Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 11.3s

Alternatives: 11

Speedup: 1.0×

• 33.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 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: 71.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot y\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := x + y \cdot t\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-199}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-131}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6200000000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* x y))) (t_2 (* z (- x t))) (t_3 (+ x (* y t))))
   (if (<= z -1.55e-9)
     t_2
     (if (<= z -2.45e-199)
       t_3
       (if (<= z -1.5e-226)
         t_1
         (if (<= z 2.4e-131)
           t_3
           (if (<= z 9.5e-24) t_1 (if (<= z 6200000000.0) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (x * y);
	double t_2 = z * (x - t);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -1.55e-9) {
		tmp = t_2;
	} else if (z <= -2.45e-199) {
		tmp = t_3;
	} else if (z <= -1.5e-226) {
		tmp = t_1;
	} else if (z <= 2.4e-131) {
		tmp = t_3;
	} else if (z <= 9.5e-24) {
		tmp = t_1;
	} else if (z <= 6200000000.0) {
		tmp = t_3;
	} 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 * y)
    t_2 = z * (x - t)
    t_3 = x + (y * t)
    if (z <= (-1.55d-9)) then
        tmp = t_2
    else if (z <= (-2.45d-199)) then
        tmp = t_3
    else if (z <= (-1.5d-226)) then
        tmp = t_1
    else if (z <= 2.4d-131) then
        tmp = t_3
    else if (z <= 9.5d-24) then
        tmp = t_1
    else if (z <= 6200000000.0d0) then
        tmp = t_3
    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 * y);
	double t_2 = z * (x - t);
	double t_3 = x + (y * t);
	double tmp;
	if (z <= -1.55e-9) {
		tmp = t_2;
	} else if (z <= -2.45e-199) {
		tmp = t_3;
	} else if (z <= -1.5e-226) {
		tmp = t_1;
	} else if (z <= 2.4e-131) {
		tmp = t_3;
	} else if (z <= 9.5e-24) {
		tmp = t_1;
	} else if (z <= 6200000000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (x * y)
	t_2 = z * (x - t)
	t_3 = x + (y * t)
	tmp = 0
	if z <= -1.55e-9:
		tmp = t_2
	elif z <= -2.45e-199:
		tmp = t_3
	elif z <= -1.5e-226:
		tmp = t_1
	elif z <= 2.4e-131:
		tmp = t_3
	elif z <= 9.5e-24:
		tmp = t_1
	elif z <= 6200000000.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(x * y))
	t_2 = Float64(z * Float64(x - t))
	t_3 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -1.55e-9)
		tmp = t_2;
	elseif (z <= -2.45e-199)
		tmp = t_3;
	elseif (z <= -1.5e-226)
		tmp = t_1;
	elseif (z <= 2.4e-131)
		tmp = t_3;
	elseif (z <= 9.5e-24)
		tmp = t_1;
	elseif (z <= 6200000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (x * y);
	t_2 = z * (x - t);
	t_3 = x + (y * t);
	tmp = 0.0;
	if (z <= -1.55e-9)
		tmp = t_2;
	elseif (z <= -2.45e-199)
		tmp = t_3;
	elseif (z <= -1.5e-226)
		tmp = t_1;
	elseif (z <= 2.4e-131)
		tmp = t_3;
	elseif (z <= 9.5e-24)
		tmp = t_1;
	elseif (z <= 6200000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e-9], t$95$2, If[LessEqual[z, -2.45e-199], t$95$3, If[LessEqual[z, -1.5e-226], t$95$1, If[LessEqual[z, 2.4e-131], t$95$3, If[LessEqual[z, 9.5e-24], t$95$1, If[LessEqual[z, 6200000000.0], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000002e-9 or 6.2e9 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.3%

