Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.8s

Alternatives: 13

Speedup: 1.0×

• 35.2% 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: 54.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ t_2 := x + y \cdot t\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+31}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+92} \lor \neg \left(y \leq 5 \cdot 10^{+160}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))) (t_2 (+ x (* y t))))
   (if (<= y -6.8e+135)
     t_1
     (if (<= y -6.2e+94)
       t_2
       (if (<= y -2.5e+56)
         t_1
         (if (<= y 1.4e+31)
           (- x (* z t))
           (if (or (<= y 8.5e+92) (not (<= y 5e+160))) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double t_2 = x + (y * t);
	double tmp;
	if (y <= -6.8e+135) {
		tmp = t_1;
	} else if (y <= -6.2e+94) {
		tmp = t_2;
	} else if (y <= -2.5e+56) {
		tmp = t_1;
	} else if (y <= 1.4e+31) {
		tmp = x - (z * t);
	} else if ((y <= 8.5e+92) || !(y <= 5e+160)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * -y
    t_2 = x + (y * t)
    if (y <= (-6.8d+135)) then
        tmp = t_1
    else if (y <= (-6.2d+94)) then
        tmp = t_2
    else if (y <= (-2.5d+56)) then
        tmp = t_1
    else if (y <= 1.4d+31) then
        tmp = x - (z * t)
    else if ((y <= 8.5d+92) .or. (.not. (y <= 5d+160))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double t_2 = x + (y * t);
	double tmp;
	if (y <= -6.8e+135) {
		tmp = t_1;
	} else if (y <= -6.2e+94) {
		tmp = t_2;
	} else if (y <= -2.5e+56) {
		tmp = t_1;
	} else if (y <= 1.4e+31) {
		tmp = x - (z * t);
	} else if ((y <= 8.5e+92) || !(y <= 5e+160)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	t_2 = x + (y * t)
	tmp = 0
	if y <= -6.8e+135:
		tmp = t_1
	elif y <= -6.2e+94:
		tmp = t_2
	elif y <= -2.5e+56:
		tmp = t_1
	elif y <= 1.4e+31:
		tmp = x - (z * t)
	elif (y <= 8.5e+92) or not (y <= 5e+160):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	t_2 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (y <= -6.8e+135)
		tmp = t_1;
	elseif (y <= -6.2e+94)
		tmp = t_2;
	elseif (y <= -2.5e+56)
		tmp = t_1;
	elseif (y <= 1.4e+31)
		tmp = Float64(x - Float64(z * t));
	elseif ((y <= 8.5e+92) || !(y <= 5e+160))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	t_2 = x + (y * t);
	tmp = 0.0;
	if (y <= -6.8e+135)
		tmp = t_1;
	elseif (y <= -6.2e+94)
		tmp = t_2;
	elseif (y <= -2.5e+56)
		tmp = t_1;
	elseif (y <= 1.4e+31)
		tmp = x - (z * t);
	elseif ((y <= 8.5e+92) || ~((y <= 5e+160)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+135], t$95$1, If[LessEqual[y, -6.2e+94], t$95$2, If[LessEqual[y, -2.5e+56], t$95$1, If[LessEqual[y, 1.4e+31], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 8.5e+92], N[Not[LessEqual[y, 5e+160]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.80000000000000019e135 or -6.19999999999999983e94 < y < -2.50000000000000012e56 or 1.40000000000000008e31 < y < 8.5000000000000001e92 or 5.0000000000000002e160 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. unsub-neg 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in y around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-lft-neg-out 58.8%

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

      3. *-commutative 58.8%

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

   8. Simplified 58.8%

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

   if -6.80000000000000019e135 < y < -6.19999999999999983e94 or 8.5000000000000001e92 < y < 5.0000000000000002e160

   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 59.1%

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

   4. Taylor expanded in y around inf 56.1%

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

   if -2.50000000000000012e56 < y < 1.40000000000000008e31

   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 y around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. unsub-neg 65.9%

