Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.8s

Alternatives: 12

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. Final simplification 100.0%

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

Alternative 2: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + y \cdot t\\ t_3 := x - x \cdot y\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-307}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* y t))) (t_3 (- x (* x y))))
   (if (<= z -7.2e+30)
     t_1
     (if (<= z -8e-83)
       t_3
       (if (<= z -7.6e-83)
         (* t (- z))
         (if (<= z -1.4e-217)
           t_2
           (if (<= z -1.6e-307)
             t_3
             (if (<= z 3.2e-187)
               t_2
               (if (<= z 1.8e-64) t_3 (if (<= z 2e-24) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double t_3 = x - (x * y);
	double tmp;
	if (z <= -7.2e+30) {
		tmp = t_1;
	} else if (z <= -8e-83) {
		tmp = t_3;
	} else if (z <= -7.6e-83) {
		tmp = t * -z;
	} else if (z <= -1.4e-217) {
		tmp = t_2;
	} else if (z <= -1.6e-307) {
		tmp = t_3;
	} else if (z <= 3.2e-187) {
		tmp = t_2;
	} else if (z <= 1.8e-64) {
		tmp = t_3;
	} else if (z <= 2e-24) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = x + (y * t)
    t_3 = x - (x * y)
    if (z <= (-7.2d+30)) then
        tmp = t_1
    else if (z <= (-8d-83)) then
        tmp = t_3
    else if (z <= (-7.6d-83)) then
        tmp = t * -z
    else if (z <= (-1.4d-217)) then
        tmp = t_2
    else if (z <= (-1.6d-307)) then
        tmp = t_3
    else if (z <= 3.2d-187) then
        tmp = t_2
    else if (z <= 1.8d-64) then
        tmp = t_3
    else if (z <= 2d-24) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double t_3 = x - (x * y);
	double tmp;
	if (z <= -7.2e+30) {
		tmp = t_1;
	} else if (z <= -8e-83) {
		tmp = t_3;
	} else if (z <= -7.6e-83) {
		tmp = t * -z;
	} else if (z <= -1.4e-217) {
		tmp = t_2;
	} else if (z <= -1.6e-307) {
		tmp = t_3;
	} else if (z <= 3.2e-187) {
		tmp = t_2;
	} else if (z <= 1.8e-64) {
		tmp = t_3;
	} else if (z <= 2e-24) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + (y * t)
	t_3 = x - (x * y)
	tmp = 0
	if z <= -7.2e+30:
		tmp = t_1
	elif z <= -8e-83:
		tmp = t_3
	elif z <= -7.6e-83:
		tmp = t * -z
	elif z <= -1.4e-217:
		tmp = t_2
	elif z <= -1.6e-307:
		tmp = t_3
	elif z <= 3.2e-187:
		tmp = t_2
	elif z <= 1.8e-64:
		tmp = t_3
	elif z <= 2e-24:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x + Float64(y * t))
	t_3 = Float64(x - Float64(x * y))
	tmp = 0.0
	if (z <= -7.2e+30)
		tmp = t_1;
	elseif (z <= -8e-83)
		tmp = t_3;
	elseif (z <= -7.6e-83)
		tmp = Float64(t * Float64(-z));
	elseif (z <= -1.4e-217)
		tmp = t_2;
	elseif (z <= -1.6e-307)
		tmp = t_3;
	elseif (z <= 3.2e-187)
		tmp = t_2;
	elseif (z <= 1.8e-64)
		tmp = t_3;
	elseif (z <= 2e-24)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x + (y * t);
	t_3 = x - (x * y);
	tmp = 0.0;
	if (z <= -7.2e+30)
		tmp = t_1;
	elseif (z <= -8e-83)
		tmp = t_3;
	elseif (z <= -7.6e-83)
		tmp = t * -z;
	elseif (z <= -1.4e-217)
		tmp = t_2;
	elseif (z <= -1.6e-307)
		tmp = t_3;
	elseif (z <= 3.2e-187)
		tmp = t_2;
	elseif (z <= 1.8e-64)
		tmp = t_3;
	elseif (z <= 2e-24)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+30], t$95$1, If[LessEqual[z, -8e-83], t$95$3, If[LessEqual[z, -7.6e-83], N[(t * (-z)), $MachinePrecision], If[LessEqual[z, -1.4e-217], t$95$2, If[LessEqual[z, -1.6e-307], t$95$3, If[LessEqual[z, 3.2e-187], t$95$2, If[LessEqual[z, 1.8e-64], t$95$3, If[LessEqual[z, 2e-24], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.2000000000000004e30 or 1.99999999999999985e-24 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. distribute-lft-neg-out 82.6%

