%

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

      1. *-commutative 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in t around inf 55.2%

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

      1. *-commutative 55.2%

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

   7. Simplified 55.2%

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

   if -5.2000000000000001e73 < y < -4.99999999999999989e-114 or 4.7999999999999997e-255 < y < 3.25000000000000018e-170

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. distribute-lft-neg-out 79.8%

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

      3. *-commutative 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in t around inf 66.5%

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

      1. associate-*r* 66.5%

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

      2. mul-1-neg 66.5%

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

   7. Simplified 66.5%

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

   if -4.99999999999999989e-114 < y < 4.7999999999999997e-255 or 3.25000000000000018e-170 < y < 3.9999999999999996e-96

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 97.3%

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

      1. mul-1-neg 97.3%

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

      2. distribute-lft-neg-out 97.3%

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

      3. *-commutative 97.3%

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

   4. Simplified 97.3%

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

   5. Taylor expanded in t around 0 72.4%

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

   if 3.79999999999999966e153 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 97.1%

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

   3. Applied egg-rr 97.1%

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

   4. Taylor expanded in t around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. distribute-rgt-neg-in 63.9%

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

      3. mul-1-neg 63.9%

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

      4. distribute-lft-in 66.6%

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

      5. +-commutative 66.6%

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

      6. mul-1-neg 66.6%

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

      7. unsub-neg 66.6%

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

   6. Simplified 66.6%

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

   7. Taylor expanded in z around 0 60.4%

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

      1. *-rgt-identity 60.4%

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

      2. mul-1-neg 60.4%

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

      3. distribute-rgt-neg-out 60.4%

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

      4. distribute-lft-in 60.4%

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

      5. unsub-neg 60.4%

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

   9. Simplified 60.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+73}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-114}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-255}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-170}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-96}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+153}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 5: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+60}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-50}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+16}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+153}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))))
   (if (<= y -5.5e+60)
     (* y t)
     (if (<= y -2e+17)
       t_1
       (if (<= y -3.25e-50)
         (* y t)
         (if (<= y 1.6e+16)
           (+ x (* x z))
           (if (<= y 4.6e+153) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (y <= -5.5e+60) {
		tmp = y * t;
	} else if (y <= -2e+17) {
		tmp = t_1;
	} else if (y <= -3.25e-50) {
		tmp = y * t;
	} else if (y <= 1.6e+16) {
		tmp = x + (x * z);
	} else if (y <= 4.6e+153) {
		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 * (1.0d0 - y)
    if (y <= (-5.5d+60)) then
        tmp = y * t
    else if (y <= (-2d+17)) then
        tmp = t_1
    else if (y <= (-3.25d-50)) then
        tmp = y * t
    else if (y <= 1.6d+16) then
        tmp = x + (x * z)
    else if (y <= 4.6d+153) 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 * (1.0 - y);
	double tmp;
	if (y <= -5.5e+60) {
		tmp = y * t;
	} else if (y <= -2e+17) {
		tmp = t_1;
	} else if (y <= -3.25e-50) {
		tmp = y * t;
	} else if (y <= 1.6e+16) {
		tmp = x + (x * z);
	} else if (y <= 4.6e+153) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	tmp = 0
	if y <= -5.5e+60:
		tmp = y * t
	elif y <= -2e+17:
		tmp = t_1
	elif y <= -3.25e-50:
		tmp = y * t
	elif y <= 1.6e+16:
		tmp = x + (x * z)
	elif y <= 4.6e+153:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (y <= -5.5e+60)
		tmp = Float64(y * t);
	elseif (y <= -2e+17)
		tmp = t_1;
	elseif (y <= -3.25e-50)
		tmp = Float64(y * t);
	elseif (y <= 1.6e+16)
		tmp = Float64(x + Float64(x * z));
	elseif (y <= 4.6e+153)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	tmp = 0.0;
	if (y <= -5.5e+60)
		tmp = y * t;
	elseif (y <= -2e+17)
		tmp = t_1;
	elseif (y <= -3.25e-50)
		tmp = y * t;
	elseif (y <= 1.6e+16)
		tmp = x + (x * z);
	elseif (y <= 4.6e+153)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+60], N[(y * t), $MachinePrecision], If[LessEqual[y, -2e+17], t$95$1, If[LessEqual[y, -3.25e-50], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.6e+16], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+153], N[(y * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000001e60 or -2e17 < y < -3.24999999999999994e-50 or 1.6e16 < y < 4.6000000000000003e153