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

      3. *-commutative 65.9%

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

   6. Simplified 65.9%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+94}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+31}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+92} \lor \neg \left(y \leq 5 \cdot 10^{+160}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ t_2 := x - z \cdot t\\ t_3 := x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{-98}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-153}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))) (t_2 (- x (* z t))) (t_3 (* x (+ (- z y) 1.0))))
   (if (<= x -1.22e-98)
     t_3
     (if (<= x 3.25e-305)
       t_1
       (if (<= x 6.2e-153)
         t_2
         (if (<= x 6e-126) t_1 (if (<= x 1.05e-76) t_2 t_3)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = x - (z * t);
	double t_3 = x * ((z - y) + 1.0);
	double tmp;
	if (x <= -1.22e-98) {
		tmp = t_3;
	} else if (x <= 3.25e-305) {
		tmp = t_1;
	} else if (x <= 6.2e-153) {
		tmp = t_2;
	} else if (x <= 6e-126) {
		tmp = t_1;
	} else if (x <= 1.05e-76) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (y * t)
    t_2 = x - (z * t)
    t_3 = x * ((z - y) + 1.0d0)
    if (x <= (-1.22d-98)) then
        tmp = t_3
    else if (x <= 3.25d-305) then
        tmp = t_1
    else if (x <= 6.2d-153) then
        tmp = t_2
    else if (x <= 6d-126) then
        tmp = t_1
    else if (x <= 1.05d-76) then
        tmp = t_2
    else
        tmp = t_3
    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);
	double t_2 = x - (z * t);
	double t_3 = x * ((z - y) + 1.0);
	double tmp;
	if (x <= -1.22e-98) {
		tmp = t_3;
	} else if (x <= 3.25e-305) {
		tmp = t_1;
	} else if (x <= 6.2e-153) {
		tmp = t_2;
	} else if (x <= 6e-126) {
		tmp = t_1;
	} else if (x <= 1.05e-76) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	t_2 = x - (z * t)
	t_3 = x * ((z - y) + 1.0)
	tmp = 0
	if x <= -1.22e-98:
		tmp = t_3
	elif x <= 3.25e-305:
		tmp = t_1
	elif x <= 6.2e-153:
		tmp = t_2
	elif x <= 6e-126:
		tmp = t_1
	elif x <= 1.05e-76:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	t_2 = Float64(x - Float64(z * t))
	t_3 = Float64(x * Float64(Float64(z - y) + 1.0))
	tmp = 0.0
	if (x <= -1.22e-98)
		tmp = t_3;
	elseif (x <= 3.25e-305)
		tmp = t_1;
	elseif (x <= 6.2e-153)
		tmp = t_2;
	elseif (x <= 6e-126)
		tmp = t_1;
	elseif (x <= 1.05e-76)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * t);
	t_2 = x - (z * t);
	t_3 = x * ((z - y) + 1.0);
	tmp = 0.0;
	if (x <= -1.22e-98)
		tmp = t_3;
	elseif (x <= 3.25e-305)
		tmp = t_1;
	elseif (x <= 6.2e-153)
		tmp = t_2;
	elseif (x <= 6e-126)
		tmp = t_1;
	elseif (x <= 1.05e-76)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.22e-98], t$95$3, If[LessEqual[x, 3.25e-305], t$95$1, If[LessEqual[x, 6.2e-153], t$95$2, If[LessEqual[x, 6e-126], t$95$1, If[LessEqual[x, 1.05e-76], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2200000000000001e-98 or 1.04999999999999996e-76 < 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 75.4%

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

      1. mul-1-neg 75.4%

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

      2. unsub-neg 75.4%

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

   5. Simplified 75.4%

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

   if -1.2200000000000001e-98 < x < 3.24999999999999996e-305 or 6.1999999999999999e-153 < x < 6.0000000000000003e-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 88.3%

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

   4. Taylor expanded in y around inf 65.7%

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

   if 3.24999999999999996e-305 < x < 6.1999999999999999e-153 or 6.0000000000000003e-126 < x < 1.04999999999999996e-76

