Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.0s

Alternatives: 14

Speedup: 1.0×

• 33.9% 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: 79.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+103} \lor \neg \left(t \leq -3.5 \cdot 10^{-33} \lor \neg \left(t \leq -4.5 \cdot 10^{-52}\right) \land t \leq 8 \cdot 10^{-52}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.1e+103)
         (not (or (<= t -3.5e-33) (and (not (<= t -4.5e-52)) (<= t 8e-52)))))
   (+ x (* (- y z) t))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.1e+103) || !((t <= -3.5e-33) || (!(t <= -4.5e-52) && (t <= 8e-52)))) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	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 <= (-1.1d+103)) .or. (.not. (t <= (-3.5d-33)) .or. (.not. (t <= (-4.5d-52))) .and. (t <= 8d-52))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.1e+103) || !((t <= -3.5e-33) || (!(t <= -4.5e-52) && (t <= 8e-52)))) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.1e+103) or not ((t <= -3.5e-33) or (not (t <= -4.5e-52) and (t <= 8e-52))):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.1e+103) || !((t <= -3.5e-33) || (!(t <= -4.5e-52) && (t <= 8e-52))))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.1e+103) || ~(((t <= -3.5e-33) || (~((t <= -4.5e-52)) && (t <= 8e-52)))))
		tmp = x + ((y - z) * t);
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.1e+103], N[Not[Or[LessEqual[t, -3.5e-33], And[N[Not[LessEqual[t, -4.5e-52]], $MachinePrecision], LessEqual[t, 8e-52]]]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.09999999999999996e103 or -3.4999999999999999e-33 < t < -4.5e-52 or 8.0000000000000001e-52 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 89.0%

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

   if -1.09999999999999996e103 < t < -3.4999999999999999e-33 or -4.5e-52 < t < 8.0000000000000001e-52

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

   4. Simplified 80.5%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+103} \lor \neg \left(t \leq -3.5 \cdot 10^{-33} \lor \neg \left(t \leq -4.5 \cdot 10^{-52}\right) \land t \leq 8 \cdot 10^{-52}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]

Alternative 3: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1450:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-111}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* x (+ (- z y) 1.0))))
   (if (<= z -7.5e+84)
     t_1
     (if (<= z -1450.0)
       t_2
       (if (<= z 1.35e-111) (+ x (* y t)) (if (<= z 9.4e+63) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x * ((z - y) + 1.0);
	double tmp;
	if (z <= -7.5e+84) {
		tmp = t_1;
	} else if (z <= -1450.0) {
		tmp = t_2;
	} else if (z <= 1.35e-111) {
		tmp = x + (y * t);
	} else if (z <= 9.4e+63) {
		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 = z * (x - t)
    t_2 = x * ((z - y) + 1.0d0)
    if (z <= (-7.5d+84)) then
        tmp = t_1
    else if (z <= (-1450.0d0)) then
        tmp = t_2
    else if (z <= 1.35d-111) then
        tmp = x + (y * t)
    else if (z <= 9.4d+63) 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 = z * (x - t);
	double t_2 = x * ((z - y) + 1.0);
	double tmp;
	if (z <= -7.5e+84) {
		tmp = t_1;
	} else if (z <= -1450.0) {
		tmp = t_2;
	} else if (z <= 1.35e-111) {
		tmp = x + (y * t);
	} else if (z <= 9.4e+63) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x * ((z - y) + 1.0)
	tmp = 0
	if z <= -7.5e+84:
		tmp = t_1
	elif z <= -1450.0:
		tmp = t_2
	elif z <= 1.35e-111:
		tmp = x + (y * t)
	elif z <= 9.4e+63:
		tmp = t_2
	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(Float64(z - y) + 1.0))
	tmp = 0.0
	if (z <= -7.5e+84)
		tmp = t_1;
	elseif (z <= -1450.0)
		tmp = t_2;
	elseif (z <= 1.35e-111)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 9.4e+63)
		tmp = t_2;
	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 * ((z - y) + 1.0);
	tmp = 0.0;
	if (z <= -7.5e+84)
		tmp = t_1;
	elseif (z <= -1450.0)
		tmp = t_2;
	elseif (z <= 1.35e-111)
		tmp = x + (y * t);
	elseif (z <= 9.4e+63)
		tmp = t_2;
	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[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+84], t$95$1, If[LessEqual[z, -1450.0], t$95$2, If[LessEqual[z, 1.35e-111], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.4e+63], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5000000000000001e84 or 9.4000000000000006e63 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.9%

