Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.1s

Alternatives: 14

Speedup: 1.0×

• 33.9% 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-def 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: 44.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+243}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+32}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-247}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.0295:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))))
   (if (<= y -5.2e+243)
     (* y t)
     (if (<= y -3.7e+88)
       (* y (- x))
       (if (<= y -1.8e+32)
         (* y t)
         (if (<= y -2.3e-77)
           t_1
           (if (<= y 2.8e-247)
             (* z (- t))
             (if (<= y 0.0295) t_1 (* y t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double tmp;
	if (y <= -5.2e+243) {
		tmp = y * t;
	} else if (y <= -3.7e+88) {
		tmp = y * -x;
	} else if (y <= -1.8e+32) {
		tmp = y * t;
	} else if (y <= -2.3e-77) {
		tmp = t_1;
	} else if (y <= 2.8e-247) {
		tmp = z * -t;
	} else if (y <= 0.0295) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    if (y <= (-5.2d+243)) then
        tmp = y * t
    else if (y <= (-3.7d+88)) then
        tmp = y * -x
    else if (y <= (-1.8d+32)) then
        tmp = y * t
    else if (y <= (-2.3d-77)) then
        tmp = t_1
    else if (y <= 2.8d-247) then
        tmp = z * -t
    else if (y <= 0.0295d0) then
        tmp = t_1
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double tmp;
	if (y <= -5.2e+243) {
		tmp = y * t;
	} else if (y <= -3.7e+88) {
		tmp = y * -x;
	} else if (y <= -1.8e+32) {
		tmp = y * t;
	} else if (y <= -2.3e-77) {
		tmp = t_1;
	} else if (y <= 2.8e-247) {
		tmp = z * -t;
	} else if (y <= 0.0295) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	tmp = 0
	if y <= -5.2e+243:
		tmp = y * t
	elif y <= -3.7e+88:
		tmp = y * -x
	elif y <= -1.8e+32:
		tmp = y * t
	elif y <= -2.3e-77:
		tmp = t_1
	elif y <= 2.8e-247:
		tmp = z * -t
	elif y <= 0.0295:
		tmp = t_1
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -5.2e+243)
		tmp = Float64(y * t);
	elseif (y <= -3.7e+88)
		tmp = Float64(y * Float64(-x));
	elseif (y <= -1.8e+32)
		tmp = Float64(y * t);
	elseif (y <= -2.3e-77)
		tmp = t_1;
	elseif (y <= 2.8e-247)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 0.0295)
		tmp = t_1;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -5.2e+243)
		tmp = y * t;
	elseif (y <= -3.7e+88)
		tmp = y * -x;
	elseif (y <= -1.8e+32)
		tmp = y * t;
	elseif (y <= -2.3e-77)
		tmp = t_1;
	elseif (y <= 2.8e-247)
		tmp = z * -t;
	elseif (y <= 0.0295)
		tmp = t_1;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+243], N[(y * t), $MachinePrecision], If[LessEqual[y, -3.7e+88], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, -1.8e+32], N[(y * t), $MachinePrecision], If[LessEqual[y, -2.3e-77], t$95$1, If[LessEqual[y, 2.8e-247], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 0.0295], t$95$1, N[(y * t), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.19999999999999993e243 or -3.69999999999999994e88 < y < -1.7999999999999998e32 or 0.029499999999999998 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 61.2%

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

   4. Taylor expanded in y around inf 51.3%

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

      1. *-commutative 51.3%

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

   6. Simplified 51.3%

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

   7. Taylor expanded in x around 0 51.3%

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

   if -5.19999999999999993e243 < y < -3.69999999999999994e88

   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 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in y around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-lft-neg-out 58.8%

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

      3. *-commutative 58.8%

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

   8. Simplified 58.8%

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

   if -1.7999999999999998e32 < y < -2.29999999999999999e-77 or 2.79999999999999986e-247 < y < 0.029499999999999998