   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 90.7%

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

   4. Taylor expanded in y around 0 67.6%

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

      1. mul-1-neg 67.6%

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

      2. unsub-neg 67.6%

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

      3. *-commutative 67.6%

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

   6. Simplified 67.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;x \leq 3.25 \cdot 10^{-305}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-153}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-126}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-76}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ t_2 := x \cdot \left(-y\right)\\ t_3 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-43}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-131}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))) (t_2 (* x (- y))) (t_3 (* z (- t))))
   (if (<= y -1.6e+56)
     t_2
     (if (<= y -6.5e-43)
       t_3
       (if (<= y 4e-229)
         t_1
         (if (<= y 2.3e-131) t_3 (if (<= y 1.55e+31) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = x * -y;
	double t_3 = z * -t;
	double tmp;
	if (y <= -1.6e+56) {
		tmp = t_2;
	} else if (y <= -6.5e-43) {
		tmp = t_3;
	} else if (y <= 4e-229) {
		tmp = t_1;
	} else if (y <= 2.3e-131) {
		tmp = t_3;
	} else if (y <= 1.55e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    t_2 = x * -y
    t_3 = z * -t
    if (y <= (-1.6d+56)) then
        tmp = t_2
    else if (y <= (-6.5d-43)) then
        tmp = t_3
    else if (y <= 4d-229) then
        tmp = t_1
    else if (y <= 2.3d-131) then
        tmp = t_3
    else if (y <= 1.55d+31) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = x * -y;
	double t_3 = z * -t;
	double tmp;
	if (y <= -1.6e+56) {
		tmp = t_2;
	} else if (y <= -6.5e-43) {
		tmp = t_3;
	} else if (y <= 4e-229) {
		tmp = t_1;
	} else if (y <= 2.3e-131) {
		tmp = t_3;
	} else if (y <= 1.55e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	t_2 = x * -y
	t_3 = z * -t
	tmp = 0
	if y <= -1.6e+56:
		tmp = t_2
	elif y <= -6.5e-43:
		tmp = t_3
	elif y <= 4e-229:
		tmp = t_1
	elif y <= 2.3e-131:
		tmp = t_3
	elif y <= 1.55e+31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	t_2 = Float64(x * Float64(-y))
	t_3 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -1.6e+56)
		tmp = t_2;
	elseif (y <= -6.5e-43)
		tmp = t_3;
	elseif (y <= 4e-229)
		tmp = t_1;
	elseif (y <= 2.3e-131)
		tmp = t_3;
	elseif (y <= 1.55e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	t_2 = x * -y;
	t_3 = z * -t;
	tmp = 0.0;
	if (y <= -1.6e+56)
		tmp = t_2;
	elseif (y <= -6.5e-43)
		tmp = t_3;
	elseif (y <= 4e-229)
		tmp = t_1;
	elseif (y <= 2.3e-131)
		tmp = t_3;
	elseif (y <= 1.55e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * (-y)), $MachinePrecision]}, Block[{t$95$3 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -1.6e+56], t$95$2, If[LessEqual[y, -6.5e-43], t$95$3, If[LessEqual[y, 4e-229], t$95$1, If[LessEqual[y, 2.3e-131], t$95$3, If[LessEqual[y, 1.55e+31], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.60000000000000002e56 or 1.5500000000000001e31 < y

   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 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in y around inf 49.4%

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

      1. mul-1-neg 49.4%

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

      2. distribute-lft-neg-out 49.4%

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

      3. *-commutative 49.4%

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

   8. Simplified 49.4%

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

   if -1.60000000000000002e56 < y < -6.50000000000000001e-43 or 4.00000000000000028e-229 < y < 2.30000000000000022e-131

   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 83.3%

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

   4. Taylor expanded in y around 0 71.9%

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

      1. mul-1-neg 71.9%

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

      2. unsub-neg 71.9%

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

      3. *-commutative 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in x around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. distribute-rgt-neg-out 59.2%

