Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.4s

Alternatives: 13

Speedup: 1.0×

• 34.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 63.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot t\\ t_2 := x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{+232}:\\ \;\;\;\;y \cdot \left(t + x\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+208}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq -2.85 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+112} \lor \neg \left(t \leq 5.3 \cdot 10^{+190}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y t))) (t_2 (* x (- (+ z 1.0) y))))
   (if (<= t -5e+232)
     (* y (+ t x))
     (if (<= t -1.65e+208)
       (* z (- t))
       (if (<= t -2.85e+150)
         t_1
         (if (<= t -3.2e+22)
           t_2
           (if (<= t -2.65e-39)
             (* y (- t x))
             (if (<= t 3e+42)
               t_2
               (if (or (<= t 3.8e+112) (not (<= t 5.3e+190)))
                 t_1
                 (- x (* z t)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = x * ((z + 1.0) - y);
	double tmp;
	if (t <= -5e+232) {
		tmp = y * (t + x);
	} else if (t <= -1.65e+208) {
		tmp = z * -t;
	} else if (t <= -2.85e+150) {
		tmp = t_1;
	} else if (t <= -3.2e+22) {
		tmp = t_2;
	} else if (t <= -2.65e-39) {
		tmp = y * (t - x);
	} else if (t <= 3e+42) {
		tmp = t_2;
	} else if ((t <= 3.8e+112) || !(t <= 5.3e+190)) {
		tmp = t_1;
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * t)
    t_2 = x * ((z + 1.0d0) - y)
    if (t <= (-5d+232)) then
        tmp = y * (t + x)
    else if (t <= (-1.65d+208)) then
        tmp = z * -t
    else if (t <= (-2.85d+150)) then
        tmp = t_1
    else if (t <= (-3.2d+22)) then
        tmp = t_2
    else if (t <= (-2.65d-39)) then
        tmp = y * (t - x)
    else if (t <= 3d+42) then
        tmp = t_2
    else if ((t <= 3.8d+112) .or. (.not. (t <= 5.3d+190))) then
        tmp = t_1
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * t);
	double t_2 = x * ((z + 1.0) - y);
	double tmp;
	if (t <= -5e+232) {
		tmp = y * (t + x);
	} else if (t <= -1.65e+208) {
		tmp = z * -t;
	} else if (t <= -2.85e+150) {
		tmp = t_1;
	} else if (t <= -3.2e+22) {
		tmp = t_2;
	} else if (t <= -2.65e-39) {
		tmp = y * (t - x);
	} else if (t <= 3e+42) {
		tmp = t_2;
	} else if ((t <= 3.8e+112) || !(t <= 5.3e+190)) {
		tmp = t_1;
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * t)
	t_2 = x * ((z + 1.0) - y)
	tmp = 0
	if t <= -5e+232:
		tmp = y * (t + x)
	elif t <= -1.65e+208:
		tmp = z * -t
	elif t <= -2.85e+150:
		tmp = t_1
	elif t <= -3.2e+22:
		tmp = t_2
	elif t <= -2.65e-39:
		tmp = y * (t - x)
	elif t <= 3e+42:
		tmp = t_2
	elif (t <= 3.8e+112) or not (t <= 5.3e+190):
		tmp = t_1
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * t))
	t_2 = Float64(x * Float64(Float64(z + 1.0) - y))
	tmp = 0.0
	if (t <= -5e+232)
		tmp = Float64(y * Float64(t + x));
	elseif (t <= -1.65e+208)
		tmp = Float64(z * Float64(-t));
	elseif (t <= -2.85e+150)
		tmp = t_1;
	elseif (t <= -3.2e+22)
		tmp = t_2;
	elseif (t <= -2.65e-39)
		tmp = Float64(y * Float64(t - x));
	elseif (t <= 3e+42)
		tmp = t_2;
	elseif ((t <= 3.8e+112) || !(t <= 5.3e+190))
		tmp = t_1;
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * t);
	t_2 = x * ((z + 1.0) - y);
	tmp = 0.0;
	if (t <= -5e+232)
		tmp = y * (t + x);
	elseif (t <= -1.65e+208)
		tmp = z * -t;
	elseif (t <= -2.85e+150)
		tmp = t_1;
	elseif (t <= -3.2e+22)
		tmp = t_2;
	elseif (t <= -2.65e-39)
		tmp = y * (t - x);
	elseif (t <= 3e+42)
		tmp = t_2;
	elseif ((t <= 3.8e+112) || ~((t <= 5.3e+190)))
		tmp = t_1;
	else
		tmp = x - (z * t);
	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[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+232], N[(y * N[(t + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.65e+208], N[(z * (-t)), $MachinePrecision], If[LessEqual[t, -2.85e+150], t$95$1, If[LessEqual[t, -3.2e+22], t$95$2, If[LessEqual[t, -2.65e-39], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+42], t$95$2, If[Or[LessEqual[t, 3.8e+112], N[Not[LessEqual[t, 5.3e+190]], $MachinePrecision]], t$95$1, N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.99999999999999987e232

