Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.4s

Alternatives: 14

Speedup: 1.0×

• 34.8% 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: 38.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+14}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-253}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= z -1.5e+14)
     (* z x)
     (if (<= z -2.2e-59)
       t_1
       (if (<= z -5.4e-104)
         x
         (if (<= z 5.2e-253)
           (* y t)
           (if (<= z 4e-127) x (if (<= z 3.25e+114) t_1 (* z (- t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (z <= -1.5e+14) {
		tmp = z * x;
	} else if (z <= -2.2e-59) {
		tmp = t_1;
	} else if (z <= -5.4e-104) {
		tmp = x;
	} else if (z <= 5.2e-253) {
		tmp = y * t;
	} else if (z <= 4e-127) {
		tmp = x;
	} else if (z <= 3.25e+114) {
		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 = y * -x
    if (z <= (-1.5d+14)) then
        tmp = z * x
    else if (z <= (-2.2d-59)) then
        tmp = t_1
    else if (z <= (-5.4d-104)) then
        tmp = x
    else if (z <= 5.2d-253) then
        tmp = y * t
    else if (z <= 4d-127) then
        tmp = x
    else if (z <= 3.25d+114) 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 = y * -x;
	double tmp;
	if (z <= -1.5e+14) {
		tmp = z * x;
	} else if (z <= -2.2e-59) {
		tmp = t_1;
	} else if (z <= -5.4e-104) {
		tmp = x;
	} else if (z <= 5.2e-253) {
		tmp = y * t;
	} else if (z <= 4e-127) {
		tmp = x;
	} else if (z <= 3.25e+114) {
		tmp = t_1;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if z <= -1.5e+14:
		tmp = z * x
	elif z <= -2.2e-59:
		tmp = t_1
	elif z <= -5.4e-104:
		tmp = x
	elif z <= 5.2e-253:
		tmp = y * t
	elif z <= 4e-127:
		tmp = x
	elif z <= 3.25e+114:
		tmp = t_1
	else:
		tmp = z * -t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (z <= -1.5e+14)
		tmp = Float64(z * x);
	elseif (z <= -2.2e-59)
		tmp = t_1;
	elseif (z <= -5.4e-104)
		tmp = x;
	elseif (z <= 5.2e-253)
		tmp = Float64(y * t);
	elseif (z <= 4e-127)
		tmp = x;
	elseif (z <= 3.25e+114)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (z <= -1.5e+14)
		tmp = z * x;
	elseif (z <= -2.2e-59)
		tmp = t_1;
	elseif (z <= -5.4e-104)
		tmp = x;
	elseif (z <= 5.2e-253)
		tmp = y * t;
	elseif (z <= 4e-127)
		tmp = x;
	elseif (z <= 3.25e+114)
		tmp = t_1;
	else
		tmp = z * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[z, -1.5e+14], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.2e-59], t$95$1, If[LessEqual[z, -5.4e-104], x, If[LessEqual[z, 5.2e-253], N[(y * t), $MachinePrecision], If[LessEqual[z, 4e-127], x, If[LessEqual[z, 3.25e+114], t$95$1, N[(z * (-t)), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.5e14

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 56.8%

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

      1. mul-1-neg 56.8%

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

      2. distribute-lft-neg-out 56.8%

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

      3. *-commutative 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in x around 0 56.8%

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

      1. mul-1-neg 56.8%

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

      2. unsub-neg 56.8%

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

   8. Simplified 56.8%

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

   9. Taylor expanded in z around inf 48.9%

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

   if -1.5e14 < z < -2.1999999999999999e-59 or 4.0000000000000001e-127 < z < 3.2500000000000001e114

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. distribute-lft-neg-out 63.8%

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

      3. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in x around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. unsub-neg 63.8%

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

   8. Simplified 63.8%

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

   9. Taylor expanded in y around inf 43.7%

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

       1. mul-1-neg 43.7%

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

       2. distribute-rgt-neg-out 43.7%

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

   11. Simplified 43.7%

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

   if -2.1999999999999999e-59 < z < -5.3999999999999997e-104 or 5.2e-253 < z < 4.0000000000000001e-127

