Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.3s

Alternatives: 11

Speedup: 1.0×

• 33.8% 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-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: 37.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+93}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-10}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-247}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+20}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.22e+93)
   (* y t)
   (if (<= y -5.2e+59)
     (* y (- x))
     (if (<= y -5.4e-10)
       (* y t)
       (if (<= y -3.5e-247)
         (* z x)
         (if (<= y 5e-54) (* z (- t)) (if (<= y 4.1e+20) (* z x) (* y t))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.22e+93) {
		tmp = y * t;
	} else if (y <= -5.2e+59) {
		tmp = y * -x;
	} else if (y <= -5.4e-10) {
		tmp = y * t;
	} else if (y <= -3.5e-247) {
		tmp = z * x;
	} else if (y <= 5e-54) {
		tmp = z * -t;
	} else if (y <= 4.1e+20) {
		tmp = z * 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 <= (-1.22d+93)) then
        tmp = y * t
    else if (y <= (-5.2d+59)) then
        tmp = y * -x
    else if (y <= (-5.4d-10)) then
        tmp = y * t
    else if (y <= (-3.5d-247)) then
        tmp = z * x
    else if (y <= 5d-54) then
        tmp = z * -t
    else if (y <= 4.1d+20) then
        tmp = z * 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 <= -1.22e+93) {
		tmp = y * t;
	} else if (y <= -5.2e+59) {
		tmp = y * -x;
	} else if (y <= -5.4e-10) {
		tmp = y * t;
	} else if (y <= -3.5e-247) {
		tmp = z * x;
	} else if (y <= 5e-54) {
		tmp = z * -t;
	} else if (y <= 4.1e+20) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.22e+93:
		tmp = y * t
	elif y <= -5.2e+59:
		tmp = y * -x
	elif y <= -5.4e-10:
		tmp = y * t
	elif y <= -3.5e-247:
		tmp = z * x
	elif y <= 5e-54:
		tmp = z * -t
	elif y <= 4.1e+20:
		tmp = z * x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.22e+93)
		tmp = Float64(y * t);
	elseif (y <= -5.2e+59)
		tmp = Float64(y * Float64(-x));
	elseif (y <= -5.4e-10)
		tmp = Float64(y * t);
	elseif (y <= -3.5e-247)
		tmp = Float64(z * x);
	elseif (y <= 5e-54)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 4.1e+20)
		tmp = Float64(z * x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.22e+93)
		tmp = y * t;
	elseif (y <= -5.2e+59)
		tmp = y * -x;
	elseif (y <= -5.4e-10)
		tmp = y * t;
	elseif (y <= -3.5e-247)
		tmp = z * x;
	elseif (y <= 5e-54)
		tmp = z * -t;
	elseif (y <= 4.1e+20)
		tmp = z * x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.22e+93], N[(y * t), $MachinePrecision], If[LessEqual[y, -5.2e+59], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, -5.4e-10], N[(y * t), $MachinePrecision], If[LessEqual[y, -3.5e-247], N[(z * x), $MachinePrecision], If[LessEqual[y, 5e-54], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 4.1e+20], N[(z * x), $MachinePrecision], N[(y * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.21999999999999995e93 or -5.19999999999999999e59 < y < -5.4e-10 or 4.1e20 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 64.6%

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

   3. Taylor expanded in y around inf 53.0%

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

   if -1.21999999999999995e93 < y < -5.19999999999999999e59

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 67.0%

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

   3. Taylor expanded in t around 0 67.4%

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

      1. mul-1-neg 67.4%

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

      2. distribute-rgt-neg-out 67.4%

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

   5. Simplified 67.4%

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

   if -5.4e-10 < y < -3.4999999999999999e-247 or 5.00000000000000015e-54 < y < 4.1e20

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. distribute-lft-neg-out 71.1%