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 82.6%

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

   3. Taylor expanded in y around inf 82.6%

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

      1. sub-neg 82.6%

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

      2. distribute-lft-in 82.6%

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

      3. add-sqr-sqrt 63.6%

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

      4. sqrt-unprod 73.6%

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

      5. sqr-neg 73.6%

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

      6. sqrt-unprod 9.9%

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

      7. add-sqr-sqrt 73.6%

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

   5. Applied egg-rr 73.6%

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

      1. distribute-lft-in 82.6%

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

   7. Simplified 82.6%

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

   if -4.99999999999999987e232 < t < -1.65e208

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   if -1.65e208 < t < -2.8500000000000001e150 or 3.00000000000000029e42 < t < 3.80000000000000008e112 or 5.30000000000000015e190 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 96.7%

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

   3. Taylor expanded in z around 0 72.1%

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

   if -2.8500000000000001e150 < t < -3.2e22 or -2.65000000000000002e-39 < t < 3.00000000000000029e42

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. mul-1-neg 79.7%

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

      3. unsub-neg 79.7%

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

      4. distribute-lft-out-- 79.7%

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

      5. *-rgt-identity 79.7%

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

   4. Simplified 79.7%

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

   5. Taylor expanded in x around 0 79.7%

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

   if -3.2e22 < t < -2.65000000000000002e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 82.4%

