Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.3s

Alternatives: 10

Speedup: 1.0×

• 34.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 56.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -8 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-193}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-19}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- t))))
   (if (<= y -8e-50)
     t_1
     (if (<= y 2.5e-193)
       t_2
       (if (<= y 3.5e-83) x (if (<= y 2.05e-19) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * -t;
	double tmp;
	if (y <= -8e-50) {
		tmp = t_1;
	} else if (y <= 2.5e-193) {
		tmp = t_2;
	} else if (y <= 3.5e-83) {
		tmp = x;
	} else if (y <= 2.05e-19) {
		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 = y * (t - x)
    t_2 = z * -t
    if (y <= (-8d-50)) then
        tmp = t_1
    else if (y <= 2.5d-193) then
        tmp = t_2
    else if (y <= 3.5d-83) then
        tmp = x
    else if (y <= 2.05d-19) 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 = y * (t - x);
	double t_2 = z * -t;
	double tmp;
	if (y <= -8e-50) {
		tmp = t_1;
	} else if (y <= 2.5e-193) {
		tmp = t_2;
	} else if (y <= 3.5e-83) {
		tmp = x;
	} else if (y <= 2.05e-19) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * -t
	tmp = 0
	if y <= -8e-50:
		tmp = t_1
	elif y <= 2.5e-193:
		tmp = t_2
	elif y <= 3.5e-83:
		tmp = x
	elif y <= 2.05e-19:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -8e-50)
		tmp = t_1;
	elseif (y <= 2.5e-193)
		tmp = t_2;
	elseif (y <= 3.5e-83)
		tmp = x;
	elseif (y <= 2.05e-19)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * -t;
	tmp = 0.0;
	if (y <= -8e-50)
		tmp = t_1;
	elseif (y <= 2.5e-193)
		tmp = t_2;
	elseif (y <= 3.5e-83)
		tmp = x;
	elseif (y <= 2.05e-19)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -8e-50], t$95$1, If[LessEqual[y, 2.5e-193], t$95$2, If[LessEqual[y, 3.5e-83], x, If[LessEqual[y, 2.05e-19], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000006e-50 or 2.04999999999999993e-19 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 75.3%

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

      1. *-commutative 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in y around inf 71.6%

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

   if -8.00000000000000006e-50 < y < 2.5000000000000002e-193 or 3.5000000000000003e-83 < y < 2.04999999999999993e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.9%

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

      1. mul-1-neg 95.9%

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

      2. unsub-neg 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in x around 0 42.3%

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

      1. mul-1-neg 42.3%

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

      2. distribute-rgt-neg-in 42.3%

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

   8. Simplified 42.3%

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

   if 2.5000000000000002e-193 < y < 3.5000000000000003e-83

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 86.9%

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

   4. Taylor expanded in x around inf 62.1%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-193}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -2.25e+23)
     t_1
     (if (<= z -6.2e-65)
       (* y (- t x))
       (if (<= z 2.7e+21) (+ x (* 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 <= -2.25e+23) {
		tmp = t_1;
	} else if (z <= -6.2e-65) {
		tmp = y * (t - x);
	} else if (z <= 2.7e+21) {
		tmp = x + (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 <= (-2.25d+23)) then
        tmp = t_1
    else if (z <= (-6.2d-65)) then
        tmp = y * (t - x)
    else if (z <= 2.7d+21) then
        tmp = x + (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 <= -2.25e+23) {
		tmp = t_1;
	} else if (z <= -6.2e-65) {
		tmp = y * (t - x);
	} else if (z <= 2.7e+21) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -2.25e+23:
		tmp = t_1
	elif z <= -6.2e-65:
		tmp = y * (t - x)
	elif z <= 2.7e+21:
		tmp = x + (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 <= -2.25e+23)
		tmp = t_1;
	elseif (z <= -6.2e-65)
		tmp = Float64(y * Float64(t - x));
	elseif (z <= 2.7e+21)
		tmp = Float64(x + 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 <= -2.25e+23)
		tmp = t_1;
	elseif (z <= -6.2e-65)
		tmp = y * (t - x);
	elseif (z <= 2.7e+21)
		tmp = x + (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, -2.25e+23], t$95$1, If[LessEqual[z, -6.2e-65], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+21], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2499999999999999e23 or 2.7e21 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. unsub-neg 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in x around 0 82.5%

