Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.3s

Alternatives: 13

Speedup: 1.0×

• 34.6% 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-def 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. Final simplification 100.0%

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

Alternative 2: 37.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-252}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-113}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+117} \lor \neg \left(z \leq 2.4 \cdot 10^{+275}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))))
   (if (<= z -1.05e-17)
     t_1
     (if (<= z 3.6e-252)
       x
       (if (<= z 4.9e-113)
         (* y t)
         (if (<= z 3.8e-51)
           x
           (if (or (<= z 1.25e+117) (not (<= z 2.4e+275))) t_1 (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (z <= -1.05e-17) {
		tmp = t_1;
	} else if (z <= 3.6e-252) {
		tmp = x;
	} else if (z <= 4.9e-113) {
		tmp = y * t;
	} else if (z <= 3.8e-51) {
		tmp = x;
	} else if ((z <= 1.25e+117) || !(z <= 2.4e+275)) {
		tmp = t_1;
	} else {
		tmp = z * 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) :: t_1
    real(8) :: tmp
    t_1 = t * -z
    if (z <= (-1.05d-17)) then
        tmp = t_1
    else if (z <= 3.6d-252) then
        tmp = x
    else if (z <= 4.9d-113) then
        tmp = y * t
    else if (z <= 3.8d-51) then
        tmp = x
    else if ((z <= 1.25d+117) .or. (.not. (z <= 2.4d+275))) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (z <= -1.05e-17) {
		tmp = t_1;
	} else if (z <= 3.6e-252) {
		tmp = x;
	} else if (z <= 4.9e-113) {
		tmp = y * t;
	} else if (z <= 3.8e-51) {
		tmp = x;
	} else if ((z <= 1.25e+117) || !(z <= 2.4e+275)) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	tmp = 0
	if z <= -1.05e-17:
		tmp = t_1
	elif z <= 3.6e-252:
		tmp = x
	elif z <= 4.9e-113:
		tmp = y * t
	elif z <= 3.8e-51:
		tmp = x
	elif (z <= 1.25e+117) or not (z <= 2.4e+275):
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	tmp = 0.0
	if (z <= -1.05e-17)
		tmp = t_1;
	elseif (z <= 3.6e-252)
		tmp = x;
	elseif (z <= 4.9e-113)
		tmp = Float64(y * t);
	elseif (z <= 3.8e-51)
		tmp = x;
	elseif ((z <= 1.25e+117) || !(z <= 2.4e+275))
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	tmp = 0.0;
	if (z <= -1.05e-17)
		tmp = t_1;
	elseif (z <= 3.6e-252)
		tmp = x;
	elseif (z <= 4.9e-113)
		tmp = y * t;
	elseif (z <= 3.8e-51)
		tmp = x;
	elseif ((z <= 1.25e+117) || ~((z <= 2.4e+275)))
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, If[LessEqual[z, -1.05e-17], t$95$1, If[LessEqual[z, 3.6e-252], x, If[LessEqual[z, 4.9e-113], N[(y * t), $MachinePrecision], If[LessEqual[z, 3.8e-51], x, If[Or[LessEqual[z, 1.25e+117], N[Not[LessEqual[z, 2.4e+275]], $MachinePrecision]], t$95$1, N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.04999999999999996e-17 or 3.80000000000000003e-51 < z < 1.24999999999999996e117 or 2.39999999999999997e275 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 61.3%

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

   3. Taylor expanded in z around inf 50.7%

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

      1. mul-1-neg 50.7%

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

      2. distribute-rgt-neg-out 50.7%

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

   5. Simplified 50.7%

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

   if -1.04999999999999996e-17 < z < 3.60000000000000023e-252 or 4.9000000000000003e-113 < z < 3.80000000000000003e-51

