Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.9s

Alternatives: 11

Speedup: 1.0×

• 34.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 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: 79.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{if}\;x \leq -4.3 \cdot 10^{+196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+99}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ (- z y) 1.0))))
   (if (<= x -4.3e+196)
     t_1
     (if (<= x -2.8e-6)
       (+ x (* y (- t x)))
       (if (<= x 1.02e+99) (+ x (* (- y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) + 1.0);
	double tmp;
	if (x <= -4.3e+196) {
		tmp = t_1;
	} else if (x <= -2.8e-6) {
		tmp = x + (y * (t - x));
	} else if (x <= 1.02e+99) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - y) + 1.0d0)
    if (x <= (-4.3d+196)) then
        tmp = t_1
    else if (x <= (-2.8d-6)) then
        tmp = x + (y * (t - x))
    else if (x <= 1.02d+99) then
        tmp = x + ((y - z) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) + 1.0);
	double tmp;
	if (x <= -4.3e+196) {
		tmp = t_1;
	} else if (x <= -2.8e-6) {
		tmp = x + (y * (t - x));
	} else if (x <= 1.02e+99) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - y) + 1.0)
	tmp = 0
	if x <= -4.3e+196:
		tmp = t_1
	elif x <= -2.8e-6:
		tmp = x + (y * (t - x))
	elif x <= 1.02e+99:
		tmp = x + ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - y) + 1.0))
	tmp = 0.0
	if (x <= -4.3e+196)
		tmp = t_1;
	elseif (x <= -2.8e-6)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	elseif (x <= 1.02e+99)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - y) + 1.0);
	tmp = 0.0;
	if (x <= -4.3e+196)
		tmp = t_1;
	elseif (x <= -2.8e-6)
		tmp = x + (y * (t - x));
	elseif (x <= 1.02e+99)
		tmp = x + ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.3e+196], t$95$1, If[LessEqual[x, -2.8e-6], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e+99], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.30000000000000012e196 or 1.01999999999999998e99 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      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. Taylor expanded in t around 0 95.5%

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

      1. *-rgt-identity 95.5%

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

      2. mul-1-neg 95.5%

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

      3. distribute-rgt-neg-in 95.5%

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

      4. mul-1-neg 95.5%

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

      5. distribute-lft-in 95.6%

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

      6. mul-1-neg 95.6%

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

      7. unsub-neg 95.6%

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

   7. Simplified 95.6%

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

   if -4.30000000000000012e196 < x < -2.79999999999999987e-6

   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 84.4%

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

      1. *-commutative 84.4%

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

   5. Simplified 84.4%

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

   if -2.79999999999999987e-6 < x < 1.01999999999999998e99

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 83.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-6}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+99}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 190000000000:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+98}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ (- z y) 1.0))))
   (if (<= z -4.5e+96)
     t_1
     (if (<= z 190000000000.0)
       (+ x (* y (- t x)))
       (if (<= z 1.12e+98) t_1 (- x (* z t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) + 1.0);
	double tmp;
	if (z <= -4.5e+96) {
		tmp = t_1;
	} else if (z <= 190000000000.0) {
		tmp = x + (y * (t - x));
	} else if (z <= 1.12e+98) {
		tmp = t_1;
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - y) + 1.0d0)
    if (z <= (-4.5d+96)) then
        tmp = t_1
    else if (z <= 190000000000.0d0) then
        tmp = x + (y * (t - x))
    else if (z <= 1.12d+98) then
        tmp = t_1
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) + 1.0);
	double tmp;
	if (z <= -4.5e+96) {
		tmp = t_1;
	} else if (z <= 190000000000.0) {
		tmp = x + (y * (t - x));
	} else if (z <= 1.12e+98) {
		tmp = t_1;
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - y) + 1.0)
	tmp = 0
	if z <= -4.5e+96:
		tmp = t_1
	elif z <= 190000000000.0:
		tmp = x + (y * (t - x))
	elif z <= 1.12e+98:
		tmp = t_1
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - y) + 1.0))
	tmp = 0.0
	if (z <= -4.5e+96)
		tmp = t_1;
	elseif (z <= 190000000000.0)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	elseif (z <= 1.12e+98)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - y) + 1.0);
	tmp = 0.0;
	if (z <= -4.5e+96)
		tmp = t_1;
	elseif (z <= 190000000000.0)
		tmp = x + (y * (t - x));
	elseif (z <= 1.12e+98)
		tmp = t_1;
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+96], t$95$1, If[LessEqual[z, 190000000000.0], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e+98], t$95$1, N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.49999999999999957e96 or 1.9e11 < z < 1.12e98