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

      1. mul-1-neg 87.9%

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

      2. *-commutative 87.9%

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

      3. distribute-rgt-neg-out 87.9%

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

   4. Simplified 87.9%

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

      1. distribute-rgt-neg-out 87.9%

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

      2. unsub-neg 87.9%

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

   6. Applied egg-rr 87.9%

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

   7. Taylor expanded in z around inf 87.9%

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

   if -7.5000000000000001e84 < z < -1450 or 1.34999999999999994e-111 < z < 9.4000000000000006e63

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. unsub-neg 66.1%

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

   4. Simplified 66.1%

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

   if -1450 < z < 1.34999999999999994e-111

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.9%

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

   3. Taylor expanded in y around inf 73.3%

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

      1. *-commutative 73.3%

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

   5. Simplified 73.3%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+84}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1450:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-111}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 4: 47.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+109}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-290}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))))
   (if (<= z -3.5e+109)
     (* z x)
     (if (<= z -8.5e-254)
       t_1
       (if (<= z -2.8e-290) (* y t) (if (<= z 2.1e+79) t_1 (* z (- t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (z <= -3.5e+109) {
		tmp = z * x;
	} else if (z <= -8.5e-254) {
		tmp = t_1;
	} else if (z <= -2.8e-290) {
		tmp = y * t;
	} else if (z <= 2.1e+79) {
		tmp = t_1;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    if (z <= (-3.5d+109)) then
        tmp = z * x
    else if (z <= (-8.5d-254)) then
        tmp = t_1
    else if (z <= (-2.8d-290)) then
        tmp = y * t
    else if (z <= 2.1d+79) then
        tmp = t_1
    else
        tmp = z * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (z <= -3.5e+109) {
		tmp = z * x;
	} else if (z <= -8.5e-254) {
		tmp = t_1;
	} else if (z <= -2.8e-290) {
		tmp = y * t;
	} else if (z <= 2.1e+79) {
		tmp = t_1;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	tmp = 0
	if z <= -3.5e+109:
		tmp = z * x
	elif z <= -8.5e-254:
		tmp = t_1
	elif z <= -2.8e-290:
		tmp = y * t
	elif z <= 2.1e+79:
		tmp = t_1
	else:
		tmp = z * -t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -3.5e+109)
		tmp = Float64(z * x);
	elseif (z <= -8.5e-254)
		tmp = t_1;
	elseif (z <= -2.8e-290)
		tmp = Float64(y * t);
	elseif (z <= 2.1e+79)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -3.5e+109)
		tmp = z * x;
	elseif (z <= -8.5e-254)
		tmp = t_1;
	elseif (z <= -2.8e-290)
		tmp = y * t;
	elseif (z <= 2.1e+79)
		tmp = t_1;
	else
		tmp = z * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+109], N[(z * x), $MachinePrecision], If[LessEqual[z, -8.5e-254], t$95$1, If[LessEqual[z, -2.8e-290], N[(y * t), $MachinePrecision], If[LessEqual[z, 2.1e+79], t$95$1, N[(z * (-t)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.49999999999999983e109

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.1%

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

      1. mul-1-neg 96.1%

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

      2. *-commutative 96.1%

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

      3. distribute-rgt-neg-out 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in t around 0 69.2%

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

   6. Taylor expanded in z around inf 69.2%

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

      1. *-commutative 69.2%

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

   8. Simplified 69.2%

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

   if -3.49999999999999983e109 < z < -8.49999999999999963e-254 or -2.79999999999999997e-290 < z < 2.10000000000000008e79

