Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.7s

Alternatives: 13

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, 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 2: 48.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -2500000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-289}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-51}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))))
   (if (<= z -2500000.0)
     (* x z)
     (if (<= z -2.4e-215)
       t_1
       (if (<= z 5.8e-289)
         (* y t)
         (if (<= z 2.15e-67)
           t_1
           (if (<= z 1.8e-51) (* y t) (if (<= z 4.1e+55) t_1 (* x z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (z <= -2500000.0) {
		tmp = x * z;
	} else if (z <= -2.4e-215) {
		tmp = t_1;
	} else if (z <= 5.8e-289) {
		tmp = y * t;
	} else if (z <= 2.15e-67) {
		tmp = t_1;
	} else if (z <= 1.8e-51) {
		tmp = y * t;
	} else if (z <= 4.1e+55) {
		tmp = t_1;
	} else {
		tmp = x * z;
	}
	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 <= (-2500000.0d0)) then
        tmp = x * z
    else if (z <= (-2.4d-215)) then
        tmp = t_1
    else if (z <= 5.8d-289) then
        tmp = y * t
    else if (z <= 2.15d-67) then
        tmp = t_1
    else if (z <= 1.8d-51) then
        tmp = y * t
    else if (z <= 4.1d+55) then
        tmp = t_1
    else
        tmp = x * z
    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 <= -2500000.0) {
		tmp = x * z;
	} else if (z <= -2.4e-215) {
		tmp = t_1;
	} else if (z <= 5.8e-289) {
		tmp = y * t;
	} else if (z <= 2.15e-67) {
		tmp = t_1;
	} else if (z <= 1.8e-51) {
		tmp = y * t;
	} else if (z <= 4.1e+55) {
		tmp = t_1;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	tmp = 0
	if z <= -2500000.0:
		tmp = x * z
	elif z <= -2.4e-215:
		tmp = t_1
	elif z <= 5.8e-289:
		tmp = y * t
	elif z <= 2.15e-67:
		tmp = t_1
	elif z <= 1.8e-51:
		tmp = y * t
	elif z <= 4.1e+55:
		tmp = t_1
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -2500000.0)
		tmp = Float64(x * z);
	elseif (z <= -2.4e-215)
		tmp = t_1;
	elseif (z <= 5.8e-289)
		tmp = Float64(y * t);
	elseif (z <= 2.15e-67)
		tmp = t_1;
	elseif (z <= 1.8e-51)
		tmp = Float64(y * t);
	elseif (z <= 4.1e+55)
		tmp = t_1;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -2500000.0)
		tmp = x * z;
	elseif (z <= -2.4e-215)
		tmp = t_1;
	elseif (z <= 5.8e-289)
		tmp = y * t;
	elseif (z <= 2.15e-67)
		tmp = t_1;
	elseif (z <= 1.8e-51)
		tmp = y * t;
	elseif (z <= 4.1e+55)
		tmp = t_1;
	else
		tmp = x * z;
	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, -2500000.0], N[(x * z), $MachinePrecision], If[LessEqual[z, -2.4e-215], t$95$1, If[LessEqual[z, 5.8e-289], N[(y * t), $MachinePrecision], If[LessEqual[z, 2.15e-67], t$95$1, If[LessEqual[z, 1.8e-51], N[(y * t), $MachinePrecision], If[LessEqual[z, 4.1e+55], t$95$1, N[(x * z), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5e6 or 4.09999999999999981e55 < 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 62.5%

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

      1. mul-1-neg 62.5%

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

      2. distribute-rgt-neg-in 62.5%

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

      3. sub-neg 62.5%

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

      4. +-commutative 62.5%

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

      5. distribute-neg-in 62.5%

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

      6. remove-double-neg 62.5%

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

      7. sub-neg 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in z around inf 51.2%

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

   if -2.5e6 < z < -2.4000000000000001e-215 or 5.80000000000000012e-289 < z < 2.15000000000000013e-67 or 1.8e-51 < z < 4.09999999999999981e55

   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 64.6%

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

      1. mul-1-neg 64.6%

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

      2. distribute-rgt-neg-in 64.6%

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

      3. sub-neg 64.6%

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

      4. +-commutative 64.6%

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

      5. distribute-neg-in 64.6%

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

      6. remove-double-neg 64.6%

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

      7. sub-neg 64.6%

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

   5. Simplified 64.6%

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

   6. Taylor expanded in z around 0 64.4%

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

      1. mul-1-neg 64.4%

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

      2. *-rgt-identity 64.4%

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

      3. distribute-rgt-neg-in 64.4%

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

      4. mul-1-neg 64.4%

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

      5. distribute-lft-in 64.4%

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

      6. mul-1-neg 64.4%

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

      7. unsub-neg 64.4%

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

   8. Simplified 64.4%

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

   if -2.4000000000000001e-215 < z < 5.80000000000000012e-289 or 2.15000000000000013e-67 < z < 1.8e-51