   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. Taylor expanded in t around 0 56.1%

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

      1. *-rgt-identity 56.1%

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

      2. mul-1-neg 56.1%

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

      3. distribute-rgt-neg-in 56.1%

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

      4. mul-1-neg 56.1%

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

      5. distribute-lft-in 56.1%

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

      6. mul-1-neg 56.1%

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

      7. unsub-neg 56.1%

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

   7. Simplified 56.1%

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

   if -4.49999999999999957e96 < z < 1.9e11

   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 90.4%

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

      1. *-commutative 90.4%

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

   5. Simplified 90.4%

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

   if 1.12e98 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in t around inf 62.5%

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

   5. Taylor expanded in z around inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. *-commutative 56.9%

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

      3. distribute-rgt-neg-in 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in x around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. sub-neg 56.9%

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

   10. Simplified 56.9%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;z \leq 190000000000:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-205}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+97}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ (- z y) 1.0))))
   (if (<= x -8e-121)
     t_1
     (if (<= x -1.85e-205)
       (- x (* z t))
       (if (<= x 7.5e+97) (+ x (* y t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) + 1.0);
	double tmp;
	if (x <= -8e-121) {
		tmp = t_1;
	} else if (x <= -1.85e-205) {
		tmp = x - (z * t);
	} else if (x <= 7.5e+97) {
		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 = x * ((z - y) + 1.0d0)
    if (x <= (-8d-121)) then
        tmp = t_1
    else if (x <= (-1.85d-205)) then
        tmp = x - (z * t)
    else if (x <= 7.5d+97) 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 = x * ((z - y) + 1.0);
	double tmp;
	if (x <= -8e-121) {
		tmp = t_1;
	} else if (x <= -1.85e-205) {
		tmp = x - (z * t);
	} else if (x <= 7.5e+97) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - y) + 1.0)
	tmp = 0
	if x <= -8e-121:
		tmp = t_1
	elif x <= -1.85e-205:
		tmp = x - (z * t)
	elif x <= 7.5e+97:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - y) + 1.0))
	tmp = 0.0
	if (x <= -8e-121)
		tmp = t_1;
	elseif (x <= -1.85e-205)
		tmp = Float64(x - Float64(z * t));
	elseif (x <= 7.5e+97)
		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 = x * ((z - y) + 1.0);
	tmp = 0.0;
	if (x <= -8e-121)
		tmp = t_1;
	elseif (x <= -1.85e-205)
		tmp = x - (z * t);
	elseif (x <= 7.5e+97)
		tmp = x + (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e-121], t$95$1, If[LessEqual[x, -1.85e-205], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+97], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.9999999999999998e-121 or 7.5000000000000004e97 < x

   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. Taylor expanded in t around 0 79.4%

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

      1. *-rgt-identity 79.4%

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

      2. mul-1-neg 79.4%

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

      3. distribute-rgt-neg-in 79.4%

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

      4. mul-1-neg 79.4%

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

      5. distribute-lft-in 79.5%

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

      6. mul-1-neg 79.5%

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

      7. unsub-neg 79.5%

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

   7. Simplified 79.5%

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

   if -7.9999999999999998e-121 < x < -1.85e-205

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 94.3%

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

   4. Taylor expanded in t around inf 83.2%

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

   5. Taylor expanded in z around inf 65.7%

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

      1. mul-1-neg 65.7%

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

      2. *-commutative 65.7%

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

      3. distribute-rgt-neg-in 65.7%

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

   7. Simplified 65.7%

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

   8. Taylor expanded in x around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. sub-neg 65.7%

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

   10. Simplified 65.7%

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

   if -1.85e-205 < x < 7.5000000000000004e97

   1. Initial program 100.0%

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

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 64.9%

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

   6. Taylor expanded in x around 0 60.4%

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

      1. *-commutative 60.4%

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

   8. Simplified 60.4%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-205}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+97}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+96} \lor \neg \left(z \leq 300000\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.1e+96) (not (<= z 300000.0)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e+96) || !(z <= 300000.0)) {
		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 <= (-4.1d+96)) .or. (.not. (z <= 300000.0d0))) 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 <= -4.1e+96) || !(z <= 300000.0)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.1e+96) or not (z <= 300000.0):
		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 <= -4.1e+96) || !(z <= 300000.0))
		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 <= -4.1e+96) || ~((z <= 300000.0)))
		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, -4.1e+96], N[Not[LessEqual[z, 300000.0]], $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 < -4.09999999999999998e96 or 3e5 < z