   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 64.1%

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

      1. +-commutative 64.1%

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

   8. Simplified 64.1%

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

   if -2.29999999999999999e-77 < y < 2.79999999999999986e-247

   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 86.8%

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

   4. Taylor expanded in y around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. unsub-neg 75.7%

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

      3. *-commutative 75.7%

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

   6. Simplified 75.7%

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

   7. Taylor expanded in x around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. *-commutative 51.3%

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

      3. distribute-rgt-neg-in 51.3%

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

   9. Simplified 51.3%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+243}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+32}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-247}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.0295:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+246}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4.35 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -0.00024:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-247}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.1e+246)
   (* y t)
   (if (<= y -4.35e+86)
     (* y (- x))
     (if (<= y -0.00024)
       (* y t)
       (if (<= y 1.32e-247) (* z (- t)) (if (<= y 6.6e-60) x (* y t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e+246) {
		tmp = y * t;
	} else if (y <= -4.35e+86) {
		tmp = y * -x;
	} else if (y <= -0.00024) {
		tmp = y * t;
	} else if (y <= 1.32e-247) {
		tmp = z * -t;
	} else if (y <= 6.6e-60) {
		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 <= (-1.1d+246)) then
        tmp = y * t
    else if (y <= (-4.35d+86)) then
        tmp = y * -x
    else if (y <= (-0.00024d0)) then
        tmp = y * t
    else if (y <= 1.32d-247) then
        tmp = z * -t
    else if (y <= 6.6d-60) 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 <= -1.1e+246) {
		tmp = y * t;
	} else if (y <= -4.35e+86) {
		tmp = y * -x;
	} else if (y <= -0.00024) {
		tmp = y * t;
	} else if (y <= 1.32e-247) {
		tmp = z * -t;
	} else if (y <= 6.6e-60) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.1e+246:
		tmp = y * t
	elif y <= -4.35e+86:
		tmp = y * -x
	elif y <= -0.00024:
		tmp = y * t
	elif y <= 1.32e-247:
		tmp = z * -t
	elif y <= 6.6e-60:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.1e+246)
		tmp = Float64(y * t);
	elseif (y <= -4.35e+86)
		tmp = Float64(y * Float64(-x));
	elseif (y <= -0.00024)
		tmp = Float64(y * t);
	elseif (y <= 1.32e-247)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 6.6e-60)
		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 <= -1.1e+246)
		tmp = y * t;
	elseif (y <= -4.35e+86)
		tmp = y * -x;
	elseif (y <= -0.00024)
		tmp = y * t;
	elseif (y <= 1.32e-247)
		tmp = z * -t;
	elseif (y <= 6.6e-60)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.1e+246], N[(y * t), $MachinePrecision], If[LessEqual[y, -4.35e+86], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, -0.00024], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.32e-247], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 6.6e-60], x, N[(y * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.09999999999999994e246 or -4.3500000000000001e86 < y < -2.40000000000000006e-4 or 6.5999999999999996e-60 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 58.1%

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

   4. Taylor expanded in y around inf 47.5%

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

      1. *-commutative 47.5%

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

   6. Simplified 47.5%

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

   7. Taylor expanded in x around 0 46.3%

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

   if -1.09999999999999994e246 < y < -4.3500000000000001e86

   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 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in y around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-lft-neg-out 58.8%

