Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.6s

Alternatives: 12

Speedup: 1.0×

• 34.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + t \cdot \left(y - z\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{-34}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+122}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (+ x (* t (- y z)))))
   (if (<= y -9.2e+108)
     t_1
     (if (<= y -1.2e-29)
       t_2
       (if (<= y 1.56e-34)
         (+ x (* z (- x t)))
         (if (<= y 1.9e+77)
           t_2
           (if (<= y 2.8e+122) (+ x (* x (- z y))) (+ x t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x + (t * (y - z));
	double tmp;
	if (y <= -9.2e+108) {
		tmp = t_1;
	} else if (y <= -1.2e-29) {
		tmp = t_2;
	} else if (y <= 1.56e-34) {
		tmp = x + (z * (x - t));
	} else if (y <= 1.9e+77) {
		tmp = t_2;
	} else if (y <= 2.8e+122) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + 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 + (t * (y - z))
    if (y <= (-9.2d+108)) then
        tmp = t_1
    else if (y <= (-1.2d-29)) then
        tmp = t_2
    else if (y <= 1.56d-34) then
        tmp = x + (z * (x - t))
    else if (y <= 1.9d+77) then
        tmp = t_2
    else if (y <= 2.8d+122) then
        tmp = x + (x * (z - y))
    else
        tmp = x + 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 + (t * (y - z));
	double tmp;
	if (y <= -9.2e+108) {
		tmp = t_1;
	} else if (y <= -1.2e-29) {
		tmp = t_2;
	} else if (y <= 1.56e-34) {
		tmp = x + (z * (x - t));
	} else if (y <= 1.9e+77) {
		tmp = t_2;
	} else if (y <= 2.8e+122) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x + (t * (y - z))
	tmp = 0
	if y <= -9.2e+108:
		tmp = t_1
	elif y <= -1.2e-29:
		tmp = t_2
	elif y <= 1.56e-34:
		tmp = x + (z * (x - t))
	elif y <= 1.9e+77:
		tmp = t_2
	elif y <= 2.8e+122:
		tmp = x + (x * (z - y))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x + Float64(t * Float64(y - z)))
	tmp = 0.0
	if (y <= -9.2e+108)
		tmp = t_1;
	elseif (y <= -1.2e-29)
		tmp = t_2;
	elseif (y <= 1.56e-34)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	elseif (y <= 1.9e+77)
		tmp = t_2;
	elseif (y <= 2.8e+122)
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x + (t * (y - z));
	tmp = 0.0;
	if (y <= -9.2e+108)
		tmp = t_1;
	elseif (y <= -1.2e-29)
		tmp = t_2;
	elseif (y <= 1.56e-34)
		tmp = x + (z * (x - t));
	elseif (y <= 1.9e+77)
		tmp = t_2;
	elseif (y <= 2.8e+122)
		tmp = x + (x * (z - y));
	else
		tmp = x + 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[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+108], t$95$1, If[LessEqual[y, -1.2e-29], t$95$2, If[LessEqual[y, 1.56e-34], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+77], t$95$2, If[LessEqual[y, 2.8e+122], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.1999999999999996e108

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 87.6%

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

      1. *-commutative 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in x around -inf 81.2%

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

      1. +-commutative 81.2%

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

      2. mul-1-neg 81.2%

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

      3. unsub-neg 81.2%

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

      4. *-commutative 81.2%

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

      5. sub-neg 81.2%

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

      6. metadata-eval 81.2%

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

      7. +-commutative 81.2%

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

   7. Simplified 81.2%

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

   8. Taylor expanded in y around inf 87.6%

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

   if -9.1999999999999996e108 < y < -1.19999999999999996e-29 or 1.55999999999999992e-34 < y < 1.9000000000000001e77

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.3%

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

   if -1.19999999999999996e-29 < y < 1.55999999999999992e-34

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. distribute-lft-neg-out 98.5%

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

      3. *-commutative 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in z around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. unsub-neg 98.5%

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

   7. Simplified 98.5%

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

   if 1.9000000000000001e77 < y < 2.8e122

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in t around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. distribute-rgt-neg-in 87.0%