   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. Taylor expanded in y around 0 84.7%

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

      1. mul-1-neg 84.7%

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

      2. unsub-neg 84.7%

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

   7. Simplified 84.7%

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

   if -4.09999999999999998e96 < z < 3e5

   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 91.0%

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

      1. *-commutative 91.0%

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

   5. Simplified 91.0%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+96} \lor \neg \left(z \leq 300000\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+94} \lor \neg \left(z \leq 6.2\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.62e+94) (not (<= z 6.2))) (* z (- t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.62e+94) || !(z <= 6.2)) {
		tmp = z * -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 <= (-1.62d+94)) .or. (.not. (z <= 6.2d0))) then
        tmp = z * -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 <= -1.62e+94) || !(z <= 6.2)) {
		tmp = z * -t;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.62e+94) or not (z <= 6.2):
		tmp = z * -t
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.62e+94) || !(z <= 6.2))
		tmp = Float64(z * Float64(-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 <= -1.62e+94) || ~((z <= 6.2)))
		tmp = z * -t;
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.62e+94], N[Not[LessEqual[z, 6.2]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.61999999999999997e94 or 6.20000000000000018 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in t around inf 54.1%

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

   5. Taylor expanded in z around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. *-commutative 46.2%

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

      3. distribute-rgt-neg-in 46.2%

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

   7. Simplified 46.2%

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

   8. Taylor expanded in x around 0 45.7%

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

      1. mul-1-neg 45.7%

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

      2. distribute-rgt-neg-in 45.7%

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

   10. Simplified 45.7%

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

   if -1.61999999999999997e94 < z < 6.20000000000000018

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing
   3. 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 97.2%

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

   4. Applied egg-rr 97.2%

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

   5. Taylor expanded in z around 0 88.7%

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

   6. Taylor expanded in x around 0 69.9%

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

      1. *-commutative 69.9%

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

   8. Simplified 69.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+94} \lor \neg \left(z \leq 6.2\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+96} \lor \neg \left(z \leq 5.3 \cdot 10^{+91}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.1e+96) (not (<= z 5.3e+91))) (* z (- t)) (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.1e+96) || !(z <= 5.3e+91)) {
		tmp = z * -t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.1d+96)) .or. (.not. (z <= 5.3d+91))) then
        tmp = z * -t
    else
        tmp = x * (1.0d0 - y)
    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+96) || !(z <= 5.3e+91)) {
		tmp = z * -t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.1e+96) or not (z <= 5.3e+91):
		tmp = z * -t
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.1e+96) || !(z <= 5.3e+91))
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.1e+96) || ~((z <= 5.3e+91)))
		tmp = z * -t;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.1e+96], N[Not[LessEqual[z, 5.3e+91]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.09999999999999998e96 or 5.29999999999999997e91 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in t around inf 58.2%

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

   5. Taylor expanded in z around inf 50.3%

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

      1. mul-1-neg 50.3%

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

      2. *-commutative 50.3%

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

      3. distribute-rgt-neg-in 50.3%

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

   7. Simplified 50.3%

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

   8. Taylor expanded in x around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. distribute-rgt-neg-in 50.3%

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

   10. Simplified 50.3%

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

   if -4.09999999999999998e96 < z < 5.29999999999999997e91

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing
   3. 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 97.6%