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 80.2%

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

      1. *-commutative 80.2%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in x around 0 55.3%

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

      1. *-commutative 55.3%

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

   7. Simplified 55.3%

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

   if -5.5000000000000001e60 < y < -2e17 or 4.6000000000000003e153 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 93.8%

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

   3. Applied egg-rr 93.8%

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

   4. Taylor expanded in t around 0 57.4%

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

      1. mul-1-neg 57.4%

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

      2. distribute-rgt-neg-in 57.4%

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

      3. mul-1-neg 57.4%

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

      4. distribute-lft-in 61.5%

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

      5. +-commutative 61.5%

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

      6. mul-1-neg 61.5%

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

      7. unsub-neg 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in z around 0 54.8%

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

      1. *-rgt-identity 54.8%

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

      2. mul-1-neg 54.8%

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

      3. distribute-rgt-neg-out 54.8%

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

      4. distribute-lft-in 54.8%

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

      5. unsub-neg 54.8%

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

   9. Simplified 54.8%

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

   if -3.24999999999999994e-50 < y < 1.6e16

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 91.7%

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

      1. mul-1-neg 91.7%

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

      2. distribute-lft-neg-out 91.7%

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

      3. *-commutative 91.7%

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

   4. Simplified 91.7%

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

   5. Taylor expanded in t around 0 62.9%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+60}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-50}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+16}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+153}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 6: 80.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+147} \lor \neg \left(x \leq -4.3 \cdot 10^{+111} \lor \neg \left(x \leq -3.5 \cdot 10^{-29}\right) \land x \leq 1.28 \cdot 10^{-23}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.35e+147)
         (not
          (or (<= x -4.3e+111) (and (not (<= x -3.5e-29)) (<= x 1.28e-23)))))
   (+ x (* x (- z y)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.35e+147) || !((x <= -4.3e+111) || (!(x <= -3.5e-29) && (x <= 1.28e-23)))) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.35d+147)) .or. (.not. (x <= (-4.3d+111)) .or. (.not. (x <= (-3.5d-29))) .and. (x <= 1.28d-23))) then
        tmp = x + (x * (z - y))
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.35e+147) || !((x <= -4.3e+111) || (!(x <= -3.5e-29) && (x <= 1.28e-23)))) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.35e+147) or not ((x <= -4.3e+111) or (not (x <= -3.5e-29) and (x <= 1.28e-23))):
		tmp = x + (x * (z - y))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.35e+147) || !((x <= -4.3e+111) || (!(x <= -3.5e-29) && (x <= 1.28e-23))))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.35e+147) || ~(((x <= -4.3e+111) || (~((x <= -3.5e-29)) && (x <= 1.28e-23)))))
		tmp = x + (x * (z - y));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.35e+147], N[Not[Or[LessEqual[x, -4.3e+111], And[N[Not[LessEqual[x, -3.5e-29]], $MachinePrecision], LessEqual[x, 1.28e-23]]]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.34999999999999999e147 or -4.29999999999999993e111 < x < -3.4999999999999997e-29 or 1.28000000000000005e-23 < x

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 95.7%

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

   3. Applied egg-rr 95.7%

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

   4. Taylor expanded in t around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. distribute-rgt-neg-in 82.3%

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

      3. mul-1-neg 82.3%

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

      4. distribute-lft-in 85.2%

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

      5. +-commutative 85.2%

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

      6. mul-1-neg 85.2%

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

      7. unsub-neg 85.2%

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

   6. Simplified 85.2%

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

   if -1.34999999999999999e147 < x < -4.29999999999999993e111 or -3.4999999999999997e-29 < x < 1.28000000000000005e-23

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 87.4%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+147} \lor \neg \left(x \leq -4.3 \cdot 10^{+111} \lor \neg \left(x \leq -3.5 \cdot 10^{-29}\right) \land x \leq 1.28 \cdot 10^{-23}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 7: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+64} \lor \neg \left(z \leq 0.00075\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.5e+64) (not (<= z 0.00075)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e+64) || !(z <= 0.00075)) {
		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 <= (-8.5d+64)) .or. (.not. (z <= 0.00075d0))) 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 <= -8.5e+64) || !(z <= 0.00075)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.5e+64) or not (z <= 0.00075):
		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 <= -8.5e+64) || !(z <= 0.00075))
		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 <= -8.5e+64) || ~((z <= 0.00075)))
		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, -8.5e+64], N[Not[LessEqual[z, 0.00075]], $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 < -8.4999999999999998e64 or 7.5000000000000002e-4 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 87.2%