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

      3. *-commutative 71.1%

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

   4. Simplified 71.1%

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

   5. Taylor expanded in t around 0 49.6%

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

   if -3.4999999999999999e-247 < y < 5.00000000000000015e-54

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 50.6%

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

   3. Taylor expanded in y around 0 47.9%

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

      1. associate-*r* 47.9%

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

      2. neg-mul-1 47.9%

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

   5. Simplified 47.9%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+93}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-10}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-247}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-54}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+20}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 3: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-58}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* x (+ z 1.0))))
   (if (<= y -5.8e-10)
     t_1
     (if (<= y 2.35e-203)
       t_2
       (if (<= y 2.3e-58) (* (- y z) t) (if (<= y 3.2e+21) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -5.8e-10) {
		tmp = t_1;
	} else if (y <= 2.35e-203) {
		tmp = t_2;
	} else if (y <= 2.3e-58) {
		tmp = (y - z) * t;
	} else if (y <= 3.2e+21) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = x * (z + 1.0d0)
    if (y <= (-5.8d-10)) then
        tmp = t_1
    else if (y <= 2.35d-203) then
        tmp = t_2
    else if (y <= 2.3d-58) then
        tmp = (y - z) * t
    else if (y <= 3.2d+21) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -5.8e-10) {
		tmp = t_1;
	} else if (y <= 2.35e-203) {
		tmp = t_2;
	} else if (y <= 2.3e-58) {
		tmp = (y - z) * t;
	} else if (y <= 3.2e+21) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -5.8e-10:
		tmp = t_1
	elif y <= 2.35e-203:
		tmp = t_2
	elif y <= 2.3e-58:
		tmp = (y - z) * t
	elif y <= 3.2e+21:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -5.8e-10)
		tmp = t_1;
	elseif (y <= 2.35e-203)
		tmp = t_2;
	elseif (y <= 2.3e-58)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= 3.2e+21)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -5.8e-10)
		tmp = t_1;
	elseif (y <= 2.35e-203)
		tmp = t_2;
	elseif (y <= 2.3e-58)
		tmp = (y - z) * t;
	elseif (y <= 3.2e+21)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e-10], t$95$1, If[LessEqual[y, 2.35e-203], t$95$2, If[LessEqual[y, 2.3e-58], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 3.2e+21], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999962e-10 or 3.2e21 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.8%

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

   if -5.79999999999999962e-10 < y < 2.35000000000000003e-203 or 2.2999999999999999e-58 < y < 3.2e21

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. distribute-rgt1-in 66.7%

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

      3. mul-1-neg 66.7%

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

      4. cancel-sign-sub-inv 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in x around 0 66.7%

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

   6. Taylor expanded in y around 0 66.2%

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

   if 2.35000000000000003e-203 < y < 2.2999999999999999e-58

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 60.7%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-203}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-58}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+65} \lor \neg \left(t \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.02e+65) (not (<= t 2.2e-71)))
   (* (- y z) t)
   (* x (- (+ z 1.0) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.02e+65) || !(t <= 2.2e-71)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z + 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 ((t <= (-1.02d+65)) .or. (.not. (t <= 2.2d-71))) then
        tmp = (y - z) * t
    else
        tmp = x * ((z + 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 ((t <= -1.02e+65) || !(t <= 2.2e-71)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z + 1.0) - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.02e+65) or not (t <= 2.2e-71):
		tmp = (y - z) * t
	else:
		tmp = x * ((z + 1.0) - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.02e+65) || !(t <= 2.2e-71))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(Float64(z + 1.0) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.02e+65) || ~((t <= 2.2e-71)))
		tmp = (y - z) * t;
	else
		tmp = x * ((z + 1.0) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.02e+65], N[Not[LessEqual[t, 2.2e-71]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.02000000000000005e65 or 2.19999999999999997e-71 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.9%

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

   if -1.02000000000000005e65 < t < 2.19999999999999997e-71

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.0%

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

      1. +-commutative 79.0%

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

      2. distribute-rgt1-in 79.0%

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

      3. mul-1-neg 79.0%

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

      4. cancel-sign-sub-inv 79.0%

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

   4. Simplified 79.0%

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

   5. Taylor expanded in x around 0 79.0%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+65} \lor \neg \left(t \leq 2.2 \cdot 10^{-71}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \end{array} \]