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

      3. *-commutative 82.6%

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

   4. Simplified 82.6%

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

   5. Taylor expanded in z around 0 82.6%

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

      1. +-commutative 82.6%

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

      2. mul-1-neg 82.6%

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

      3. unsub-neg 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in z around inf 82.6%

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

   if -7.2000000000000004e30 < z < -8.0000000000000003e-83 or -1.4e-217 < z < -1.60000000000000005e-307 or 3.1999999999999998e-187 < z < 1.7999999999999999e-64

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. distribute-rgt-neg-out 75.3%

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

   4. Simplified 75.3%

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

   5. Taylor expanded in z around 0 73.9%

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

      1. +-commutative 73.9%

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

      2. mul-1-neg 73.9%

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

      3. unsub-neg 73.9%

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

      4. *-commutative 73.9%

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

   7. Simplified 73.9%

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

   if -8.0000000000000003e-83 < z < -7.59999999999999953e-83

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

   if -7.59999999999999953e-83 < z < -1.4e-217 or -1.60000000000000005e-307 < z < 3.1999999999999998e-187 or 1.7999999999999999e-64 < z < 1.99999999999999985e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 84.5%

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

   3. Taylor expanded in z around 0 80.3%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-83}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-83}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-217}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-307}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-187}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-64}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-24}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 3: 36.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-292}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-261}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -1500.0)
     t_1
     (if (<= y -1.04e-253)
       x
       (if (<= y 2.6e-292)
         (* x z)
         (if (<= y 6e-261) x (if (<= y 3e+47) (* t (- z)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -1500.0) {
		tmp = t_1;
	} else if (y <= -1.04e-253) {
		tmp = x;
	} else if (y <= 2.6e-292) {
		tmp = x * z;
	} else if (y <= 6e-261) {
		tmp = x;
	} else if (y <= 3e+47) {
		tmp = t * -z;
	} 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 <= (-1500.0d0)) then
        tmp = t_1
    else if (y <= (-1.04d-253)) then
        tmp = x
    else if (y <= 2.6d-292) then
        tmp = x * z
    else if (y <= 6d-261) then
        tmp = x
    else if (y <= 3d+47) then
        tmp = t * -z
    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 <= -1500.0) {
		tmp = t_1;
	} else if (y <= -1.04e-253) {
		tmp = x;
	} else if (y <= 2.6e-292) {
		tmp = x * z;
	} else if (y <= 6e-261) {
		tmp = x;
	} else if (y <= 3e+47) {
		tmp = t * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -1500.0:
		tmp = t_1
	elif y <= -1.04e-253:
		tmp = x
	elif y <= 2.6e-292:
		tmp = x * z
	elif y <= 6e-261:
		tmp = x
	elif y <= 3e+47:
		tmp = t * -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1500.0)
		tmp = t_1;
	elseif (y <= -1.04e-253)
		tmp = x;
	elseif (y <= 2.6e-292)
		tmp = Float64(x * z);
	elseif (y <= 6e-261)
		tmp = x;
	elseif (y <= 3e+47)
		tmp = Float64(t * Float64(-z));
	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 <= -1500.0)
		tmp = t_1;
	elseif (y <= -1.04e-253)
		tmp = x;
	elseif (y <= 2.6e-292)
		tmp = x * z;
	elseif (y <= 6e-261)
		tmp = x;
	elseif (y <= 3e+47)
		tmp = t * -z;
	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, -1500.0], t$95$1, If[LessEqual[y, -1.04e-253], x, If[LessEqual[y, 2.6e-292], N[(x * z), $MachinePrecision], If[LessEqual[y, 6e-261], x, If[LessEqual[y, 3e+47], N[(t * (-z)), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1500 or 3.0000000000000001e47 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-rgt-neg-out 60.4%