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

   3. Taylor expanded in y around inf 73.9%

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

   if 3.80000000000000008e112 < t < 5.30000000000000015e190

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 95.4%

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

   3. Taylor expanded in y around 0 90.4%

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

      1. +-commutative 90.4%

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

      2. mul-1-neg 90.4%

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

      3. unsub-neg 90.4%

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

   5. Simplified 90.4%

      \[\leadsto \color{blue}{x - t \cdot z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+232}:\\ \;\;\;\;y \cdot \left(t + x\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+208}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq -2.85 \cdot 10^{+150}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+112} \lor \neg \left(t \leq 5.3 \cdot 10^{+190}\right):\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 3: 37.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t + x\right)\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-237}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (+ t x))) (t_2 (* z (- t))))
   (if (<= y -2.7e+39)
     t_1
     (if (<= y -1.35e-43)
       t_2
       (if (<= y -1.42e-105)
         x
         (if (<= y -1.35e-237)
           t_2
           (if (<= y 4.1e-275)
             x
             (if (<= y 2.05e-196)
               t_2
               (if (<= y 2e-106) x (if (<= y 3.8e-64) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t + x);
	double t_2 = z * -t;
	double tmp;
	if (y <= -2.7e+39) {
		tmp = t_1;
	} else if (y <= -1.35e-43) {
		tmp = t_2;
	} else if (y <= -1.42e-105) {
		tmp = x;
	} else if (y <= -1.35e-237) {
		tmp = t_2;
	} else if (y <= 4.1e-275) {
		tmp = x;
	} else if (y <= 2.05e-196) {
		tmp = t_2;
	} else if (y <= 2e-106) {
		tmp = x;
	} else if (y <= 3.8e-64) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t + x)
    t_2 = z * -t
    if (y <= (-2.7d+39)) then
        tmp = t_1
    else if (y <= (-1.35d-43)) then
        tmp = t_2
    else if (y <= (-1.42d-105)) then
        tmp = x
    else if (y <= (-1.35d-237)) then
        tmp = t_2
    else if (y <= 4.1d-275) then
        tmp = x
    else if (y <= 2.05d-196) then
        tmp = t_2
    else if (y <= 2d-106) then
        tmp = x
    else if (y <= 3.8d-64) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t + x);
	double t_2 = z * -t;
	double tmp;
	if (y <= -2.7e+39) {
		tmp = t_1;
	} else if (y <= -1.35e-43) {
		tmp = t_2;
	} else if (y <= -1.42e-105) {
		tmp = x;
	} else if (y <= -1.35e-237) {
		tmp = t_2;
	} else if (y <= 4.1e-275) {
		tmp = x;
	} else if (y <= 2.05e-196) {
		tmp = t_2;
	} else if (y <= 2e-106) {
		tmp = x;
	} else if (y <= 3.8e-64) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t + x)
	t_2 = z * -t
	tmp = 0
	if y <= -2.7e+39:
		tmp = t_1
	elif y <= -1.35e-43:
		tmp = t_2
	elif y <= -1.42e-105:
		tmp = x
	elif y <= -1.35e-237:
		tmp = t_2
	elif y <= 4.1e-275:
		tmp = x
	elif y <= 2.05e-196:
		tmp = t_2
	elif y <= 2e-106:
		tmp = x
	elif y <= 3.8e-64:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t + x))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -2.7e+39)
		tmp = t_1;
	elseif (y <= -1.35e-43)
		tmp = t_2;
	elseif (y <= -1.42e-105)
		tmp = x;
	elseif (y <= -1.35e-237)
		tmp = t_2;
	elseif (y <= 4.1e-275)
		tmp = x;
	elseif (y <= 2.05e-196)
		tmp = t_2;
	elseif (y <= 2e-106)
		tmp = x;
	elseif (y <= 3.8e-64)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t + x);
	t_2 = z * -t;
	tmp = 0.0;
	if (y <= -2.7e+39)
		tmp = t_1;
	elseif (y <= -1.35e-43)
		tmp = t_2;
	elseif (y <= -1.42e-105)
		tmp = x;
	elseif (y <= -1.35e-237)
		tmp = t_2;
	elseif (y <= 4.1e-275)
		tmp = x;
	elseif (y <= 2.05e-196)
		tmp = t_2;
	elseif (y <= 2e-106)
		tmp = x;
	elseif (y <= 3.8e-64)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -2.7e+39], t$95$1, If[LessEqual[y, -1.35e-43], t$95$2, If[LessEqual[y, -1.42e-105], x, If[LessEqual[y, -1.35e-237], t$95$2, If[LessEqual[y, 4.1e-275], x, If[LessEqual[y, 2.05e-196], t$95$2, If[LessEqual[y, 2e-106], x, If[LessEqual[y, 3.8e-64], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.70000000000000003e39 or 3.8000000000000002e-64 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 78.8%

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

   3. Taylor expanded in y around inf 73.8%

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

      1. sub-neg 73.8%

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

      2. distribute-lft-in 72.9%

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

      3. add-sqr-sqrt 41.4%

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

      4. sqrt-unprod 58.1%

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

      5. sqr-neg 58.1%

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

      6. sqrt-unprod 17.6%

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

      7. add-sqr-sqrt 43.7%

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

   5. Applied egg-rr 43.7%

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

      1. distribute-lft-in 45.4%

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

   7. Simplified 45.4%

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

   if -2.70000000000000003e39 < y < -1.34999999999999996e-43 or -1.4199999999999999e-105 < y < -1.34999999999999992e-237 or 4.09999999999999975e-275 < y < 2.05000000000000011e-196 or 1.99999999999999988e-106 < y < 3.8000000000000002e-64

