Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.0s

Alternatives: 17

Speedup: 1.0×

• 34.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - z, t - x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 53.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y - z \leq -1 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{+101} \lor \neg \left(y - z \leq 10^{+163}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= (- y z) -1e-15)
     t_1
     (if (<= (- y z) 2e-88)
       x
       (if (or (<= (- y z) 2e+101) (not (<= (- y z) 1e+163))) t_1 (* z x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -1e-15) {
		tmp = t_1;
	} else if ((y - z) <= 2e-88) {
		tmp = x;
	} else if (((y - z) <= 2e+101) || !((y - z) <= 1e+163)) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if ((y - z) <= (-1d-15)) then
        tmp = t_1
    else if ((y - z) <= 2d-88) then
        tmp = x
    else if (((y - z) <= 2d+101) .or. (.not. ((y - z) <= 1d+163))) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -1e-15) {
		tmp = t_1;
	} else if ((y - z) <= 2e-88) {
		tmp = x;
	} else if (((y - z) <= 2e+101) || !((y - z) <= 1e+163)) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if (y - z) <= -1e-15:
		tmp = t_1
	elif (y - z) <= 2e-88:
		tmp = x
	elif ((y - z) <= 2e+101) or not ((y - z) <= 1e+163):
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (Float64(y - z) <= -1e-15)
		tmp = t_1;
	elseif (Float64(y - z) <= 2e-88)
		tmp = x;
	elseif ((Float64(y - z) <= 2e+101) || !(Float64(y - z) <= 1e+163))
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if ((y - z) <= -1e-15)
		tmp = t_1;
	elseif ((y - z) <= 2e-88)
		tmp = x;
	elseif (((y - z) <= 2e+101) || ~(((y - z) <= 1e+163)))
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(y - z), $MachinePrecision], -1e-15], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 2e-88], x, If[Or[LessEqual[N[(y - z), $MachinePrecision], 2e+101], N[Not[LessEqual[N[(y - z), $MachinePrecision], 1e+163]], $MachinePrecision]], t$95$1, N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 y z) < -1.0000000000000001e-15 or 1.99999999999999987e-88 < (-.f64 y z) < 2e101 or 9.9999999999999994e162 < (-.f64 y z)

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 58.8%

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

   4. Taylor expanded in x around 0 57.0%

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

   if -1.0000000000000001e-15 < (-.f64 y z) < 1.99999999999999987e-88

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 100.0%

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

   4. Taylor expanded in x around inf 81.8%

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

   if 2e101 < (-.f64 y z) < 9.9999999999999994e162

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. unsub-neg 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in z around inf 59.1%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -1 \cdot 10^{-15}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{+101} \lor \neg \left(y - z \leq 10^{+163}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-102}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-305}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -1.9e+57)
     (* x (- y))
     (if (<= y -1.75e-102)
       (* z x)
       (if (<= y -7.5e-203)
         t_1
         (if (<= y -1.6e-305) x (if (<= y 4.6e-29) t_1 (* y t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -1.9e+57) {
		tmp = x * -y;
	} else if (y <= -1.75e-102) {
		tmp = z * x;
	} else if (y <= -7.5e-203) {
		tmp = t_1;
	} else if (y <= -1.6e-305) {
		tmp = x;
	} else if (y <= 4.6e-29) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (y <= (-1.9d+57)) then
        tmp = x * -y
    else if (y <= (-1.75d-102)) then
        tmp = z * x
    else if (y <= (-7.5d-203)) then
        tmp = t_1
    else if (y <= (-1.6d-305)) then
        tmp = x
    else if (y <= 4.6d-29) then
        tmp = t_1
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -1.9e+57) {
		tmp = x * -y;
	} else if (y <= -1.75e-102) {
		tmp = z * x;
	} else if (y <= -7.5e-203) {
		tmp = t_1;
	} else if (y <= -1.6e-305) {
		tmp = x;
	} else if (y <= 4.6e-29) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -1.9e+57:
		tmp = x * -y
	elif y <= -1.75e-102:
		tmp = z * x
	elif y <= -7.5e-203:
		tmp = t_1
	elif y <= -1.6e-305:
		tmp = x
	elif y <= 4.6e-29:
		tmp = t_1
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -1.9e+57)
		tmp = Float64(x * Float64(-y));
	elseif (y <= -1.75e-102)
		tmp = Float64(z * x);
	elseif (y <= -7.5e-203)
		tmp = t_1;
	elseif (y <= -1.6e-305)
		tmp = x;
	elseif (y <= 4.6e-29)
		tmp = t_1;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (y <= -1.9e+57)
		tmp = x * -y;
	elseif (y <= -1.75e-102)
		tmp = z * x;
	elseif (y <= -7.5e-203)
		tmp = t_1;
	elseif (y <= -1.6e-305)
		tmp = x;
	elseif (y <= 4.6e-29)
		tmp = t_1;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -1.9e+57], N[(x * (-y)), $MachinePrecision], If[LessEqual[y, -1.75e-102], N[(z * x), $MachinePrecision], If[LessEqual[y, -7.5e-203], t$95$1, If[LessEqual[y, -1.6e-305], x, If[LessEqual[y, 4.6e-29], t$95$1, N[(y * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.8999999999999999e57