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

   9. Simplified 59.2%

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

   if -6.50000000000000001e-43 < y < 4.00000000000000028e-229 or 2.30000000000000022e-131 < y < 1.5500000000000001e31

   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 62.5%

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

      1. mul-1-neg 62.5%

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

      2. unsub-neg 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in y around 0 60.7%

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

      1. +-commutative 60.7%

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

   8. Simplified 60.7%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-43}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-229}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-131}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* x (- 1.0 y))))
   (if (<= t -6.5e+34)
     t_1
     (if (<= t 3.5e-70)
       t_2
       (if (<= t 2.05e-10) (* x (+ z 1.0)) (if (<= t 9.5e+78) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x * (1.0 - y);
	double tmp;
	if (t <= -6.5e+34) {
		tmp = t_1;
	} else if (t <= 3.5e-70) {
		tmp = t_2;
	} else if (t <= 2.05e-10) {
		tmp = x * (z + 1.0);
	} else if (t <= 9.5e+78) {
		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 * -t
    t_2 = x * (1.0d0 - y)
    if (t <= (-6.5d+34)) then
        tmp = t_1
    else if (t <= 3.5d-70) then
        tmp = t_2
    else if (t <= 2.05d-10) then
        tmp = x * (z + 1.0d0)
    else if (t <= 9.5d+78) 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 * -t;
	double t_2 = x * (1.0 - y);
	double tmp;
	if (t <= -6.5e+34) {
		tmp = t_1;
	} else if (t <= 3.5e-70) {
		tmp = t_2;
	} else if (t <= 2.05e-10) {
		tmp = x * (z + 1.0);
	} else if (t <= 9.5e+78) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x * (1.0 - y)
	tmp = 0
	if t <= -6.5e+34:
		tmp = t_1
	elif t <= 3.5e-70:
		tmp = t_2
	elif t <= 2.05e-10:
		tmp = x * (z + 1.0)
	elif t <= 9.5e+78:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (t <= -6.5e+34)
		tmp = t_1;
	elseif (t <= 3.5e-70)
		tmp = t_2;
	elseif (t <= 2.05e-10)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (t <= 9.5e+78)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = x * (1.0 - y);
	tmp = 0.0;
	if (t <= -6.5e+34)
		tmp = t_1;
	elseif (t <= 3.5e-70)
		tmp = t_2;
	elseif (t <= 2.05e-10)
		tmp = x * (z + 1.0);
	elseif (t <= 9.5e+78)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+34], t$95$1, If[LessEqual[t, 3.5e-70], t$95$2, If[LessEqual[t, 2.05e-10], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+78], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.50000000000000017e34 or 9.5000000000000006e78 < 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 92.7%

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

   4. Taylor expanded in y around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. unsub-neg 54.4%

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

      3. *-commutative 54.4%

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

   6. Simplified 54.4%

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

   7. Taylor expanded in x around 0 49.3%

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

      1. mul-1-neg 49.3%

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

      2. distribute-rgt-neg-out 49.3%

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

   9. Simplified 49.3%

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

   if -6.50000000000000017e34 < t < 3.49999999999999974e-70 or 2.0499999999999999e-10 < t < 9.5000000000000006e78

   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 74.0%

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

      1. mul-1-neg 74.0%

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

      2. unsub-neg 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in z around 0 56.1%

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

   if 3.49999999999999974e-70 < t < 2.0499999999999999e-10

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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 y around 0 61.0%