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

      1. mul-1-neg 83.3%

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

      2. distribute-lft-neg-out 83.3%

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

      3. *-commutative 83.3%

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

   4. Simplified 83.3%

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

   5. Taylor expanded in z around 0 83.3%

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

      1. associate-*r* 83.3%

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

      2. sub-neg 83.3%

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

      3. mul-1-neg 83.3%

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

      4. associate-*r* 83.3%

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

      5. mul-1-neg 83.3%

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

      6. unsub-neg 83.3%

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

      7. mul-1-neg 83.3%

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

      8. sub-neg 83.3%

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

   7. Simplified 83.3%

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

   8. Taylor expanded in z around inf 83.4%

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

   if -1.55000000000000002e-9 < z < -2.45e-199 or -1.49999999999999998e-226 < z < 2.4e-131 or 9.50000000000000029e-24 < z < 6.2e9

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 98.9%

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

   3. Applied egg-rr 98.9%

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

   4. Taylor expanded in z around 0 93.1%

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

   5. Taylor expanded in x around 0 79.7%

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

   if -2.45e-199 < z < -1.49999999999999998e-226 or 2.4e-131 < z < 9.50000000000000029e-24

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-lft-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around 0 79.0%

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

   5. Taylor expanded in x around inf 75.2%

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

      1. associate-*r* 75.2%

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

      2. mul-1-neg 75.2%

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

   7. Simplified 75.2%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-199}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-226}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-131}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-24}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 6200000000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 3: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-214}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* (- y z) t))))
   (if (<= z -4.4e+69)
     t_1
     (if (<= z -3.2e-199)
       t_2
       (if (<= z -8.5e-214) (- x (* x y)) (if (<= z 5e+25) 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 - z) * t);
	double tmp;
	if (z <= -4.4e+69) {
		tmp = t_1;
	} else if (z <= -3.2e-199) {
		tmp = t_2;
	} else if (z <= -8.5e-214) {
		tmp = x - (x * y);
	} else if (z <= 5e+25) {
		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 - z) * t)
    if (z <= (-4.4d+69)) then
        tmp = t_1
    else if (z <= (-3.2d-199)) then
        tmp = t_2
    else if (z <= (-8.5d-214)) then
        tmp = x - (x * y)
    else if (z <= 5d+25) 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 - z) * t);
	double tmp;
	if (z <= -4.4e+69) {
		tmp = t_1;
	} else if (z <= -3.2e-199) {
		tmp = t_2;
	} else if (z <= -8.5e-214) {
		tmp = x - (x * y);
	} else if (z <= 5e+25) {
		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 - z) * t)
	tmp = 0
	if z <= -4.4e+69:
		tmp = t_1
	elif z <= -3.2e-199:
		tmp = t_2
	elif z <= -8.5e-214:
		tmp = x - (x * y)
	elif z <= 5e+25:
		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(Float64(y - z) * t))
	tmp = 0.0
	if (z <= -4.4e+69)
		tmp = t_1;
	elseif (z <= -3.2e-199)
		tmp = t_2;
	elseif (z <= -8.5e-214)
		tmp = Float64(x - Float64(x * y));
	elseif (z <= 5e+25)
		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 - z) * t);
	tmp = 0.0;
	if (z <= -4.4e+69)
		tmp = t_1;
	elseif (z <= -3.2e-199)
		tmp = t_2;
	elseif (z <= -8.5e-214)
		tmp = x - (x * y);
	elseif (z <= 5e+25)
		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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+69], t$95$1, If[LessEqual[z, -3.2e-199], t$95$2, If[LessEqual[z, -8.5e-214], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+25], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4000000000000003e69 or 5.00000000000000024e25 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. distribute-lft-neg-out 86.5%

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

      3. *-commutative 86.5%

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

   4. Simplified 86.5%

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

   5. Taylor expanded in z around 0 86.5%

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

      1. associate-*r* 86.5%

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

      2. sub-neg 86.5%

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

      3. mul-1-neg 86.5%

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

      4. associate-*r* 86.5%

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

      5. mul-1-neg 86.5%

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

      6. unsub-neg 86.5%

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

      7. mul-1-neg 86.5%

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

      8. sub-neg 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in z around inf 86.5%

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

   if -4.4000000000000003e69 < z < -3.1999999999999999e-199 or -8.5000000000000006e-214 < z < 5.00000000000000024e25