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.6%

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

      1. *-commutative 83.6%

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

   4. Simplified 83.6%

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

   5. Taylor expanded in x around inf 54.1%

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

      1. mul-1-neg 54.1%

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

      2. unsub-neg 54.1%

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

   7. Simplified 54.1%

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

   if -8.49999999999999963e-254 < z < -2.79999999999999997e-290

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 96.3%

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

   3. Taylor expanded in y around inf 96.3%

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

      1. *-commutative 96.3%

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

   5. Simplified 96.3%

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

   6. Taylor expanded in x around 0 79.3%

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

   if 2.10000000000000008e79 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. *-commutative 85.6%

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

      3. distribute-rgt-neg-out 85.6%

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

   4. Simplified 85.6%

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

      1. distribute-rgt-neg-out 85.6%

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

      2. unsub-neg 85.6%

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

   6. Applied egg-rr 85.6%

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

   7. Taylor expanded in x around 0 51.1%

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

      1. mul-1-neg 51.1%

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

      2. distribute-rgt-neg-out 51.1%

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

   9. Simplified 51.1%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+109}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-290}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]

Alternative 5: 70.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -118000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-107}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -118000.0)
     t_1
     (if (<= z 7.5e-107)
       (+ x (* y t))
       (if (<= z 3.6e+48) (* x (- 1.0 y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -118000.0) {
		tmp = t_1;
	} else if (z <= 7.5e-107) {
		tmp = x + (y * t);
	} else if (z <= 3.6e+48) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-118000.0d0)) then
        tmp = t_1
    else if (z <= 7.5d-107) then
        tmp = x + (y * t)
    else if (z <= 3.6d+48) then
        tmp = x * (1.0d0 - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -118000.0) {
		tmp = t_1;
	} else if (z <= 7.5e-107) {
		tmp = x + (y * t);
	} else if (z <= 3.6e+48) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -118000.0:
		tmp = t_1
	elif z <= 7.5e-107:
		tmp = x + (y * t)
	elif z <= 3.6e+48:
		tmp = x * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -118000.0)
		tmp = t_1;
	elseif (z <= 7.5e-107)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 3.6e+48)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -118000.0)
		tmp = t_1;
	elseif (z <= 7.5e-107)
		tmp = x + (y * t);
	elseif (z <= 3.6e+48)
		tmp = x * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -118000.0], t$95$1, If[LessEqual[z, 7.5e-107], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+48], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -118000 or 3.59999999999999983e48 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.3%

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

      1. mul-1-neg 80.3%

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

      2. *-commutative 80.3%

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

      3. distribute-rgt-neg-out 80.3%

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

   4. Simplified 80.3%

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

      1. distribute-rgt-neg-out 80.3%

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

      2. unsub-neg 80.3%

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

   6. Applied egg-rr 80.3%

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

   7. Taylor expanded in z around inf 79.9%

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

   if -118000 < z < 7.50000000000000047e-107

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.9%

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

   3. Taylor expanded in y around inf 73.3%

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

      1. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if 7.50000000000000047e-107 < z < 3.59999999999999983e48

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 87.8%

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

      1. *-commutative 87.8%

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

   4. Simplified 87.8%

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

   5. Taylor expanded in x around inf 66.9%

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

      1. mul-1-neg 66.9%

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

      2. unsub-neg 66.9%

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

   7. Simplified 66.9%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -118000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-107}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 6: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+84} \lor \neg \left(z \leq 8.4 \cdot 10^{+48}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.4e+84) (not (<= z 8.4e+48)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.4e+84) || !(z <= 8.4e+48)) {
		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 <= (-6.4d+84)) .or. (.not. (z <= 8.4d+48))) 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 <= -6.4e+84) || !(z <= 8.4e+48)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.4e+84) or not (z <= 8.4e+48):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.4e+84) || !(z <= 8.4e+48))
		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 <= -6.4e+84) || ~((z <= 8.4e+48)))
		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, -6.4e+84], N[Not[LessEqual[z, 8.4e+48]], $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 < -6.4000000000000002e84 or 8.3999999999999994e48 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.9%