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

      1. +-commutative 61.0%

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

   8. Simplified 61.0%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+34}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{-88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))))
   (if (<= t -6.2e-88)
     t_1
     (if (<= t 3.5e-67)
       (* x (- 1.0 y))
       (if (<= t 5.9e+38)
         (* x (+ z 1.0))
         (if (<= t 2.3e+91) (* z (- t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double tmp;
	if (t <= -6.2e-88) {
		tmp = t_1;
	} else if (t <= 3.5e-67) {
		tmp = x * (1.0 - y);
	} else if (t <= 5.9e+38) {
		tmp = x * (z + 1.0);
	} else if (t <= 2.3e+91) {
		tmp = 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 + (y * t)
    if (t <= (-6.2d-88)) then
        tmp = t_1
    else if (t <= 3.5d-67) then
        tmp = x * (1.0d0 - y)
    else if (t <= 5.9d+38) then
        tmp = x * (z + 1.0d0)
    else if (t <= 2.3d+91) then
        tmp = 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 + (y * t);
	double tmp;
	if (t <= -6.2e-88) {
		tmp = t_1;
	} else if (t <= 3.5e-67) {
		tmp = x * (1.0 - y);
	} else if (t <= 5.9e+38) {
		tmp = x * (z + 1.0);
	} else if (t <= 2.3e+91) {
		tmp = z * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	tmp = 0
	if t <= -6.2e-88:
		tmp = t_1
	elif t <= 3.5e-67:
		tmp = x * (1.0 - y)
	elif t <= 5.9e+38:
		tmp = x * (z + 1.0)
	elif t <= 2.3e+91:
		tmp = z * -t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (t <= -6.2e-88)
		tmp = t_1;
	elseif (t <= 3.5e-67)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (t <= 5.9e+38)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (t <= 2.3e+91)
		tmp = Float64(z * Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * t);
	tmp = 0.0;
	if (t <= -6.2e-88)
		tmp = t_1;
	elseif (t <= 3.5e-67)
		tmp = x * (1.0 - y);
	elseif (t <= 5.9e+38)
		tmp = x * (z + 1.0);
	elseif (t <= 2.3e+91)
		tmp = z * -t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e-88], t$95$1, If[LessEqual[t, 3.5e-67], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.9e+38], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+91], N[(z * (-t)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.1999999999999995e-88 or 2.29999999999999991e91 < 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 88.9%

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

   4. Taylor expanded in y around inf 49.1%

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

   if -6.1999999999999995e-88 < t < 3.5e-67

   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 82.6%

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

      1. mul-1-neg 82.6%

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

      2. unsub-neg 82.6%

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

   5. Simplified 82.6%

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

   6. Taylor expanded in z around 0 62.4%

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

   if 3.5e-67 < t < 5.89999999999999981e38

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in y around 0 57.2%

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

      1. +-commutative 57.2%

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

   8. Simplified 57.2%

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

   if 5.89999999999999981e38 < t < 2.29999999999999991e91

   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 67.9%

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

   4. Taylor expanded in y around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. unsub-neg 67.9%

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

      3. *-commutative 67.9%

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

   6. Simplified 67.9%

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

   7. Taylor expanded in x around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. distribute-rgt-neg-out 51.6%

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

   9. Simplified 51.6%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-88}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))) (t_2 (* z (- t))))
   (if (<= y -1.45e+57)
     t_1
     (if (<= y -4.2e-89)
       t_2
       (if (<= y -1.26e-238) x (if (<= y 1.55e+31) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double t_2 = z * -t;
	double tmp;
	if (y <= -1.45e+57) {
		tmp = t_1;
	} else if (y <= -4.2e-89) {
		tmp = t_2;
	} else if (y <= -1.26e-238) {
		tmp = x;
	} else if (y <= 1.55e+31) {
		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 = x * -y
    t_2 = z * -t
    if (y <= (-1.45d+57)) then
        tmp = t_1
    else if (y <= (-4.2d-89)) then
        tmp = t_2
    else if (y <= (-1.26d-238)) then
        tmp = x
    else if (y <= 1.55d+31) 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 = x * -y;
	double t_2 = z * -t;
	double tmp;
	if (y <= -1.45e+57) {
		tmp = t_1;
	} else if (y <= -4.2e-89) {
		tmp = t_2;
	} else if (y <= -1.26e-238) {
		tmp = x;
	} else if (y <= 1.55e+31) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -y
	t_2 = z * -t
	tmp = 0
	if y <= -1.45e+57:
		tmp = t_1
	elif y <= -4.2e-89:
		tmp = t_2
	elif y <= -1.26e-238:
		tmp = x
	elif y <= 1.55e+31:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -1.45e+57)
		tmp = t_1;
	elseif (y <= -4.2e-89)
		tmp = t_2;
	elseif (y <= -1.26e-238)
		tmp = x;
	elseif (y <= 1.55e+31)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -y;
	t_2 = z * -t;
	tmp = 0.0;
	if (y <= -1.45e+57)
		tmp = t_1;
	elseif (y <= -4.2e-89)
		tmp = t_2;
	elseif (y <= -1.26e-238)
		tmp = x;
	elseif (y <= 1.55e+31)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -1.45e+57], t$95$1, If[LessEqual[y, -4.2e-89], t$95$2, If[LessEqual[y, -1.26e-238], x, If[LessEqual[y, 1.55e+31], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4500000000000001e57 or 1.5500000000000001e31 < y