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

      1. mul-1-neg 87.2%

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

      2. distribute-lft-neg-out 87.2%

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

      3. *-commutative 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in t around 0 80.5%

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

      1. associate-*r* 80.5%

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

      2. distribute-rgt-in 87.2%

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

      3. +-commutative 87.2%

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

      4. mul-1-neg 87.2%

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

      5. sub-neg 87.2%

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

   7. Simplified 87.2%

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

   if -8.4999999999999998e64 < z < 7.5000000000000002e-4

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 88.0%

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

      1. *-commutative 88.0%

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

   4. Simplified 88.0%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+64} \lor \neg \left(z \leq 0.00075\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 8: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-28} \lor \neg \left(x \leq 3.5 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.6e-28) (not (<= x 3.5e-25))) (* x (- 1.0 y)) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.6e-28) || !(x <= 3.5e-25)) {
		tmp = x * (1.0 - y);
	} 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 ((x <= (-3.6d-28)) .or. (.not. (x <= 3.5d-25))) then
        tmp = x * (1.0d0 - y)
    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 ((x <= -3.6e-28) || !(x <= 3.5e-25)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.6e-28) or not (x <= 3.5e-25):
		tmp = x * (1.0 - y)
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.6e-28) || !(x <= 3.5e-25))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.6e-28) || ~((x <= 3.5e-25)))
		tmp = x * (1.0 - y);
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.6e-28], N[Not[LessEqual[x, 3.5e-25]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5999999999999999e-28 or 3.5000000000000002e-25 < x

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 95.2%

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

   3. Applied egg-rr 95.2%

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

   4. Taylor expanded in t around 0 79.4%

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

      1. mul-1-neg 79.4%

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

      2. distribute-rgt-neg-in 79.4%

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

      3. mul-1-neg 79.4%

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

      4. distribute-lft-in 82.1%

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

      5. +-commutative 82.1%

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

      6. mul-1-neg 82.1%

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

      7. unsub-neg 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in z around 0 54.0%

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

      1. *-rgt-identity 54.0%

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

      2. mul-1-neg 54.0%

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

      3. distribute-rgt-neg-out 54.0%

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

      4. distribute-lft-in 54.0%

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

      5. unsub-neg 54.0%

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

   9. Simplified 54.0%

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

   if -3.5999999999999999e-28 < x < 3.5000000000000002e-25

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 56.5%

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

      1. *-commutative 56.5%

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

   4. Simplified 56.5%

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

   5. Taylor expanded in x around 0 46.6%

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

      1. *-commutative 46.6%

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

   7. Simplified 46.6%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{-28} \lor \neg \left(x \leq 3.5 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 9: 36.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-53}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e-53) (* y t) (if (<= y 1.6e-80) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-53) {
		tmp = y * t;
	} else if (y <= 1.6e-80) {
		tmp = 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 <= (-3.4d-53)) then
        tmp = y * t
    else if (y <= 1.6d-80) then
        tmp = 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 <= -3.4e-53) {
		tmp = y * t;
	} else if (y <= 1.6e-80) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e-53:
		tmp = y * t
	elif y <= 1.6e-80:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e-53)
		tmp = Float64(y * t);
	elseif (y <= 1.6e-80)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e-53)
		tmp = y * t;
	elseif (y <= 1.6e-80)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e-53], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.6e-80], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4e-53 or 1.5999999999999999e-80 < y

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 74.4%

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

      1. *-commutative 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in x around 0 45.4%

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

      1. *-commutative 45.4%

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

   7. Simplified 45.4%

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

   if -3.4e-53 < y < 1.5999999999999999e-80

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around inf 33.8%

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

      1. *-commutative 33.8%

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

   4. Simplified 33.8%

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

   5. Taylor expanded in y around 0 30.7%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-53}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 10: 18.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]

2. Taylor expanded in y around inf 59.5%

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

   1. *-commutative 59.5%

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

4. Simplified 59.5%

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

5. Taylor expanded in y around 0 13.3%

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

6. Final simplification 13.3%

   \[\leadsto x \]

Developer target: 96.2% 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 2023275 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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