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

   4. Simplified 60.4%

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

   5. Taylor expanded in x around 0 60.4%

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

      1. *-commutative 60.4%

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

      2. mul-1-neg 60.4%

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

      3. unsub-neg 60.4%

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

   7. Simplified 60.4%

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

   8. Taylor expanded in y around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. distribute-rgt-neg-in 54.7%

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

   10. Simplified 54.7%

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

   if -1500 < y < -1.04e-253 or 2.60000000000000013e-292 < y < 6.0000000000000001e-261

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.5%

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

   3. Taylor expanded in x around inf 42.8%

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

   if -1.04e-253 < y < 2.60000000000000013e-292

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. distribute-rgt-neg-out 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in x around 0 70.0%

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

      1. *-commutative 70.0%

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

      2. mul-1-neg 70.0%

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

      3. unsub-neg 70.0%

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

   7. Simplified 70.0%

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

   8. Taylor expanded in z around inf 55.1%

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

   if 6.0000000000000001e-261 < y < 3.0000000000000001e47

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 72.7%

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

   3. Taylor expanded in y around 0 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in x around 0 41.7%

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

      1. associate-*r* 41.7%

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

      2. neg-mul-1 41.7%

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

   8. Simplified 41.7%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1500:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-292}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-261}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 4: 70.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + y \cdot t\\ \mathbf{if}\;z \leq -5 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* y t))))
   (if (<= z -5e-21)
     t_1
     (if (<= z 4.05e-143)
       t_2
       (if (<= z 4.7e-66) (* x (- y)) (if (<= z 3.15e-24) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -5e-21) {
		tmp = t_1;
	} else if (z <= 4.05e-143) {
		tmp = t_2;
	} else if (z <= 4.7e-66) {
		tmp = x * -y;
	} else if (z <= 3.15e-24) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = x + (y * t)
    if (z <= (-5d-21)) then
        tmp = t_1
    else if (z <= 4.05d-143) then
        tmp = t_2
    else if (z <= 4.7d-66) then
        tmp = x * -y
    else if (z <= 3.15d-24) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -5e-21) {
		tmp = t_1;
	} else if (z <= 4.05e-143) {
		tmp = t_2;
	} else if (z <= 4.7e-66) {
		tmp = x * -y;
	} else if (z <= 3.15e-24) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + (y * t)
	tmp = 0
	if z <= -5e-21:
		tmp = t_1
	elif z <= 4.05e-143:
		tmp = t_2
	elif z <= 4.7e-66:
		tmp = x * -y
	elif z <= 3.15e-24:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -5e-21)
		tmp = t_1;
	elseif (z <= 4.05e-143)
		tmp = t_2;
	elseif (z <= 4.7e-66)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 3.15e-24)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (z <= -5e-21)
		tmp = t_1;
	elseif (z <= 4.05e-143)
		tmp = t_2;
	elseif (z <= 4.7e-66)
		tmp = x * -y;
	elseif (z <= 3.15e-24)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-21], t$95$1, If[LessEqual[z, 4.05e-143], t$95$2, If[LessEqual[z, 4.7e-66], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 3.15e-24], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999973e-21 or 3.1499999999999999e-24 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. distribute-lft-neg-out 79.5%

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

      3. *-commutative 79.5%

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

   4. Simplified 79.5%

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

   5. Taylor expanded in z around 0 79.5%

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

      1. +-commutative 79.5%

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

      2. mul-1-neg 79.5%

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

      3. unsub-neg 79.5%

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

   7. Simplified 79.5%

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

   8. Taylor expanded in z around inf 79.4%

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

   if -4.99999999999999973e-21 < z < 4.0499999999999999e-143 or 4.6999999999999999e-66 < z < 3.1499999999999999e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.2%

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

   3. Taylor expanded in z around 0 72.1%

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

   if 4.0499999999999999e-143 < z < 4.6999999999999999e-66

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 65.8%

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

      1. mul-1-neg 65.8%

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

      2. distribute-rgt-neg-out 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in x around 0 65.8%

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

      1. *-commutative 65.8%

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

      2. mul-1-neg 65.8%

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

      3. unsub-neg 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in y around inf 58.3%