   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 83.8%

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

   4. Taylor expanded in x around inf 51.3%

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

   if -5.3999999999999997e-104 < z < 5.2e-253

   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 76.3%

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

   4. Taylor expanded in z around 0 74.1%

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

      1. +-commutative 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in t around inf 47.7%

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

      1. *-commutative 47.7%

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

   9. Simplified 47.7%

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

   if 3.2500000000000001e114 < 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 64.3%

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

   4. Taylor expanded in y around 0 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

   6. Simplified 60.9%

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

   7. Taylor expanded in t around inf 59.9%

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

      1. associate-*r* 59.9%

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

      2. neg-mul-1 59.9%

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

   9. Simplified 59.9%

      \[\leadsto \color{blue}{\left(-t\right) \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+14}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-104}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-253}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-127}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{+114}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+142}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+23}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-159}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))))
   (if (<= z -2.5e+142)
     (* z x)
     (if (<= z -1.7e+80)
       t_1
       (if (<= z -1.22e+23)
         (* z x)
         (if (<= z 2.8e-159)
           (+ x (* y t))
           (if (<= z 3.6e+114) (* x (- 1.0 y)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (z <= -2.5e+142) {
		tmp = z * x;
	} else if (z <= -1.7e+80) {
		tmp = t_1;
	} else if (z <= -1.22e+23) {
		tmp = z * x;
	} else if (z <= 2.8e-159) {
		tmp = x + (y * t);
	} else if (z <= 3.6e+114) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (z * t)
    if (z <= (-2.5d+142)) then
        tmp = z * x
    else if (z <= (-1.7d+80)) then
        tmp = t_1
    else if (z <= (-1.22d+23)) then
        tmp = z * x
    else if (z <= 2.8d-159) then
        tmp = x + (y * t)
    else if (z <= 3.6d+114) then
        tmp = x * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (z <= -2.5e+142) {
		tmp = z * x;
	} else if (z <= -1.7e+80) {
		tmp = t_1;
	} else if (z <= -1.22e+23) {
		tmp = z * x;
	} else if (z <= 2.8e-159) {
		tmp = x + (y * t);
	} else if (z <= 3.6e+114) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	tmp = 0
	if z <= -2.5e+142:
		tmp = z * x
	elif z <= -1.7e+80:
		tmp = t_1
	elif z <= -1.22e+23:
		tmp = z * x
	elif z <= 2.8e-159:
		tmp = x + (y * t)
	elif z <= 3.6e+114:
		tmp = x * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (z <= -2.5e+142)
		tmp = Float64(z * x);
	elseif (z <= -1.7e+80)
		tmp = t_1;
	elseif (z <= -1.22e+23)
		tmp = Float64(z * x);
	elseif (z <= 2.8e-159)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 3.6e+114)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (z * t);
	tmp = 0.0;
	if (z <= -2.5e+142)
		tmp = z * x;
	elseif (z <= -1.7e+80)
		tmp = t_1;
	elseif (z <= -1.22e+23)
		tmp = z * x;
	elseif (z <= 2.8e-159)
		tmp = x + (y * t);
	elseif (z <= 3.6e+114)
		tmp = x * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+142], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.7e+80], t$95$1, If[LessEqual[z, -1.22e+23], N[(z * x), $MachinePrecision], If[LessEqual[z, 2.8e-159], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+114], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.5000000000000001e142 or -1.69999999999999996e80 < z < -1.22e23

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. distribute-lft-neg-out 61.7%

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

      3. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in x around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   8. Simplified 61.7%

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

   9. Taylor expanded in z around inf 57.6%

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

   if -2.5000000000000001e142 < z < -1.69999999999999996e80 or 3.6000000000000001e114 < 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 64.0%