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

      1. mul-1-neg 87.9%

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

      2. *-commutative 87.9%

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

      3. distribute-rgt-neg-out 87.9%

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

   4. Simplified 87.9%

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

      1. distribute-rgt-neg-out 87.9%

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

      2. unsub-neg 87.9%

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

   6. Applied egg-rr 87.9%

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

   7. Taylor expanded in z around inf 87.9%

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

   if -6.4000000000000002e84 < z < 8.3999999999999994e48

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 86.6%

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

      1. *-commutative 86.6%

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

   4. Simplified 86.6%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+84} \lor \neg \left(z \leq 8.4 \cdot 10^{+48}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 7: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+53}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -6.4e+84) t_1 (if (<= z 4.9e+53) (+ x (* y (- t x))) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -6.4e+84) {
		tmp = t_1;
	} else if (z <= 4.9e+53) {
		tmp = x + (y * (t - x));
	} 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) :: tmp
    t_1 = z * (x - t)
    if (z <= (-6.4d+84)) then
        tmp = t_1
    else if (z <= 4.9d+53) then
        tmp = x + (y * (t - x))
    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 = z * (x - t);
	double tmp;
	if (z <= -6.4e+84) {
		tmp = t_1;
	} else if (z <= 4.9e+53) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -6.4e+84:
		tmp = t_1
	elif z <= 4.9e+53:
		tmp = x + (y * (t - x))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -6.4e+84)
		tmp = t_1;
	elseif (z <= 4.9e+53)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -6.4e+84)
		tmp = t_1;
	elseif (z <= 4.9e+53)
		tmp = x + (y * (t - x));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e+84], t$95$1, If[LessEqual[z, 4.9e+53], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4000000000000002e84

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 92.8%

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

      1. mul-1-neg 92.8%

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

      2. *-commutative 92.8%

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

      3. distribute-rgt-neg-out 92.8%

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

   4. Simplified 92.8%

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

      1. distribute-rgt-neg-out 92.8%

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

      2. unsub-neg 92.8%

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

   6. Applied egg-rr 92.8%

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

   7. Taylor expanded in z around inf 92.8%

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

   if -6.4000000000000002e84 < z < 4.90000000000000018e53

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 86.6%

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

      1. *-commutative 86.6%

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

   4. Simplified 86.6%

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

   if 4.90000000000000018e53 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.5%

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

      1. mul-1-neg 83.5%

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

      2. *-commutative 83.5%

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

      3. distribute-rgt-neg-out 83.5%

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

   4. Simplified 83.5%

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

      1. distribute-rgt-neg-out 83.5%

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

      2. unsub-neg 83.5%

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

   6. Applied egg-rr 83.5%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+84}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+53}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 8: 37.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+104}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-108}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.6e+104)
   (* z x)
   (if (<= z 5e-108) (* y t) (if (<= z 1.26e+79) (* y (- x)) (* z (- t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e+104) {
		tmp = z * x;
	} else if (z <= 5e-108) {
		tmp = y * t;
	} else if (z <= 1.26e+79) {
		tmp = y * -x;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.6d+104)) then
        tmp = z * x
    else if (z <= 5d-108) then
        tmp = y * t
    else if (z <= 1.26d+79) then
        tmp = y * -x
    else
        tmp = z * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e+104) {
		tmp = z * x;
	} else if (z <= 5e-108) {
		tmp = y * t;
	} else if (z <= 1.26e+79) {
		tmp = y * -x;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.6e+104:
		tmp = z * x
	elif z <= 5e-108:
		tmp = y * t
	elif z <= 1.26e+79:
		tmp = y * -x
	else:
		tmp = z * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.6e+104)
		tmp = Float64(z * x);
	elseif (z <= 5e-108)
		tmp = Float64(y * t);
	elseif (z <= 1.26e+79)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(z * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.6e+104)
		tmp = z * x;
	elseif (z <= 5e-108)
		tmp = y * t;
	elseif (z <= 1.26e+79)
		tmp = y * -x;
	else
		tmp = z * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.6e+104], N[(z * x), $MachinePrecision], If[LessEqual[z, 5e-108], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.26e+79], N[(y * (-x)), $MachinePrecision], N[(z * (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.59999999999999969e104