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

      3. mul-1-neg 87.0%

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

      4. distribute-lft-in 87.0%

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

      5. +-commutative 87.0%

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

      6. mul-1-neg 87.0%

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

      7. sub-neg 87.0%

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

   6. Simplified 87.0%

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

   if 2.8e122 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 91.8%

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

      1. *-commutative 91.8%

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

   4. Simplified 91.8%

      \[\leadsto x + \color{blue}{\left(t - x\right) \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+108}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-29}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{-34}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+77}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+122}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 3: 68.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-253}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-170}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))) (t_3 (* x (- 1.0 y))))
   (if (<= z -6.2e-5)
     t_2
     (if (<= z -5.1e-253)
       t_3
       (if (<= z 6e-286)
         t_1
         (if (<= z 5.5e-170) t_3 (if (<= z 6e+17) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (z <= -6.2e-5) {
		tmp = t_2;
	} else if (z <= -5.1e-253) {
		tmp = t_3;
	} else if (z <= 6e-286) {
		tmp = t_1;
	} else if (z <= 5.5e-170) {
		tmp = t_3;
	} else if (z <= 6e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * (x - t)
    t_3 = x * (1.0d0 - y)
    if (z <= (-6.2d-5)) then
        tmp = t_2
    else if (z <= (-5.1d-253)) then
        tmp = t_3
    else if (z <= 6d-286) then
        tmp = t_1
    else if (z <= 5.5d-170) then
        tmp = t_3
    else if (z <= 6d+17) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (z <= -6.2e-5) {
		tmp = t_2;
	} else if (z <= -5.1e-253) {
		tmp = t_3;
	} else if (z <= 6e-286) {
		tmp = t_1;
	} else if (z <= 5.5e-170) {
		tmp = t_3;
	} else if (z <= 6e+17) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * (x - t)
	t_3 = x * (1.0 - y)
	tmp = 0
	if z <= -6.2e-5:
		tmp = t_2
	elif z <= -5.1e-253:
		tmp = t_3
	elif z <= 6e-286:
		tmp = t_1
	elif z <= 5.5e-170:
		tmp = t_3
	elif z <= 6e+17:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(x - t))
	t_3 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -6.2e-5)
		tmp = t_2;
	elseif (z <= -5.1e-253)
		tmp = t_3;
	elseif (z <= 6e-286)
		tmp = t_1;
	elseif (z <= 5.5e-170)
		tmp = t_3;
	elseif (z <= 6e+17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * (x - t);
	t_3 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -6.2e-5)
		tmp = t_2;
	elseif (z <= -5.1e-253)
		tmp = t_3;
	elseif (z <= 6e-286)
		tmp = t_1;
	elseif (z <= 5.5e-170)
		tmp = t_3;
	elseif (z <= 6e+17)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e-5], t$95$2, If[LessEqual[z, -5.1e-253], t$95$3, If[LessEqual[z, 6e-286], t$95$1, If[LessEqual[z, 5.5e-170], t$95$3, If[LessEqual[z, 6e+17], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.20000000000000027e-5 or 6e17 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. distribute-lft-neg-out 77.3%

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

      3. *-commutative 77.3%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in z around 0 77.3%

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

      1. mul-1-neg 77.3%

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

      2. unsub-neg 77.3%

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

   7. Simplified 77.3%

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

   8. Taylor expanded in z around inf 76.5%

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

   if -6.20000000000000027e-5 < z < -5.10000000000000008e-253 or 6.0000000000000001e-286 < z < 5.50000000000000018e-170

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 94.7%

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

      1. *-commutative 94.7%

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

   4. Simplified 94.7%

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

   5. Taylor expanded in x around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. unsub-neg 78.3%

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

   7. Simplified 78.3%

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

   if -5.10000000000000008e-253 < z < 6.0000000000000001e-286 or 5.50000000000000018e-170 < z < 6e17

