Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.1s

Alternatives: 13

Speedup: 1.0×

• 34.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 69.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{if}\;y \leq -6.1 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-266}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+26}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* x (+ (- z y) 1.0))))
   (if (<= y -6.1e+96)
     t_1
     (if (<= y -3.5e-12)
       t_2
       (if (<= y -1.6e-266) (- x (* z t)) (if (<= y 4.6e+26) 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 <= -6.1e+96) {
		tmp = t_1;
	} else if (y <= -3.5e-12) {
		tmp = t_2;
	} else if (y <= -1.6e-266) {
		tmp = x - (z * t);
	} else if (y <= 4.6e+26) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = x * ((z - y) + 1.0d0)
    if (y <= (-6.1d+96)) then
        tmp = t_1
    else if (y <= (-3.5d-12)) then
        tmp = t_2
    else if (y <= (-1.6d-266)) then
        tmp = x - (z * t)
    else if (y <= 4.6d+26) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * ((z - y) + 1.0);
	double tmp;
	if (y <= -6.1e+96) {
		tmp = t_1;
	} else if (y <= -3.5e-12) {
		tmp = t_2;
	} else if (y <= -1.6e-266) {
		tmp = x - (z * t);
	} else if (y <= 4.6e+26) {
		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 <= -6.1e+96:
		tmp = t_1
	elif y <= -3.5e-12:
		tmp = t_2
	elif y <= -1.6e-266:
		tmp = x - (z * t)
	elif y <= 4.6e+26:
		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 <= -6.1e+96)
		tmp = t_1;
	elseif (y <= -3.5e-12)
		tmp = t_2;
	elseif (y <= -1.6e-266)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 4.6e+26)
		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 <= -6.1e+96)
		tmp = t_1;
	elseif (y <= -3.5e-12)
		tmp = t_2;
	elseif (y <= -1.6e-266)
		tmp = x - (z * t);
	elseif (y <= 4.6e+26)
		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, -6.1e+96], t$95$1, If[LessEqual[y, -3.5e-12], t$95$2, If[LessEqual[y, -1.6e-266], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+26], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.09999999999999984e96 or 4.6000000000000001e26 < 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 81.8%

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

      1. *-commutative 81.8%

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

   5. Simplified 81.8%

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

      1. *-commutative 81.8%

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

      2. sub-neg 81.8%

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

      3. distribute-lft-in 76.4%

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

   7. Applied egg-rr 76.4%

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

      1. associate-+r+ 76.4%

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

      2. distribute-rgt-neg-out 76.4%

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

      3. unsub-neg 76.4%

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

      4. +-commutative 76.4%

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

   9. Applied egg-rr 76.4%

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

   10. Taylor expanded in y around inf 81.8%

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

   if -6.09999999999999984e96 < y < -3.5e-12 or -1.6e-266 < y < 4.6000000000000001e26

   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 69.0%

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

      1. mul-1-neg 69.0%

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

      2. unsub-neg 69.0%

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

   5. Simplified 69.0%

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

   if -3.5e-12 < y < -1.6e-266

   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 95.3%

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

      1. mul-1-neg 95.3%

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

      2. unsub-neg 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in t around inf 72.6%

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

      1. *-commutative 72.6%

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

   8. Simplified 72.6%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-266}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 36.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+107}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-112}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2500000000:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.6e+107)
   (* y t)
   (if (<= y -4.8e-112)
     (* z x)
     (if (<= y 7.4e-128) x (if (<= y 2500000000.0) (* z x) (* x (- y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+107) {
		tmp = y * t;
	} else if (y <= -4.8e-112) {
		tmp = z * x;
	} else if (y <= 7.4e-128) {
		tmp = x;
	} else if (y <= 2500000000.0) {
		tmp = z * x;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.6d+107)) then
        tmp = y * t
    else if (y <= (-4.8d-112)) then
        tmp = z * x
    else if (y <= 7.4d-128) then
        tmp = x
    else if (y <= 2500000000.0d0) then
        tmp = z * x
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+107) {
		tmp = y * t;
	} else if (y <= -4.8e-112) {
		tmp = z * x;
	} else if (y <= 7.4e-128) {
		tmp = x;
	} else if (y <= 2500000000.0) {
		tmp = z * x;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.6e+107:
		tmp = y * t
	elif y <= -4.8e-112:
		tmp = z * x
	elif y <= 7.4e-128:
		tmp = x
	elif y <= 2500000000.0:
		tmp = z * x
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.6e+107)
		tmp = Float64(y * t);
	elseif (y <= -4.8e-112)
		tmp = Float64(z * x);
	elseif (y <= 7.4e-128)
		tmp = x;
	elseif (y <= 2500000000.0)
		tmp = Float64(z * x);
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.6e+107)
		tmp = y * t;
	elseif (y <= -4.8e-112)
		tmp = z * x;
	elseif (y <= 7.4e-128)
		tmp = x;
	elseif (y <= 2500000000.0)
		tmp = z * x;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.6e+107], N[(y * t), $MachinePrecision], If[LessEqual[y, -4.8e-112], N[(z * x), $MachinePrecision], If[LessEqual[y, 7.4e-128], x, If[LessEqual[y, 2500000000.0], N[(z * x), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.6000000000000001e107