   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 93.4%

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

   4. Taylor expanded in y around -inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. *-commutative 87.1%

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

      3. distribute-rgt-neg-in 87.1%

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

      4. neg-mul-1 87.1%

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

      5. +-commutative 87.1%

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

      6. associate-/l* 87.1%

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

      7. neg-mul-1 87.1%

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

      8. *-commutative 87.1%

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

      9. distribute-lft-out 87.1%

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

   6. Simplified 87.1%

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

   7. Taylor expanded in x around 0 93.5%

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

      1. mul-1-neg 93.5%

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

      2. sub-neg 93.5%

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

      3. metadata-eval 93.5%

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

      4. associate-*r* 93.4%

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

      5. distribute-lft-neg-in 93.4%

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

      6. cancel-sign-sub-inv 93.4%

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

      7. +-commutative 93.4%

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

   9. Simplified 93.4%

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

   10. Taylor expanded in y around inf 73.6%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2500000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-215}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-289}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-51}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ t_2 := x + y \cdot t\\ t_3 := x - z \cdot t\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-257}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-266}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-112}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+119}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x z))) (t_2 (+ x (* y t))) (t_3 (- x (* z t))))
   (if (<= y -2.7e-70)
     t_2
     (if (<= y -4e-257)
       t_3
       (if (<= y 2.85e-266)
         t_1
         (if (<= y 1.3e-112)
           t_3
           (if (<= y 7.8e+18) t_1 (if (<= y 3.8e+119) t_2 (* x (- y))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x + (y * t);
	double t_3 = x - (z * t);
	double tmp;
	if (y <= -2.7e-70) {
		tmp = t_2;
	} else if (y <= -4e-257) {
		tmp = t_3;
	} else if (y <= 2.85e-266) {
		tmp = t_1;
	} else if (y <= 1.3e-112) {
		tmp = t_3;
	} else if (y <= 7.8e+18) {
		tmp = t_1;
	} else if (y <= 3.8e+119) {
		tmp = t_2;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (x * z)
    t_2 = x + (y * t)
    t_3 = x - (z * t)
    if (y <= (-2.7d-70)) then
        tmp = t_2
    else if (y <= (-4d-257)) then
        tmp = t_3
    else if (y <= 2.85d-266) then
        tmp = t_1
    else if (y <= 1.3d-112) then
        tmp = t_3
    else if (y <= 7.8d+18) then
        tmp = t_1
    else if (y <= 3.8d+119) then
        tmp = t_2
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x + (y * t);
	double t_3 = x - (z * t);
	double tmp;
	if (y <= -2.7e-70) {
		tmp = t_2;
	} else if (y <= -4e-257) {
		tmp = t_3;
	} else if (y <= 2.85e-266) {
		tmp = t_1;
	} else if (y <= 1.3e-112) {
		tmp = t_3;
	} else if (y <= 7.8e+18) {
		tmp = t_1;
	} else if (y <= 3.8e+119) {
		tmp = t_2;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * z)
	t_2 = x + (y * t)
	t_3 = x - (z * t)
	tmp = 0
	if y <= -2.7e-70:
		tmp = t_2
	elif y <= -4e-257:
		tmp = t_3
	elif y <= 2.85e-266:
		tmp = t_1
	elif y <= 1.3e-112:
		tmp = t_3
	elif y <= 7.8e+18:
		tmp = t_1
	elif y <= 3.8e+119:
		tmp = t_2
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * z))
	t_2 = Float64(x + Float64(y * t))
	t_3 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (y <= -2.7e-70)
		tmp = t_2;
	elseif (y <= -4e-257)
		tmp = t_3;
	elseif (y <= 2.85e-266)
		tmp = t_1;
	elseif (y <= 1.3e-112)
		tmp = t_3;
	elseif (y <= 7.8e+18)
		tmp = t_1;
	elseif (y <= 3.8e+119)
		tmp = t_2;
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * z);
	t_2 = x + (y * t);
	t_3 = x - (z * t);
	tmp = 0.0;
	if (y <= -2.7e-70)
		tmp = t_2;
	elseif (y <= -4e-257)
		tmp = t_3;
	elseif (y <= 2.85e-266)
		tmp = t_1;
	elseif (y <= 1.3e-112)
		tmp = t_3;
	elseif (y <= 7.8e+18)
		tmp = t_1;
	elseif (y <= 3.8e+119)
		tmp = t_2;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e-70], t$95$2, If[LessEqual[y, -4e-257], t$95$3, If[LessEqual[y, 2.85e-266], t$95$1, If[LessEqual[y, 1.3e-112], t$95$3, If[LessEqual[y, 7.8e+18], t$95$1, If[LessEqual[y, 3.8e+119], t$95$2, N[(x * (-y)), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7000000000000001e-70 or 7.8e18 < y < 3.7999999999999999e119

   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 57.9%

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

   4. Taylor expanded in y around inf 52.4%

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

      1. *-commutative 52.4%

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

   6. Simplified 52.4%

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

   if -2.7000000000000001e-70 < y < -3.9999999999999999e-257 or 2.8500000000000001e-266 < y < 1.29999999999999996e-112

   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 83.0%

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

   4. Taylor expanded in y around 0 78.7%

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

      1. mul-1-neg 78.7%

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

      2. unsub-neg 78.7%

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

   6. Simplified 78.7%

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

   if -3.9999999999999999e-257 < y < 2.8500000000000001e-266 or 1.29999999999999996e-112 < y < 7.8e18

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. distribute-rgt-neg-in 72.8%

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

      3. sub-neg 72.8%

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

      4. +-commutative 72.8%

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

      5. distribute-neg-in 72.8%

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

      6. remove-double-neg 72.8%

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

      7. sub-neg 72.8%

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

   5. Simplified 72.8%

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

   6. Taylor expanded in y around 0 72.8%

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

   if 3.7999999999999999e119 < 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 64.7%