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. unsub-neg 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y around inf 56.8%

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

      1. mul-1-neg 56.8%

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

      2. distribute-lft-neg-out 56.8%

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

      3. *-commutative 56.8%

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

   8. Simplified 56.8%

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

   if -1.8999999999999999e57 < y < -1.74999999999999993e-102

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. unsub-neg 77.4%

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

   5. Simplified 77.4%

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

   6. Taylor expanded in z around inf 40.5%

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

   if -1.74999999999999993e-102 < y < -7.50000000000000027e-203 or -1.60000000000000004e-305 < y < 4.59999999999999982e-29

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.6%

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

   4. Taylor expanded in z around inf 51.7%

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

      1. associate-*r* 51.7%

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

      2. mul-1-neg 51.7%

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

   6. Simplified 51.7%

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

   if -7.50000000000000027e-203 < y < -1.60000000000000004e-305

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 74.2%

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

   4. Taylor expanded in x around inf 52.8%

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

   if 4.59999999999999982e-29 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 59.0%

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

   4. Taylor expanded in y around inf 43.6%

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

      1. *-commutative 43.6%

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

   6. Simplified 43.6%

      \[\leadsto \color{blue}{y \cdot t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-102}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-305}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + y \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-33}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* y (- t x)))))
   (if (<= z -1.12e+36)
     t_1
     (if (<= z -6e+18)
       t_2
       (if (<= z -1.7e-33)
         (- x (* t (- z y)))
         (if (<= z 1.75e+28) 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 + (y * (t - x));
	double tmp;
	if (z <= -1.12e+36) {
		tmp = t_1;
	} else if (z <= -6e+18) {
		tmp = t_2;
	} else if (z <= -1.7e-33) {
		tmp = x - (t * (z - y));
	} else if (z <= 1.75e+28) {
		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 + (y * (t - x))
    if (z <= (-1.12d+36)) then
        tmp = t_1
    else if (z <= (-6d+18)) then
        tmp = t_2
    else if (z <= (-1.7d-33)) then
        tmp = x - (t * (z - y))
    else if (z <= 1.75d+28) 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 + (y * (t - x));
	double tmp;
	if (z <= -1.12e+36) {
		tmp = t_1;
	} else if (z <= -6e+18) {
		tmp = t_2;
	} else if (z <= -1.7e-33) {
		tmp = x - (t * (z - y));
	} else if (z <= 1.75e+28) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + (y * (t - x))
	tmp = 0
	if z <= -1.12e+36:
		tmp = t_1
	elif z <= -6e+18:
		tmp = t_2
	elif z <= -1.7e-33:
		tmp = x - (t * (z - y))
	elif z <= 1.75e+28:
		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(y * Float64(t - x)))
	tmp = 0.0
	if (z <= -1.12e+36)
		tmp = t_1;
	elseif (z <= -6e+18)
		tmp = t_2;
	elseif (z <= -1.7e-33)
		tmp = Float64(x - Float64(t * Float64(z - y)));
	elseif (z <= 1.75e+28)
		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 + (y * (t - x));
	tmp = 0.0;
	if (z <= -1.12e+36)
		tmp = t_1;
	elseif (z <= -6e+18)
		tmp = t_2;
	elseif (z <= -1.7e-33)
		tmp = x - (t * (z - y));
	elseif (z <= 1.75e+28)
		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[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e+36], t$95$1, If[LessEqual[z, -6e+18], t$95$2, If[LessEqual[z, -1.7e-33], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+28], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.11999999999999999e36 or 1.75e28 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.7%