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.6%

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

   if -3.1999999999999999e-199 < z < -8.5000000000000006e-214

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+69}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-199}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-214}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+25}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 4: 38.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+70}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-305}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+25}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.02e+70)
   (* x z)
   (if (<= z -2.5e-42)
     (* z (- t))
     (if (<= z 3.3e-305)
       (* y t)
       (if (<= z 8.5e-38) x (if (<= z 1.75e+25) (* y t) (* x z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.02e+70) {
		tmp = x * z;
	} else if (z <= -2.5e-42) {
		tmp = z * -t;
	} else if (z <= 3.3e-305) {
		tmp = y * t;
	} else if (z <= 8.5e-38) {
		tmp = x;
	} else if (z <= 1.75e+25) {
		tmp = y * t;
	} 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 <= (-1.02d+70)) then
        tmp = x * z
    else if (z <= (-2.5d-42)) then
        tmp = z * -t
    else if (z <= 3.3d-305) then
        tmp = y * t
    else if (z <= 8.5d-38) then
        tmp = x
    else if (z <= 1.75d+25) then
        tmp = y * t
    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 <= -1.02e+70) {
		tmp = x * z;
	} else if (z <= -2.5e-42) {
		tmp = z * -t;
	} else if (z <= 3.3e-305) {
		tmp = y * t;
	} else if (z <= 8.5e-38) {
		tmp = x;
	} else if (z <= 1.75e+25) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.02e+70:
		tmp = x * z
	elif z <= -2.5e-42:
		tmp = z * -t
	elif z <= 3.3e-305:
		tmp = y * t
	elif z <= 8.5e-38:
		tmp = x
	elif z <= 1.75e+25:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.02e+70)
		tmp = Float64(x * z);
	elseif (z <= -2.5e-42)
		tmp = Float64(z * Float64(-t));
	elseif (z <= 3.3e-305)
		tmp = Float64(y * t);
	elseif (z <= 8.5e-38)
		tmp = x;
	elseif (z <= 1.75e+25)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.02e+70)
		tmp = x * z;
	elseif (z <= -2.5e-42)
		tmp = z * -t;
	elseif (z <= 3.3e-305)
		tmp = y * t;
	elseif (z <= 8.5e-38)
		tmp = x;
	elseif (z <= 1.75e+25)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.02e+70], N[(x * z), $MachinePrecision], If[LessEqual[z, -2.5e-42], N[(z * (-t)), $MachinePrecision], If[LessEqual[z, 3.3e-305], N[(y * t), $MachinePrecision], If[LessEqual[z, 8.5e-38], x, If[LessEqual[z, 1.75e+25], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.02e70 or 1.75e25 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. distribute-lft-neg-out 86.5%

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

      3. *-commutative 86.5%

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

   4. Simplified 86.5%

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

   5. Taylor expanded in t around 0 52.1%

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

   6. Taylor expanded in z around inf 52.1%

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

      1. *-commutative 52.1%

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

   8. Simplified 52.1%

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

   if -1.02e70 < z < -2.50000000000000001e-42

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. distribute-lft-neg-out 68.8%

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

      3. *-commutative 68.8%

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

   4. Simplified 68.8%

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

   5. Taylor expanded in z around 0 68.8%

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

      1. associate-*r* 68.8%

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

      2. sub-neg 68.8%

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

      3. mul-1-neg 68.8%

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

      4. associate-*r* 68.8%

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

      5. mul-1-neg 68.8%

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

      6. unsub-neg 68.8%

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

      7. mul-1-neg 68.8%

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

      8. sub-neg 68.8%

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

   7. Simplified 68.8%

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

   8. Taylor expanded in x around 0 50.0%

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

      1. associate-*r* 50.0%

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

      2. mul-1-neg 50.0%

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

   10. Simplified 50.0%

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

   if -2.50000000000000001e-42 < z < 3.29999999999999982e-305 or 8.50000000000000046e-38 < z < 1.75e25

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 98.6%

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

   3. Applied egg-rr 98.6%

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

   4. Taylor expanded in z around 0 88.5%

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

   5. Taylor expanded in x around 0 71.5%

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

   6. Taylor expanded in x around 0 44.8%

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

   if 3.29999999999999982e-305 < z < 8.50000000000000046e-38

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. distribute-lft-neg-out 51.0%