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

      1. mul-1-neg 58.3%

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

      2. distribute-rgt-neg-in 58.3%

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

   10. Simplified 58.3%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{-143}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-24}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 5: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -7.6e-83)
     t_1
     (if (<= z 4.6e-143) x (if (<= z 3.4e-82) (* x (- y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -7.6e-83) {
		tmp = t_1;
	} else if (z <= 4.6e-143) {
		tmp = x;
	} else if (z <= 3.4e-82) {
		tmp = x * -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-7.6d-83)) then
        tmp = t_1
    else if (z <= 4.6d-143) then
        tmp = x
    else if (z <= 3.4d-82) then
        tmp = x * -y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -7.6e-83) {
		tmp = t_1;
	} else if (z <= 4.6e-143) {
		tmp = x;
	} else if (z <= 3.4e-82) {
		tmp = x * -y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -7.6e-83:
		tmp = t_1
	elif z <= 4.6e-143:
		tmp = x
	elif z <= 3.4e-82:
		tmp = x * -y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -7.6e-83)
		tmp = t_1;
	elseif (z <= 4.6e-143)
		tmp = x;
	elseif (z <= 3.4e-82)
		tmp = Float64(x * Float64(-y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -7.6e-83)
		tmp = t_1;
	elseif (z <= 4.6e-143)
		tmp = x;
	elseif (z <= 3.4e-82)
		tmp = x * -y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.6e-83], t$95$1, If[LessEqual[z, 4.6e-143], x, If[LessEqual[z, 3.4e-82], N[(x * (-y)), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.59999999999999953e-83 or 3.39999999999999975e-82 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. distribute-lft-neg-out 72.9%

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

      3. *-commutative 72.9%

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

   4. Simplified 72.9%

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

   5. Taylor expanded in z around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in z around inf 71.8%

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

   if -7.59999999999999953e-83 < z < 4.60000000000000023e-143

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.6%

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

   3. Taylor expanded in x around inf 39.1%

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

   if 4.60000000000000023e-143 < z < 3.39999999999999975e-82

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 73.7%

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

      1. mul-1-neg 73.7%

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

      2. distribute-rgt-neg-out 73.7%

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

   4. Simplified 73.7%

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

   5. Taylor expanded in x around 0 73.7%

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

      1. *-commutative 73.7%

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

      2. mul-1-neg 73.7%

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

      3. unsub-neg 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in y around inf 64.8%

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

      1. mul-1-neg 64.8%

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

      2. distribute-rgt-neg-in 64.8%

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

   10. Simplified 64.8%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-83}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 6: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -380000 \lor \neg \left(t \leq 3100000000000\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(y - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -380000.0) (not (<= t 3100000000000.0)))
   (+ x (* (- y z) t))
   (* x (- 1.0 (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -380000.0) || !(t <= 3100000000000.0)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * (1.0 - (y - 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) :: tmp
    if ((t <= (-380000.0d0)) .or. (.not. (t <= 3100000000000.0d0))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x * (1.0d0 - (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -380000.0) || !(t <= 3100000000000.0)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * (1.0 - (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -380000.0) or not (t <= 3100000000000.0):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * (1.0 - (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -380000.0) || !(t <= 3100000000000.0))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -380000.0) || ~((t <= 3100000000000.0)))
		tmp = x + ((y - z) * t);
	else
		tmp = x * (1.0 - (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -380000.0], N[Not[LessEqual[t, 3100000000000.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8e5 or 3.1e12 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 87.1%

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

   if -3.8e5 < t < 3.1e12

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 82.7%

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

      1. mul-1-neg 82.7%

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

      2. distribute-rgt-neg-out 82.7%

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

   4. Simplified 82.7%

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

   5. Taylor expanded in x around 0 82.7%

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

      1. *-commutative 82.7%

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

      2. mul-1-neg 82.7%

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

      3. unsub-neg 82.7%

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

   7. Simplified 82.7%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -380000 \lor \neg \left(t \leq 3100000000000\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(y - z\right)\right)\\ \end{array} \]