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

      3. *-commutative 58.8%

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

   8. Simplified 58.8%

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

   if -2.40000000000000006e-4 < y < 1.3200000000000001e-247

   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 82.6%

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

   4. Taylor expanded in y around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

      3. *-commutative 71.4%

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

   6. Simplified 71.4%

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

   7. Taylor expanded in x around 0 45.6%

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

      1. mul-1-neg 45.6%

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

      2. *-commutative 45.6%

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

      3. distribute-rgt-neg-in 45.6%

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

   9. Simplified 45.6%

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

   if 1.3200000000000001e-247 < y < 6.5999999999999996e-60

   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 82.5%

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

   4. Taylor expanded in x around inf 50.9%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+246}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4.35 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -0.00024:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-247}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-230}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))))
   (if (<= z -1.6e+19)
     (* z x)
     (if (<= z -5.8e-179)
       t_1
       (if (<= z -2.2e-230) (* y t) (if (<= z 1.55e+34) t_1 (* z (- t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (z <= -1.6e+19) {
		tmp = z * x;
	} else if (z <= -5.8e-179) {
		tmp = t_1;
	} else if (z <= -2.2e-230) {
		tmp = y * t;
	} else if (z <= 1.55e+34) {
		tmp = t_1;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    if (z <= (-1.6d+19)) then
        tmp = z * x
    else if (z <= (-5.8d-179)) then
        tmp = t_1
    else if (z <= (-2.2d-230)) then
        tmp = y * t
    else if (z <= 1.55d+34) then
        tmp = t_1
    else
        tmp = z * -t
    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 (z <= -1.6e+19) {
		tmp = z * x;
	} else if (z <= -5.8e-179) {
		tmp = t_1;
	} else if (z <= -2.2e-230) {
		tmp = y * t;
	} else if (z <= 1.55e+34) {
		tmp = t_1;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	tmp = 0
	if z <= -1.6e+19:
		tmp = z * x
	elif z <= -5.8e-179:
		tmp = t_1
	elif z <= -2.2e-230:
		tmp = y * t
	elif z <= 1.55e+34:
		tmp = t_1
	else:
		tmp = z * -t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -1.6e+19)
		tmp = Float64(z * x);
	elseif (z <= -5.8e-179)
		tmp = t_1;
	elseif (z <= -2.2e-230)
		tmp = Float64(y * t);
	elseif (z <= 1.55e+34)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -1.6e+19)
		tmp = z * x;
	elseif (z <= -5.8e-179)
		tmp = t_1;
	elseif (z <= -2.2e-230)
		tmp = y * t;
	elseif (z <= 1.55e+34)
		tmp = t_1;
	else
		tmp = z * -t;
	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[z, -1.6e+19], N[(z * x), $MachinePrecision], If[LessEqual[z, -5.8e-179], t$95$1, If[LessEqual[z, -2.2e-230], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.55e+34], t$95$1, N[(z * (-t)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6e19

   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 50.7%

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

      1. mul-1-neg 50.7%

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

      2. unsub-neg 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around 0 42.1%

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

      1. +-commutative 42.1%

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

   8. Simplified 42.1%

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

   9. Taylor expanded in z around inf 42.1%

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

       1. *-commutative 42.1%

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

   11. Simplified 42.1%

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

   if -1.6e19 < z < -5.7999999999999998e-179 or -2.1999999999999998e-230 < z < 1.54999999999999989e34

   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 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in z around 0 61.7%

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

   if -5.7999999999999998e-179 < z < -2.1999999999999998e-230

   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 78.9%

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

   4. Taylor expanded in y around inf 78.9%

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

      1. *-commutative 78.9%

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

   6. Simplified 78.9%

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

   7. Taylor expanded in x around 0 78.1%

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

   if 1.54999999999999989e34 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 70.1%

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

   4. Taylor expanded in y around 0 56.5%

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

      1. mul-1-neg 56.5%

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

      2. unsub-neg 56.5%

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

      3. *-commutative 56.5%

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

   6. Simplified 56.5%

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

   7. Taylor expanded in x around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. *-commutative 56.1%

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

      3. distribute-rgt-neg-in 56.1%

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

   9. Simplified 56.1%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+19}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-230}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-230}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 11500000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* x (- 1.0 y))))
   (if (<= z -1.75e-14)
     t_1
     (if (<= z -2.5e-182)
       t_2
       (if (<= z -2.4e-230) (* y t) (if (<= z 11500000000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -1.75e-14) {
		tmp = t_1;
	} else if (z <= -2.5e-182) {
		tmp = t_2;
	} else if (z <= -2.4e-230) {
		tmp = y * t;
	} else if (z <= 11500000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = x * (1.0d0 - y)
    if (z <= (-1.75d-14)) then
        tmp = t_1
    else if (z <= (-2.5d-182)) then
        tmp = t_2
    else if (z <= (-2.4d-230)) then
        tmp = y * t
    else if (z <= 11500000000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x * (1.0 - y);
	double tmp;
	if (z <= -1.75e-14) {
		tmp = t_1;
	} else if (z <= -2.5e-182) {
		tmp = t_2;
	} else if (z <= -2.4e-230) {
		tmp = y * t;
	} else if (z <= 11500000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x * (1.0 - y)
	tmp = 0
	if z <= -1.75e-14:
		tmp = t_1
	elif z <= -2.5e-182:
		tmp = t_2
	elif z <= -2.4e-230:
		tmp = y * t
	elif z <= 11500000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -1.75e-14)
		tmp = t_1;
	elseif (z <= -2.5e-182)
		tmp = t_2;
	elseif (z <= -2.4e-230)
		tmp = Float64(y * t);
	elseif (z <= 11500000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -1.75e-14)
		tmp = t_1;
	elseif (z <= -2.5e-182)
		tmp = t_2;
	elseif (z <= -2.4e-230)
		tmp = y * t;
	elseif (z <= 11500000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e-14], t$95$1, If[LessEqual[z, -2.5e-182], t$95$2, If[LessEqual[z, -2.4e-230], N[(y * t), $MachinePrecision], If[LessEqual[z, 11500000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7500000000000001e-14 or 1.15e10 < 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 75.8%