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.0%

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

   3. Taylor expanded in x around inf 49.1%

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

   if 3.60000000000000023e-252 < z < 4.9000000000000003e-113

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 50.7%

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

   3. Taylor expanded in y around inf 34.3%

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

   if 1.24999999999999996e117 < z < 2.39999999999999997e275

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 54.3%

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

      1. *-commutative 54.3%

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

      2. mul-1-neg 54.3%

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

      3. unsub-neg 54.3%

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

      4. distribute-lft-out-- 54.3%

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

      5. *-rgt-identity 54.3%

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

   4. Simplified 54.3%

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

   5. Taylor expanded in z around inf 55.9%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-252}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-113}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+117} \lor \neg \left(z \leq 2.4 \cdot 10^{+275}\right):\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+65}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+89}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z (- x t)))))
   (if (<= z -4.6e-17)
     t_1
     (if (<= z 8e-53)
       (+ x (* y (- t x)))
       (if (<= z 1.2e+65)
         (+ x (* (- y z) t))
         (if (<= z 6.5e+89) (+ x (* x (- z y))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (x - t));
	double tmp;
	if (z <= -4.6e-17) {
		tmp = t_1;
	} else if (z <= 8e-53) {
		tmp = x + (y * (t - x));
	} else if (z <= 1.2e+65) {
		tmp = x + ((y - z) * t);
	} else if (z <= 6.5e+89) {
		tmp = x + (x * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (x - t))
    if (z <= (-4.6d-17)) then
        tmp = t_1
    else if (z <= 8d-53) then
        tmp = x + (y * (t - x))
    else if (z <= 1.2d+65) then
        tmp = x + ((y - z) * t)
    else if (z <= 6.5d+89) then
        tmp = x + (x * (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (x - t));
	double tmp;
	if (z <= -4.6e-17) {
		tmp = t_1;
	} else if (z <= 8e-53) {
		tmp = x + (y * (t - x));
	} else if (z <= 1.2e+65) {
		tmp = x + ((y - z) * t);
	} else if (z <= 6.5e+89) {
		tmp = x + (x * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * (x - t))
	tmp = 0
	if z <= -4.6e-17:
		tmp = t_1
	elif z <= 8e-53:
		tmp = x + (y * (t - x))
	elif z <= 1.2e+65:
		tmp = x + ((y - z) * t)
	elif z <= 6.5e+89:
		tmp = x + (x * (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * Float64(x - t)))
	tmp = 0.0
	if (z <= -4.6e-17)
		tmp = t_1;
	elseif (z <= 8e-53)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	elseif (z <= 1.2e+65)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	elseif (z <= 6.5e+89)
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * (x - t));
	tmp = 0.0;
	if (z <= -4.6e-17)
		tmp = t_1;
	elseif (z <= 8e-53)
		tmp = x + (y * (t - x));
	elseif (z <= 1.2e+65)
		tmp = x + ((y - z) * t);
	elseif (z <= 6.5e+89)
		tmp = x + (x * (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e-17], t$95$1, If[LessEqual[z, 8e-53], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+65], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+89], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.60000000000000018e-17 or 6.4999999999999996e89 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.3%