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 68.6%

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

   3. Taylor expanded in y around 0 59.7%

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

      1. +-commutative 59.7%

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

      2. mul-1-neg 59.7%

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

      3. unsub-neg 59.7%

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

   5. Simplified 59.7%

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

   6. Taylor expanded in x around 0 50.1%

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

      1. associate-*r* 50.1%

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

      2. neg-mul-1 50.1%

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

      3. *-commutative 50.1%

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

   8. Simplified 50.1%

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

   if -1.34999999999999996e-43 < y < -1.4199999999999999e-105 or -1.34999999999999992e-237 < y < 4.09999999999999975e-275 or 2.05000000000000011e-196 < y < 1.99999999999999988e-106

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.2%

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

   3. Taylor expanded in x around inf 55.7%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+39}:\\ \;\;\;\;y \cdot \left(t + x\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-43}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-237}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-196}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t + x\right)\\ \end{array} \]

Alternative 4: 71.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot x\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := x - z \cdot t\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-214}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-21}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 23000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z x))) (t_2 (* y (- t x))) (t_3 (- x (* z t))))
   (if (<= y -4.2e+19)
     t_2
     (if (<= y -2.7e-150)
       t_3
       (if (<= y -3.4e-192)
         t_1
         (if (<= y 4.8e-214)
           t_3
           (if (<= y 3.7e-102)
             t_1
             (if (<= y 3.5e-21) t_3 (if (<= y 23000.0) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * x);
	double t_2 = y * (t - x);
	double t_3 = x - (z * t);
	double tmp;
	if (y <= -4.2e+19) {
		tmp = t_2;
	} else if (y <= -2.7e-150) {
		tmp = t_3;
	} else if (y <= -3.4e-192) {
		tmp = t_1;
	} else if (y <= 4.8e-214) {
		tmp = t_3;
	} else if (y <= 3.7e-102) {
		tmp = t_1;
	} else if (y <= 3.5e-21) {
		tmp = t_3;
	} else if (y <= 23000.0) {
		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 * x)
    t_2 = y * (t - x)
    t_3 = x - (z * t)
    if (y <= (-4.2d+19)) then
        tmp = t_2
    else if (y <= (-2.7d-150)) then
        tmp = t_3
    else if (y <= (-3.4d-192)) then
        tmp = t_1
    else if (y <= 4.8d-214) then
        tmp = t_3
    else if (y <= 3.7d-102) then
        tmp = t_1
    else if (y <= 3.5d-21) then
        tmp = t_3
    else if (y <= 23000.0d0) 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 * x);
	double t_2 = y * (t - x);
	double t_3 = x - (z * t);
	double tmp;
	if (y <= -4.2e+19) {
		tmp = t_2;
	} else if (y <= -2.7e-150) {
		tmp = t_3;
	} else if (y <= -3.4e-192) {
		tmp = t_1;
	} else if (y <= 4.8e-214) {
		tmp = t_3;
	} else if (y <= 3.7e-102) {
		tmp = t_1;
	} else if (y <= 3.5e-21) {
		tmp = t_3;
	} else if (y <= 23000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * x)
	t_2 = y * (t - x)
	t_3 = x - (z * t)
	tmp = 0
	if y <= -4.2e+19:
		tmp = t_2
	elif y <= -2.7e-150:
		tmp = t_3
	elif y <= -3.4e-192:
		tmp = t_1
	elif y <= 4.8e-214:
		tmp = t_3
	elif y <= 3.7e-102:
		tmp = t_1
	elif y <= 3.5e-21:
		tmp = t_3
	elif y <= 23000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * x))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(x - Float64(z * t))
	tmp = 0.0
	if (y <= -4.2e+19)
		tmp = t_2;
	elseif (y <= -2.7e-150)
		tmp = t_3;
	elseif (y <= -3.4e-192)
		tmp = t_1;
	elseif (y <= 4.8e-214)
		tmp = t_3;
	elseif (y <= 3.7e-102)
		tmp = t_1;
	elseif (y <= 3.5e-21)
		tmp = t_3;
	elseif (y <= 23000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * x);
	t_2 = y * (t - x);
	t_3 = x - (z * t);
	tmp = 0.0;
	if (y <= -4.2e+19)
		tmp = t_2;
	elseif (y <= -2.7e-150)
		tmp = t_3;
	elseif (y <= -3.4e-192)
		tmp = t_1;
	elseif (y <= 4.8e-214)
		tmp = t_3;
	elseif (y <= 3.7e-102)
		tmp = t_1;
	elseif (y <= 3.5e-21)
		tmp = t_3;
	elseif (y <= 23000.0)
		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 * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+19], t$95$2, If[LessEqual[y, -2.7e-150], t$95$3, If[LessEqual[y, -3.4e-192], t$95$1, If[LessEqual[y, 4.8e-214], t$95$3, If[LessEqual[y, 3.7e-102], t$95$1, If[LessEqual[y, 3.5e-21], t$95$3, If[LessEqual[y, 23000.0], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2e19 or 23000 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 79.2%