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

   4. Taylor expanded in y around 0 59.5%

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

      1. +-commutative 59.5%

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

      2. mul-1-neg 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in t around 0 59.5%

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

      1. mul-1-neg 59.5%

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

      2. sub-neg 59.5%

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

   9. Simplified 59.5%

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

   if -1.22e23 < z < 2.8000000000000002e-159

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 77.8%

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

   4. Taylor expanded in z around 0 72.7%

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

      1. +-commutative 72.7%

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

   6. Simplified 72.7%

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

   if 2.8000000000000002e-159 < z < 3.6000000000000001e114

   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 76.0%

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

      1. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in x around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. unsub-neg 55.4%

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

   8. Simplified 55.4%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+142}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+80}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{+23}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-159}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot t\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+140}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+20}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-160}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+116}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* z t))))
   (if (<= z -2.6e+140)
     (* z x)
     (if (<= z -5.4e+76)
       t_1
       (if (<= z -9.2e+20)
         (* z x)
         (if (<= z 8e-160)
           (+ x (* y t))
           (if (<= z 2.35e+116) (- x (* y x)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (z <= -2.6e+140) {
		tmp = z * x;
	} else if (z <= -5.4e+76) {
		tmp = t_1;
	} else if (z <= -9.2e+20) {
		tmp = z * x;
	} else if (z <= 8e-160) {
		tmp = x + (y * t);
	} else if (z <= 2.35e+116) {
		tmp = x - (y * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (z * t)
    if (z <= (-2.6d+140)) then
        tmp = z * x
    else if (z <= (-5.4d+76)) then
        tmp = t_1
    else if (z <= (-9.2d+20)) then
        tmp = z * x
    else if (z <= 8d-160) then
        tmp = x + (y * t)
    else if (z <= 2.35d+116) then
        tmp = x - (y * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (z * t);
	double tmp;
	if (z <= -2.6e+140) {
		tmp = z * x;
	} else if (z <= -5.4e+76) {
		tmp = t_1;
	} else if (z <= -9.2e+20) {
		tmp = z * x;
	} else if (z <= 8e-160) {
		tmp = x + (y * t);
	} else if (z <= 2.35e+116) {
		tmp = x - (y * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (z * t)
	tmp = 0
	if z <= -2.6e+140:
		tmp = z * x
	elif z <= -5.4e+76:
		tmp = t_1
	elif z <= -9.2e+20:
		tmp = z * x
	elif z <= 8e-160:
		tmp = x + (y * t)
	elif z <= 2.35e+116:
		tmp = x - (y * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (z <= -2.6e+140)
		tmp = Float64(z * x);
	elseif (z <= -5.4e+76)
		tmp = t_1;
	elseif (z <= -9.2e+20)
		tmp = Float64(z * x);
	elseif (z <= 8e-160)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 2.35e+116)
		tmp = Float64(x - Float64(y * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (z * t);
	tmp = 0.0;
	if (z <= -2.6e+140)
		tmp = z * x;
	elseif (z <= -5.4e+76)
		tmp = t_1;
	elseif (z <= -9.2e+20)
		tmp = z * x;
	elseif (z <= 8e-160)
		tmp = x + (y * t);
	elseif (z <= 2.35e+116)
		tmp = x - (y * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+140], N[(z * x), $MachinePrecision], If[LessEqual[z, -5.4e+76], t$95$1, If[LessEqual[z, -9.2e+20], N[(z * x), $MachinePrecision], If[LessEqual[z, 8e-160], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+116], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.6000000000000001e140 or -5.3999999999999998e76 < z < -9.2e20

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. distribute-lft-neg-out 61.7%

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

      3. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in x around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

   8. Simplified 61.7%

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

   9. Taylor expanded in z around inf 57.6%

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

   if -2.6000000000000001e140 < z < -5.3999999999999998e76 or 2.3500000000000002e116 < 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 64.0%

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

   4. Taylor expanded in y around 0 59.5%

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

      1. +-commutative 59.5%

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

      2. mul-1-neg 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in t around 0 59.5%

