Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.4s

Alternatives: 10

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

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

FPCore

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

C

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

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) * (x - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

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%

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

      1. +-commutative 83.3%

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

      2. mul-1-neg 83.3%

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

      3. unsub-neg 83.3%

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

   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%

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

   5. Taylor expanded in t around inf 79.7%

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

   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%

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

   5. Taylor expanded in t around 0 75.2%

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

      1. associate-*r* 75.2%

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

      2. neg-mul-1 75.2%

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

   7. Simplified 75.2%

      \[\leadsto x + \color{blue}{\left(-y\right) \cdot x} \]
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: 37.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+72}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+108} \lor \neg \left(z \leq 1.65 \cdot 10^{+184}\right) \land z \leq 4.4 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -1.12e+72)
     (* x z)
     (if (<= z -2.6e-16)
       t_1
       (if (<= z 7.5)
         x
         (if (or (<= z 2.2e+108) (and (not (<= z 1.65e+184)) (<= z 4.4e+229)))
           t_1
           (* x z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1.12e+72) {
		tmp = x * z;
	} else if (z <= -2.6e-16) {
		tmp = t_1;
	} else if (z <= 7.5) {
		tmp = x;
	} else if ((z <= 2.2e+108) || (!(z <= 1.65e+184) && (z <= 4.4e+229))) {
		tmp = t_1;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-1.12d+72)) then
        tmp = x * z
    else if (z <= (-2.6d-16)) then
        tmp = t_1
    else if (z <= 7.5d0) then
        tmp = x
    else if ((z <= 2.2d+108) .or. (.not. (z <= 1.65d+184)) .and. (z <= 4.4d+229)) then
        tmp = t_1
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -1.12e+72) {
		tmp = x * z;
	} else if (z <= -2.6e-16) {
		tmp = t_1;
	} else if (z <= 7.5) {
		tmp = x;
	} else if ((z <= 2.2e+108) || (!(z <= 1.65e+184) && (z <= 4.4e+229))) {
		tmp = t_1;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -1.12e+72:
		tmp = x * z
	elif z <= -2.6e-16:
		tmp = t_1
	elif z <= 7.5:
		tmp = x
	elif (z <= 2.2e+108) or (not (z <= 1.65e+184) and (z <= 4.4e+229)):
		tmp = t_1
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -1.12e+72)
		tmp = Float64(x * z);
	elseif (z <= -2.6e-16)
		tmp = t_1;
	elseif (z <= 7.5)
		tmp = x;
	elseif ((z <= 2.2e+108) || (!(z <= 1.65e+184) && (z <= 4.4e+229)))
		tmp = t_1;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -1.12e+72)
		tmp = x * z;
	elseif (z <= -2.6e-16)
		tmp = t_1;
	elseif (z <= 7.5)
		tmp = x;
	elseif ((z <= 2.2e+108) || (~((z <= 1.65e+184)) && (z <= 4.4e+229)))
		tmp = t_1;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -1.12e+72], N[(x * z), $MachinePrecision], If[LessEqual[z, -2.6e-16], t$95$1, If[LessEqual[z, 7.5], x, If[Or[LessEqual[z, 2.2e+108], And[N[Not[LessEqual[z, 1.65e+184]], $MachinePrecision], LessEqual[z, 4.4e+229]]], t$95$1, N[(x * z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.12000000000000001e72 or 2.2000000000000001e108 < z < 1.6499999999999999e184 or 4.40000000000000007e229 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.0%

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

      1. mul-1-neg 89.0%

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

      2. distribute-lft-neg-out 89.0%

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

      3. *-commutative 89.0%

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

   4. Simplified 89.0%

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

   5. Taylor expanded in t around 0 60.6%

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

   6. Taylor expanded in z around inf 60.6%

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

   if -1.12000000000000001e72 < z < -2.5999999999999998e-16 or 7.5 < z < 2.2000000000000001e108 or 1.6499999999999999e184 < z < 4.40000000000000007e229

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. distribute-lft-neg-out 71.2%

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

      3. *-commutative 71.2%

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

   4. Simplified 71.2%

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

   5. Taylor expanded in z around 0 71.2%

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

      1. +-commutative 71.2%

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

      2. mul-1-neg 71.2%

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

      3. unsub-neg 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in x around 0 54.0%

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

      1. mul-1-neg 54.0%

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

      2. distribute-rgt-neg-in 54.0%

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

   10. Simplified 54.0%

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

   if -2.5999999999999998e-16 < z < 7.5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 44.4%

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

      1. mul-1-neg 44.4%

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

      2. distribute-lft-neg-out 44.4%

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

      3. *-commutative 44.4%

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

   4. Simplified 44.4%

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

   5. Taylor expanded in z around 0 36.2%

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

4. Final simplification 48.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+72}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 7.5:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+108} \lor \neg \left(z \leq 1.65 \cdot 10^{+184}\right) \land z \leq 4.4 \cdot 10^{+229}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 4: 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%