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

      1. +-commutative 85.3%

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

      2. mul-1-neg 85.3%

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

      3. unsub-neg 85.3%

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

      4. *-commutative 85.3%

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

   4. Simplified 85.3%

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

   if -4.60000000000000018e-17 < z < 8.00000000000000025e-53

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 96.6%

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

   if 8.00000000000000025e-53 < z < 1.2000000000000001e65

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 68.0%

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

   if 1.2000000000000001e65 < z < 6.4999999999999996e89

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-lft-out-- 100.0%

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

      5. *-rgt-identity 100.0%

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

   4. Simplified 100.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-17}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+65}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+89}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 4: 55.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y - z \leq -1 \cdot 10^{-35} \lor \neg \left(y - z \leq 4 \cdot 10^{-22}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (- y z) -1e-35) (not (<= (- y z) 4e-22))) (* (- y z) t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -1e-35) || !((y - z) <= 4e-22)) {
		tmp = (y - 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 (((y - z) <= (-1d-35)) .or. (.not. ((y - z) <= 4d-22))) then
        tmp = (y - 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 (((y - z) <= -1e-35) || !((y - z) <= 4e-22)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y - z) <= -1e-35) or not ((y - z) <= 4e-22):
		tmp = (y - z) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y - z) <= -1e-35) || !(Float64(y - z) <= 4e-22))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y - z) <= -1e-35) || ~(((y - z) <= 4e-22)))
		tmp = (y - z) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y - z), $MachinePrecision], -1e-35], N[Not[LessEqual[N[(y - z), $MachinePrecision], 4e-22]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -1.00000000000000001e-35 or 4.0000000000000002e-22 < (-.f64 y z)

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 54.6%

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

   3. Taylor expanded in x around 0 53.2%

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

   if -1.00000000000000001e-35 < (-.f64 y z) < 4.0000000000000002e-22

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 100.0%

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

   3. Taylor expanded in x around inf 76.7%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -1 \cdot 10^{-35} \lor \neg \left(y - z \leq 4 \cdot 10^{-22}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 37.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-112}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 27000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.7e-16)
   (* z x)
   (if (<= z 8.2e-251)
     x
     (if (<= z 9.5e-112) (* y t) (if (<= z 27000000.0) x (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e-16) {
		tmp = z * x;
	} else if (z <= 8.2e-251) {
		tmp = x;
	} else if (z <= 9.5e-112) {
		tmp = y * t;
	} else if (z <= 27000000.0) {
		tmp = x;
	} else {
		tmp = z * 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 <= (-1.7d-16)) then
        tmp = z * x
    else if (z <= 8.2d-251) then
        tmp = x
    else if (z <= 9.5d-112) then
        tmp = y * t
    else if (z <= 27000000.0d0) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e-16) {
		tmp = z * x;
	} else if (z <= 8.2e-251) {
		tmp = x;
	} else if (z <= 9.5e-112) {
		tmp = y * t;
	} else if (z <= 27000000.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.7e-16:
		tmp = z * x
	elif z <= 8.2e-251:
		tmp = x
	elif z <= 9.5e-112:
		tmp = y * t
	elif z <= 27000000.0:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.7e-16)
		tmp = Float64(z * x);
	elseif (z <= 8.2e-251)
		tmp = x;
	elseif (z <= 9.5e-112)
		tmp = Float64(y * t);
	elseif (z <= 27000000.0)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.7e-16)
		tmp = z * x;
	elseif (z <= 8.2e-251)
		tmp = x;
	elseif (z <= 9.5e-112)
		tmp = y * t;
	elseif (z <= 27000000.0)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.7e-16], N[(z * x), $MachinePrecision], If[LessEqual[z, 8.2e-251], x, If[LessEqual[z, 9.5e-112], N[(y * t), $MachinePrecision], If[LessEqual[z, 27000000.0], x, N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e-16 or 2.7e7 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

      4. distribute-lft-out-- 48.8%

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

      5. *-rgt-identity 48.8%

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

   4. Simplified 48.8%

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

   5. Taylor expanded in z around inf 37.6%

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

   if -1.7e-16 < z < 8.1999999999999997e-251 or 9.50000000000000056e-112 < z < 2.7e7