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

      1. mul-1-neg 59.5%

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

      2. sub-neg 59.5%

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

   9. Simplified 59.5%

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

   if -9.2e20 < z < 7.9999999999999999e-160

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 77.8%

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

   4. Taylor expanded in z around 0 72.7%

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

      1. +-commutative 72.7%

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

   6. Simplified 72.7%

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

   if 7.9999999999999999e-160 < z < 2.3500000000000002e116

   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 76.0%

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

      1. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in x around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. unsub-neg 55.4%

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

   8. Simplified 55.4%

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

      1. sub-neg 55.4%

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

      2. distribute-rgt-in 55.4%

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

      3. *-un-lft-identity 55.4%

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

   10. Applied egg-rr 55.4%

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

       1. distribute-lft-neg-out 55.4%

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

       2. unsub-neg 55.4%

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

       3. *-commutative 55.4%

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

   12. Applied egg-rr 55.4%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+140}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+76}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{+20}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-160}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+116}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -76000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-157}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))))
   (if (<= z -76000000.0)
     (* z x)
     (if (<= z -1.55e-112)
       t_1
       (if (<= z -7.4e-157) (* y t) (if (<= z 2.9e+114) 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 <= -76000000.0) {
		tmp = z * x;
	} else if (z <= -1.55e-112) {
		tmp = t_1;
	} else if (z <= -7.4e-157) {
		tmp = y * t;
	} else if (z <= 2.9e+114) {
		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 <= (-76000000.0d0)) then
        tmp = z * x
    else if (z <= (-1.55d-112)) then
        tmp = t_1
    else if (z <= (-7.4d-157)) then
        tmp = y * t
    else if (z <= 2.9d+114) 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 <= -76000000.0) {
		tmp = z * x;
	} else if (z <= -1.55e-112) {
		tmp = t_1;
	} else if (z <= -7.4e-157) {
		tmp = y * t;
	} else if (z <= 2.9e+114) {
		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 <= -76000000.0:
		tmp = z * x
	elif z <= -1.55e-112:
		tmp = t_1
	elif z <= -7.4e-157:
		tmp = y * t
	elif z <= 2.9e+114:
		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 <= -76000000.0)
		tmp = Float64(z * x);
	elseif (z <= -1.55e-112)
		tmp = t_1;
	elseif (z <= -7.4e-157)
		tmp = Float64(y * t);
	elseif (z <= 2.9e+114)
		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 <= -76000000.0)
		tmp = z * x;
	elseif (z <= -1.55e-112)
		tmp = t_1;
	elseif (z <= -7.4e-157)
		tmp = y * t;
	elseif (z <= 2.9e+114)
		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, -76000000.0], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.55e-112], t$95$1, If[LessEqual[z, -7.4e-157], N[(y * t), $MachinePrecision], If[LessEqual[z, 2.9e+114], t$95$1, N[(z * (-t)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.6e7

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 56.8%

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

      1. mul-1-neg 56.8%

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

      2. distribute-lft-neg-out 56.8%

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

      3. *-commutative 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in x around 0 56.8%

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

      1. mul-1-neg 56.8%

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

      2. unsub-neg 56.8%

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

   8. Simplified 56.8%

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

   9. Taylor expanded in z around inf 48.9%

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

   if -7.6e7 < z < -1.5499999999999999e-112 or -7.3999999999999995e-157 < z < 2.9e114

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 87.4%

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

      1. *-commutative 87.4%

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

   5. Simplified 87.4%

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

   6. Taylor expanded in x around inf 61.3%

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

      1. mul-1-neg 61.3%

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

      2. unsub-neg 61.3%

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

   8. Simplified 61.3%

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

   if -1.5499999999999999e-112 < z < -7.3999999999999995e-157

   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 92.6%

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

   4. Taylor expanded in z around 0 84.7%

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

      1. +-commutative 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in t around inf 68.8%