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

      1. mul-1-neg 64.7%

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

      2. distribute-rgt-neg-in 64.7%

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

      3. sub-neg 64.7%

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

      4. +-commutative 64.7%

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

      5. distribute-neg-in 64.7%

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

      6. remove-double-neg 64.7%

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

      7. sub-neg 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in y around inf 59.6%

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

      1. mul-1-neg 59.6%

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

      2. distribute-lft-neg-out 59.6%

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

      3. *-commutative 59.6%

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

   8. Simplified 59.6%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-70}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-257}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-266}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-112}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+18}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+119}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-70}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.000185:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -1.6e+58)
     t_1
     (if (<= y -2.2e-70)
       (* y t)
       (if (<= y 2.1e-234)
         x
         (if (<= y 1.25e-115)
           (* z (- t))
           (if (<= y 0.000185) (* x z) (if (<= y 3.05e+119) (* y t) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -1.6e+58) {
		tmp = t_1;
	} else if (y <= -2.2e-70) {
		tmp = y * t;
	} else if (y <= 2.1e-234) {
		tmp = x;
	} else if (y <= 1.25e-115) {
		tmp = z * -t;
	} else if (y <= 0.000185) {
		tmp = x * z;
	} else if (y <= 3.05e+119) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * -y
    if (y <= (-1.6d+58)) then
        tmp = t_1
    else if (y <= (-2.2d-70)) then
        tmp = y * t
    else if (y <= 2.1d-234) then
        tmp = x
    else if (y <= 1.25d-115) then
        tmp = z * -t
    else if (y <= 0.000185d0) then
        tmp = x * z
    else if (y <= 3.05d+119) then
        tmp = y * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -1.6e+58) {
		tmp = t_1;
	} else if (y <= -2.2e-70) {
		tmp = y * t;
	} else if (y <= 2.1e-234) {
		tmp = x;
	} else if (y <= 1.25e-115) {
		tmp = z * -t;
	} else if (y <= 0.000185) {
		tmp = x * z;
	} else if (y <= 3.05e+119) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -1.6e+58:
		tmp = t_1
	elif y <= -2.2e-70:
		tmp = y * t
	elif y <= 2.1e-234:
		tmp = x
	elif y <= 1.25e-115:
		tmp = z * -t
	elif y <= 0.000185:
		tmp = x * z
	elif y <= 3.05e+119:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1.6e+58)
		tmp = t_1;
	elseif (y <= -2.2e-70)
		tmp = Float64(y * t);
	elseif (y <= 2.1e-234)
		tmp = x;
	elseif (y <= 1.25e-115)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 0.000185)
		tmp = Float64(x * z);
	elseif (y <= 3.05e+119)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	tmp = 0.0;
	if (y <= -1.6e+58)
		tmp = t_1;
	elseif (y <= -2.2e-70)
		tmp = y * t;
	elseif (y <= 2.1e-234)
		tmp = x;
	elseif (y <= 1.25e-115)
		tmp = z * -t;
	elseif (y <= 0.000185)
		tmp = x * z;
	elseif (y <= 3.05e+119)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.6e+58], t$95$1, If[LessEqual[y, -2.2e-70], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.1e-234], x, If[LessEqual[y, 1.25e-115], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 0.000185], N[(x * z), $MachinePrecision], If[LessEqual[y, 3.05e+119], N[(y * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.60000000000000008e58 or 3.05e119 < 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 62.9%

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

      1. mul-1-neg 62.9%

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

      2. distribute-rgt-neg-in 62.9%

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

      3. sub-neg 62.9%

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

      4. +-commutative 62.9%

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

      5. distribute-neg-in 62.9%

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

      6. remove-double-neg 62.9%

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

      7. sub-neg 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in y around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. distribute-lft-neg-out 55.2%

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

      3. *-commutative 55.2%

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

   8. Simplified 55.2%

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

   if -1.60000000000000008e58 < y < -2.1999999999999999e-70 or 1.85e-4 < y < 3.05e119

   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 65.5%

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

   4. Taylor expanded in y around -inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. *-commutative 65.5%

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

      3. distribute-rgt-neg-in 65.5%

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

      4. neg-mul-1 65.5%

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

      5. +-commutative 65.5%

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

      6. associate-/l* 65.5%

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

      7. neg-mul-1 65.5%

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

      8. *-commutative 65.5%

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

      9. distribute-lft-out 65.5%

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

   6. Simplified 65.5%

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

   7. Taylor expanded in x around 0 65.5%

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

      1. mul-1-neg 65.5%

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

      2. sub-neg 65.5%

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

      3. metadata-eval 65.5%

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

      4. associate-*r* 65.5%

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

      5. distribute-lft-neg-in 65.5%

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

      6. cancel-sign-sub-inv 65.5%

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

      7. +-commutative 65.5%

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

   9. Simplified 65.5%

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

   10. Taylor expanded in y around inf 51.9%

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

   if -2.1999999999999999e-70 < y < 2.09999999999999991e-234

   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 77.2%

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

   4. Taylor expanded in x around inf 45.3%

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

   if 2.09999999999999991e-234 < y < 1.2500000000000001e-115

   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 79.5%

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

   4. Taylor expanded in y around -inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. *-commutative 76.7%

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

      3. distribute-rgt-neg-in 76.7%

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

      4. neg-mul-1 76.7%

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

      5. +-commutative 76.7%

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

      6. associate-/l* 76.4%

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

      7. neg-mul-1 76.4%

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

      8. *-commutative 76.4%

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

      9. distribute-lft-out 76.4%

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

   6. Simplified 76.4%

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

   7. Taylor expanded in x around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. sub-neg 79.3%

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

      3. metadata-eval 79.3%

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

      4. associate-*r* 76.4%

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

      5. distribute-lft-neg-in 76.4%

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

      6. cancel-sign-sub-inv 76.4%

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

      7. +-commutative 76.4%

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

   9. Simplified 76.4%

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

   10. Taylor expanded in z around inf 53.4%

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

       1. associate-*r* 53.4%

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

       2. mul-1-neg 53.4%

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

   12. Simplified 53.4%

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

   if 1.2500000000000001e-115 < y < 1.85e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 68.5%