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.5%

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

   3. Taylor expanded in x around inf 47.2%

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

   if 8.1999999999999997e-251 < z < 9.50000000000000056e-112

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 50.7%

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

   3. Taylor expanded in y around inf 34.3%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-16}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-251}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-112}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 27000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 6: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.66 \cdot 10^{-40}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-31}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))))
   (if (<= x -7.8e+163)
     t_1
     (if (<= x -1.66e-40)
       (- x (* y x))
       (if (<= x 1.1e-31) (* (- y z) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double tmp;
	if (x <= -7.8e+163) {
		tmp = t_1;
	} else if (x <= -1.66e-40) {
		tmp = x - (y * x);
	} else if (x <= 1.1e-31) {
		tmp = (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 + 1.0d0)
    if (x <= (-7.8d+163)) then
        tmp = t_1
    else if (x <= (-1.66d-40)) then
        tmp = x - (y * x)
    else if (x <= 1.1d-31) then
        tmp = (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 + 1.0);
	double tmp;
	if (x <= -7.8e+163) {
		tmp = t_1;
	} else if (x <= -1.66e-40) {
		tmp = x - (y * x);
	} else if (x <= 1.1e-31) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	tmp = 0
	if x <= -7.8e+163:
		tmp = t_1
	elif x <= -1.66e-40:
		tmp = x - (y * x)
	elif x <= 1.1e-31:
		tmp = (y - z) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (x <= -7.8e+163)
		tmp = t_1;
	elseif (x <= -1.66e-40)
		tmp = Float64(x - Float64(y * x));
	elseif (x <= 1.1e-31)
		tmp = 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 + 1.0);
	tmp = 0.0;
	if (x <= -7.8e+163)
		tmp = t_1;
	elseif (x <= -1.66e-40)
		tmp = x - (y * x);
	elseif (x <= 1.1e-31)
		tmp = (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[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.8e+163], t$95$1, If[LessEqual[x, -1.66e-40], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e-31], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.80000000000000047e163 or 1.10000000000000005e-31 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. *-commutative 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in x around -inf 64.2%

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

   if -7.80000000000000047e163 < x < -1.6600000000000001e-40

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 68.1%

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

      1. *-commutative 68.1%

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

      2. mul-1-neg 68.1%

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

      3. unsub-neg 68.1%

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

      4. distribute-lft-out-- 68.2%

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

      5. *-rgt-identity 68.2%

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

   4. Simplified 68.2%

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

   5. Taylor expanded in z around 0 57.5%

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

   if -1.6600000000000001e-40 < x < 1.10000000000000005e-31

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.3%

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

   3. Taylor expanded in x around 0 75.4%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+163}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -1.66 \cdot 10^{-40}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-31}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 7: 69.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+120} \lor \neg \left(x \leq 5.9 \cdot 10^{+184}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.5e+120) (not (<= x 5.9e+184)))
   (* x (+ z 1.0))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.5e+120) || !(x <= 5.9e+184)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = x + ((y - 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 ((x <= (-8.5d+120)) .or. (.not. (x <= 5.9d+184))) then
        tmp = x * (z + 1.0d0)
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.5e+120) || !(x <= 5.9e+184)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.5e+120) or not (x <= 5.9e+184):
		tmp = x * (z + 1.0)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.5e+120) || !(x <= 5.9e+184))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8.5e+120) || ~((x <= 5.9e+184)))
		tmp = x * (z + 1.0);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.5e+120], N[Not[LessEqual[x, 5.9e+184]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.50000000000000026e120 or 5.9000000000000001e184 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.3%

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

      1. +-commutative 72.3%

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

      2. mul-1-neg 72.3%

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

      3. unsub-neg 72.3%

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

      4. *-commutative 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in x around -inf 72.0%

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

   if -8.50000000000000026e120 < x < 5.9000000000000001e184

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 72.6%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+120} \lor \neg \left(x \leq 5.9 \cdot 10^{+184}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 8: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.46 \lor \neg \left(y \leq 7200000000\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.46) (not (<= y 7200000000.0)))
   (+ x (* y (- t x)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.46) || !(y <= 7200000000.0)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + ((y - 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 ((y <= (-0.46d0)) .or. (.not. (y <= 7200000000.0d0))) then
        tmp = x + (y * (t - x))
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.46) || !(y <= 7200000000.0)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.46) or not (y <= 7200000000.0):
		tmp = x + (y * (t - x))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.46) || !(y <= 7200000000.0))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.46) || ~((y <= 7200000000.0)))
		tmp = x + (y * (t - x));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.46], N[Not[LessEqual[y, 7200000000.0]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.46000000000000002 or 7.2e9 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 75.7%