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

      1. *-commutative 68.8%

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

   9. Simplified 68.8%

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

   if 2.9e114 < 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 64.3%

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

   4. Taylor expanded in y around 0 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

   6. Simplified 60.9%

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

   7. Taylor expanded in t around inf 59.9%

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

      1. associate-*r* 59.9%

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

      2. neg-mul-1 59.9%

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

   9. Simplified 59.9%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -76000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-157}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-33}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 140000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+150} \lor \neg \left(y \leq 3.8 \cdot 10^{+209}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.55e-33)
   (* y t)
   (if (<= y 140000000.0)
     x
     (if (or (<= y 2.2e+150) (not (<= y 3.8e+209))) (* y (- x)) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.55e-33) {
		tmp = y * t;
	} else if (y <= 140000000.0) {
		tmp = x;
	} else if ((y <= 2.2e+150) || !(y <= 3.8e+209)) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.55d-33)) then
        tmp = y * t
    else if (y <= 140000000.0d0) then
        tmp = x
    else if ((y <= 2.2d+150) .or. (.not. (y <= 3.8d+209))) then
        tmp = y * -x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.55e-33) {
		tmp = y * t;
	} else if (y <= 140000000.0) {
		tmp = x;
	} else if ((y <= 2.2e+150) || !(y <= 3.8e+209)) {
		tmp = y * -x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.55e-33:
		tmp = y * t
	elif y <= 140000000.0:
		tmp = x
	elif (y <= 2.2e+150) or not (y <= 3.8e+209):
		tmp = y * -x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.55e-33)
		tmp = Float64(y * t);
	elseif (y <= 140000000.0)
		tmp = x;
	elseif ((y <= 2.2e+150) || !(y <= 3.8e+209))
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.55e-33)
		tmp = y * t;
	elseif (y <= 140000000.0)
		tmp = x;
	elseif ((y <= 2.2e+150) || ~((y <= 3.8e+209)))
		tmp = y * -x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.55e-33], N[(y * t), $MachinePrecision], If[LessEqual[y, 140000000.0], x, If[Or[LessEqual[y, 2.2e+150], N[Not[LessEqual[y, 3.8e+209]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999998e-33 or 2.19999999999999999e150 < y < 3.79999999999999984e209

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 58.9%

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

   4. Taylor expanded in z around 0 46.2%

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

      1. +-commutative 46.2%

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

   6. Simplified 46.2%

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

   7. Taylor expanded in t around inf 43.3%

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

      1. *-commutative 43.3%

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

   9. Simplified 43.3%

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

   if -1.54999999999999998e-33 < y < 1.4e8

   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 76.6%

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

   4. Taylor expanded in x around inf 35.4%

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

   if 1.4e8 < y < 2.19999999999999999e150 or 3.79999999999999984e209 < 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 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. distribute-lft-neg-out 70.2%

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

      3. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in x around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. unsub-neg 70.2%

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

   8. Simplified 70.2%

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

   9. Taylor expanded in y around inf 57.0%

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

       1. mul-1-neg 57.0%

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

       2. distribute-rgt-neg-out 57.0%

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

   11. Simplified 57.0%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-33}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 140000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+150} \lor \neg \left(y \leq 3.8 \cdot 10^{+209}\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+22}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-154}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 7.3 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e+22)
   (* z x)
   (if (<= z 2.8e-154)
     (+ x (* y t))
     (if (<= z 7.3e+115) (* x (- 1.0 y)) (* z (- t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+22) {
		tmp = z * x;
	} else if (z <= 2.8e-154) {
		tmp = x + (y * t);
	} else if (z <= 7.3e+115) {
		tmp = x * (1.0 - y);
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.6d+22)) then
        tmp = z * x
    else if (z <= 2.8d-154) then
        tmp = x + (y * t)
    else if (z <= 7.3d+115) then
        tmp = x * (1.0d0 - y)
    else
        tmp = z * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+22) {
		tmp = z * x;
	} else if (z <= 2.8e-154) {
		tmp = x + (y * t);
	} else if (z <= 7.3e+115) {
		tmp = x * (1.0 - y);
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e+22:
		tmp = z * x
	elif z <= 2.8e-154:
		tmp = x + (y * t)
	elif z <= 7.3e+115:
		tmp = x * (1.0 - y)
	else:
		tmp = z * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e+22)
		tmp = Float64(z * x);
	elseif (z <= 2.8e-154)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 7.3e+115)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(z * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e+22)
		tmp = z * x;
	elseif (z <= 2.8e-154)
		tmp = x + (y * t);
	elseif (z <= 7.3e+115)
		tmp = x * (1.0 - y);
	else
		tmp = z * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e+22], N[(z * x), $MachinePrecision], If[LessEqual[z, 2.8e-154], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.3e+115], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(z * (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6e22