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

      1. mul-1-neg 68.5%

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

      2. distribute-rgt-neg-in 68.5%

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

      3. sub-neg 68.5%

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

      4. +-commutative 68.5%

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

      5. distribute-neg-in 68.5%

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

      6. remove-double-neg 68.5%

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

      7. sub-neg 68.5%

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

   5. Simplified 68.5%

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

   6. Taylor expanded in z around inf 47.6%

      \[\leadsto \color{blue}{x \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-70}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.000185:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ t_2 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-15}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-164}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x z))) (t_2 (* x (- y))))
   (if (<= y -9e+58)
     t_2
     (if (<= y -4.2e-15)
       (* y t)
       (if (<= y 2.4e-187)
         t_1
         (if (<= y 6e-164)
           (* z (- t))
           (if (<= y 3.1e+18) t_1 (if (<= y 3.05e+119) (* y t) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x * -y;
	double tmp;
	if (y <= -9e+58) {
		tmp = t_2;
	} else if (y <= -4.2e-15) {
		tmp = y * t;
	} else if (y <= 2.4e-187) {
		tmp = t_1;
	} else if (y <= 6e-164) {
		tmp = z * -t;
	} else if (y <= 3.1e+18) {
		tmp = t_1;
	} else if (y <= 3.05e+119) {
		tmp = y * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (x * z)
    t_2 = x * -y
    if (y <= (-9d+58)) then
        tmp = t_2
    else if (y <= (-4.2d-15)) then
        tmp = y * t
    else if (y <= 2.4d-187) then
        tmp = t_1
    else if (y <= 6d-164) then
        tmp = z * -t
    else if (y <= 3.1d+18) then
        tmp = t_1
    else if (y <= 3.05d+119) then
        tmp = y * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x * -y;
	double tmp;
	if (y <= -9e+58) {
		tmp = t_2;
	} else if (y <= -4.2e-15) {
		tmp = y * t;
	} else if (y <= 2.4e-187) {
		tmp = t_1;
	} else if (y <= 6e-164) {
		tmp = z * -t;
	} else if (y <= 3.1e+18) {
		tmp = t_1;
	} else if (y <= 3.05e+119) {
		tmp = y * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * z)
	t_2 = x * -y
	tmp = 0
	if y <= -9e+58:
		tmp = t_2
	elif y <= -4.2e-15:
		tmp = y * t
	elif y <= 2.4e-187:
		tmp = t_1
	elif y <= 6e-164:
		tmp = z * -t
	elif y <= 3.1e+18:
		tmp = t_1
	elif y <= 3.05e+119:
		tmp = y * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * z))
	t_2 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -9e+58)
		tmp = t_2;
	elseif (y <= -4.2e-15)
		tmp = Float64(y * t);
	elseif (y <= 2.4e-187)
		tmp = t_1;
	elseif (y <= 6e-164)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 3.1e+18)
		tmp = t_1;
	elseif (y <= 3.05e+119)
		tmp = Float64(y * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * z);
	t_2 = x * -y;
	tmp = 0.0;
	if (y <= -9e+58)
		tmp = t_2;
	elseif (y <= -4.2e-15)
		tmp = y * t;
	elseif (y <= 2.4e-187)
		tmp = t_1;
	elseif (y <= 6e-164)
		tmp = z * -t;
	elseif (y <= 3.1e+18)
		tmp = t_1;
	elseif (y <= 3.05e+119)
		tmp = y * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -9e+58], t$95$2, If[LessEqual[y, -4.2e-15], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.4e-187], t$95$1, If[LessEqual[y, 6e-164], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 3.1e+18], t$95$1, If[LessEqual[y, 3.05e+119], N[(y * t), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.9999999999999996e58 or 3.05e119 < 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 62.9%

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

      1. mul-1-neg 62.9%

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

      2. distribute-rgt-neg-in 62.9%

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

      3. sub-neg 62.9%

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

      4. +-commutative 62.9%

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

      5. distribute-neg-in 62.9%

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

      6. remove-double-neg 62.9%

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

      7. sub-neg 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in y around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. distribute-lft-neg-out 55.2%

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

      3. *-commutative 55.2%

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

   8. Simplified 55.2%

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

   if -8.9999999999999996e58 < y < -4.19999999999999962e-15 or 3.1e18 < y < 3.05e119