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

      1. mul-1-neg 75.8%

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

      2. unsub-neg 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in t around 0 70.2%

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

   7. Taylor expanded in z around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. neg-mul-1 75.7%

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

      3. +-commutative 75.7%

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

      4. *-commutative 75.7%

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

      5. associate-*l* 75.7%

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

      6. distribute-lft-out 75.7%

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

      7. neg-mul-1 75.7%

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

      8. remove-double-neg 75.7%

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

      9. neg-mul-1 75.7%

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

      10. unsub-neg 75.7%

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

   9. Simplified 75.7%

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

   if -1.7500000000000001e-14 < z < -2.50000000000000012e-182 or -2.4000000000000002e-230 < z < 1.15e10

   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 64.5%

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

      1. mul-1-neg 64.5%

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

      2. unsub-neg 64.5%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in z around 0 64.5%

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

   if -2.50000000000000012e-182 < z < -2.4000000000000002e-230

   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 78.9%

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

   4. Taylor expanded in y around inf 78.9%

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

      1. *-commutative 78.9%

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

   6. Simplified 78.9%

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

   7. Taylor expanded in x around 0 78.1%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-182}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-230}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 11500000000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + y \cdot t\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 125000000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* y t))))
   (if (<= z -8.5e+16)
     t_1
     (if (<= z -1.9e-231)
       t_2
       (if (<= z 4.3e-172)
         (* x (- 1.0 y))
         (if (<= z 125000000000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -8.5e+16) {
		tmp = t_1;
	} else if (z <= -1.9e-231) {
		tmp = t_2;
	} else if (z <= 4.3e-172) {
		tmp = x * (1.0 - y);
	} else if (z <= 125000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = x + (y * t)
    if (z <= (-8.5d+16)) then
        tmp = t_1
    else if (z <= (-1.9d-231)) then
        tmp = t_2
    else if (z <= 4.3d-172) then
        tmp = x * (1.0d0 - y)
    else if (z <= 125000000000.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -8.5e+16) {
		tmp = t_1;
	} else if (z <= -1.9e-231) {
		tmp = t_2;
	} else if (z <= 4.3e-172) {
		tmp = x * (1.0 - y);
	} else if (z <= 125000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + (y * t)
	tmp = 0
	if z <= -8.5e+16:
		tmp = t_1
	elif z <= -1.9e-231:
		tmp = t_2
	elif z <= 4.3e-172:
		tmp = x * (1.0 - y)
	elif z <= 125000000000.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -8.5e+16)
		tmp = t_1;
	elseif (z <= -1.9e-231)
		tmp = t_2;
	elseif (z <= 4.3e-172)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 125000000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (z <= -8.5e+16)
		tmp = t_1;
	elseif (z <= -1.9e-231)
		tmp = t_2;
	elseif (z <= 4.3e-172)
		tmp = x * (1.0 - y);
	elseif (z <= 125000000000.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+16], t$95$1, If[LessEqual[z, -1.9e-231], t$95$2, If[LessEqual[z, 4.3e-172], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 125000000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5e16 or 1.25e11 < 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 77.4%

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

      1. mul-1-neg 77.4%

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

      2. unsub-neg 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in t around 0 71.6%

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

   7. Taylor expanded in z around inf 77.3%

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

      1. associate-*r* 77.3%

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

      2. neg-mul-1 77.3%

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

      3. +-commutative 77.3%

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

      4. *-commutative 77.3%

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

      5. associate-*l* 77.3%

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

      6. distribute-lft-out 77.3%

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

      7. neg-mul-1 77.3%

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

      8. remove-double-neg 77.3%

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

      9. neg-mul-1 77.3%

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

      10. unsub-neg 77.3%

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

   9. Simplified 77.3%

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

   if -8.5e16 < z < -1.90000000000000007e-231 or 4.2999999999999997e-172 < z < 1.25e11