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

      1. mul-1-neg 82.7%

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

      2. unsub-neg 82.7%

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

   5. Simplified 82.7%

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

      1. sub-neg 82.7%

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

      2. distribute-lft-in 79.3%

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

   7. Applied egg-rr 79.3%

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

   8. Taylor expanded in z around inf 82.7%

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

      1. mul-1-neg 82.7%

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

      2. distribute-rgt-neg-in 82.7%

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

      3. +-commutative 82.7%

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

      4. distribute-neg-in 82.7%

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

      5. unsub-neg 82.7%

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

      6. mul-1-neg 82.7%

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

      7. remove-double-neg 82.7%

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

   10. Simplified 82.7%

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

   if -1.11999999999999999e36 < z < -6e18 or -1.7e-33 < z < 1.75e28

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 95.2%

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

      1. *-commutative 95.2%

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

   5. Simplified 95.2%

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

   if -6e18 < z < -1.7e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 74.3%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+36}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-33}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+28}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4500000000:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-16}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (- t x)))))
   (if (<= y -1.06e+89)
     t_1
     (if (<= y -4500000000.0)
       (* x (+ (- z y) 1.0))
       (if (<= y -7.2e-16)
         (- x (* t (- z y)))
         (if (<= y 6e-5) (+ x (* z (- x t))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (t - x));
	double tmp;
	if (y <= -1.06e+89) {
		tmp = t_1;
	} else if (y <= -4500000000.0) {
		tmp = x * ((z - y) + 1.0);
	} else if (y <= -7.2e-16) {
		tmp = x - (t * (z - y));
	} else if (y <= 6e-5) {
		tmp = x + (z * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (t - x))
    if (y <= (-1.06d+89)) then
        tmp = t_1
    else if (y <= (-4500000000.0d0)) then
        tmp = x * ((z - y) + 1.0d0)
    else if (y <= (-7.2d-16)) then
        tmp = x - (t * (z - y))
    else if (y <= 6d-5) then
        tmp = x + (z * (x - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (t - x));
	double tmp;
	if (y <= -1.06e+89) {
		tmp = t_1;
	} else if (y <= -4500000000.0) {
		tmp = x * ((z - y) + 1.0);
	} else if (y <= -7.2e-16) {
		tmp = x - (t * (z - y));
	} else if (y <= 6e-5) {
		tmp = x + (z * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (t - x))
	tmp = 0
	if y <= -1.06e+89:
		tmp = t_1
	elif y <= -4500000000.0:
		tmp = x * ((z - y) + 1.0)
	elif y <= -7.2e-16:
		tmp = x - (t * (z - y))
	elif y <= 6e-5:
		tmp = x + (z * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(t - x)))
	tmp = 0.0
	if (y <= -1.06e+89)
		tmp = t_1;
	elseif (y <= -4500000000.0)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	elseif (y <= -7.2e-16)
		tmp = Float64(x - Float64(t * Float64(z - y)));
	elseif (y <= 6e-5)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (t - x));
	tmp = 0.0;
	if (y <= -1.06e+89)
		tmp = t_1;
	elseif (y <= -4500000000.0)
		tmp = x * ((z - y) + 1.0);
	elseif (y <= -7.2e-16)
		tmp = x - (t * (z - y));
	elseif (y <= 6e-5)
		tmp = x + (z * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e+89], t$95$1, If[LessEqual[y, -4500000000.0], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e-16], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-5], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.05999999999999997e89 or 6.00000000000000015e-5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.0%