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

   if -0.46000000000000002 < y < 7.2e9

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.7%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.46 \lor \neg \left(y \leq 7200000000\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 9: 80.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+97} \lor \neg \left(x \leq 2.3 \cdot 10^{-60}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.4e+97) (not (<= x 2.3e-60)))
   (+ x (* x (- z y)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.4e+97) || !(x <= 2.3e-60)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - 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 ((x <= (-4.4d+97)) .or. (.not. (x <= 2.3d-60))) then
        tmp = x + (x * (z - y))
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.4e+97) || !(x <= 2.3e-60)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.4e+97) or not (x <= 2.3e-60):
		tmp = x + (x * (z - y))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.4e+97) || !(x <= 2.3e-60))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.4e+97) || ~((x <= 2.3e-60)))
		tmp = x + (x * (z - y));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.4e+97], N[Not[LessEqual[x, 2.3e-60]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.4000000000000002e97 or 2.3000000000000001e-60 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 84.4%

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

      1. *-commutative 84.4%

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

      2. mul-1-neg 84.4%

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

      3. unsub-neg 84.4%

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

      4. distribute-lft-out-- 84.5%

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

      5. *-rgt-identity 84.5%

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

   4. Simplified 84.5%

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

   if -4.4000000000000002e97 < x < 2.3000000000000001e-60

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.9%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+97} \lor \neg \left(x \leq 2.3 \cdot 10^{-60}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 10: 62.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+70} \lor \neg \left(x \leq 2.9 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.7e+70) (not (<= x 2.9e-31))) (* x (+ z 1.0)) (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e+70) || !(x <= 2.9e-31)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - 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 ((x <= (-1.7d+70)) .or. (.not. (x <= 2.9d-31))) then
        tmp = x * (z + 1.0d0)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e+70) || !(x <= 2.9e-31)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.7e+70) or not (x <= 2.9e-31):
		tmp = x * (z + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.7e+70) || !(x <= 2.9e-31))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.7e+70) || ~((x <= 2.9e-31)))
		tmp = x * (z + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.7e+70], N[Not[LessEqual[x, 2.9e-31]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e70 or 2.9000000000000001e-31 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 67.6%

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

      1. +-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

      4. *-commutative 67.6%

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

   4. Simplified 67.6%

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

   5. Taylor expanded in x around -inf 61.7%

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

   if -1.7e70 < x < 2.9000000000000001e-31

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.3%

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

   3. Taylor expanded in x around 0 69.7%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+70} \lor \neg \left(x \leq 2.9 \cdot 10^{-31}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 12: 37.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-37}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.75e-37) (* y t) (if (<= y 2.4e-19) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e-37) {
		tmp = y * t;
	} else if (y <= 2.4e-19) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.75d-37)) then
        tmp = y * t
    else if (y <= 2.4d-19) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e-37) {
		tmp = y * t;
	} else if (y <= 2.4e-19) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.75e-37:
		tmp = y * t
	elif y <= 2.4e-19:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.75e-37)
		tmp = Float64(y * t);
	elseif (y <= 2.4e-19)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.75e-37)
		tmp = y * t;
	elseif (y <= 2.4e-19)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.75e-37], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.4e-19], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7500000000000001e-37 or 2.40000000000000023e-19 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 49.5%

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

   3. Taylor expanded in y around inf 32.1%

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

   if -1.7500000000000001e-37 < y < 2.40000000000000023e-19

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.0%

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

   3. Taylor expanded in x around inf 37.7%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-37}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 13: 17.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in t around inf 64.4%

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

3. Taylor expanded in x around inf 19.7%

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

4. Final simplification 19.7%

   \[\leadsto x \]

Developer target: 96.2% 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 2023238 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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