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

      1. neg-mul-1 82.5%

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

      2. *-commutative 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in z around inf 85.6%

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

   if -2.2499999999999999e23 < z < -6.20000000000000032e-65

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 87.7%

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

      1. *-commutative 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in y around inf 81.5%

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

   if -6.20000000000000032e-65 < z < 2.7e21

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 78.3%

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

   4. Taylor expanded in y around inf 73.1%

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

Alternative 4: 37.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -3.35 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-143}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -3.35e+19)
     t_1
     (if (<= z -1.65e-143) (* y (- x)) (if (<= z 8.5e-20) x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -3.35e+19) {
		tmp = t_1;
	} else if (z <= -1.65e-143) {
		tmp = y * -x;
	} else if (z <= 8.5e-20) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-3.35d+19)) then
        tmp = t_1
    else if (z <= (-1.65d-143)) then
        tmp = y * -x
    else if (z <= 8.5d-20) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -3.35e+19) {
		tmp = t_1;
	} else if (z <= -1.65e-143) {
		tmp = y * -x;
	} else if (z <= 8.5e-20) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -3.35e+19:
		tmp = t_1
	elif z <= -1.65e-143:
		tmp = y * -x
	elif z <= 8.5e-20:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -3.35e+19)
		tmp = t_1;
	elseif (z <= -1.65e-143)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 8.5e-20)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -3.35e+19)
		tmp = t_1;
	elseif (z <= -1.65e-143)
		tmp = y * -x;
	elseif (z <= 8.5e-20)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -3.35e+19], t$95$1, If[LessEqual[z, -1.65e-143], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 8.5e-20], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.35e19 or 8.5000000000000005e-20 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.0%

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

      1. mul-1-neg 83.0%

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

      2. unsub-neg 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in x around 0 43.1%

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

      1. mul-1-neg 43.1%

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

      2. distribute-rgt-neg-in 43.1%

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

   8. Simplified 43.1%

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

   if -3.35e19 < z < -1.65e-143

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. distribute-rgt-neg-in 62.1%

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

      3. sub-neg 62.1%

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

      4. +-commutative 62.1%

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

      5. distribute-neg-in 62.1%

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

      6. remove-double-neg 62.1%

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

      7. sub-neg 62.1%

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

   5. Simplified 62.1%

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

   6. Taylor expanded in z around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. unsub-neg 62.1%

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

   8. Simplified 62.1%

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

   9. Taylor expanded in y around inf 41.8%

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

       1. mul-1-neg 41.8%

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

       2. distribute-rgt-neg-out 41.8%

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

   11. Simplified 41.8%

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

   if -1.65e-143 < z < 8.5000000000000005e-20

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 80.5%

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

   4. Taylor expanded in x around inf 41.1%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-143}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+21} \lor \neg \left(z \leq 7 \cdot 10^{+27}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.1e+21) (not (<= z 7e+27)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e+21) || !(z <= 7e+27)) {
		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 <= (-4.1d+21)) .or. (.not. (z <= 7d+27))) 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 <= -4.1e+21) || !(z <= 7e+27)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.1e+21) or not (z <= 7e+27):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.1e+21) || !(z <= 7e+27))
		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 <= -4.1e+21) || ~((z <= 7e+27)))
		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, -4.1e+21], N[Not[LessEqual[z, 7e+27]], $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 < -4.1e21 or 7.0000000000000004e27 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. unsub-neg 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in x around 0 82.5%

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

      1. neg-mul-1 82.5%

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

      2. *-commutative 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in z around inf 85.6%