   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 76.9%

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

      1. *-commutative 76.9%

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

   5. Simplified 76.9%

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

      1. *-commutative 76.9%

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

      2. sub-neg 76.9%

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

      3. distribute-lft-in 68.4%

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

   7. Applied egg-rr 68.4%

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

      1. associate-+r+ 68.4%

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

      2. distribute-rgt-neg-out 68.4%

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

      3. unsub-neg 68.4%

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

      4. +-commutative 68.4%

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

   9. Applied egg-rr 68.4%

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

   10. Taylor expanded in t around inf 50.0%

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

       1. *-commutative 50.0%

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

   12. Simplified 50.0%

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

   if -2.6000000000000001e107 < y < -4.8000000000000001e-112 or 7.4e-128 < y < 2.5e9

   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 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

   5. Simplified 53.0%

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

      1. associate--r- 53.0%

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

      2. distribute-rgt-in 53.0%

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

   7. Applied egg-rr 53.0%

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

   8. Taylor expanded in z around inf 34.7%

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

   if -4.8000000000000001e-112 < y < 7.4e-128

   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 50.3%

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

      1. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in y around 0 47.8%

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

   if 2.5e9 < 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 85.9%

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

      1. *-commutative 85.9%

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

   5. Simplified 85.9%

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

      1. *-commutative 85.9%

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

      2. sub-neg 85.9%

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

      3. distribute-lft-in 82.8%

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

   7. Applied egg-rr 82.8%

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

   8. Taylor expanded in t around 0 54.4%

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

      1. associate-*r* 54.4%

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

      2. mul-1-neg 54.4%

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

   10. Simplified 54.4%

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

   11. Taylor expanded in y around inf 53.5%

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

       1. associate-*r* 53.5%

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

       2. mul-1-neg 53.5%

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

   13. Simplified 53.5%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+107}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-112}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2500000000:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 36.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+107}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-112}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+33}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.7e+107)
   (* y t)
   (if (<= y -4.1e-112)
     (* z x)
     (if (<= y 6.5e-128) x (if (<= y 3.1e+33) (* z x) (* y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e+107) {
		tmp = y * t;
	} else if (y <= -4.1e-112) {
		tmp = z * x;
	} else if (y <= 6.5e-128) {
		tmp = x;
	} else if (y <= 3.1e+33) {
		tmp = z * 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 <= (-2.7d+107)) then
        tmp = y * t
    else if (y <= (-4.1d-112)) then
        tmp = z * x
    else if (y <= 6.5d-128) then
        tmp = x
    else if (y <= 3.1d+33) then
        tmp = z * 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 <= -2.7e+107) {
		tmp = y * t;
	} else if (y <= -4.1e-112) {
		tmp = z * x;
	} else if (y <= 6.5e-128) {
		tmp = x;
	} else if (y <= 3.1e+33) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.7e+107:
		tmp = y * t
	elif y <= -4.1e-112:
		tmp = z * x
	elif y <= 6.5e-128:
		tmp = x
	elif y <= 3.1e+33:
		tmp = z * x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.7e+107)
		tmp = Float64(y * t);
	elseif (y <= -4.1e-112)
		tmp = Float64(z * x);
	elseif (y <= 6.5e-128)
		tmp = x;
	elseif (y <= 3.1e+33)
		tmp = Float64(z * x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.7e+107)
		tmp = y * t;
	elseif (y <= -4.1e-112)
		tmp = z * x;
	elseif (y <= 6.5e-128)
		tmp = x;
	elseif (y <= 3.1e+33)
		tmp = z * x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.7e+107], N[(y * t), $MachinePrecision], If[LessEqual[y, -4.1e-112], N[(z * x), $MachinePrecision], If[LessEqual[y, 6.5e-128], x, If[LessEqual[y, 3.1e+33], N[(z * x), $MachinePrecision], N[(y * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7000000000000001e107 or 3.1e33 < 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 82.3%