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 95.4%

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

      1. *-commutative 95.4%

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

   4. Simplified 95.4%

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

   5. Taylor expanded in x around -inf 93.6%

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

      1. +-commutative 93.6%

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

      2. mul-1-neg 93.6%

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

      3. unsub-neg 93.6%

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

      4. *-commutative 93.6%

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

      5. sub-neg 93.6%

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

      6. metadata-eval 93.6%

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

      7. +-commutative 93.6%

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

   7. Simplified 93.6%

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

   8. Taylor expanded in y around inf 76.0%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-253}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-286}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 4: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + y \cdot t\\ \mathbf{if}\;z \leq -70:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-287}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* y t))))
   (if (<= z -70.0)
     t_1
     (if (<= z 7.6e-287)
       t_2
       (if (<= z 1.45e-186)
         (* x (- 1.0 y))
         (if (<= z 1.55e-102) t_2 (if (<= z 2.65e+17) (* y (- t x)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -70.0) {
		tmp = t_1;
	} else if (z <= 7.6e-287) {
		tmp = t_2;
	} else if (z <= 1.45e-186) {
		tmp = x * (1.0 - y);
	} else if (z <= 1.55e-102) {
		tmp = t_2;
	} else if (z <= 2.65e+17) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x - t)
    t_2 = x + (y * t)
    if (z <= (-70.0d0)) then
        tmp = t_1
    else if (z <= 7.6d-287) then
        tmp = t_2
    else if (z <= 1.45d-186) then
        tmp = x * (1.0d0 - y)
    else if (z <= 1.55d-102) then
        tmp = t_2
    else if (z <= 2.65d+17) then
        tmp = y * (t - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + (y * t);
	double tmp;
	if (z <= -70.0) {
		tmp = t_1;
	} else if (z <= 7.6e-287) {
		tmp = t_2;
	} else if (z <= 1.45e-186) {
		tmp = x * (1.0 - y);
	} else if (z <= 1.55e-102) {
		tmp = t_2;
	} else if (z <= 2.65e+17) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + (y * t)
	tmp = 0
	if z <= -70.0:
		tmp = t_1
	elif z <= 7.6e-287:
		tmp = t_2
	elif z <= 1.45e-186:
		tmp = x * (1.0 - y)
	elif z <= 1.55e-102:
		tmp = t_2
	elif z <= 2.65e+17:
		tmp = y * (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (z <= -70.0)
		tmp = t_1;
	elseif (z <= 7.6e-287)
		tmp = t_2;
	elseif (z <= 1.45e-186)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 1.55e-102)
		tmp = t_2;
	elseif (z <= 2.65e+17)
		tmp = Float64(y * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x + (y * t);
	tmp = 0.0;
	if (z <= -70.0)
		tmp = t_1;
	elseif (z <= 7.6e-287)
		tmp = t_2;
	elseif (z <= 1.45e-186)
		tmp = x * (1.0 - y);
	elseif (z <= 1.55e-102)
		tmp = t_2;
	elseif (z <= 2.65e+17)
		tmp = y * (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -70.0], t$95$1, If[LessEqual[z, 7.6e-287], t$95$2, If[LessEqual[z, 1.45e-186], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-102], t$95$2, If[LessEqual[z, 2.65e+17], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -70 or 2.65e17 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. distribute-lft-neg-out 77.5%

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

      3. *-commutative 77.5%

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

   4. Simplified 77.5%

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

   5. Taylor expanded in z around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. unsub-neg 77.5%

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

   7. Simplified 77.5%

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

   8. Taylor expanded in z around inf 77.5%

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

   if -70 < z < 7.59999999999999964e-287 or 1.4500000000000001e-186 < z < 1.55000000000000006e-102

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 95.0%

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

      1. *-commutative 95.0%

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

   4. Simplified 95.0%

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

   5. Taylor expanded in t around inf 79.2%

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

      1. *-commutative 79.2%

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

   7. Simplified 79.2%

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

   if 7.59999999999999964e-287 < z < 1.4500000000000001e-186

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 94.6%

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

      1. *-commutative 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in x around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. unsub-neg 83.3%

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

   7. Simplified 83.3%

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

   if 1.55000000000000006e-102 < z < 2.65e17

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 89.4%

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

      1. *-commutative 89.4%

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

   4. Simplified 89.4%

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

   5. Taylor expanded in x around -inf 85.2%

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

      1. +-commutative 85.2%

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

      2. mul-1-neg 85.2%

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

      3. unsub-neg 85.2%

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

      4. *-commutative 85.2%

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

      5. sub-neg 85.2%

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

      6. metadata-eval 85.2%

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

      7. +-commutative 85.2%

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

   7. Simplified 85.2%

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

   8. Taylor expanded in y around inf 77.9%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -70:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-287}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-102}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 5: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+108} \lor \neg \left(y \leq 2.2 \cdot 10^{+52}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.2e+108) (not (<= y 2.2e+52)))
   (* y (- t x))
   (+ x (* t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.2e+108) || !(y <= 2.2e+52)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9.2d+108)) .or. (.not. (y <= 2.2d+52))) then
        tmp = y * (t - x)
    else
        tmp = x + (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.2e+108) || !(y <= 2.2e+52)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.2e+108) or not (y <= 2.2e+52):
		tmp = y * (t - x)
	else:
		tmp = x + (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.2e+108) || !(y <= 2.2e+52))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x + Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.2e+108) || ~((y <= 2.2e+52)))
		tmp = y * (t - x);
	else
		tmp = x + (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.2e+108], N[Not[LessEqual[y, 2.2e+52]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.1999999999999996e108 or 2.2e52 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 87.7%