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. distribute-lft-neg-out 58.6%

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

      3. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in x around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. unsub-neg 58.6%

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

   8. Simplified 58.6%

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

   9. Taylor expanded in z around inf 50.3%

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

   if -1.6e22 < z < 2.80000000000000012e-154

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 77.8%

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

   4. Taylor expanded in z around 0 72.7%

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

      1. +-commutative 72.7%

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

   6. Simplified 72.7%

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

   if 2.80000000000000012e-154 < z < 7.29999999999999968e115

   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 76.0%

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

      1. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in x around inf 55.4%

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

      1. mul-1-neg 55.4%

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

      2. unsub-neg 55.4%

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

   8. Simplified 55.4%

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

   if 7.29999999999999968e115 < 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 64.3%

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

   4. Taylor expanded in y around 0 60.9%

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

      1. +-commutative 60.9%

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

      2. mul-1-neg 60.9%

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

   6. Simplified 60.9%

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

   7. Taylor expanded in t around inf 59.9%

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

      1. associate-*r* 59.9%

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

      2. neg-mul-1 59.9%

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

   9. Simplified 59.9%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+22}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-154}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 7.3 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-69} \lor \neg \left(x \leq 1.35 \cdot 10^{-137}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.35e-69) (not (<= x 1.35e-137)))
   (* x (+ (- z y) 1.0))
   (- x (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.35e-69) || !(x <= 1.35e-137)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.35d-69)) .or. (.not. (x <= 1.35d-137))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.35e-69) || !(x <= 1.35e-137)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.35e-69) or not (x <= 1.35e-137):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.35e-69) || !(x <= 1.35e-137))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.35e-69) || ~((x <= 1.35e-137)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.35e-69], N[Not[LessEqual[x, 1.35e-137]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3499999999999999e-69 or 1.34999999999999996e-137 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. distribute-lft-neg-out 77.8%

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

      3. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in x around 0 77.8%

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

      1. mul-1-neg 77.8%

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

      2. unsub-neg 77.8%

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

   8. Simplified 77.8%

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

   if -1.3499999999999999e-69 < x < 1.34999999999999996e-137

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 88.1%

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

   4. Taylor expanded in y around 0 57.1%

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

      1. +-commutative 57.1%

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

      2. mul-1-neg 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in t around 0 57.1%

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

      1. mul-1-neg 57.1%

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

      2. sub-neg 57.1%

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

   9. Simplified 57.1%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-69} \lor \neg \left(x \leq 1.35 \cdot 10^{-137}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-69} \lor \neg \left(x \leq 9.5 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.05e-69) (not (<= x 9.5e-16)))
   (* x (+ (- z y) 1.0))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.05e-69) || !(x <= 9.5e-16)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.05d-69)) .or. (.not. (x <= 9.5d-16))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.05e-69) || !(x <= 9.5e-16)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.05e-69) or not (x <= 9.5e-16):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.05e-69) || !(x <= 9.5e-16))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.05e-69) || ~((x <= 9.5e-16)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.05e-69], N[Not[LessEqual[x, 9.5e-16]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e-69 or 9.5000000000000005e-16 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 82.8%