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

   3. Taylor expanded in y around inf 79.0%

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

   if -4.2e19 < y < -2.7000000000000001e-150 or -3.40000000000000002e-192 < y < 4.80000000000000041e-214 or 3.6999999999999997e-102 < y < 3.5000000000000003e-21

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.0%

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

   3. Taylor expanded in y around 0 72.4%

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

      1. +-commutative 72.4%

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

      2. mul-1-neg 72.4%

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

      3. unsub-neg 72.4%

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

   5. Simplified 72.4%

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

   if -2.7000000000000001e-150 < y < -3.40000000000000002e-192 or 4.80000000000000041e-214 < y < 3.6999999999999997e-102 or 3.5000000000000003e-21 < y < 23000

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.1%

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

      1. *-commutative 82.1%

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

      2. mul-1-neg 82.1%

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

      3. unsub-neg 82.1%

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

      4. distribute-lft-out-- 82.1%

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

      5. *-rgt-identity 82.1%

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

   4. Simplified 82.1%

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

   5. Taylor expanded in y around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. distribute-rgt-neg-in 80.7%

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

   7. Simplified 80.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-150}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-192}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-214}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-102}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-21}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 23000:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 5: 56.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-233}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-276}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- t))))
   (if (<= y -4.2e+19)
     t_1
     (if (<= y -8.2e-233)
       t_2
       (if (<= y 4.9e-276)
         x
         (if (<= y 1.2e-196)
           t_2
           (if (<= y 1.45e-106) x (if (<= y 8.6e-63) t_2 t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * -t;
	double tmp;
	if (y <= -4.2e+19) {
		tmp = t_1;
	} else if (y <= -8.2e-233) {
		tmp = t_2;
	} else if (y <= 4.9e-276) {
		tmp = x;
	} else if (y <= 1.2e-196) {
		tmp = t_2;
	} else if (y <= 1.45e-106) {
		tmp = x;
	} else if (y <= 8.6e-63) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * -t
    if (y <= (-4.2d+19)) then
        tmp = t_1
    else if (y <= (-8.2d-233)) then
        tmp = t_2
    else if (y <= 4.9d-276) then
        tmp = x
    else if (y <= 1.2d-196) then
        tmp = t_2
    else if (y <= 1.45d-106) then
        tmp = x
    else if (y <= 8.6d-63) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * -t;
	double tmp;
	if (y <= -4.2e+19) {
		tmp = t_1;
	} else if (y <= -8.2e-233) {
		tmp = t_2;
	} else if (y <= 4.9e-276) {
		tmp = x;
	} else if (y <= 1.2e-196) {
		tmp = t_2;
	} else if (y <= 1.45e-106) {
		tmp = x;
	} else if (y <= 8.6e-63) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * -t
	tmp = 0
	if y <= -4.2e+19:
		tmp = t_1
	elif y <= -8.2e-233:
		tmp = t_2
	elif y <= 4.9e-276:
		tmp = x
	elif y <= 1.2e-196:
		tmp = t_2
	elif y <= 1.45e-106:
		tmp = x
	elif y <= 8.6e-63:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -4.2e+19)