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

      1. *-commutative 82.3%

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

   5. Simplified 82.3%

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

      1. *-commutative 82.3%

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

      2. sub-neg 82.3%

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

      3. distribute-lft-in 76.7%

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

   7. Applied egg-rr 76.7%

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

      1. associate-+r+ 76.7%

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

      2. distribute-rgt-neg-out 76.7%

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

      3. unsub-neg 76.7%

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

      4. +-commutative 76.7%

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

   9. Applied egg-rr 76.7%

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

   10. Taylor expanded in t around inf 45.8%

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

       1. *-commutative 45.8%

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

   12. Simplified 45.8%

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

   if -2.7000000000000001e107 < y < -4.09999999999999996e-112 or 6.49999999999999977e-128 < y < 3.1e33

   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 55.6%

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

      1. mul-1-neg 55.6%

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

      2. unsub-neg 55.6%

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

   5. Simplified 55.6%

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

      1. associate--r- 55.6%

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

      2. distribute-rgt-in 55.6%

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

   7. Applied egg-rr 55.6%

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

   8. Taylor expanded in z around inf 34.3%

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

   if -4.09999999999999996e-112 < y < 6.49999999999999977e-128

   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 50.3%

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

      1. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in y around 0 47.8%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+107}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-112}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+33}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -3.25 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-266}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 75000000:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -3.25e+66)
     t_1
     (if (<= y -5e-266)
       (- x (* z t))
       (if (<= y 75000000.0) (* x (+ z 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -3.25e+66) {
		tmp = t_1;
	} else if (y <= -5e-266) {
		tmp = x - (z * t);
	} else if (y <= 75000000.0) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-3.25d+66)) then
        tmp = t_1
    else if (y <= (-5d-266)) then
        tmp = x - (z * t)
    else if (y <= 75000000.0d0) then
        tmp = x * (z + 1.0d0)
    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 tmp;
	if (y <= -3.25e+66) {
		tmp = t_1;
	} else if (y <= -5e-266) {
		tmp = x - (z * t);
	} else if (y <= 75000000.0) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -3.25e+66:
		tmp = t_1
	elif y <= -5e-266:
		tmp = x - (z * t)
	elif y <= 75000000.0:
		tmp = x * (z + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -3.25e+66)
		tmp = t_1;
	elseif (y <= -5e-266)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 75000000.0)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -3.25e+66)
		tmp = t_1;
	elseif (y <= -5e-266)
		tmp = x - (z * t);
	elseif (y <= 75000000.0)
		tmp = x * (z + 1.0);
	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]}, If[LessEqual[y, -3.25e+66], t$95$1, If[LessEqual[y, -5e-266], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 75000000.0], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2500000000000001e66 or 7.5e7 < 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 77.3%

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

      1. *-commutative 77.3%

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

   5. Simplified 77.3%

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

      1. *-commutative 77.3%

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

      2. sub-neg 77.3%

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

      3. distribute-lft-in 72.6%

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

   7. Applied egg-rr 72.6%

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

      1. associate-+r+ 72.6%

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

      2. distribute-rgt-neg-out 72.6%

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

      3. unsub-neg 72.6%

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

      4. +-commutative 72.6%

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

   9. Applied egg-rr 72.6%

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

   10. Taylor expanded in y around inf 76.9%

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

   if -3.2500000000000001e66 < y < -4.99999999999999992e-266

   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 87.9%

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

      1. mul-1-neg 87.9%

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

      2. unsub-neg 87.9%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in t around inf 65.4%

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

      1. *-commutative 65.4%

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

   8. Simplified 65.4%

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

   if -4.99999999999999992e-266 < y < 7.5e7

   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 71.1%

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

      1. mul-1-neg 71.1%

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

      2. unsub-neg 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in y around 0 69.4%

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

      1. +-commutative 69.4%

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

   8. Simplified 69.4%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+66}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-266}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 75000000:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.94 \lor \neg \left(t \leq 4.8 \cdot 10^{-76}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.94) (not (<= t 4.8e-76)))
   (+ x (* (- y z) t))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.94) || !(t <= 4.8e-76)) {
		tmp = x + ((y - z) * t);
	} 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 <= (-0.94d0)) .or. (.not. (t <= 4.8d-76))) then
        tmp = x + ((y - z) * t)
    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 <= -0.94) || !(t <= 4.8e-76)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -0.94) or not (t <= 4.8e-76):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -0.94) || !(t <= 4.8e-76))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	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 <= -0.94) || ~((t <= 4.8e-76)))
		tmp = x + ((y - z) * t);
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -0.94], N[Not[LessEqual[t, 4.8e-76]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.93999999999999995 or 4.80000000000000026e-76 < 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 82.8%