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 63.8%

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

   4. Taylor expanded in y around -inf 63.8%

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

      1. mul-1-neg 63.8%

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

      2. *-commutative 63.8%

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

      3. distribute-rgt-neg-in 63.8%

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

      4. neg-mul-1 63.8%

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

      5. +-commutative 63.8%

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

      6. associate-/l* 63.8%

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

      7. neg-mul-1 63.8%

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

      8. *-commutative 63.8%

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

      9. distribute-lft-out 63.8%

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

   6. Simplified 63.8%

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

   7. Taylor expanded in x around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. sub-neg 63.8%

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

      3. metadata-eval 63.8%

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

      4. associate-*r* 63.8%

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

      5. distribute-lft-neg-in 63.8%

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

      6. cancel-sign-sub-inv 63.8%

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

      7. +-commutative 63.8%

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

   9. Simplified 63.8%

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

   10. Taylor expanded in y around inf 60.1%

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

   if -4.19999999999999962e-15 < y < 2.40000000000000013e-187 or 6.0000000000000002e-164 < y < 3.1e18

   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 64.0%

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

      1. mul-1-neg 64.0%

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

      2. distribute-rgt-neg-in 64.0%

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

      3. sub-neg 64.0%

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

      4. +-commutative 64.0%

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

      5. distribute-neg-in 64.0%

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

      6. remove-double-neg 64.0%

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

      7. sub-neg 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in y around 0 64.0%

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

   if 2.40000000000000013e-187 < y < 6.0000000000000002e-164

   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 100.0%

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

   4. Taylor expanded in y around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. *-commutative 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. neg-mul-1 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-/l* 99.8%

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

      7. neg-mul-1 99.8%

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

      8. *-commutative 99.8%

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

      9. distribute-lft-out 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around 0 99.6%

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

      1. mul-1-neg 99.6%

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

      2. sub-neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. associate-*r* 88.2%

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

      5. distribute-lft-neg-in 88.2%

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

      6. cancel-sign-sub-inv 88.2%

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

      7. +-commutative 88.2%

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

   9. Simplified 88.2%

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

   10. Taylor expanded in z around inf 87.9%

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

       1. associate-*r* 87.9%

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

       2. mul-1-neg 87.9%

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

   12. Simplified 87.9%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-15}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-187}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-164}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+18}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot z\\ t_2 := x + y \cdot t\\ t_3 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-89}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-66}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* x z))) (t_2 (+ x (* y t))) (t_3 (* x (- 1.0 y))))
   (if (<= t -1.65e+40)
     t_2
     (if (<= t -2.3e-89)
       t_3
       (if (<= t -5.2e-278)
         t_1
         (if (<= t 1.2e-66) t_3 (if (<= t 1.85e+67) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x + (y * t);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (t <= -1.65e+40) {
		tmp = t_2;
	} else if (t <= -2.3e-89) {
		tmp = t_3;
	} else if (t <= -5.2e-278) {
		tmp = t_1;
	} else if (t <= 1.2e-66) {
		tmp = t_3;
	} else if (t <= 1.85e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (x * z)
    t_2 = x + (y * t)
    t_3 = x * (1.0d0 - y)
    if (t <= (-1.65d+40)) then
        tmp = t_2
    else if (t <= (-2.3d-89)) then
        tmp = t_3
    else if (t <= (-5.2d-278)) then
        tmp = t_1
    else if (t <= 1.2d-66) then
        tmp = t_3
    else if (t <= 1.85d+67) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (x * z);
	double t_2 = x + (y * t);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (t <= -1.65e+40) {
		tmp = t_2;
	} else if (t <= -2.3e-89) {
		tmp = t_3;
	} else if (t <= -5.2e-278) {
		tmp = t_1;
	} else if (t <= 1.2e-66) {
		tmp = t_3;
	} else if (t <= 1.85e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (x * z)
	t_2 = x + (y * t)
	t_3 = x * (1.0 - y)
	tmp = 0
	if t <= -1.65e+40:
		tmp = t_2
	elif t <= -2.3e-89:
		tmp = t_3
	elif t <= -5.2e-278:
		tmp = t_1
	elif t <= 1.2e-66:
		tmp = t_3
	elif t <= 1.85e+67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(x * z))
	t_2 = Float64(x + Float64(y * t))
	t_3 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (t <= -1.65e+40)
		tmp = t_2;
	elseif (t <= -2.3e-89)
		tmp = t_3;
	elseif (t <= -5.2e-278)
		tmp = t_1;
	elseif (t <= 1.2e-66)
		tmp = t_3;
	elseif (t <= 1.85e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (x * z);
	t_2 = x + (y * t);
	t_3 = x * (1.0 - y);
	tmp = 0.0;
	if (t <= -1.65e+40)
		tmp = t_2;
	elseif (t <= -2.3e-89)
		tmp = t_3;
	elseif (t <= -5.2e-278)
		tmp = t_1;
	elseif (t <= 1.2e-66)
		tmp = t_3;
	elseif (t <= 1.85e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.65e+40], t$95$2, If[LessEqual[t, -2.3e-89], t$95$3, If[LessEqual[t, -5.2e-278], t$95$1, If[LessEqual[t, 1.2e-66], t$95$3, If[LessEqual[t, 1.85e+67], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6499999999999999e40 or 1.8499999999999999e67 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 89.8%

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

   4. Taylor expanded in y around inf 58.4%

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

      1. *-commutative 58.4%

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

   6. Simplified 58.4%

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

   if -1.6499999999999999e40 < t < -2.3e-89 or -5.1999999999999997e-278 < t < 1.20000000000000013e-66

   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 82.1%

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

      1. mul-1-neg 82.1%

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

      2. distribute-rgt-neg-in 82.1%

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

      3. sub-neg 82.1%

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

      4. +-commutative 82.1%

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

      5. distribute-neg-in 82.1%

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

      6. remove-double-neg 82.1%

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

      7. sub-neg 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in z around 0 68.0%