Alternative 7: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+29} \lor \neg \left(z \leq 3.15 \cdot 10^{-24}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.1e+29) (not (<= z 3.15e-24)))
   (* z (- x t))
   (- x (* y (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.1e+29) || !(z <= 3.15e-24)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (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 ((z <= (-2.1d+29)) .or. (.not. (z <= 3.15d-24))) then
        tmp = z * (x - t)
    else
        tmp = x - (y * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.1e+29) || !(z <= 3.15e-24)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.1e+29) or not (z <= 3.15e-24):
		tmp = z * (x - t)
	else:
		tmp = x - (y * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.1e+29) || !(z <= 3.15e-24))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x - Float64(y * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.1e+29) || ~((z <= 3.15e-24)))
		tmp = z * (x - t);
	else
		tmp = x - (y * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.1e+29], N[Not[LessEqual[z, 3.15e-24]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1000000000000002e29 or 3.1499999999999999e-24 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. distribute-lft-neg-out 82.6%

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

      3. *-commutative 82.6%

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

   4. Simplified 82.6%

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

   5. Taylor expanded in z around 0 82.6%

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

      1. +-commutative 82.6%

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

      2. mul-1-neg 82.6%

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

      3. unsub-neg 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in z around inf 82.6%

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

   if -2.1000000000000002e29 < z < 3.1499999999999999e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 91.4%

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

      1. *-commutative 91.4%

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

   4. Simplified 91.4%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+29} \lor \neg \left(z \leq 3.15 \cdot 10^{-24}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \]

Alternative 8: 64.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+70}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(1 - \left(y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3e+70)
   (+ x (* y t))
   (if (<= t 1.05e+118) (* x (- 1.0 (- y z))) (- x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3e+70) {
		tmp = x + (y * t);
	} else if (t <= 1.05e+118) {
		tmp = x * (1.0 - (y - z));
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3d+70)) then
        tmp = x + (y * t)
    else if (t <= 1.05d+118) then
        tmp = x * (1.0d0 - (y - z))
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3e+70) {
		tmp = x + (y * t);
	} else if (t <= 1.05e+118) {
		tmp = x * (1.0 - (y - z));
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3e+70:
		tmp = x + (y * t)
	elif t <= 1.05e+118:
		tmp = x * (1.0 - (y - z))
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3e+70)
		tmp = Float64(x + Float64(y * t));
	elseif (t <= 1.05e+118)
		tmp = Float64(x * Float64(1.0 - Float64(y - z)));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3e+70)
		tmp = x + (y * t);
	elseif (t <= 1.05e+118)
		tmp = x * (1.0 - (y - z));
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3e+70], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+118], N[(x * N[(1.0 - N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.99999999999999976e70

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 89.7%

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

   3. Taylor expanded in z around 0 59.1%

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

   if -2.99999999999999976e70 < t < 1.05e118

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. distribute-rgt-neg-out 78.3%

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

   4. Simplified 78.3%

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

   5. Taylor expanded in x around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. mul-1-neg 78.3%

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

      3. unsub-neg 78.3%

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

   7. Simplified 78.3%

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

   if 1.05e118 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 96.3%

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

   3. Taylor expanded in y around 0 68.3%

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

      1. +-commutative 68.3%

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

      2. mul-1-neg 68.3%

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

      3. unsub-neg 68.3%

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

   5. Simplified 68.3%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+70}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(1 - \left(y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 9: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-24}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.55e+29) t_1 (if (<= z 3e-24) (- x (* y (- x t))) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.55e+29) {
		tmp = t_1;
	} else if (z <= 3e-24) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-1.55d+29)) then
        tmp = t_1
    else if (z <= 3d-24) then
        tmp = x - (y * (x - t))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.55e+29) {
		tmp = t_1;
	} else if (z <= 3e-24) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1.55e+29:
		tmp = t_1
	elif z <= 3e-24:
		tmp = x - (y * (x - t))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1.55e+29)
		tmp = t_1;
	elseif (z <= 3e-24)
		tmp = Float64(x - Float64(y * Float64(x - t)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1.55e+29)
		tmp = t_1;
	elseif (z <= 3e-24)
		tmp = x - (y * (x - t));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+29], t$95$1, If[LessEqual[z, 3e-24], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5499999999999999e29

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.0%

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

      1. mul-1-neg 88.0%

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

      2. distribute-lft-neg-out 88.0%

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

      3. *-commutative 88.0%

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

   4. Simplified 88.0%

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

   5. Taylor expanded in z around 0 88.0%

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

      1. +-commutative 88.0%

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

      2. mul-1-neg 88.0%

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

      3. unsub-neg 88.0%

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

   7. Simplified 88.0%

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

   8. Taylor expanded in z around inf 88.0%

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

   if -1.5499999999999999e29 < z < 2.99999999999999995e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 91.4%