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

      1. *-commutative 84.0%

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

   5. Simplified 84.0%

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

   if -1.05999999999999997e89 < y < -4.5e9

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   if -4.5e9 < y < -7.19999999999999965e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 84.2%

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

   if -7.19999999999999965e-16 < y < 6.00000000000000015e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.2%

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

      1. mul-1-neg 94.2%

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

      2. unsub-neg 94.2%

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

   5. Simplified 94.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+89}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -4500000000:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-16}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -32000000000000:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(\left(y + \frac{x}{t}\right) - z\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (- t x)))))
   (if (<= y -1e+89)
     t_1
     (if (<= y -32000000000000.0)
       (* x (+ (- z y) 1.0))
       (if (<= y -1.35e-15)
         (* t (- (+ y (/ x t)) z))
         (if (<= y 8.8e-5) (+ x (* z (- x t))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (t - x));
	double tmp;
	if (y <= -1e+89) {
		tmp = t_1;
	} else if (y <= -32000000000000.0) {
		tmp = x * ((z - y) + 1.0);
	} else if (y <= -1.35e-15) {
		tmp = t * ((y + (x / t)) - z);
	} else if (y <= 8.8e-5) {
		tmp = x + (z * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (t - x))
    if (y <= (-1d+89)) then
        tmp = t_1
    else if (y <= (-32000000000000.0d0)) then
        tmp = x * ((z - y) + 1.0d0)
    else if (y <= (-1.35d-15)) then
        tmp = t * ((y + (x / t)) - z)
    else if (y <= 8.8d-5) then
        tmp = x + (z * (x - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (t - x));
	double tmp;
	if (y <= -1e+89) {
		tmp = t_1;
	} else if (y <= -32000000000000.0) {
		tmp = x * ((z - y) + 1.0);
	} else if (y <= -1.35e-15) {
		tmp = t * ((y + (x / t)) - z);
	} else if (y <= 8.8e-5) {
		tmp = x + (z * (x - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (t - x))
	tmp = 0
	if y <= -1e+89:
		tmp = t_1
	elif y <= -32000000000000.0:
		tmp = x * ((z - y) + 1.0)
	elif y <= -1.35e-15:
		tmp = t * ((y + (x / t)) - z)
	elif y <= 8.8e-5:
		tmp = x + (z * (x - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(t - x)))
	tmp = 0.0
	if (y <= -1e+89)
		tmp = t_1;
	elseif (y <= -32000000000000.0)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	elseif (y <= -1.35e-15)
		tmp = Float64(t * Float64(Float64(y + Float64(x / t)) - z));
	elseif (y <= 8.8e-5)
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (t - x));
	tmp = 0.0;
	if (y <= -1e+89)
		tmp = t_1;
	elseif (y <= -32000000000000.0)
		tmp = x * ((z - y) + 1.0);
	elseif (y <= -1.35e-15)
		tmp = t * ((y + (x / t)) - z);
	elseif (y <= 8.8e-5)
		tmp = x + (z * (x - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+89], t$95$1, If[LessEqual[y, -32000000000000.0], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-15], N[(t * N[(N[(y + N[(x / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e-5], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.99999999999999995e88 or 8.7999999999999998e-5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 84.0%

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

      1. *-commutative 84.0%

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

   5. Simplified 84.0%

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

   if -9.99999999999999995e88 < y < -3.2e13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   if -3.2e13 < y < -1.35000000000000005e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 84.2%

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

   4. Taylor expanded in t around inf 84.2%

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

   if -1.35000000000000005e-15 < y < 8.7999999999999998e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.2%