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

      1. *-commutative 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in x around -inf 82.5%

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

      1. +-commutative 82.5%

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

      2. mul-1-neg 82.5%

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

      3. unsub-neg 82.5%

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

      4. *-commutative 82.5%

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

      5. sub-neg 82.5%

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

      6. metadata-eval 82.5%

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

      7. +-commutative 82.5%

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

   7. Simplified 82.5%

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

   8. Taylor expanded in y around inf 87.7%

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

   if -9.1999999999999996e108 < y < 2.2e52

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.7%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+108} \lor \neg \left(y \leq 2.2 \cdot 10^{+52}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \]

Alternative 6: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-14} \lor \neg \left(x \leq 1.25 \cdot 10^{+66}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.95e-14) (not (<= x 1.25e+66)))
   (+ x (* x (- z y)))
   (+ x (* t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.95e-14) || !(x <= 1.25e+66)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.95d-14)) .or. (.not. (x <= 1.25d+66))) then
        tmp = x + (x * (z - y))
    else
        tmp = x + (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.95e-14) || !(x <= 1.25e+66)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.95e-14) or not (x <= 1.25e+66):
		tmp = x + (x * (z - y))
	else:
		tmp = x + (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.95e-14) || !(x <= 1.25e+66))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.95e-14) || ~((x <= 1.25e+66)))
		tmp = x + (x * (z - y));
	else
		tmp = x + (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.95e-14], N[Not[LessEqual[x, 1.25e+66]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9499999999999999e-14 or 1.24999999999999998e66 < 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%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 95.6%

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

   3. Applied egg-rr 95.6%

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

   4. Taylor expanded in t around 0 83.5%

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

      1. mul-1-neg 83.5%

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

      2. distribute-rgt-neg-in 83.5%

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

      3. mul-1-neg 83.5%

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

      4. distribute-lft-in 86.1%

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

      5. +-commutative 86.1%

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

      6. mul-1-neg 86.1%

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

      7. sub-neg 86.1%

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

   6. Simplified 86.1%

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

   if -1.9499999999999999e-14 < x < 1.24999999999999998e66

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 85.5%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-14} \lor \neg \left(x \leq 1.25 \cdot 10^{+66}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \]

Alternative 7: 81.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4400000 \lor \neg \left(z \leq 1.7 \cdot 10^{+130}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4400000.0) (not (<= z 1.7e+130)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4400000.0) || !(z <= 1.7e+130)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4400000.0d0)) .or. (.not. (z <= 1.7d+130))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4400000.0) || !(z <= 1.7e+130)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4400000.0) or not (z <= 1.7e+130):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4400000.0) || !(z <= 1.7e+130))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4400000.0) || ~((z <= 1.7e+130)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4400000.0], N[Not[LessEqual[z, 1.7e+130]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e6 or 1.7e130 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. distribute-lft-neg-out 81.7%

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

      3. *-commutative 81.7%

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

   4. Simplified 81.7%

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

   5. Taylor expanded in z around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. unsub-neg 81.7%

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

   7. Simplified 81.7%

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

   8. Taylor expanded in z around inf 81.7%

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

   if -4.4e6 < z < 1.7e130

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 88.9%

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

      1. *-commutative 88.9%

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

   4. Simplified 88.9%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4400000 \lor \neg \left(z \leq 1.7 \cdot 10^{+130}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 8: 55.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00048 \lor \neg \left(y \leq 3000000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.00048) (not (<= y 3000000.0)))
   (* y (- t x))
   (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.00048) || !(y <= 3000000.0)) {
		tmp = y * (t - x);
	} 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 ((y <= (-0.00048d0)) .or. (.not. (y <= 3000000.0d0))) then
        tmp = y * (t - x)
    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 ((y <= -0.00048) || !(y <= 3000000.0)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.00048) or not (y <= 3000000.0):
		tmp = y * (t - x)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.00048) || !(y <= 3000000.0))
		tmp = Float64(y * Float64(t - x));
	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 ((y <= -0.00048) || ~((y <= 3000000.0)))
		tmp = y * (t - x);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.00048], N[Not[LessEqual[y, 3000000.0]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000012e-4 or 3e6 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.6%

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

      1. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   5. Taylor expanded in x around -inf 75.8%

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

      1. +-commutative 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. *-commutative 75.8%

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

      5. sub-neg 75.8%

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

      6. metadata-eval 75.8%

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

      7. +-commutative 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in y around inf 79.6%