   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 76.4%

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

   4. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

   6. Simplified 66.9%

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

   if -1.90000000000000007e-231 < z < 4.2999999999999997e-172

   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 72.5%

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

      1. mul-1-neg 72.5%

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

      2. unsub-neg 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in z around 0 72.5%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-231}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-172}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 125000000000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+31}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-88}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-126} \lor \neg \left(y \leq 7.2 \cdot 10^{-60}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e+31)
   (* y t)
   (if (<= y -2.9e-88)
     (* z x)
     (if (or (<= y -2.4e-126) (not (<= y 7.2e-60))) (* y t) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e+31) {
		tmp = y * t;
	} else if (y <= -2.9e-88) {
		tmp = z * x;
	} else if ((y <= -2.4e-126) || !(y <= 7.2e-60)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.8d+31)) then
        tmp = y * t
    else if (y <= (-2.9d-88)) then
        tmp = z * x
    else if ((y <= (-2.4d-126)) .or. (.not. (y <= 7.2d-60))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e+31) {
		tmp = y * t;
	} else if (y <= -2.9e-88) {
		tmp = z * x;
	} else if ((y <= -2.4e-126) || !(y <= 7.2e-60)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e+31:
		tmp = y * t
	elif y <= -2.9e-88:
		tmp = z * x
	elif (y <= -2.4e-126) or not (y <= 7.2e-60):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e+31)
		tmp = Float64(y * t);
	elseif (y <= -2.9e-88)
		tmp = Float64(z * x);
	elseif ((y <= -2.4e-126) || !(y <= 7.2e-60))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.8e+31)
		tmp = y * t;
	elseif (y <= -2.9e-88)
		tmp = z * x;
	elseif ((y <= -2.4e-126) || ~((y <= 7.2e-60)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e+31], N[(y * t), $MachinePrecision], If[LessEqual[y, -2.9e-88], N[(z * x), $MachinePrecision], If[Or[LessEqual[y, -2.4e-126], N[Not[LessEqual[y, 7.2e-60]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.79999999999999998e31 or -2.9000000000000001e-88 < y < -2.40000000000000007e-126 or 7.2e-60 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 56.1%

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

   4. Taylor expanded in y around inf 44.1%

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

      1. *-commutative 44.1%

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

   6. Simplified 44.1%

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

   7. Taylor expanded in x around 0 43.1%

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

   if -1.79999999999999998e31 < y < -2.9000000000000001e-88

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 54.1%

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

      1. mul-1-neg 54.1%

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

      2. unsub-neg 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in y around 0 49.7%

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

      1. +-commutative 49.7%

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

   8. Simplified 49.7%

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

   9. Taylor expanded in z around inf 31.6%

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

       1. *-commutative 31.6%

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

   11. Simplified 31.6%

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

   if -2.40000000000000007e-126 < y < 7.2e-60

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 85.2%

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

   4. Taylor expanded in x around inf 42.4%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+31}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-88}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-126} \lor \neg \left(y \leq 7.2 \cdot 10^{-60}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+32} \lor \neg \left(x \leq 150000000\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5e+32) (not (<= x 150000000.0)))
   (* x (+ (- z y) 1.0))
   (- x (* t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5e+32) || !(x <= 150000000.0)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5d+32)) .or. (.not. (x <= 150000000.0d0))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = x - (t * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5e+32) || !(x <= 150000000.0)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5e+32) or not (x <= 150000000.0):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x - (t * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5e+32) || !(x <= 150000000.0))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(x - Float64(t * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5e+32) || ~((x <= 150000000.0)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x - (t * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5e+32], N[Not[LessEqual[x, 150000000.0]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.9999999999999997e32 or 1.5e8 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.4%

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

      1. mul-1-neg 86.4%

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

      2. unsub-neg 86.4%

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

   5. Simplified 86.4%

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

   if -4.9999999999999997e32 < x < 1.5e8

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.5%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+32} \lor \neg \left(x \leq 150000000\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+18} \lor \neg \left(z \leq 5.2 \cdot 10^{+47}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.4e+18) (not (<= z 5.2e+47)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.4e+18) || !(z <= 5.2e+47)) {
		tmp = 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 <= (-4.4d+18)) .or. (.not. (z <= 5.2d+47))) then
        tmp = 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 <= -4.4e+18) || !(z <= 5.2e+47)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.4e+18) or not (z <= 5.2e+47):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.4e+18) || !(z <= 5.2e+47))
		tmp = 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 <= -4.4e+18) || ~((z <= 5.2e+47)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.4e+18], N[Not[LessEqual[z, 5.2e+47]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e18 or 5.20000000000000007e47 < 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 79.4%

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

      1. mul-1-neg 79.4%

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

      2. unsub-neg 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in t around 0 73.1%