		tmp = t_1;
	elseif (y <= -8.2e-233)
		tmp = t_2;
	elseif (y <= 4.9e-276)
		tmp = x;
	elseif (y <= 1.2e-196)
		tmp = t_2;
	elseif (y <= 1.45e-106)
		tmp = x;
	elseif (y <= 8.6e-63)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * -t;
	tmp = 0.0;
	if (y <= -4.2e+19)
		tmp = t_1;
	elseif (y <= -8.2e-233)
		tmp = t_2;
	elseif (y <= 4.9e-276)
		tmp = x;
	elseif (y <= 1.2e-196)
		tmp = t_2;
	elseif (y <= 1.45e-106)
		tmp = x;
	elseif (y <= 8.6e-63)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -4.2e+19], t$95$1, If[LessEqual[y, -8.2e-233], t$95$2, If[LessEqual[y, 4.9e-276], x, If[LessEqual[y, 1.2e-196], t$95$2, If[LessEqual[y, 1.45e-106], x, If[LessEqual[y, 8.6e-63], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2e19 or 8.5999999999999997e-63 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 77.8%

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

   3. Taylor expanded in y around inf 73.1%

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

   if -4.2e19 < y < -8.2000000000000009e-233 or 4.89999999999999966e-276 < y < 1.2000000000000001e-196 or 1.45e-106 < y < 8.5999999999999997e-63

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 72.2%

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

   3. Taylor expanded in y around 0 63.7%

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

      1. +-commutative 63.7%

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

      2. mul-1-neg 63.7%

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

      3. unsub-neg 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in x around 0 46.4%

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

      1. associate-*r* 46.4%

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

      2. neg-mul-1 46.4%

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

      3. *-commutative 46.4%

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

   8. Simplified 46.4%

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

   if -8.2000000000000009e-233 < y < 4.89999999999999966e-276 or 1.2000000000000001e-196 < y < 1.45e-106

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 74.8%

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

   3. Taylor expanded in x around inf 55.1%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-276}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-196}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-63}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 6: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-41} \lor \neg \left(t \leq 2.5 \cdot 10^{-56}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.8e-41) (not (<= t 2.5e-56)))
   (+ x (* (- y z) t))
   (* x (- (+ z 1.0) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e-41) || !(t <= 2.5e-56)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z + 1.0) - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.8d-41)) .or. (.not. (t <= 2.5d-56))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x * ((z + 1.0d0) - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e-41) || !(t <= 2.5e-56)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z + 1.0) - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.8e-41) or not (t <= 2.5e-56):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * ((z + 1.0) - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.8e-41) || !(t <= 2.5e-56))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x * Float64(Float64(z + 1.0) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.8e-41) || ~((t <= 2.5e-56)))
		tmp = x + ((y - z) * t);
	else
		tmp = x * ((z + 1.0) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.8e-41], N[Not[LessEqual[t, 2.5e-56]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8000000000000002e-41 or 2.49999999999999999e-56 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 87.1%