   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 58.7%

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

      1. mul-1-neg 58.7%

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

      2. unsub-neg 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in y around inf 49.4%

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

      1. mul-1-neg 49.4%

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

      2. distribute-lft-neg-out 49.4%

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

      3. *-commutative 49.4%

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

   8. Simplified 49.4%

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

   if -1.4500000000000001e57 < y < -4.2000000000000002e-89 or -1.26000000000000004e-238 < y < 1.5500000000000001e31

   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 76.0%

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

   4. Taylor expanded in y around 0 65.7%

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

      1. mul-1-neg 65.7%

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

      2. unsub-neg 65.7%

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

      3. *-commutative 65.7%

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

   6. Simplified 65.7%

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

   7. Taylor expanded in x around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. distribute-rgt-neg-out 45.3%

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

   9. Simplified 45.3%

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

   if -4.2000000000000002e-89 < y < -1.26000000000000004e-238

   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 79.5%

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

   4. Taylor expanded in x around inf 44.8%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 34.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+92}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.3e+92)
   (* z x)
   (if (<= x 1.16e+42) (* z (- t)) (if (<= x 1.5e+103) x (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.3e+92) {
		tmp = z * x;
	} else if (x <= 1.16e+42) {
		tmp = z * -t;
	} else if (x <= 1.5e+103) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.3d+92)) then
        tmp = z * x
    else if (x <= 1.16d+42) then
        tmp = z * -t
    else if (x <= 1.5d+103) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.3e+92) {
		tmp = z * x;
	} else if (x <= 1.16e+42) {
		tmp = z * -t;
	} else if (x <= 1.5e+103) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.3e+92:
		tmp = z * x
	elif x <= 1.16e+42:
		tmp = z * -t
	elif x <= 1.5e+103:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.3e+92)
		tmp = Float64(z * x);
	elseif (x <= 1.16e+42)
		tmp = Float64(z * Float64(-t));
	elseif (x <= 1.5e+103)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.3e+92)
		tmp = z * x;
	elseif (x <= 1.16e+42)
		tmp = z * -t;
	elseif (x <= 1.5e+103)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.3e+92], N[(z * x), $MachinePrecision], If[LessEqual[x, 1.16e+42], N[(z * (-t)), $MachinePrecision], If[LessEqual[x, 1.5e+103], x, N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2999999999999998e92 or 1.5e103 < 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 inf 40.0%