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

      1. mul-1-neg 94.2%

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

      2. unsub-neg 94.2%

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

   5. Simplified 94.2%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+89}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -32000000000000:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(\left(y + \frac{x}{t}\right) - z\right)\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-5}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 11000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* x (- 1.0 y))))
   (if (<= z -2e-74)
     t_1
     (if (<= z 2.4e-92)
       t_2
       (if (<= z 11000.0) (* (- y z) t) (if (<= z 6.4e+27) 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 * (1.0 - y);
	double tmp;
	if (z <= -2e-74) {
		tmp = t_1;
	} else if (z <= 2.4e-92) {
		tmp = t_2;
	} else if (z <= 11000.0) {
		tmp = (y - z) * t;
	} else if (z <= 6.4e+27) {
		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 * (1.0d0 - y)
    if (z <= (-2d-74)) then
        tmp = t_1
    else if (z <= 2.4d-92) then
        tmp = t_2
    else if (z <= 11000.0d0) then
        tmp = (y - z) * t
    else if (z <= 6.4d+27) 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 * (1.0 - y);
	double tmp;
	if (z <= -2e-74) {
		tmp = t_1;
	} else if (z <= 2.4e-92) {
		tmp = t_2;
	} else if (z <= 11000.0) {
		tmp = (y - z) * t;
	} else if (z <= 6.4e+27) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x * (1.0 - y)
	tmp = 0
	if z <= -2e-74:
		tmp = t_1
	elif z <= 2.4e-92:
		tmp = t_2
	elif z <= 11000.0:
		tmp = (y - z) * t
	elif z <= 6.4e+27:
		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(1.0 - y))
	tmp = 0.0
	if (z <= -2e-74)
		tmp = t_1;
	elseif (z <= 2.4e-92)
		tmp = t_2;
	elseif (z <= 11000.0)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= 6.4e+27)
		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 * (1.0 - y);
	tmp = 0.0;
	if (z <= -2e-74)
		tmp = t_1;
	elseif (z <= 2.4e-92)
		tmp = t_2;
	elseif (z <= 11000.0)
		tmp = (y - z) * t;
	elseif (z <= 6.4e+27)
		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[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e-74], t$95$1, If[LessEqual[z, 2.4e-92], t$95$2, If[LessEqual[z, 11000.0], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 6.4e+27], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.99999999999999992e-74 or 6.4000000000000003e27 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. unsub-neg 78.6%

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

   5. Simplified 78.6%

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

      1. sub-neg 78.6%

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

      2. distribute-lft-in 75.6%

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

   7. Applied egg-rr 75.6%

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

   8. Taylor expanded in z around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. distribute-rgt-neg-in 77.4%

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

      3. +-commutative 77.4%

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

      4. distribute-neg-in 77.4%

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

      5. unsub-neg 77.4%

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

      6. mul-1-neg 77.4%

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

      7. remove-double-neg 77.4%

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

   10. Simplified 77.4%

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

   if -1.99999999999999992e-74 < z < 2.4000000000000001e-92 or 11000 < z < 6.4000000000000003e27

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 73.7%

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

      1. mul-1-neg 73.7%

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

      2. unsub-neg 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in z around 0 72.8%

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

   if 2.4000000000000001e-92 < z < 11000

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 93.8%

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

   4. Taylor expanded in x around 0 74.4%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-74}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-92}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 11000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -8.4 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-90}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 110000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -8.4e-75)
     t_1
     (if (<= z 3.25e-90)
       (- x (* y x))
       (if (<= z 110000.0)
         (* (- y z) t)
         (if (<= z 6.4e+27) (* 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 <= -8.4e-75) {
		tmp = t_1;
	} else if (z <= 3.25e-90) {
		tmp = x - (y * x);
	} else if (z <= 110000.0) {
		tmp = (y - z) * t;
	} else if (z <= 6.4e+27) {
		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 <= (-8.4d-75)) then
        tmp = t_1
    else if (z <= 3.25d-90) then
        tmp = x - (y * x)
    else if (z <= 110000.0d0) then
        tmp = (y - z) * t
    else if (z <= 6.4d+27) 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 <= -8.4e-75) {
		tmp = t_1;
	} else if (z <= 3.25e-90) {
		tmp = x - (y * x);
	} else if (z <= 110000.0) {
		tmp = (y - z) * t;
	} else if (z <= 6.4e+27) {
		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 <= -8.4e-75:
		tmp = t_1
	elif z <= 3.25e-90:
		tmp = x - (y * x)
	elif z <= 110000.0:
		tmp = (y - z) * t
	elif z <= 6.4e+27:
		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 <= -8.4e-75)
		tmp = t_1;
	elseif (z <= 3.25e-90)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 110000.0)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= 6.4e+27)
		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 <= -8.4e-75)
		tmp = t_1;
	elseif (z <= 3.25e-90)
		tmp = x - (y * x);
	elseif (z <= 110000.0)
		tmp = (y - z) * t;
	elseif (z <= 6.4e+27)
		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, -8.4e-75], t$95$1, If[LessEqual[z, 3.25e-90], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 110000.0], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 6.4e+27], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.4000000000000004e-75 or 6.4000000000000003e27 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. unsub-neg 78.6%