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

      3. *-commutative 51.0%

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

   4. Simplified 51.0%

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

   5. Taylor expanded in z around 0 41.7%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+70}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-305}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+25}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 5: 55.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-301}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6100000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -2.5e-48)
     t_1
     (if (<= z 1.52e-301)
       (* y t)
       (if (<= z 2.7e-39) x (if (<= z 6100000000.0) (* y t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -2.5e-48) {
		tmp = t_1;
	} else if (z <= 1.52e-301) {
		tmp = y * t;
	} else if (z <= 2.7e-39) {
		tmp = x;
	} else if (z <= 6100000000.0) {
		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 = z * (x - t)
    if (z <= (-2.5d-48)) then
        tmp = t_1
    else if (z <= 1.52d-301) then
        tmp = y * t
    else if (z <= 2.7d-39) then
        tmp = x
    else if (z <= 6100000000.0d0) 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 = z * (x - t);
	double tmp;
	if (z <= -2.5e-48) {
		tmp = t_1;
	} else if (z <= 1.52e-301) {
		tmp = y * t;
	} else if (z <= 2.7e-39) {
		tmp = x;
	} else if (z <= 6100000000.0) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -2.5e-48:
		tmp = t_1
	elif z <= 1.52e-301:
		tmp = y * t
	elif z <= 2.7e-39:
		tmp = x
	elif z <= 6100000000.0:
		tmp = y * t
	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 <= -2.5e-48)
		tmp = t_1;
	elseif (z <= 1.52e-301)
		tmp = Float64(y * t);
	elseif (z <= 2.7e-39)
		tmp = x;
	elseif (z <= 6100000000.0)
		tmp = Float64(y * t);
	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 <= -2.5e-48)
		tmp = t_1;
	elseif (z <= 1.52e-301)
		tmp = y * t;
	elseif (z <= 2.7e-39)
		tmp = x;
	elseif (z <= 6100000000.0)
		tmp = y * t;
	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, -2.5e-48], t$95$1, If[LessEqual[z, 1.52e-301], N[(y * t), $MachinePrecision], If[LessEqual[z, 2.7e-39], x, If[LessEqual[z, 6100000000.0], N[(y * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4999999999999999e-48 or 6.1e9 < 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%

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

      1. associate-*r* 82.6%

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

      2. sub-neg 82.6%

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

      3. mul-1-neg 82.6%

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

      4. associate-*r* 82.6%

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

      5. mul-1-neg 82.6%

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

      6. unsub-neg 82.6%

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

      7. mul-1-neg 82.6%

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

      8. sub-neg 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in z around inf 80.7%

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

   if -2.4999999999999999e-48 < z < 1.52e-301 or 2.7000000000000001e-39 < z < 6.1e9

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 98.6%

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

   3. Applied egg-rr 98.6%

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

   4. Taylor expanded in z around 0 90.7%

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

   5. Taylor expanded in x around 0 73.0%

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

   6. Taylor expanded in x around 0 45.2%

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

   if 1.52e-301 < z < 2.7000000000000001e-39

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. distribute-lft-neg-out 51.0%