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.1%

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

      1. mul-1-neg 94.1%

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

      2. *-commutative 94.1%

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

      3. distribute-rgt-neg-out 94.1%

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

   4. Simplified 94.1%

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

   5. Taylor expanded in t around 0 67.8%

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

   6. Taylor expanded in z around inf 67.8%

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

      1. *-commutative 67.8%

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

   8. Simplified 67.8%

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

   if -4.59999999999999969e104 < z < 5e-108

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 74.8%

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

   3. Taylor expanded in y around inf 63.4%

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

      1. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in x around 0 43.5%

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

   if 5e-108 < z < 1.26e79

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 81.7%

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

      1. *-commutative 81.7%

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

   4. Simplified 81.7%

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

   5. Taylor expanded in x around inf 60.9%

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

      1. mul-1-neg 60.9%

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

      2. unsub-neg 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in y around inf 45.4%

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

      1. mul-1-neg 45.4%

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

      2. distribute-rgt-neg-out 45.4%

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

   10. Simplified 45.4%

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

   if 1.26e79 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. *-commutative 85.6%

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

      3. distribute-rgt-neg-out 85.6%

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

   4. Simplified 85.6%

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

      1. distribute-rgt-neg-out 85.6%

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

      2. unsub-neg 85.6%

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

   6. Applied egg-rr 85.6%

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

   7. Taylor expanded in x around 0 51.1%

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

      1. mul-1-neg 51.1%

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

      2. distribute-rgt-neg-out 51.1%

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

   9. Simplified 51.1%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+104}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-108}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]

Alternative 9: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+30} \lor \neg \left(z \leq 3.6 \cdot 10^{+48}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.6e+30) (not (<= z 3.6e+48))) (* z (- x t)) (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e+30) || !(z <= 3.6e+48)) {
		tmp = z * (x - t);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.6d+30)) .or. (.not. (z <= 3.6d+48))) then
        tmp = z * (x - t)
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.6e+30) || !(z <= 3.6e+48)) {
		tmp = z * (x - t);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.6e+30) or not (z <= 3.6e+48):
		tmp = z * (x - t)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.6e+30) || !(z <= 3.6e+48))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.6e+30) || ~((z <= 3.6e+48)))
		tmp = z * (x - t);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.6e+30], N[Not[LessEqual[z, 3.6e+48]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999988e30 or 3.59999999999999983e48 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. *-commutative 83.6%

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

      3. distribute-rgt-neg-out 83.6%

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

   4. Simplified 83.6%

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

      1. distribute-rgt-neg-out 83.6%

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

      2. unsub-neg 83.6%

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

   6. Applied egg-rr 83.6%

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

   7. Taylor expanded in z around inf 83.6%

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

   if -2.59999999999999988e30 < z < 3.59999999999999983e48

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 89.7%

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

      1. *-commutative 89.7%

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

   4. Simplified 89.7%

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

   5. Taylor expanded in x around inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. unsub-neg 55.5%

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

   7. Simplified 55.5%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+30} \lor \neg \left(z \leq 3.6 \cdot 10^{+48}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 10: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 11: 37.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+106}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+81}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+106) (* z x) (if (<= z 6.6e+81) (* y t) (* z (- t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+106) {
		tmp = z * x;
	} else if (z <= 6.6e+81) {
		tmp = y * t;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.8d+106)) then
        tmp = z * x
    else if (z <= 6.6d+81) then
        tmp = y * t
    else
        tmp = z * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+106) {
		tmp = z * x;
	} else if (z <= 6.6e+81) {
		tmp = y * t;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+106:
		tmp = z * x
	elif z <= 6.6e+81:
		tmp = y * t
	else:
		tmp = z * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+106)
		tmp = Float64(z * x);
	elseif (z <= 6.6e+81)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+106)
		tmp = z * x;
	elseif (z <= 6.6e+81)
		tmp = y * t;
	else
		tmp = z * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+106], N[(z * x), $MachinePrecision], If[LessEqual[z, 6.6e+81], N[(y * t), $MachinePrecision], N[(z * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999993e106