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

   if -4.1e21 < z < 7.0000000000000004e27

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 92.6%

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

      1. *-commutative 92.6%

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

   5. Simplified 92.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+21} \lor \neg \left(z \leq 7 \cdot 10^{+27}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.2e+18)
   (* z (- x t))
   (if (<= z 1.4e+25) (+ x (* y (- t x))) (- (* z x) (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+18) {
		tmp = z * (x - t);
	} else if (z <= 1.4e+25) {
		tmp = x + (y * (t - x));
	} else {
		tmp = (z * x) - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.2d+18)) then
        tmp = z * (x - t)
    else if (z <= 1.4d+25) then
        tmp = x + (y * (t - x))
    else
        tmp = (z * x) - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+18) {
		tmp = z * (x - t);
	} else if (z <= 1.4e+25) {
		tmp = x + (y * (t - x));
	} else {
		tmp = (z * x) - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e+18:
		tmp = z * (x - t)
	elif z <= 1.4e+25:
		tmp = x + (y * (t - x))
	else:
		tmp = (z * x) - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.2e+18)
		tmp = Float64(z * Float64(x - t));
	elseif (z <= 1.4e+25)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(Float64(z * x) - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.2e+18)
		tmp = z * (x - t);
	elseif (z <= 1.4e+25)
		tmp = x + (y * (t - x));
	else
		tmp = (z * x) - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.2e+18], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+25], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in x around 0 75.7%

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

      1. neg-mul-1 75.7%

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

      2. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   9. Taylor expanded in z around inf 81.4%

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

   if -4.2e18 < z < 1.4000000000000001e25

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 92.6%

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

      1. *-commutative 92.6%

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

   5. Simplified 92.6%

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

   if 1.4000000000000001e25 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 91.0%

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

      1. mul-1-neg 91.0%

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

      2. unsub-neg 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in x around 0 91.0%

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

      1. neg-mul-1 91.0%

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

      2. *-commutative 91.0%

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

   8. Simplified 91.0%

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

   9. Taylor expanded in z around inf 91.0%

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

       1. *-commutative 91.0%

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

   11. Simplified 91.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x - z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+20} \lor \neg \left(z \leq 6400000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.2e+20) (not (<= z 6400000000000.0)))
   (* z (- x t))
   (* y (- t x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.2e+20) || !(z <= 6400000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = 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 <= (-1.2d+20)) .or. (.not. (z <= 6400000000000.0d0))) then
        tmp = z * (x - t)
    else
        tmp = 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 <= -1.2e+20) || !(z <= 6400000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = y * (t - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.2e+20) or not (z <= 6400000000000.0):
		tmp = z * (x - t)
	else:
		tmp = y * (t - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.2e+20) || !(z <= 6400000000000.0))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(y * Float64(t - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.2e+20) || ~((z <= 6400000000000.0)))
		tmp = z * (x - t);
	else
		tmp = y * (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.2e+20], N[Not[LessEqual[z, 6400000000000.0]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e20 or 6.4e12 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. unsub-neg 85.1%

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

   5. Simplified 85.1%

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

   6. Taylor expanded in x around 0 82.1%

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

      1. neg-mul-1 82.1%

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

      2. *-commutative 82.1%

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

   8. Simplified 82.1%

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

   9. Taylor expanded in z around inf 85.1%

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

   if -1.2e20 < z < 6.4e12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 93.2%

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

      1. *-commutative 93.2%

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

   5. Simplified 93.2%

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

   6. Taylor expanded in y around inf 59.8%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+20} \lor \neg \left(z \leq 6400000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 37.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-30} \lor \neg \left(z \leq 10^{-16}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.7e-30) (not (<= z 1e-16))) (* z (- t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.7e-30) || !(z <= 1e-16)) {
		tmp = z * -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 <= (-2.7d-30)) .or. (.not. (z <= 1d-16))) then
        tmp = z * -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 <= -2.7e-30) || !(z <= 1e-16)) {
		tmp = z * -t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.7e-30) or not (z <= 1e-16):
		tmp = z * -t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.7e-30) || !(z <= 1e-16))
		tmp = Float64(z * Float64(-t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.7e-30) || ~((z <= 1e-16)))
		tmp = z * -t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.7e-30], N[Not[LessEqual[z, 1e-16]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999987e-30 or 9.9999999999999998e-17 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in x around 0 41.5%

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

      1. mul-1-neg 41.5%

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

      2. distribute-rgt-neg-in 41.5%

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

   8. Simplified 41.5%

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

   if -2.69999999999999987e-30 < z < 9.9999999999999998e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 79.1%

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

   4. Taylor expanded in x around inf 39.5%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-30} \lor \neg \left(z \leq 10^{-16}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 10: 18.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 64.8%

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

4. Taylor expanded in x around inf 18.6%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Developer Target 1: 96.7% 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 2024139 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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