Alternative 5: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+62} \lor \neg \left(t \leq 2.4 \cdot 10^{-71}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.8e+62) (not (<= t 2.4e-71)))
   (* (- y z) t)
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.8e+62) || !(t <= 2.4e-71)) {
		tmp = (y - z) * t;
	} else {
		tmp = x + (x * (z - 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 ((t <= (-5.8d+62)) .or. (.not. (t <= 2.4d-71))) then
        tmp = (y - z) * t
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.8e+62) || !(t <= 2.4e-71)) {
		tmp = (y - z) * t;
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.8e+62) or not (t <= 2.4e-71):
		tmp = (y - z) * t
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.8e+62) || !(t <= 2.4e-71))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.8e+62) || ~((t <= 2.4e-71)))
		tmp = (y - z) * t;
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.8e+62], N[Not[LessEqual[t, 2.4e-71]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.79999999999999968e62 or 2.4e-71 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.9%

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

   if -5.79999999999999968e62 < t < 2.4e-71

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.0%

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

      1. +-commutative 79.0%

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

      2. distribute-rgt1-in 79.0%

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

      3. mul-1-neg 79.0%

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

      4. cancel-sign-sub-inv 79.0%

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

   4. Simplified 79.0%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+62} \lor \neg \left(t \leq 2.4 \cdot 10^{-71}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 6: 32.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+111}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-206}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.1e+111)
   (* y t)
   (if (<= t 7.2e-206) (* z x) (if (<= t 5.2e-34) x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.1e+111) {
		tmp = y * t;
	} else if (t <= 7.2e-206) {
		tmp = z * x;
	} else if (t <= 5.2e-34) {
		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 (t <= (-4.1d+111)) then
        tmp = y * t
    else if (t <= 7.2d-206) then
        tmp = z * x
    else if (t <= 5.2d-34) 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 (t <= -4.1e+111) {
		tmp = y * t;
	} else if (t <= 7.2e-206) {
		tmp = z * x;
	} else if (t <= 5.2e-34) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.1e+111:
		tmp = y * t
	elif t <= 7.2e-206:
		tmp = z * x
	elif t <= 5.2e-34:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.1e+111)
		tmp = Float64(y * t);
	elseif (t <= 7.2e-206)
		tmp = Float64(z * x);
	elseif (t <= 5.2e-34)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.1e+111)
		tmp = y * t;
	elseif (t <= 7.2e-206)
		tmp = z * x;
	elseif (t <= 5.2e-34)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.1e+111], N[(y * t), $MachinePrecision], If[LessEqual[t, 7.2e-206], N[(z * x), $MachinePrecision], If[LessEqual[t, 5.2e-34], x, N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.09999999999999986e111 or 5.1999999999999999e-34 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.9%

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

   3. Taylor expanded in y around inf 47.9%

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

   if -4.09999999999999986e111 < t < 7.19999999999999987e-206

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. distribute-lft-neg-out 58.2%

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

      3. *-commutative 58.2%

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

   4. Simplified 58.2%

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

   5. Taylor expanded in t around 0 43.9%

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

   if 7.19999999999999987e-206 < t < 5.1999999999999999e-34

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. distribute-rgt1-in 66.5%

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

      3. mul-1-neg 66.5%

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

      4. cancel-sign-sub-inv 66.5%

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

   4. Simplified 66.5%

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

   5. Taylor expanded in z around 0 52.9%

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

   6. Taylor expanded in y around 0 36.5%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+111}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-206}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 7: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+15} \lor \neg \left(y \leq 2.25 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.15e+15) (not (<= y 2.25e+22))) (* y (- t x)) (* z (- x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.15e+15) || !(y <= 2.25e+22)) {
		tmp = y * (t - x);
	} else {
		tmp = z * (x - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.15d+15)) .or. (.not. (y <= 2.25d+22))) then
        tmp = y * (t - x)
    else
        tmp = z * (x - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.15e+15) || !(y <= 2.25e+22)) {
		tmp = y * (t - x);
	} else {
		tmp = z * (x - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.15e+15) or not (y <= 2.25e+22):
		tmp = y * (t - x)
	else:
		tmp = z * (x - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.15e+15) || !(y <= 2.25e+22))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(z * Float64(x - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.15e+15) || ~((y <= 2.25e+22)))
		tmp = y * (t - x);
	else
		tmp = z * (x - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.15e+15], N[Not[LessEqual[y, 2.25e+22]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.15e15 or 2.2499999999999999e22 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.8%