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

      1. mul-1-neg 68.0%

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

      2. *-rgt-identity 68.0%

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

      3. distribute-rgt-neg-in 68.0%

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

      4. mul-1-neg 68.0%

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

      5. distribute-lft-in 68.0%

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

      6. mul-1-neg 68.0%

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

      7. unsub-neg 68.0%

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

   8. Simplified 68.0%

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

   if -2.3e-89 < t < -5.1999999999999997e-278 or 1.20000000000000013e-66 < t < 1.8499999999999999e67

   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 81.2%

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

      1. mul-1-neg 81.2%

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

      2. distribute-rgt-neg-in 81.2%

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

      3. sub-neg 81.2%

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

      4. +-commutative 81.2%

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

      5. distribute-neg-in 81.2%

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

      6. remove-double-neg 81.2%

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

      7. sub-neg 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in y around 0 65.3%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+40}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-278}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+67}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-70}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-196}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.007:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -4.8e+57)
     t_1
     (if (<= y -2.65e-70)
       (* y t)
       (if (<= y 3e-196)
         x
         (if (<= y 0.007) (* x z) (if (<= y 5.1e+119) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -4.8e+57) {
		tmp = t_1;
	} else if (y <= -2.65e-70) {
		tmp = y * t;
	} else if (y <= 3e-196) {
		tmp = x;
	} else if (y <= 0.007) {
		tmp = x * z;
	} else if (y <= 5.1e+119) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * -y
    if (y <= (-4.8d+57)) then
        tmp = t_1
    else if (y <= (-2.65d-70)) then
        tmp = y * t
    else if (y <= 3d-196) then
        tmp = x
    else if (y <= 0.007d0) then
        tmp = x * z
    else if (y <= 5.1d+119) then
        tmp = y * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -4.8e+57) {
		tmp = t_1;
	} else if (y <= -2.65e-70) {
		tmp = y * t;
	} else if (y <= 3e-196) {
		tmp = x;
	} else if (y <= 0.007) {
		tmp = x * z;
	} else if (y <= 5.1e+119) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -4.8e+57:
		tmp = t_1
	elif y <= -2.65e-70:
		tmp = y * t
	elif y <= 3e-196:
		tmp = x
	elif y <= 0.007:
		tmp = x * z
	elif y <= 5.1e+119:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -4.8e+57)
		tmp = t_1;
	elseif (y <= -2.65e-70)
		tmp = Float64(y * t);
	elseif (y <= 3e-196)
		tmp = x;
	elseif (y <= 0.007)
		tmp = Float64(x * z);
	elseif (y <= 5.1e+119)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	tmp = 0.0;
	if (y <= -4.8e+57)
		tmp = t_1;
	elseif (y <= -2.65e-70)
		tmp = y * t;
	elseif (y <= 3e-196)
		tmp = x;
	elseif (y <= 0.007)
		tmp = x * z;
	elseif (y <= 5.1e+119)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -4.8e+57], t$95$1, If[LessEqual[y, -2.65e-70], N[(y * t), $MachinePrecision], If[LessEqual[y, 3e-196], x, If[LessEqual[y, 0.007], N[(x * z), $MachinePrecision], If[LessEqual[y, 5.1e+119], N[(y * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.80000000000000009e57 or 5.09999999999999984e119 < 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 62.9%

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

      1. mul-1-neg 62.9%

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

      2. distribute-rgt-neg-in 62.9%

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

      3. sub-neg 62.9%

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

      4. +-commutative 62.9%

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

      5. distribute-neg-in 62.9%

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

      6. remove-double-neg 62.9%

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

      7. sub-neg 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in y around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. distribute-lft-neg-out 55.2%

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

      3. *-commutative 55.2%

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

   8. Simplified 55.2%

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

   if -4.80000000000000009e57 < y < -2.64999999999999992e-70 or 0.00700000000000000015 < y < 5.09999999999999984e119