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

   if -4.80000000000000012e-4 < y < 3e6

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 46.8%

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

      1. *-commutative 46.8%

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

   4. Simplified 46.8%

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

   5. Taylor expanded in x around inf 43.6%

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

      1. mul-1-neg 43.6%

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

      2. unsub-neg 43.6%

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

   7. Simplified 43.6%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00048 \lor \neg \left(y \leq 3000000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 9: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1960 \lor \neg \left(y \leq 170000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1960.0) (not (<= y 170000.0))) (* y (- t x)) (- x (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1960.0) || !(y <= 170000.0)) {
		tmp = y * (t - x);
	} 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 ((y <= (-1960.0d0)) .or. (.not. (y <= 170000.0d0))) then
        tmp = y * (t - x)
    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 ((y <= -1960.0) || !(y <= 170000.0)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1960.0) or not (y <= 170000.0):
		tmp = y * (t - x)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1960.0) || !(y <= 170000.0))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1960.0) || ~((y <= 170000.0)))
		tmp = y * (t - x);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1960.0], N[Not[LessEqual[y, 170000.0]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1960 or 1.7e5 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.4%

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

      1. *-commutative 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in x around -inf 76.6%

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

      1. +-commutative 76.6%

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

      2. mul-1-neg 76.6%

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

      3. unsub-neg 76.6%

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

      4. *-commutative 76.6%

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

      5. sub-neg 76.6%

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

      6. metadata-eval 76.6%

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

      7. +-commutative 76.6%

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

   7. Simplified 76.6%

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

   8. Taylor expanded in y around inf 80.0%

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

   if -1960 < y < 1.7e5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.5%

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

      1. mul-1-neg 95.5%

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

      2. distribute-lft-neg-out 95.5%

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

      3. *-commutative 95.5%

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

   4. Simplified 95.5%

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

   5. Taylor expanded in t around inf 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-rgt-neg-in 76.3%

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

   7. Simplified 76.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1960 \lor \neg \left(y \leq 170000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 10: 37.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -760 \lor \neg \left(y \leq 0.66\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -760.0) (not (<= y 0.66))) (* y (- x)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -760.0) || !(y <= 0.66)) {
		tmp = y * -x;
	} 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 <= (-760.0d0)) .or. (.not. (y <= 0.66d0))) then
        tmp = y * -x
    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 <= -760.0) || !(y <= 0.66)) {
		tmp = y * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -760.0) or not (y <= 0.66):
		tmp = y * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -760.0) || !(y <= 0.66))
		tmp = Float64(y * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -760.0) || ~((y <= 0.66)))
		tmp = y * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -760.0], N[Not[LessEqual[y, 0.66]], $MachinePrecision]], N[(y * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -760 or 0.660000000000000031 < 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%

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

      1. *-commutative 79.8%

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

   4. Simplified 79.8%

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

   5. Taylor expanded in x around inf 40.9%

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

      1. mul-1-neg 40.9%

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

      2. unsub-neg 40.9%

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

   7. Simplified 40.9%

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

   8. Taylor expanded in y around inf 40.5%

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

      1. mul-1-neg 40.5%

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

      2. distribute-rgt-neg-out 40.5%

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

   10. Simplified 40.5%

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

   if -760 < y < 0.660000000000000031

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 46.4%

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

      1. *-commutative 46.4%

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

   4. Simplified 46.4%

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

   5. Taylor expanded in y around 0 42.5%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -760 \lor \neg \left(y \leq 0.66\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 37.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* x (- 1.0 y)))

C

double code(double x, double y, double z, double t) {
	return x * (1.0 - y);
}

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 * (1.0d0 - y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * (1.0 - y);
}

Python

def code(x, y, z, t):
	return x * (1.0 - y)

Julia

function code(x, y, z, t)
	return Float64(x * Float64(1.0 - y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * (1.0 - y);
end

Wolfram

code[x_, y_, z_, t_] := N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around inf 63.4%

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

   1. *-commutative 63.4%

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

4. Simplified 63.4%

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

5. Taylor expanded in x around inf 42.0%

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

   1. mul-1-neg 42.0%

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

   2. unsub-neg 42.0%

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

7. Simplified 42.0%

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

8. Final simplification 42.0%

   \[\leadsto x \cdot \left(1 - y\right) \]

Alternative 12: 18.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around inf 63.4%

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

   1. *-commutative 63.4%

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

4. Simplified 63.4%

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

5. Taylor expanded in y around 0 22.4%

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

6. Final simplification 22.4%

   \[\leadsto x \]

Developer target: 96.9% 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 2023318 
(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))))