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

   if -0.93999999999999995 < t < 4.80000000000000026e-76

   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 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

   5. Simplified 84.9%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.94 \lor \neg \left(t \leq 4.8 \cdot 10^{-76}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+22} \lor \neg \left(z \leq 6.2 \cdot 10^{+75}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e+22) (not (<= z 6.2e+75)))
   (- x (* z (- t x)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e+22) || !(z <= 6.2e+75)) {
		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 <= (-1.7d+22)) .or. (.not. (z <= 6.2d+75))) 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 <= -1.7e+22) || !(z <= 6.2e+75)) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e+22) or not (z <= 6.2e+75):
		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 <= -1.7e+22) || !(z <= 6.2e+75))
		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 <= -1.7e+22) || ~((z <= 6.2e+75)))
		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, -1.7e+22], N[Not[LessEqual[z, 6.2e+75]], $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 < -1.7e22 or 6.2000000000000002e75 < 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 81.8%

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

      1. mul-1-neg 81.8%

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

      2. unsub-neg 81.8%

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

   5. Simplified 81.8%

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

   if -1.7e22 < z < 6.2000000000000002e75

   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 93.0%

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

      1. *-commutative 93.0%

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

   5. Simplified 93.0%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+22} \lor \neg \left(z \leq 6.2 \cdot 10^{+75}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+27} \lor \neg \left(y \leq 40000000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.2e+27) (not (<= y 40000000.0)))
   (* y (- t x))
   (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e+27) || !(y <= 40000000.0)) {
		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+27)) .or. (.not. (y <= 40000000.0d0))) 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+27) || !(y <= 40000000.0)) {
		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+27) or not (y <= 40000000.0):
		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+27) || !(y <= 40000000.0))
		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+27) || ~((y <= 40000000.0)))
		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+27], N[Not[LessEqual[y, 40000000.0]], $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 < -1.19999999999999999e27 or 4e7 < 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 75.7%

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

      1. *-commutative 75.7%

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

   5. Simplified 75.7%

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

      1. *-commutative 75.7%

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

      2. sub-neg 75.7%

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

      3. distribute-lft-in 70.5%

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

   7. Applied egg-rr 70.5%

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

      1. associate-+r+ 70.5%

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

      2. distribute-rgt-neg-out 70.5%

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

      3. unsub-neg 70.5%

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

      4. +-commutative 70.5%

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

   9. Applied egg-rr 70.5%

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

   10. Taylor expanded in y around inf 75.3%

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

   if -1.19999999999999999e27 < y < 4e7

   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 66.0%

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

      1. mul-1-neg 66.0%

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

      2. unsub-neg 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in y around 0 64.2%

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

      1. +-commutative 64.2%

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

   8. Simplified 64.2%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+27} \lor \neg \left(y \leq 40000000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+107}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 5000000000:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.6e+107)
   (* y t)
   (if (<= y 5000000000.0) (* x (+ z 1.0)) (* x (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+107) {
		tmp = y * t;
	} else if (y <= 5000000000.0) {
		tmp = x * (z + 1.0);
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.6d+107)) then
        tmp = y * t
    else if (y <= 5000000000.0d0) then
        tmp = x * (z + 1.0d0)
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+107) {
		tmp = y * t;
	} else if (y <= 5000000000.0) {
		tmp = x * (z + 1.0);
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.6e+107:
		tmp = y * t
	elif y <= 5000000000.0:
		tmp = x * (z + 1.0)
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.6e+107)
		tmp = Float64(y * t);
	elseif (y <= 5000000000.0)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.6e+107)
		tmp = y * t;
	elseif (y <= 5000000000.0)
		tmp = x * (z + 1.0);
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.6e+107], N[(y * t), $MachinePrecision], If[LessEqual[y, 5000000000.0], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6000000000000001e107