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

      1. +-commutative 86.5%

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

      2. mul-1-neg 86.5%

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

      3. unsub-neg 86.5%

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

   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%

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

   5. Taylor expanded in t around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

   7. Simplified 100.0%

      \[\leadsto x + \color{blue}{\left(-y\right) \cdot x} \]
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 5: 84.1% accurate, 0.8× speedup

Math

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

FPCore

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

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 * (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 <= (-0.115d0)) .or. (.not. (z <= 1.45d+29))) 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 <= -0.115) || !(z <= 1.45e+29)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (x - t));
	}
	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 * (x - t))
	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(x - t)));
	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 * (x - t));
	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[(x - t), $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%

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

      1. +-commutative 85.5%

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

      2. mul-1-neg 85.5%

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

      3. unsub-neg 85.5%

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

   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%

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

Alternative 6: 84.3% accurate, 0.8× speedup

Math

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

FPCore

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

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 * (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 <= (-0.105d0)) .or. (.not. (z <= 1.8d+29))) then
        tmp = x + (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 <= -0.105) || !(z <= 1.8e+29)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x - (y * (x - t));
	}
	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 * (x - t))
	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(x - t)));
	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 * (x - t));
	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[(x - t), $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%

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

      1. +-commutative 85.5%

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

      2. mul-1-neg 85.5%

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

      3. unsub-neg 85.5%

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

   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%

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

Alternative 7: 55.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-12} \lor \neg \left(z \leq 3.8 \cdot 10^{-6}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.3e-12) (not (<= z 3.8e-6))) (* z (- x t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.3e-12) || !(z <= 3.8e-6)) {
		tmp = z * (x - t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.3d-12)) .or. (.not. (z <= 3.8d-6))) then
        tmp = z * (x - t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.3e-12) || !(z <= 3.8e-6)) {
		tmp = z * (x - t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.3e-12) or not (z <= 3.8e-6):
		tmp = z * (x - t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.3e-12) || !(z <= 3.8e-6))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.3e-12) || ~((z <= 3.8e-6)))
		tmp = z * (x - t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.3e-12], N[Not[LessEqual[z, 3.8e-6]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.29999999999999991e-12 or 3.8e-6 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. distribute-lft-neg-out 80.5%

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

      3. *-commutative 80.5%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in z around 0 80.5%

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

      1. +-commutative 80.5%

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

      2. mul-1-neg 80.5%

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

      3. unsub-neg 80.5%

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

   7. Simplified 80.5%

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

   8. Taylor expanded in z around inf 80.5%

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

   if -1.29999999999999991e-12 < z < 3.8e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 45.5%

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

      1. mul-1-neg 45.5%

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

      2. distribute-lft-neg-out 45.5%

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

      3. *-commutative 45.5%

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

   4. Simplified 45.5%

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

   5. Taylor expanded in z around 0 37.0%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-12} \lor \neg \left(z \leq 3.8 \cdot 10^{-6}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 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%

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

      1. +-commutative 83.3%

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

      2. mul-1-neg 83.3%

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

      3. unsub-neg 83.3%

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

   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%

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

   5. Taylor expanded in t around inf 70.0%

      \[\leadsto x + \color{blue}{y \cdot t} \]
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 9: 36.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1550000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 0.019:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1550000000.0) (* x z) (if (<= z 0.019) x (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1550000000.0) {
		tmp = x * z;
	} else if (z <= 0.019) {
		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 <= (-1550000000.0d0)) then
        tmp = x * z
    else if (z <= 0.019d0) 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 <= -1550000000.0) {
		tmp = x * z;
	} else if (z <= 0.019) {
		tmp = x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1550000000.0:
		tmp = x * z
	elif z <= 0.019:
		tmp = x
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1550000000.0)
		tmp = Float64(x * z);
	elseif (z <= 0.019)
		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 <= -1550000000.0)
		tmp = x * z;
	elseif (z <= 0.019)
		tmp = x;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1550000000.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 0.019], x, N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e9 or 0.0189999999999999995 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 82.4%

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

      1. mul-1-neg 82.4%

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

      2. distribute-lft-neg-out 82.4%

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

      3. *-commutative 82.4%

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

   4. Simplified 82.4%

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

   5. Taylor expanded in t around 0 46.1%

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

   6. Taylor expanded in z around inf 46.0%

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

   if -1.55e9 < z < 0.0189999999999999995

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 45.4%

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

      1. mul-1-neg 45.4%

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

      2. distribute-lft-neg-out 45.4%

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

      3. *-commutative 45.4%

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

   4. Simplified 45.4%

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

   5. Taylor expanded in z around 0 35.1%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1550000000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 0.019:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 10: 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))))