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.1%

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

      1. mul-1-neg 94.1%

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

      2. *-commutative 94.1%

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

      3. distribute-rgt-neg-out 94.1%

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

   4. Simplified 94.1%

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

   5. Taylor expanded in t around 0 67.8%

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

   6. Taylor expanded in z around inf 67.8%

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

      1. *-commutative 67.8%

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

   8. Simplified 67.8%

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

   if -2.79999999999999993e106 < z < 6.6e81

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 70.9%

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

   3. Taylor expanded in y around inf 59.7%

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

      1. *-commutative 59.7%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in x around 0 40.7%

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

   if 6.6e81 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. *-commutative 85.6%

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

      3. distribute-rgt-neg-out 85.6%

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

   4. Simplified 85.6%

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

      1. distribute-rgt-neg-out 85.6%

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

      2. unsub-neg 85.6%

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

   6. Applied egg-rr 85.6%

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

   7. Taylor expanded in x around 0 51.1%

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

      1. mul-1-neg 51.1%

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

      2. distribute-rgt-neg-out 51.1%

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

   9. Simplified 51.1%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+106}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+81}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]

Alternative 12: 37.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-54} \lor \neg \left(y \leq 1.45 \cdot 10^{-22}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.1e-54) (not (<= y 1.45e-22))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.1e-54) || !(y <= 1.45e-22)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.1d-54)) .or. (.not. (y <= 1.45d-22))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.1e-54) || !(y <= 1.45e-22)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.1e-54) or not (y <= 1.45e-22):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.1e-54) || !(y <= 1.45e-22))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.1e-54) || ~((y <= 1.45e-22)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.1e-54], N[Not[LessEqual[y, 1.45e-22]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.1000000000000001e-54 or 1.4500000000000001e-22 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 59.6%

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

   3. Taylor expanded in y around inf 46.6%

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

      1. *-commutative 46.6%

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

   5. Simplified 46.6%

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

   6. Taylor expanded in x around 0 45.0%

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

   if -4.1000000000000001e-54 < y < 1.4500000000000001e-22

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 70.3%

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

   3. Taylor expanded in x around inf 30.9%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-54} \lor \neg \left(y \leq 1.45 \cdot 10^{-22}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 38.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+96} \lor \neg \left(z \leq 3.4 \cdot 10^{+101}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.75e+96) (not (<= z 3.4e+101))) (* z x) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.75e+96) || !(z <= 3.4e+101)) {
		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 ((z <= (-1.75d+96)) .or. (.not. (z <= 3.4d+101))) 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 ((z <= -1.75e+96) || !(z <= 3.4e+101)) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.75e+96) or not (z <= 3.4e+101):
		tmp = z * x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.75e+96) || !(z <= 3.4e+101))
		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 ((z <= -1.75e+96) || ~((z <= 3.4e+101)))
		tmp = z * x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.75e+96], N[Not[LessEqual[z, 3.4e+101]], $MachinePrecision]], N[(z * x), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7499999999999999e96 or 3.40000000000000017e101 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.0%

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

      1. mul-1-neg 91.0%

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

      2. *-commutative 91.0%

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

      3. distribute-rgt-neg-out 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in t around 0 55.4%

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

   6. Taylor expanded in z around inf 55.4%

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

      1. *-commutative 55.4%

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

   8. Simplified 55.4%

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

   if -1.7499999999999999e96 < z < 3.40000000000000017e101

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 70.9%

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

   3. Taylor expanded in y around inf 58.2%

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

      1. *-commutative 58.2%

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

   5. Simplified 58.2%

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

   6. Taylor expanded in x around 0 39.9%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+96} \lor \neg \left(z \leq 3.4 \cdot 10^{+101}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 14: 17.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in t around inf 63.5%

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

3. Taylor expanded in x around inf 14.1%

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

4. Final simplification 14.1%

   \[\leadsto x \]

Developer target: 96.5% 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 2023301 
(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))))