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

   if -2.15e15 < y < 2.2499999999999999e22

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. distribute-lft-neg-out 69.6%

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

      3. *-commutative 69.6%

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

   4. Simplified 69.6%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+15} \lor \neg \left(y \leq 2.25 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 8: 54.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{+99}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+73}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.04e+99) (* z x) (if (<= x 1.26e+73) (* (- y z) t) (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.04e+99) {
		tmp = z * x;
	} else if (x <= 1.26e+73) {
		tmp = (y - z) * t;
	} 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 (x <= (-1.04d+99)) then
        tmp = z * x
    else if (x <= 1.26d+73) then
        tmp = (y - z) * t
    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 (x <= -1.04e+99) {
		tmp = z * x;
	} else if (x <= 1.26e+73) {
		tmp = (y - z) * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.04e+99:
		tmp = z * x
	elif x <= 1.26e+73:
		tmp = (y - z) * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.04e+99)
		tmp = Float64(z * x);
	elseif (x <= 1.26e+73)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.04e+99)
		tmp = z * x;
	elseif (x <= 1.26e+73)
		tmp = (y - z) * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.04e+99], N[(z * x), $MachinePrecision], If[LessEqual[x, 1.26e+73], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.04e99 or 1.25999999999999993e73 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 53.5%

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

      1. mul-1-neg 53.5%

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

      2. distribute-lft-neg-out 53.5%

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

      3. *-commutative 53.5%

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

   4. Simplified 53.5%

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

   5. Taylor expanded in t around 0 48.0%

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

   if -1.04e99 < x < 1.25999999999999993e73

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 69.8%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{+99}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{+73}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 9: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 10: 36.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-58}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 300000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e-58) (* y t) (if (<= y 300000.0) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-58) {
		tmp = y * t;
	} else if (y <= 300000.0) {
		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 <= (-4.8d-58)) then
        tmp = y * t
    else if (y <= 300000.0d0) 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 <= -4.8e-58) {
		tmp = y * t;
	} else if (y <= 300000.0) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e-58:
		tmp = y * t
	elif y <= 300000.0:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e-58)
		tmp = Float64(y * t);
	elseif (y <= 300000.0)
		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 <= -4.8e-58)
		tmp = y * t;
	elseif (y <= 300000.0)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e-58], N[(y * t), $MachinePrecision], If[LessEqual[y, 300000.0], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8000000000000001e-58 or 3e5 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 60.4%

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

   3. Taylor expanded in y around inf 46.9%

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

   if -4.8000000000000001e-58 < y < 3e5

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 62.0%

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

      1. +-commutative 62.0%

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

      2. distribute-rgt1-in 62.0%

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

      3. mul-1-neg 62.0%

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

      4. cancel-sign-sub-inv 62.0%

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

   4. Simplified 62.0%

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

   5. Taylor expanded in z around 0 29.0%

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

   6. Taylor expanded in y around 0 29.0%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-58}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 300000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 11: 17.5% 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 x around inf 52.6%

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

   1. +-commutative 52.6%

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

   2. distribute-rgt1-in 52.6%

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

   3. mul-1-neg 52.6%

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

   4. cancel-sign-sub-inv 52.6%

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

4. Simplified 52.6%

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

5. Taylor expanded in z around 0 30.5%

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

6. Taylor expanded in y around 0 15.7%

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

7. Final simplification 15.7%

   \[\leadsto x \]

Developer target: 96.1% 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 2023200 
(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))))