   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 65.5%

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

   4. Taylor expanded in y around -inf 65.5%

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

      1. mul-1-neg 65.5%

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

      2. *-commutative 65.5%

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

      3. distribute-rgt-neg-in 65.5%

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

      4. neg-mul-1 65.5%

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

      5. +-commutative 65.5%

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

      6. associate-/l* 65.5%

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

      7. neg-mul-1 65.5%

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

      8. *-commutative 65.5%

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

      9. distribute-lft-out 65.5%

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

   6. Simplified 65.5%

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

   7. Taylor expanded in x around 0 65.5%

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

      1. mul-1-neg 65.5%

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

      2. sub-neg 65.5%

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

      3. metadata-eval 65.5%

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

      4. associate-*r* 65.5%

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

      5. distribute-lft-neg-in 65.5%

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

      6. cancel-sign-sub-inv 65.5%

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

      7. +-commutative 65.5%

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

   9. Simplified 65.5%

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

   10. Taylor expanded in y around inf 51.9%

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

   if -2.64999999999999992e-70 < y < 3e-196

   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 79.5%

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

   4. Taylor expanded in x around inf 44.3%

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

   if 3e-196 < y < 0.00700000000000000015

   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 58.9%

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

      1. mul-1-neg 58.9%

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

      2. distribute-rgt-neg-in 58.9%

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

      3. sub-neg 58.9%

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

      4. +-commutative 58.9%

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

      5. distribute-neg-in 58.9%

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

      6. remove-double-neg 58.9%

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

      7. sub-neg 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in z around inf 39.7%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-70}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-196}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.007:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+119}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{-32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-269}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (+ x (* (- y z) t))))
   (if (<= t -2.15e-32)
     t_2
     (if (<= t -2.95e-92)
       t_1
       (if (<= t -3.5e-269) (+ x (* x z)) (if (<= t 5.5e-131) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (t <= -2.15e-32) {
		tmp = t_2;
	} else if (t <= -2.95e-92) {
		tmp = t_1;
	} else if (t <= -3.5e-269) {
		tmp = x + (x * z);
	} else if (t <= 5.5e-131) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = x + ((y - z) * t)
    if (t <= (-2.15d-32)) then
        tmp = t_2
    else if (t <= (-2.95d-92)) then
        tmp = t_1
    else if (t <= (-3.5d-269)) then
        tmp = x + (x * z)
    else if (t <= 5.5d-131) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (t <= -2.15e-32) {
		tmp = t_2;
	} else if (t <= -2.95e-92) {
		tmp = t_1;
	} else if (t <= -3.5e-269) {
		tmp = x + (x * z);
	} else if (t <= 5.5e-131) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = x + ((y - z) * t)
	tmp = 0
	if t <= -2.15e-32:
		tmp = t_2
	elif t <= -2.95e-92:
		tmp = t_1
	elif t <= -3.5e-269:
		tmp = x + (x * z)
	elif t <= 5.5e-131:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (t <= -2.15e-32)
		tmp = t_2;
	elseif (t <= -2.95e-92)
		tmp = t_1;
	elseif (t <= -3.5e-269)
		tmp = Float64(x + Float64(x * z));
	elseif (t <= 5.5e-131)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = x + ((y - z) * t);
	tmp = 0.0;
	if (t <= -2.15e-32)
		tmp = t_2;
	elseif (t <= -2.95e-92)
		tmp = t_1;
	elseif (t <= -3.5e-269)
		tmp = x + (x * z);
	elseif (t <= 5.5e-131)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.15e-32], t$95$2, If[LessEqual[t, -2.95e-92], t$95$1, If[LessEqual[t, -3.5e-269], N[(x + N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-131], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.14999999999999995e-32 or 5.4999999999999997e-131 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.4%

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

   if -2.14999999999999995e-32 < t < -2.95e-92 or -3.50000000000000019e-269 < t < 5.4999999999999997e-131

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 89.6%

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

      1. mul-1-neg 89.6%

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

      2. distribute-rgt-neg-in 89.6%

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

      3. sub-neg 89.6%

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

      4. +-commutative 89.6%

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

      5. distribute-neg-in 89.6%

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

      6. remove-double-neg 89.6%

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

      7. sub-neg 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in z around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. *-rgt-identity 71.7%

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

      3. distribute-rgt-neg-in 71.7%

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

      4. mul-1-neg 71.7%

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

      5. distribute-lft-in 71.7%

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

      6. mul-1-neg 71.7%

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

      7. unsub-neg 71.7%

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

   8. Simplified 71.7%

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

   if -2.95e-92 < t < -3.50000000000000019e-269

   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 90.7%

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

      1. mul-1-neg 90.7%

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

      2. distribute-rgt-neg-in 90.7%

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

      3. sub-neg 90.7%

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

      4. +-commutative 90.7%

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

      5. distribute-neg-in 90.7%

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

      6. remove-double-neg 90.7%

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

      7. sub-neg 90.7%

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

   5. Simplified 90.7%

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

   6. Taylor expanded in y around 0 70.2%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-32}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-269}:\\ \;\;\;\;x + x \cdot z\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-72}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.024:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.2e-72)
   (* y t)
   (if (<= y 3.5e-197) x (if (<= y 0.024) (* x z) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.2e-72) {
		tmp = y * t;
	} else if (y <= 3.5e-197) {
		tmp = x;
	} else if (y <= 0.024) {
		tmp = x * z;
	} 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 <= (-6.2d-72)) then
        tmp = y * t
    else if (y <= 3.5d-197) then
        tmp = x
    else if (y <= 0.024d0) then
        tmp = x * z
    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 <= -6.2e-72) {
		tmp = y * t;
	} else if (y <= 3.5e-197) {
		tmp = x;
	} else if (y <= 0.024) {
		tmp = x * z;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.2e-72:
		tmp = y * t
	elif y <= 3.5e-197:
		tmp = x
	elif y <= 0.024:
		tmp = x * z
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.2e-72)
		tmp = Float64(y * t);
	elseif (y <= 3.5e-197)
		tmp = x;
	elseif (y <= 0.024)
		tmp = Float64(x * z);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.2e-72)
		tmp = y * t;
	elseif (y <= 3.5e-197)
		tmp = x;
	elseif (y <= 0.024)
		tmp = x * z;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.2e-72], N[(y * t), $MachinePrecision], If[LessEqual[y, 3.5e-197], x, If[LessEqual[y, 0.024], N[(x * z), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.1999999999999996e-72 or 0.024 < 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 55.0%

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

   4. Taylor expanded in y around -inf 52.1%

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

      1. mul-1-neg 52.1%

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

      2. *-commutative 52.1%

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

      3. distribute-rgt-neg-in 52.1%

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

      4. neg-mul-1 52.1%

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

      5. +-commutative 52.1%

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

      6. associate-/l* 55.0%

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

      7. neg-mul-1 55.0%

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

      8. *-commutative 55.0%

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

      9. distribute-lft-out 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in x around 0 55.0%