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

   if -2.8000000000000002e-41 < t < 2.49999999999999999e-56

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 91.4%

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

      1. *-commutative 91.4%

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

      2. mul-1-neg 91.4%

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

      3. unsub-neg 91.4%

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

      4. distribute-lft-out-- 91.4%

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

      5. *-rgt-identity 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in x around 0 91.4%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-41} \lor \neg \left(t \leq 2.5 \cdot 10^{-56}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \end{array} \]

Alternative 7: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-42} \lor \neg \left(t \leq 1.3 \cdot 10^{-56}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.9e-42) (not (<= t 1.3e-56)))
   (+ x (* (- y z) t))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.9e-42) || !(t <= 1.3e-56)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.9d-42)) .or. (.not. (t <= 1.3d-56))) then
        tmp = x + ((y - z) * t)
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.9e-42) || !(t <= 1.3e-56)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.9e-42) or not (t <= 1.3e-56):
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.9e-42) || !(t <= 1.3e-56))
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.9e-42) || ~((t <= 1.3e-56)))
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.9e-42], N[Not[LessEqual[t, 1.3e-56]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.9000000000000003e-42 or 1.29999999999999998e-56 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 87.1%

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

   if -2.9000000000000003e-42 < t < 1.29999999999999998e-56

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. associate-+r+ 96.0%

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

      3. associate-*r* 96.0%

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

      4. *-commutative 96.0%

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

      5. distribute-rgt-in 96.0%

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

      6. *-commutative 96.0%

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

      7. mul-1-neg 96.0%

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

      8. distribute-lft-in 96.0%

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

      9. distribute-rgt-neg-in 96.0%

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

      10. mul-1-neg 96.0%

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

      11. fma-def 97.0%

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

      12. +-commutative 97.0%

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

      13. mul-1-neg 97.0%

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

      14. sub-neg 97.0%

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

      15. mul-1-neg 97.0%

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

      16. distribute-rgt-neg-in 97.0%

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

      17. distribute-lft-in 97.0%

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

      18. sub-neg 97.0%

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

      19. *-commutative 97.0%

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

   6. Simplified 97.0%

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

   7. Taylor expanded in t around 0 91.2%

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

      1. associate-*r* 91.2%

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

      2. neg-mul-1 91.2%

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

   9. Simplified 91.2%

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

   10. Taylor expanded in x around inf 91.4%

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

       1. *-commutative 91.4%

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

       2. mul-1-neg 91.4%

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

       3. unsub-neg 91.4%

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

   12. Simplified 91.4%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-42} \lor \neg \left(t \leq 1.3 \cdot 10^{-56}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 8: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.066 \lor \neg \left(z \leq 5.8 \cdot 10^{-8}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.066) (not (<= z 5.8e-8)))
   (- x (* z (- t x)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.066) || !(z <= 5.8e-8)) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-0.066d0)) .or. (.not. (z <= 5.8d-8))) then
        tmp = x - (z * (t - x))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.066) || !(z <= 5.8e-8)) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.066) or not (z <= 5.8e-8):
		tmp = x - (z * (t - x))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.066) || !(z <= 5.8e-8))
		tmp = Float64(x - Float64(z * Float64(t - x)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.066) || ~((z <= 5.8e-8)))
		tmp = x - (z * (t - x));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.066], N[Not[LessEqual[z, 5.8e-8]], $MachinePrecision]], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.066000000000000003 or 5.8000000000000003e-8 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.6%

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

      1. +-commutative 86.6%

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

      2. mul-1-neg 86.6%

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

      3. unsub-neg 86.6%

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

      4. *-commutative 86.6%

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

   4. Simplified 86.6%

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

   if -0.066000000000000003 < z < 5.8000000000000003e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 92.2%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.066 \lor \neg \left(z \leq 5.8 \cdot 10^{-8}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 9: 52.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+65} \lor \neg \left(z \leq 1.7 \cdot 10^{+43}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.5e+65) (not (<= z 1.7e+43))) (* z (- t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+65) || !(z <= 1.7e+43)) {
		tmp = z * -t;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.5d+65)) .or. (.not. (z <= 1.7d+43))) then
        tmp = z * -t
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+65) || !(z <= 1.7e+43)) {
		tmp = z * -t;
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.5e+65) or not (z <= 1.7e+43):
		tmp = z * -t
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.5e+65) || !(z <= 1.7e+43))
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.5e+65) || ~((z <= 1.7e+43)))
		tmp = z * -t;
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.5e+65], N[Not[LessEqual[z, 1.7e+43]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999996e65 or 1.70000000000000006e43 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 55.8%