   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 76.9%

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

      1. *-commutative 76.9%

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

   5. Simplified 76.9%

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

      1. *-commutative 76.9%

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

      2. sub-neg 76.9%

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

      3. distribute-lft-in 68.4%

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

   7. Applied egg-rr 68.4%

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

      1. associate-+r+ 68.4%

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

      2. distribute-rgt-neg-out 68.4%

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

      3. unsub-neg 68.4%

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

      4. +-commutative 68.4%

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

   9. Applied egg-rr 68.4%

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

   10. Taylor expanded in t around inf 50.0%

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

       1. *-commutative 50.0%

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

   12. Simplified 50.0%

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

   if -2.6000000000000001e107 < y < 5e9

   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 64.6%

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

      1. mul-1-neg 64.6%

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

      2. unsub-neg 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around 0 60.1%

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

      1. +-commutative 60.1%

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

   8. Simplified 60.1%

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

   if 5e9 < 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 85.9%

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

      1. *-commutative 85.9%

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

   5. Simplified 85.9%

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

      1. *-commutative 85.9%

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

      2. sub-neg 85.9%

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

      3. distribute-lft-in 82.8%

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

   7. Applied egg-rr 82.8%

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

   8. Taylor expanded in t around 0 54.4%

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

      1. associate-*r* 54.4%

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

      2. mul-1-neg 54.4%

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

   10. Simplified 54.4%

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

   11. Taylor expanded in y around inf 53.5%

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

       1. associate-*r* 53.5%

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

       2. mul-1-neg 53.5%

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

   13. Simplified 53.5%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+107}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 5000000000:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+107}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 130000000:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e+107)
   (* y t)
   (if (<= y 130000000.0) (* x (+ z 1.0)) (* x (- 1.0 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+107) {
		tmp = y * t;
	} else if (y <= 130000000.0) {
		tmp = x * (z + 1.0);
	} 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) :: tmp
    if (y <= (-2.8d+107)) then
        tmp = y * t
    else if (y <= 130000000.0d0) then
        tmp = x * (z + 1.0d0)
    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 tmp;
	if (y <= -2.8e+107) {
		tmp = y * t;
	} else if (y <= 130000000.0) {
		tmp = x * (z + 1.0);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e+107:
		tmp = y * t
	elif y <= 130000000.0:
		tmp = x * (z + 1.0)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e+107)
		tmp = Float64(y * t);
	elseif (y <= 130000000.0)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e+107)
		tmp = y * t;
	elseif (y <= 130000000.0)
		tmp = x * (z + 1.0);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e+107], N[(y * t), $MachinePrecision], If[LessEqual[y, 130000000.0], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.79999999999999985e107

   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 76.9%

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

      1. *-commutative 76.9%

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

   5. Simplified 76.9%

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

      1. *-commutative 76.9%

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

      2. sub-neg 76.9%

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

      3. distribute-lft-in 68.4%

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

   7. Applied egg-rr 68.4%

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

      1. associate-+r+ 68.4%

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

      2. distribute-rgt-neg-out 68.4%

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

      3. unsub-neg 68.4%

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

      4. +-commutative 68.4%

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

   9. Applied egg-rr 68.4%

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

   10. Taylor expanded in t around inf 50.0%

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

       1. *-commutative 50.0%

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

   12. Simplified 50.0%

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

   if -2.79999999999999985e107 < y < 1.3e8

   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 64.6%

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

      1. mul-1-neg 64.6%

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

      2. unsub-neg 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in y around 0 60.1%

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

      1. +-commutative 60.1%

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

   8. Simplified 60.1%

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

   if 1.3e8 < 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 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in z around 0 54.4%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+107}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 130000000:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{-15} \lor \neg \left(z \leq 110\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.62e-15) (not (<= z 110.0))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.62e-15) || !(z <= 110.0)) {
		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 <= (-1.62d-15)) .or. (.not. (z <= 110.0d0))) 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 <= -1.62e-15) || !(z <= 110.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.62e-15) or not (z <= 110.0):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.62e-15) || !(z <= 110.0))
		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 <= -1.62e-15) || ~((z <= 110.0)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.62e-15], N[Not[LessEqual[z, 110.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.62000000000000009e-15 or 110 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 56.3%

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

      1. mul-1-neg 56.3%

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

      2. unsub-neg 56.3%

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

   5. Simplified 56.3%

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

      1. associate--r- 56.3%

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

      2. distribute-rgt-in 49.9%

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

   7. Applied egg-rr 49.9%

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

   8. Taylor expanded in z around inf 42.2%

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

   if -1.62000000000000009e-15 < z < 110

   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 95.3%

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

      1. *-commutative 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in y around 0 38.0%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{-15} \lor \neg \left(z \leq 110\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 13: 17.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 60.5%

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

   1. *-commutative 60.5%

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

5. Simplified 60.5%

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

6. Taylor expanded in y around 0 18.6%

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

7. Final simplification 18.6%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 96.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024053 
(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))))