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

      1. *-commutative 40.0%

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

   8. Simplified 40.0%

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

   if -4.2999999999999998e92 < x < 1.15999999999999995e42

   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 76.0%

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

   4. Taylor expanded in y around 0 45.2%

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

      1. mul-1-neg 45.2%

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

      2. unsub-neg 45.2%

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

      3. *-commutative 45.2%

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

   6. Simplified 45.2%

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

   7. Taylor expanded in x around 0 34.8%

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

      1. mul-1-neg 34.8%

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

      2. distribute-rgt-neg-out 34.8%

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

   9. Simplified 34.8%

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

   if 1.15999999999999995e42 < x < 1.5e103

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 72.6%

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

   4. Taylor expanded in x around inf 43.6%

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

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{+92}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+42}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-87} \lor \neg \left(t \leq 1.3 \cdot 10^{+40}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.15e-87) (not (<= t 1.3e+40)))
   (- x (* t (- z y)))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.15e-87) || !(t <= 1.3e+40)) {
		tmp = x - (t * (z - y));
	} 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 <= (-1.15d-87)) .or. (.not. (t <= 1.3d+40))) then
        tmp = x - (t * (z - y))
    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 <= -1.15e-87) || !(t <= 1.3e+40)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.15e-87) or not (t <= 1.3e+40):
		tmp = x - (t * (z - y))
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.15e-87) || !(t <= 1.3e+40))
		tmp = Float64(x - Float64(t * Float64(z - y)));
	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 <= -1.15e-87) || ~((t <= 1.3e+40)))
		tmp = x - (t * (z - y));
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.15e-87], N[Not[LessEqual[t, 1.3e+40]], $MachinePrecision]], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1500000000000001e-87 or 1.3e40 < 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 88.6%

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

   if -1.1500000000000001e-87 < t < 1.3e40

   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 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

   5. Simplified 81.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{-87} \lor \neg \left(t \leq 1.3 \cdot 10^{+40}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6800000000 \lor \neg \left(y \leq 1.05 \cdot 10^{+20}\right):\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6800000000.0) (not (<= y 1.05e+20)))
   (- x (* y (- x t)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6800000000.0) || !(y <= 1.05e+20)) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6800000000.0d0)) .or. (.not. (y <= 1.05d+20))) then
        tmp = x - (y * (x - t))
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6800000000.0) || !(y <= 1.05e+20)) {
		tmp = x - (y * (x - t));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6800000000.0) or not (y <= 1.05e+20):
		tmp = x - (y * (x - t))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6800000000.0) || !(y <= 1.05e+20))
		tmp = Float64(x - Float64(y * Float64(x - t)));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6800000000.0) || ~((y <= 1.05e+20)))
		tmp = x - (y * (x - t));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6800000000.0], N[Not[LessEqual[y, 1.05e+20]], $MachinePrecision]], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8e9 or 1.05e20 < 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 83.0%

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

      1. *-commutative 83.0%

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

   5. Simplified 83.0%

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

   if -6.8e9 < y < 1.05e20

   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 91.2%

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

      1. mul-1-neg 91.2%

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

      2. unsub-neg 91.2%

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

   5. Simplified 91.2%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6800000000 \lor \neg \left(y \leq 1.05 \cdot 10^{+20}\right):\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+28} \lor \neg \left(z \leq 2.2 \cdot 10^{-6}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6e+28) (not (<= z 2.2e-6))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e+28) || !(z <= 2.2e-6)) {
		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 <= (-6d+28)) .or. (.not. (z <= 2.2d-6))) 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 <= -6e+28) || !(z <= 2.2e-6)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6e+28) or not (z <= 2.2e-6):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e+28) || !(z <= 2.2e-6))
		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 <= -6e+28) || ~((z <= 2.2e-6)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6e+28], N[Not[LessEqual[z, 2.2e-6]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000002e28 or 2.2000000000000001e-6 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 53.2%

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

      1. mul-1-neg 53.2%

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

      2. unsub-neg 53.2%

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

   5. Simplified 53.2%

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

   6. Taylor expanded in z around inf 40.7%

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

      1. *-commutative 40.7%

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

   8. Simplified 40.7%

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

   if -6.0000000000000002e28 < z < 2.2000000000000001e-6

   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 66.5%

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

   4. Taylor expanded in x around inf 25.3%

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

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+28} \lor \neg \left(z \leq 2.2 \cdot 10^{-6}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 13: 18.2% 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 62.0%

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

4. Taylor expanded in x around inf 15.1%

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

5. Final simplification 15.1%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024076 
(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))))