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

   4. Applied egg-rr 97.6%

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

   5. Taylor expanded in z around 0 82.0%

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

   6. Taylor expanded in x around inf 77.5%

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

      1. +-commutative 77.5%

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

      2. mul-1-neg 77.5%

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

      3. unsub-neg 77.5%

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

      4. associate-/l* 76.4%

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

   8. Simplified 76.4%

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

   9. Taylor expanded in x around inf 50.3%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+96} \lor \neg \left(z \leq 5.3 \cdot 10^{+91}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+94}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 650:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.12e+94)
   (* z (- t))
   (if (<= z 650.0) (+ x (* y t)) (- x (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.12e+94) {
		tmp = z * -t;
	} else if (z <= 650.0) {
		tmp = x + (y * t);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.12d+94)) then
        tmp = z * -t
    else if (z <= 650.0d0) then
        tmp = x + (y * t)
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.12e+94) {
		tmp = z * -t;
	} else if (z <= 650.0) {
		tmp = x + (y * t);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.12e+94:
		tmp = z * -t
	elif z <= 650.0:
		tmp = x + (y * t)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.12e+94)
		tmp = Float64(z * Float64(-t));
	elseif (z <= 650.0)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.12e+94)
		tmp = z * -t;
	elseif (z <= 650.0)
		tmp = x + (y * t);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.12e+94], N[(z * (-t)), $MachinePrecision], If[LessEqual[z, 650.0], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.11999999999999996e94

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in t around inf 53.9%

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

   5. Taylor expanded in z around inf 44.5%

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

      1. mul-1-neg 44.5%

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

      2. *-commutative 44.5%

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

      3. distribute-rgt-neg-in 44.5%

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

   7. Simplified 44.5%

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

   8. Taylor expanded in x around 0 45.0%

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

      1. mul-1-neg 45.0%

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

      2. distribute-rgt-neg-in 45.0%

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

   10. Simplified 45.0%

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

   if -1.11999999999999996e94 < z < 650

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing
   3. 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 97.2%

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

   4. Applied egg-rr 97.2%

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

   5. Taylor expanded in z around 0 88.7%

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

   6. Taylor expanded in x around 0 69.9%

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

      1. *-commutative 69.9%

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

   8. Simplified 69.9%

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

   if 650 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in t around inf 54.3%

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

   5. Taylor expanded in z around inf 47.6%

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

      1. mul-1-neg 47.6%

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

      2. *-commutative 47.6%

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

      3. distribute-rgt-neg-in 47.6%

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

   7. Simplified 47.6%

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

   8. Taylor expanded in x around 0 47.6%

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

      1. mul-1-neg 47.6%

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

      2. sub-neg 47.6%

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

   10. Simplified 47.6%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+94}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 650:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{-75} \lor \neg \left(z \leq 4.9 \cdot 10^{-64}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.36e-75) (not (<= z 4.9e-64))) (* z (- t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.36e-75) || !(z <= 4.9e-64)) {
		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 <= (-1.36d-75)) .or. (.not. (z <= 4.9d-64))) 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 <= -1.36e-75) || !(z <= 4.9e-64)) {
		tmp = z * -t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.36e-75) or not (z <= 4.9e-64):
		tmp = z * -t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.36e-75) || !(z <= 4.9e-64))
		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 <= -1.36e-75) || ~((z <= 4.9e-64)))
		tmp = z * -t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.36e-75], N[Not[LessEqual[z, 4.9e-64]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.36e-75 or 4.9000000000000002e-64 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in t around inf 59.8%

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

   5. Taylor expanded in z around inf 41.1%

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

      1. mul-1-neg 41.1%

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

      2. *-commutative 41.1%

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

      3. distribute-rgt-neg-in 41.1%

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

   7. Simplified 41.1%

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

   8. Taylor expanded in x around 0 38.2%

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

      1. mul-1-neg 38.2%

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

      2. distribute-rgt-neg-in 38.2%

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

   10. Simplified 38.2%

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

   if -1.36e-75 < z < 4.9000000000000002e-64

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing
   3. 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 97.1%

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

   4. Applied egg-rr 97.1%

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

   5. Taylor expanded in z around 0 95.5%

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

   6. Taylor expanded in x around inf 93.5%

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

      1. +-commutative 93.5%

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

      2. mul-1-neg 93.5%

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

      3. unsub-neg 93.5%

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

      4. associate-/l* 91.6%

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

   8. Simplified 91.6%

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

   9. Taylor expanded in y around 0 38.4%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{-75} \lor \neg \left(z \leq 4.9 \cdot 10^{-64}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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 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. Add Preprocessing
3. 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 97.6%

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

4. Applied egg-rr 97.6%

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

5. Taylor expanded in z around 0 60.1%

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

6. Taylor expanded in x around inf 57.9%

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

   1. +-commutative 57.9%

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

   2. mul-1-neg 57.9%

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

   3. unsub-neg 57.9%

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

   4. associate-/l* 56.8%

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

8. Simplified 56.8%

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

9. Taylor expanded in y around 0 18.8%

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

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 2024111 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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