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

      1. mul-1-neg 55.0%

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

      2. sub-neg 55.0%

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

      3. metadata-eval 55.0%

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

      4. associate-*r* 55.0%

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

      5. distribute-lft-neg-in 55.0%

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

      6. cancel-sign-sub-inv 55.0%

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

      7. +-commutative 55.0%

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

   9. Simplified 55.0%

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

   10. Taylor expanded in y around inf 46.6%

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

   if -6.1999999999999996e-72 < y < 3.4999999999999998e-197

   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 79.5%

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

   4. Taylor expanded in x around inf 44.3%

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

   if 3.4999999999999998e-197 < y < 0.024

   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 58.9%

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

      1. mul-1-neg 58.9%

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

      2. distribute-rgt-neg-in 58.9%

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

      3. sub-neg 58.9%

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

      4. +-commutative 58.9%

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

      5. distribute-neg-in 58.9%

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

      6. remove-double-neg 58.9%

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

      7. sub-neg 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in z around inf 39.7%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-72}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.024:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 80.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+39} \lor \neg \left(t \leq 1.85 \cdot 10^{+67}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9e+39) (not (<= t 1.85e+67)))
   (+ x (* (- y z) t))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9e+39) || !(t <= 1.85e+67)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (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 ((t <= (-9d+39)) .or. (.not. (t <= 1.85d+67))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9e+39) || !(t <= 1.85e+67)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9e+39) or not (t <= 1.85e+67):
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9e+39) || !(t <= 1.85e+67))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9e+39) || ~((t <= 1.85e+67)))
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9e+39], N[Not[LessEqual[t, 1.85e+67]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.99999999999999991e39 or 1.8499999999999999e67 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 89.8%

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

   if -8.99999999999999991e39 < t < 1.8499999999999999e67

   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 81.7%

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

      1. mul-1-neg 81.7%

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

      2. distribute-rgt-neg-in 81.7%

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

      3. sub-neg 81.7%

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

      4. +-commutative 81.7%

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

      5. distribute-neg-in 81.7%

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

      6. remove-double-neg 81.7%

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

      7. sub-neg 81.7%

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

   5. Simplified 81.7%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+39} \lor \neg \left(t \leq 1.85 \cdot 10^{+67}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{-27} \lor \neg \left(y \leq 0.00021\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.38e-27) (not (<= y 0.00021)))
   (+ x (* y (- t x)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.38e-27) || !(y <= 0.00021)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - 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 <= (-1.38d-27)) .or. (.not. (y <= 0.00021d0))) then
        tmp = x + (y * (t - x))
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.38e-27) || !(y <= 0.00021)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.38e-27) or not (y <= 0.00021):
		tmp = x + (y * (t - x))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.38e-27) || !(y <= 0.00021))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.38e-27) || ~((y <= 0.00021)))
		tmp = x + (y * (t - x));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.38e-27], N[Not[LessEqual[y, 0.00021]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.38e-27 or 2.1000000000000001e-4 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 86.9%

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

      1. *-commutative 86.9%

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

   5. Simplified 86.9%

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

   if -1.38e-27 < y < 2.1000000000000001e-4

   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 93.0%

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

      1. mul-1-neg 93.0%

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

      2. distribute-rgt-neg-in 93.0%

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

      3. sub-neg 93.0%

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

      4. +-commutative 93.0%

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

      5. distribute-neg-in 93.0%

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

      6. remove-double-neg 93.0%

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

      7. sub-neg 93.0%

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

   5. Simplified 93.0%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{-27} \lor \neg \left(y \leq 0.00021\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-70} \lor \neg \left(y \leq 1.75 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.35e-70) (not (<= y 1.75e-29))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.35e-70) || !(y <= 1.75e-29)) {
		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 <= (-2.35d-70)) .or. (.not. (y <= 1.75d-29))) 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 <= -2.35e-70) || !(y <= 1.75e-29)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.35e-70) or not (y <= 1.75e-29):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.35e-70) || !(y <= 1.75e-29))
		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 <= -2.35e-70) || ~((y <= 1.75e-29)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.35e-70], N[Not[LessEqual[y, 1.75e-29]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.3499999999999999e-70 or 1.7499999999999999e-29 < 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 51.7%

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

      1. mul-1-neg 51.7%

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

      2. *-commutative 51.7%

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

      3. distribute-rgt-neg-in 51.7%

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

      4. neg-mul-1 51.7%

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

      5. +-commutative 51.7%

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

      6. associate-/l* 54.5%

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

      7. neg-mul-1 54.5%

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

      8. *-commutative 54.5%

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

      9. distribute-lft-out 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in x around 0 54.5%

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

      1. mul-1-neg 54.5%

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

      2. sub-neg 54.5%

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

      3. metadata-eval 54.5%

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

      4. associate-*r* 54.5%

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

      5. distribute-lft-neg-in 54.5%

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

      6. cancel-sign-sub-inv 54.5%

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

      7. +-commutative 54.5%

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

   9. Simplified 54.5%

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

   10. Taylor expanded in y around inf 45.7%

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

   if -2.3499999999999999e-70 < y < 1.7499999999999999e-29

   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 75.3%

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

   4. Taylor expanded in x around inf 36.4%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-70} \lor \neg \left(y \leq 1.75 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 17.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 63.6%

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

4. Taylor expanded in x around inf 18.7%

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

5. Final simplification 18.7%

   \[\leadsto x \]
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 2024058 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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