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

      1. *-commutative 91.4%

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

   4. Simplified 91.4%

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

   if 2.99999999999999995e-24 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-lft-neg-out 76.3%

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

      3. *-commutative 76.3%

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

   4. Simplified 76.3%

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

   5. Taylor expanded in z around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. mul-1-neg 76.3%

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

      3. unsub-neg 76.3%

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

   7. Simplified 76.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-24}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 10: 34.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2450000:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -1500.0)
     t_1
     (if (<= y -6.6e-253) x (if (<= y 2450000.0) (* x z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -1500.0) {
		tmp = t_1;
	} else if (y <= -6.6e-253) {
		tmp = x;
	} else if (y <= 2450000.0) {
		tmp = x * z;
	} 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 <= (-1500.0d0)) then
        tmp = t_1
    else if (y <= (-6.6d-253)) then
        tmp = x
    else if (y <= 2450000.0d0) then
        tmp = x * z
    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 <= -1500.0) {
		tmp = t_1;
	} else if (y <= -6.6e-253) {
		tmp = x;
	} else if (y <= 2450000.0) {
		tmp = x * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -1500.0:
		tmp = t_1
	elif y <= -6.6e-253:
		tmp = x
	elif y <= 2450000.0:
		tmp = x * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1500.0)
		tmp = t_1;
	elseif (y <= -6.6e-253)
		tmp = x;
	elseif (y <= 2450000.0)
		tmp = Float64(x * z);
	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 <= -1500.0)
		tmp = t_1;
	elseif (y <= -6.6e-253)
		tmp = x;
	elseif (y <= 2450000.0)
		tmp = x * z;
	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, -1500.0], t$95$1, If[LessEqual[y, -6.6e-253], x, If[LessEqual[y, 2450000.0], N[(x * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1500 or 2.45e6 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-rgt-neg-out 56.4%

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

   4. Simplified 56.4%

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

   5. Taylor expanded in x around 0 56.4%

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

      1. *-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in y around inf 50.4%

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

      1. mul-1-neg 50.4%

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

      2. distribute-rgt-neg-in 50.4%

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

   10. Simplified 50.4%

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

   if -1500 < y < -6.6000000000000002e-253

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 75.2%

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

   3. Taylor expanded in x around inf 40.2%

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

   if -6.6000000000000002e-253 < y < 2.45e6

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 57.5%

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

      1. mul-1-neg 57.5%

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

      2. distribute-rgt-neg-out 57.5%

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

   4. Simplified 57.5%

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

   5. Taylor expanded in x around 0 57.5%

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

      1. *-commutative 57.5%

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

      2. mul-1-neg 57.5%

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

      3. unsub-neg 57.5%

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

   7. Simplified 57.5%

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

   8. Taylor expanded in z around inf 34.4%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1500:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-253}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2450000:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 11: 37.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.0) (* x z) (if (<= z 3.15e-24) x (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 3.15e-24) {
		tmp = x;
	} 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) :: tmp
    if (z <= (-1.0d0)) then
        tmp = x * z
    else if (z <= 3.15d-24) then
        tmp = x
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.0) {
		tmp = x * z;
	} else if (z <= 3.15e-24) {
		tmp = x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.0:
		tmp = x * z
	elif z <= 3.15e-24:
		tmp = x
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(x * z);
	elseif (z <= 3.15e-24)
		tmp = x;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = x * z;
	elseif (z <= 3.15e-24)
		tmp = x;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 3.15e-24], x, N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 3.1499999999999999e-24 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 57.7%

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

      1. mul-1-neg 57.7%

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

      2. distribute-rgt-neg-out 57.7%

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

   4. Simplified 57.7%

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

   5. Taylor expanded in x around 0 57.7%

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

      1. *-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. unsub-neg 57.7%

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

   7. Simplified 57.7%

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

   8. Taylor expanded in z around inf 45.0%

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

   if -1 < z < 3.1499999999999999e-24

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 72.7%

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

   3. Taylor expanded in x around inf 31.2%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-24}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 12: 18.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in t around inf 60.2%

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

3. Taylor expanded in x around inf 17.4%

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

4. Final simplification 17.4%

   \[\leadsto x \]

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 2023229 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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