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

      3. *-commutative 51.0%

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

   4. Simplified 51.0%

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

   5. Taylor expanded in z around 0 41.7%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-48}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-301}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6100000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 6: 37.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+71}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-302}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+25}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.22e+71)
   (* x z)
   (if (<= z 3.8e-302)
     (* y t)
     (if (<= z 8.2e-36) x (if (<= z 1.75e+25) (* y t) (* x z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.22e+71) {
		tmp = x * z;
	} else if (z <= 3.8e-302) {
		tmp = y * t;
	} else if (z <= 8.2e-36) {
		tmp = x;
	} else if (z <= 1.75e+25) {
		tmp = y * t;
	} 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 <= (-1.22d+71)) then
        tmp = x * z
    else if (z <= 3.8d-302) then
        tmp = y * t
    else if (z <= 8.2d-36) then
        tmp = x
    else if (z <= 1.75d+25) then
        tmp = y * t
    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 <= -1.22e+71) {
		tmp = x * z;
	} else if (z <= 3.8e-302) {
		tmp = y * t;
	} else if (z <= 8.2e-36) {
		tmp = x;
	} else if (z <= 1.75e+25) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.22e+71:
		tmp = x * z
	elif z <= 3.8e-302:
		tmp = y * t
	elif z <= 8.2e-36:
		tmp = x
	elif z <= 1.75e+25:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.22e+71)
		tmp = Float64(x * z);
	elseif (z <= 3.8e-302)
		tmp = Float64(y * t);
	elseif (z <= 8.2e-36)
		tmp = x;
	elseif (z <= 1.75e+25)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.22e+71)
		tmp = x * z;
	elseif (z <= 3.8e-302)
		tmp = y * t;
	elseif (z <= 8.2e-36)
		tmp = x;
	elseif (z <= 1.75e+25)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.22e+71], N[(x * z), $MachinePrecision], If[LessEqual[z, 3.8e-302], N[(y * t), $MachinePrecision], If[LessEqual[z, 8.2e-36], x, If[LessEqual[z, 1.75e+25], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.22000000000000001e71 or 1.75e25 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. distribute-lft-neg-out 86.5%

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

      3. *-commutative 86.5%

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

   4. Simplified 86.5%

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

   5. Taylor expanded in t around 0 52.1%

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

   6. Taylor expanded in z around inf 52.1%

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

      1. *-commutative 52.1%

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

   8. Simplified 52.1%

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

   if -1.22000000000000001e71 < z < 3.8e-302 or 8.20000000000000025e-36 < z < 1.75e25

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 99.0%

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

   3. Applied egg-rr 99.0%

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

   4. Taylor expanded in z around 0 77.4%

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

   5. Taylor expanded in x around 0 59.2%

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

   6. Taylor expanded in x around 0 37.1%

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

   if 3.8e-302 < z < 8.20000000000000025e-36

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 51.0%

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

      1. mul-1-neg 51.0%

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

      2. distribute-lft-neg-out 51.0%

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

      3. *-commutative 51.0%

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

   4. Simplified 51.0%

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

   5. Taylor expanded in z around 0 41.7%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+71}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-302}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+25}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 7: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.115 \lor \neg \left(z \leq 1.45 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.115) (not (<= z 1.45e+29)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.115) || !(z <= 1.45e+29)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-0.115d0)) .or. (.not. (z <= 1.45d+29))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.115) || !(z <= 1.45e+29)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.115) or not (z <= 1.45e+29):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.115) || !(z <= 1.45e+29))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.115) || ~((z <= 1.45e+29)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.115], N[Not[LessEqual[z, 1.45e+29]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.115000000000000005 or 1.45e29 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.5%

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

      1. mul-1-neg 85.5%

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

      2. distribute-lft-neg-out 85.5%

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

      3. *-commutative 85.5%

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

   4. Simplified 85.5%

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

   5. Taylor expanded in z around 0 85.5%

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

      1. associate-*r* 85.5%

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

      2. sub-neg 85.5%

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

      3. mul-1-neg 85.5%

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

      4. associate-*r* 85.5%

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

      5. mul-1-neg 85.5%

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

      6. unsub-neg 85.5%

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

      7. mul-1-neg 85.5%

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

      8. sub-neg 85.5%

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

   7. Simplified 85.5%

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

   8. Taylor expanded in z around inf 85.5%

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

   if -0.115000000000000005 < z < 1.45e29

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 90.1%

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

      1. *-commutative 90.1%

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

   4. Simplified 90.1%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.115 \lor \neg \left(z \leq 1.45 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 8: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.105 \lor \neg \left(z \leq 1.8 \cdot 10^{+29}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.105) (not (<= z 1.8e+29)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.105) || !(z <= 1.8e+29)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-0.105d0)) .or. (.not. (z <= 1.8d+29))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.105) || !(z <= 1.8e+29)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.105) or not (z <= 1.8e+29):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.105) || !(z <= 1.8e+29))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.105) || ~((z <= 1.8e+29)))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.105], N[Not[LessEqual[z, 1.8e+29]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.104999999999999996 or 1.79999999999999988e29 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.5%