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

   7. Taylor expanded in z around inf 79.4%

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

      1. associate-*r* 79.4%

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

      2. neg-mul-1 79.4%

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

      3. +-commutative 79.4%

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

      4. *-commutative 79.4%

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

      5. associate-*l* 79.4%

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

      6. distribute-lft-out 79.4%

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

      7. neg-mul-1 79.4%

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

      8. remove-double-neg 79.4%

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

      9. neg-mul-1 79.4%

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

      10. unsub-neg 79.4%

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

   9. Simplified 79.4%

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

   if -4.4e18 < z < 5.20000000000000007e47

   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 91.0%

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

      1. *-commutative 91.0%

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

   5. Simplified 91.0%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+18} \lor \neg \left(z \leq 5.2 \cdot 10^{+47}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+47}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.9e+19) t_1 (if (<= z 7e+47) (+ x (* y (- t x))) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.9e+19) {
		tmp = t_1;
	} else if (z <= 7e+47) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + 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 = z * (x - t)
    if (z <= (-1.9d+19)) then
        tmp = t_1
    else if (z <= 7d+47) then
        tmp = x + (y * (t - x))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.9e+19) {
		tmp = t_1;
	} else if (z <= 7e+47) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1.9e+19:
		tmp = t_1
	elif z <= 7e+47:
		tmp = x + (y * (t - x))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1.9e+19)
		tmp = t_1;
	elseif (z <= 7e+47)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1.9e+19)
		tmp = t_1;
	elseif (z <= 7e+47)
		tmp = x + (y * (t - x));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+19], t$95$1, If[LessEqual[z, 7e+47], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. unsub-neg 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in t around 0 73.3%

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

   7. Taylor expanded in z around inf 80.2%

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

      1. associate-*r* 80.2%

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

      2. neg-mul-1 80.2%

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

      3. +-commutative 80.2%

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

      4. *-commutative 80.2%

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

      5. associate-*l* 80.2%

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

      6. distribute-lft-out 80.2%

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

      7. neg-mul-1 80.2%

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

      8. remove-double-neg 80.2%

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

      9. neg-mul-1 80.2%

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

      10. unsub-neg 80.2%

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

   9. Simplified 80.2%

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

   if -1.9e19 < z < 7.00000000000000031e47

   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 91.0%

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

      1. *-commutative 91.0%

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

   5. Simplified 91.0%

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

   if 7.00000000000000031e47 < 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 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

   5. Simplified 78.5%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+47}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 12: 35.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+20} \lor \neg \left(x \leq 1.4 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.1e+20) (not (<= x 1.4e-20))) (* y (- x)) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.1e+20) || !(x <= 1.4e-20)) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.1d+20)) .or. (.not. (x <= 1.4d-20))) then
        tmp = y * -x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.1e+20) || !(x <= 1.4e-20)) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.1e+20) or not (x <= 1.4e-20):
		tmp = y * -x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.1e+20) || !(x <= 1.4e-20))
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.1e+20) || ~((x <= 1.4e-20)))
		tmp = y * -x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.1e+20], N[Not[LessEqual[x, 1.4e-20]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1e20 or 1.4000000000000001e-20 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.3%

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

      1. mul-1-neg 84.3%

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

      2. unsub-neg 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in y around inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. distribute-lft-neg-out 44.9%

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

      3. *-commutative 44.9%

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

   8. Simplified 44.9%

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

   if -1.1e20 < x < 1.4000000000000001e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.2%

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

   4. Taylor expanded in y around inf 50.7%

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

      1. *-commutative 50.7%

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

   6. Simplified 50.7%

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

   7. Taylor expanded in x around 0 38.8%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+20} \lor \neg \left(x \leq 1.4 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-7} \lor \neg \left(y \leq 5.2 \cdot 10^{-60}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.45e-7) (not (<= y 5.2e-60))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.45e-7) || !(y <= 5.2e-60)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.45d-7)) .or. (.not. (y <= 5.2d-60))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.45e-7) || !(y <= 5.2e-60)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.45e-7) or not (y <= 5.2e-60):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.45e-7) || !(y <= 5.2e-60))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.45e-7) || ~((y <= 5.2e-60)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.45e-7], N[Not[LessEqual[y, 5.2e-60]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.4499999999999999e-7 or 5.1999999999999995e-60 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 54.5%

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

   4. Taylor expanded in y around inf 42.6%

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

      1. *-commutative 42.6%

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

   6. Simplified 42.6%

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

   7. Taylor expanded in x around 0 41.5%

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

   if -1.4499999999999999e-7 < y < 5.1999999999999995e-60

   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 82.4%

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

   4. Taylor expanded in x around inf 37.2%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-7} \lor \neg \left(y \leq 5.2 \cdot 10^{-60}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 18.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 66.2%

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

4. Taylor expanded in x around inf 17.7%

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

5. Final simplification 17.7%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024013 
(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))))