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

   5. Simplified 78.6%

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

      1. sub-neg 78.6%

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

      2. distribute-lft-in 75.6%

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

   7. Applied egg-rr 75.6%

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

   8. Taylor expanded in z around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. distribute-rgt-neg-in 77.4%

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

      3. +-commutative 77.4%

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

      4. distribute-neg-in 77.4%

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

      5. unsub-neg 77.4%

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

      6. mul-1-neg 77.4%

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

      7. remove-double-neg 77.4%

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

   10. Simplified 77.4%

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

   if -8.4000000000000004e-75 < z < 3.2499999999999998e-90

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in z around 0 72.2%

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

      1. sub-neg 72.2%

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

      2. distribute-rgt-in 72.2%

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

      3. *-un-lft-identity 72.2%

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

   8. Applied egg-rr 72.2%

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

   if 3.2499999999999998e-90 < z < 1.1e5

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 93.8%

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

   4. Taylor expanded in x around 0 74.4%

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

   if 1.1e5 < z < 6.4000000000000003e27

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. unsub-neg 89.7%

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

   5. Simplified 89.7%

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

   6. Taylor expanded in z around 0 79.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{-75}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-90}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 110000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+144} \lor \neg \left(y \leq 1.6 \cdot 10^{+192}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -1.0)
     t_1
     (if (<= y 5.5e-129)
       x
       (if (or (<= y 7.4e+144) (not (<= y 1.6e+192))) (* y t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -1.0) {
		tmp = t_1;
	} else if (y <= 5.5e-129) {
		tmp = x;
	} else if ((y <= 7.4e+144) || !(y <= 1.6e+192)) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * -y
    if (y <= (-1.0d0)) then
        tmp = t_1
    else if (y <= 5.5d-129) then
        tmp = x
    else if ((y <= 7.4d+144) .or. (.not. (y <= 1.6d+192))) then
        tmp = y * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -1.0) {
		tmp = t_1;
	} else if (y <= 5.5e-129) {
		tmp = x;
	} else if ((y <= 7.4e+144) || !(y <= 1.6e+192)) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	tmp = 0
	if y <= -1.0:
		tmp = t_1
	elif y <= 5.5e-129:
		tmp = x
	elif (y <= 7.4e+144) or not (y <= 1.6e+192):
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_1;
	elseif (y <= 5.5e-129)
		tmp = x;
	elseif ((y <= 7.4e+144) || !(y <= 1.6e+192))
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_1;
	elseif (y <= 5.5e-129)
		tmp = x;
	elseif ((y <= 7.4e+144) || ~((y <= 1.6e+192)))
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$1, If[LessEqual[y, 5.5e-129], x, If[Or[LessEqual[y, 7.4e+144], N[Not[LessEqual[y, 1.6e+192]], $MachinePrecision]], N[(y * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 7.3999999999999993e144 < y < 1.60000000000000012e192

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 63.6%

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

      1. mul-1-neg 63.6%

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

      2. unsub-neg 63.6%

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

   5. Simplified 63.6%

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

   6. Taylor expanded in y around inf 56.8%

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

      1. mul-1-neg 56.8%

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

      2. distribute-lft-neg-out 56.8%

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

      3. *-commutative 56.8%

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

   8. Simplified 56.8%

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

   if -1 < y < 5.50000000000000023e-129

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 74.8%

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

   4. Taylor expanded in x around inf 37.3%

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

   if 5.50000000000000023e-129 < y < 7.3999999999999993e144 or 1.60000000000000012e192 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 67.1%