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

      1. mul-1-neg 85.5%

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

      2. distribute-lft-neg-out 85.5%

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

      3. *-commutative 85.5%

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

   4. Simplified 85.5%

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

   5. Taylor expanded in z around 0 85.5%

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

      1. associate-*r* 85.5%

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

      2. sub-neg 85.5%

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

      3. mul-1-neg 85.5%

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

      4. associate-*r* 85.5%

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

      5. mul-1-neg 85.5%

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

      6. unsub-neg 85.5%

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

      7. mul-1-neg 85.5%

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

      8. sub-neg 85.5%

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

   7. Simplified 85.5%

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

   if -0.104999999999999996 < z < 1.79999999999999988e29

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 90.1%

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

      1. *-commutative 90.1%

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

   4. Simplified 90.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.105 \lor \neg \left(z \leq 1.8 \cdot 10^{+29}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 9: 71.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-14} \lor \neg \left(z \leq 2550000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.5e-14) (not (<= z 2550000000000.0)))
   (* z (- x t))
   (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.5e-14) || !(z <= 2550000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (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 ((z <= (-4.5d-14)) .or. (.not. (z <= 2550000000000.0d0))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.5e-14) || !(z <= 2550000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.5e-14) or not (z <= 2550000000000.0):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.5e-14) || !(z <= 2550000000000.0))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.5e-14) || ~((z <= 2550000000000.0)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.5e-14], N[Not[LessEqual[z, 2550000000000.0]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999998e-14 or 2.55e12 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.3%

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

      1. mul-1-neg 83.3%

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

      2. distribute-lft-neg-out 83.3%

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

      3. *-commutative 83.3%

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

   4. Simplified 83.3%

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

   5. Taylor expanded in z around 0 83.3%

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

      1. associate-*r* 83.3%

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

      2. sub-neg 83.3%

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

      3. mul-1-neg 83.3%

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

      4. associate-*r* 83.3%

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

      5. mul-1-neg 83.3%

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

      6. unsub-neg 83.3%

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

      7. mul-1-neg 83.3%

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

      8. sub-neg 83.3%

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

   7. Simplified 83.3%

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

   8. Taylor expanded in z around inf 83.4%

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

   if -4.4999999999999998e-14 < z < 2.55e12

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 99.1%

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

   3. Applied egg-rr 99.1%

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

   4. Taylor expanded in z around 0 90.4%

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

   5. Taylor expanded in x around 0 70.0%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-14} \lor \neg \left(z \leq 2550000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 10: 36.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+45}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e+45) (* y t) (if (<= y 1.8e-28) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e+45) {
		tmp = y * t;
	} else if (y <= 1.8e-28) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.2d+45)) then
        tmp = y * t
    else if (y <= 1.8d-28) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e+45) {
		tmp = y * t;
	} else if (y <= 1.8e-28) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e+45:
		tmp = y * t
	elif y <= 1.8e-28:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e+45)
		tmp = Float64(y * t);
	elseif (y <= 1.8e-28)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.2e+45)
		tmp = y * t;
	elseif (y <= 1.8e-28)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e+45], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.8e-28], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.19999999999999995e45 or 1.7999999999999999e-28 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 94.9%

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

   3. Applied egg-rr 94.9%

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

   4. Taylor expanded in z around 0 73.1%

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

   5. Taylor expanded in x around 0 47.2%

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

   6. Taylor expanded in x around 0 46.6%

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

   if -1.19999999999999995e45 < y < 1.7999999999999999e-28

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.8%

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

      1. mul-1-neg 89.8%

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

      2. distribute-lft-neg-out 89.8%

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

      3. *-commutative 89.8%

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

   4. Simplified 89.8%

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

   5. Taylor expanded in z around 0 30.5%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+45}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 11: 17.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0 64.9%

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

   1. mul-1-neg 64.9%

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

   2. distribute-lft-neg-out 64.9%

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

   3. *-commutative 64.9%

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

4. Simplified 64.9%

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

5. Taylor expanded in z around 0 17.9%

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

6. Final simplification 17.9%

   \[\leadsto x \]

Developer target: 96.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(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))))