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

      1. mul-1-neg 82.8%

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

      2. distribute-lft-neg-out 82.8%

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

      3. *-commutative 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in x around 0 82.8%

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

      1. mul-1-neg 82.8%

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

      2. unsub-neg 82.8%

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

   8. Simplified 82.8%

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

   if -1.05e-69 < x < 9.5000000000000005e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 82.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-69} \lor \neg \left(x \leq 9.5 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+23} \lor \neg \left(z \leq 4.2 \cdot 10^{+41}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e+23) (not (<= z 4.2e+41)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+23) || !(z <= 4.2e+41)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1d+23)) .or. (.not. (z <= 4.2d+41))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+23) || !(z <= 4.2e+41)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1e+23) or not (z <= 4.2e+41):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1e+23) || !(z <= 4.2e+41))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1e+23) || ~((z <= 4.2e+41)))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1e+23], N[Not[LessEqual[z, 4.2e+41]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999992e22 or 4.1999999999999999e41 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.9%

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

      1. mul-1-neg 82.9%

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

      2. distribute-lft-neg-out 82.9%

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

      3. *-commutative 82.9%

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

   5. Simplified 82.9%

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

   if -9.9999999999999992e22 < z < 4.1999999999999999e41

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.8%

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

      1. *-commutative 90.8%

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

   5. Simplified 90.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+23} \lor \neg \left(z \leq 4.2 \cdot 10^{+41}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.28 \lor \neg \left(z \leq 2.8 \cdot 10^{-28}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.28) (not (<= z 2.8e-28))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.28) || !(z <= 2.8e-28)) {
		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 <= (-0.28d0)) .or. (.not. (z <= 2.8d-28))) 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 <= -0.28) || !(z <= 2.8e-28)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.28) or not (z <= 2.8e-28):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.28) || !(z <= 2.8e-28))
		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 <= -0.28) || ~((z <= 2.8e-28)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.28], N[Not[LessEqual[z, 2.8e-28]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.28000000000000003 or 2.7999999999999998e-28 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 54.0%

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

      1. mul-1-neg 54.0%

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

      2. distribute-lft-neg-out 54.0%

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

      3. *-commutative 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in x around 0 54.0%

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

      1. mul-1-neg 54.0%

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

      2. unsub-neg 54.0%

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

   8. Simplified 54.0%

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

   9. Taylor expanded in z around inf 37.8%

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

   if -0.28000000000000003 < z < 2.7999999999999998e-28

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 74.2%

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

   4. Taylor expanded in x around inf 34.6%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.28 \lor \neg \left(z \leq 2.8 \cdot 10^{-28}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-31} \lor \neg \left(y \leq 6 \cdot 10^{-99}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.7e-31) (not (<= y 6e-99))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.7e-31) || !(y <= 6e-99)) {
		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 <= (-3.7d-31)) .or. (.not. (y <= 6d-99))) 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 <= -3.7e-31) || !(y <= 6e-99)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.7e-31) or not (y <= 6e-99):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.7e-31) || !(y <= 6e-99))
		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 <= -3.7e-31) || ~((y <= 6e-99)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.7e-31], N[Not[LessEqual[y, 6e-99]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.6999999999999998e-31 or 6.00000000000000012e-99 < 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 53.6%

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

   4. Taylor expanded in z around 0 39.7%

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

      1. +-commutative 39.7%

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

   6. Simplified 39.7%

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

   7. Taylor expanded in t around inf 36.5%

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

      1. *-commutative 36.5%

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

   9. Simplified 36.5%

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

   if -3.6999999999999998e-31 < y < 6.00000000000000012e-99

   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 76.2%

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

   4. Taylor expanded in x around inf 38.6%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-31} \lor \neg \left(y \leq 6 \cdot 10^{-99}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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 14: 17.9% 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 62.3%

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

4. Taylor expanded in x around inf 18.0%

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

5. Final simplification 18.0%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.4% 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 2024029 
(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))))