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

   4. Taylor expanded in y around inf 41.6%

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

      1. *-commutative 41.6%

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

   6. Simplified 41.6%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+144} \lor \neg \left(y \leq 1.6 \cdot 10^{+192}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+56}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))))
   (if (<= x -3.5e+70)
     t_1
     (if (<= x -5e+20)
       (* x (+ z 1.0))
       (if (<= x 5.4e+56) (* (- y z) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (x <= -3.5e+70) {
		tmp = t_1;
	} else if (x <= -5e+20) {
		tmp = x * (z + 1.0);
	} else if (x <= 5.4e+56) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    if (x <= (-3.5d+70)) then
        tmp = t_1
    else if (x <= (-5d+20)) then
        tmp = x * (z + 1.0d0)
    else if (x <= 5.4d+56) then
        tmp = (y - z) * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (x <= -3.5e+70) {
		tmp = t_1;
	} else if (x <= -5e+20) {
		tmp = x * (z + 1.0);
	} else if (x <= 5.4e+56) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	tmp = 0
	if x <= -3.5e+70:
		tmp = t_1
	elif x <= -5e+20:
		tmp = x * (z + 1.0)
	elif x <= 5.4e+56:
		tmp = (y - z) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (x <= -3.5e+70)
		tmp = t_1;
	elseif (x <= -5e+20)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (x <= 5.4e+56)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	tmp = 0.0;
	if (x <= -3.5e+70)
		tmp = t_1;
	elseif (x <= -5e+20)
		tmp = x * (z + 1.0);
	elseif (x <= 5.4e+56)
		tmp = (y - z) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e+70], t$95$1, If[LessEqual[x, -5e+20], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.4e+56], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.50000000000000002e70 or 5.40000000000000019e56 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.9%

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

      1. mul-1-neg 88.9%

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

      2. unsub-neg 88.9%

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

   5. Simplified 88.9%

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

   6. Taylor expanded in z around 0 68.8%

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

   if -3.50000000000000002e70 < x < -5e20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.8%

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

      1. mul-1-neg 80.8%

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

      2. unsub-neg 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in y around 0 74.2%

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

      1. +-commutative 74.2%

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

   8. Simplified 74.2%

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

   if -5e20 < x < 5.40000000000000019e56

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.4%

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

   4. Taylor expanded in x around 0 71.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+56}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+89}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-49}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.6e+89)
   (* y t)
   (if (<= y -5e-49) (* z x) (if (<= y 5.5e-129) x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+89) {
		tmp = y * t;
	} else if (y <= -5e-49) {
		tmp = z * x;
	} else if (y <= 5.5e-129) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.6d+89)) then
        tmp = y * t
    else if (y <= (-5d-49)) then
        tmp = z * x
    else if (y <= 5.5d-129) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+89) {
		tmp = y * t;
	} else if (y <= -5e-49) {
		tmp = z * x;
	} else if (y <= 5.5e-129) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.6e+89:
		tmp = y * t
	elif y <= -5e-49:
		tmp = z * x
	elif y <= 5.5e-129:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.6e+89)
		tmp = Float64(y * t);
	elseif (y <= -5e-49)
		tmp = Float64(z * x);
	elseif (y <= 5.5e-129)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.6e+89)
		tmp = y * t;
	elseif (y <= -5e-49)
		tmp = z * x;
	elseif (y <= 5.5e-129)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.6e+89], N[(y * t), $MachinePrecision], If[LessEqual[y, -5e-49], N[(z * x), $MachinePrecision], If[LessEqual[y, 5.5e-129], x, N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6000000000000001e89 or 5.50000000000000023e-129 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 58.4%

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

   4. Taylor expanded in y around inf 40.0%

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

      1. *-commutative 40.0%

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

   6. Simplified 40.0%

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

   if -2.6000000000000001e89 < y < -4.9999999999999999e-49

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. unsub-neg 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in z around inf 34.5%