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

   3. Taylor expanded in y around 0 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in x around 0 50.2%

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

      1. associate-*r* 50.2%

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

      2. neg-mul-1 50.2%

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

      3. *-commutative 50.2%

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

   8. Simplified 50.2%

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

   if -5.4999999999999996e65 < z < 1.70000000000000006e43

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 73.6%

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

   3. Taylor expanded in z around 0 65.4%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+65} \lor \neg \left(z \leq 1.7 \cdot 10^{+43}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 10: 72.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+19} \lor \neg \left(y \leq 10500000000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2e+19) (not (<= y 10500000000.0)))
   (* y (- t x))
   (- x (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e+19) || !(y <= 10500000000.0)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.2d+19)) .or. (.not. (y <= 10500000000.0d0))) then
        tmp = y * (t - x)
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e+19) || !(y <= 10500000000.0)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.2e+19) or not (y <= 10500000000.0):
		tmp = y * (t - x)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.2e+19) || !(y <= 10500000000.0))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.2e+19) || ~((y <= 10500000000.0)))
		tmp = y * (t - x);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.2e+19], N[Not[LessEqual[y, 10500000000.0]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e19 or 1.05e10 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 79.9%

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

   3. Taylor expanded in y around inf 79.6%

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

   if -4.2e19 < y < 1.05e10

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 73.6%

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

   3. Taylor expanded in y around 0 64.4%

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

      1. +-commutative 64.4%

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

      2. mul-1-neg 64.4%

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

      3. unsub-neg 64.4%

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

   5. Simplified 64.4%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+19} \lor \neg \left(y \leq 10500000000\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 12: 37.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0029 \lor \neg \left(z \leq 2.5 \cdot 10^{-17}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.0029) (not (<= z 2.5e-17))) (* z (- t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.0029) || !(z <= 2.5e-17)) {
		tmp = z * -t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-0.0029d0)) .or. (.not. (z <= 2.5d-17))) then
        tmp = z * -t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.0029) || !(z <= 2.5e-17)) {
		tmp = z * -t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -0.0029) or not (z <= 2.5e-17):
		tmp = z * -t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.0029) || !(z <= 2.5e-17))
		tmp = Float64(z * Float64(-t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.0029) || ~((z <= 2.5e-17)))
		tmp = z * -t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.0029], N[Not[LessEqual[z, 2.5e-17]], $MachinePrecision]], N[(z * (-t)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.0029 or 2.4999999999999999e-17 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 53.6%

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

   3. Taylor expanded in y around 0 44.9%

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

      1. +-commutative 44.9%

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

      2. mul-1-neg 44.9%

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

      3. unsub-neg 44.9%

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

   5. Simplified 44.9%

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

   6. Taylor expanded in x around 0 44.2%

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

      1. associate-*r* 44.2%

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

      2. neg-mul-1 44.2%

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

      3. *-commutative 44.2%

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

   8. Simplified 44.2%

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

   if -0.0029 < z < 2.4999999999999999e-17

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.8%

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

   3. Taylor expanded in x around inf 35.8%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0029 \lor \neg \left(z \leq 2.5 \cdot 10^{-17}\right):\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 18.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in t around inf 66.7%

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

3. Taylor expanded in x around inf 20.1%

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

4. Final simplification 20.1%

   \[\leadsto x \]

Developer target: 96.4% 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 2023230 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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