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

   if -4.9999999999999999e-49 < y < 5.50000000000000023e-129

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 76.6%

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

   4. Taylor expanded in x around inf 38.6%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+89}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-49}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+19} \lor \neg \left(x \leq 5.2 \cdot 10^{-126}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.5e+19) (not (<= x 5.2e-126)))
   (* x (+ (- z y) 1.0))
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.5e+19) || !(x <= 5.2e-126)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-8.5d+19)) .or. (.not. (x <= 5.2d-126))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.5e+19) || !(x <= 5.2e-126)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.5e+19) or not (x <= 5.2e-126):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.5e+19) || !(x <= 5.2e-126))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8.5e+19) || ~((x <= 5.2e-126)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.5e+19], N[Not[LessEqual[x, 5.2e-126]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5e19 or 5.19999999999999998e-126 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.6%

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

      1. mul-1-neg 79.6%

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

      2. unsub-neg 79.6%

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

   5. Simplified 79.6%

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

   if -8.5e19 < x < 5.19999999999999998e-126

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 89.1%

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

   4. Taylor expanded in x around 0 80.6%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+19} \lor \neg \left(x \leq 5.2 \cdot 10^{-126}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+24} \lor \neg \left(x \leq 8.2 \cdot 10^{+58}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.6e+24) (not (<= x 8.2e+58)))
   (* x (+ (- z y) 1.0))
   (- x (* t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.6e+24) || !(x <= 8.2e+58)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-8.6d+24)) .or. (.not. (x <= 8.2d+58))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = x - (t * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.6e+24) || !(x <= 8.2e+58)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x - (t * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.6e+24) or not (x <= 8.2e+58):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x - (t * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.6e+24) || !(x <= 8.2e+58))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(x - Float64(t * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -8.6e+24) || ~((x <= 8.2e+58)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x - (t * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.6e+24], N[Not[LessEqual[x, 8.2e+58]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.59999999999999975e24 or 8.2e58 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.7%

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

      1. mul-1-neg 87.7%

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

      2. unsub-neg 87.7%

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

   5. Simplified 87.7%

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

   if -8.59999999999999975e24 < x < 8.2e58

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 81.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+24} \lor \neg \left(x \leq 8.2 \cdot 10^{+58}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-116} \lor \neg \left(t \leq 1.35 \cdot 10^{+22}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.8e-116) (not (<= t 1.35e+22)))
   (* (- y z) t)
   (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.8e-116) || !(t <= 1.35e+22)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 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 <= (-8.8d-116)) .or. (.not. (t <= 1.35d+22))) then
        tmp = (y - z) * t
    else
        tmp = x * (z + 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 <= -8.8e-116) || !(t <= 1.35e+22)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.8e-116) or not (t <= 1.35e+22):
		tmp = (y - z) * t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.8e-116) || !(t <= 1.35e+22))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.8e-116) || ~((t <= 1.35e+22)))
		tmp = (y - z) * t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.8e-116], N[Not[LessEqual[t, 1.35e+22]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.8000000000000004e-116 or 1.3500000000000001e22 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 78.2%

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

   4. Taylor expanded in x around 0 66.6%

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

   if -8.8000000000000004e-116 < t < 1.3500000000000001e22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.2%

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

      1. mul-1-neg 82.2%

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

      2. unsub-neg 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in y around 0 59.1%

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

      1. +-commutative 59.1%

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

   8. Simplified 59.1%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-116} \lor \neg \left(t \leq 1.35 \cdot 10^{+22}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.215\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.215))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.215)) {
		tmp = z * 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 ((z <= (-1.0d0)) .or. (.not. (z <= 0.215d0))) then
        tmp = z * 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 ((z <= -1.0) || !(z <= 0.215)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.215):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.215))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 0.215)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.215]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.214999999999999997 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 49.0%

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

      1. mul-1-neg 49.0%

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

      2. unsub-neg 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in z around inf 34.6%

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

   if -1 < z < 0.214999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 71.1%

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

   4. Taylor expanded in x around inf 37.1%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.215\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 17: 17.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in t around inf 64.1%

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

4. Taylor expanded in x around inf 18.4%

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

5. Final simplification 18.4%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.0% 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 2024075 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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