Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.5s

Alternatives: 14

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-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: 37.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-104}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-265}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-258}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+59}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.5e+17)
   (* z x)
   (if (<= z -3.9e-104)
     (* y t)
     (if (<= z -1.05e-265)
       x
       (if (<= z -5.8e-306)
         (* y (- x))
         (if (<= z 4.7e-298)
           x
           (if (<= z 4.8e-258)
             (* y t)
             (if (<= z 3e-167) x (if (<= z 1.9e+59) (* y t) (* z x))))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e+17) {
		tmp = z * x;
	} else if (z <= -3.9e-104) {
		tmp = y * t;
	} else if (z <= -1.05e-265) {
		tmp = x;
	} else if (z <= -5.8e-306) {
		tmp = y * -x;
	} else if (z <= 4.7e-298) {
		tmp = x;
	} else if (z <= 4.8e-258) {
		tmp = y * t;
	} else if (z <= 3e-167) {
		tmp = x;
	} else if (z <= 1.9e+59) {
		tmp = y * t;
	} 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 (z <= (-9.5d+17)) then
        tmp = z * x
    else if (z <= (-3.9d-104)) then
        tmp = y * t
    else if (z <= (-1.05d-265)) then
        tmp = x
    else if (z <= (-5.8d-306)) then
        tmp = y * -x
    else if (z <= 4.7d-298) then
        tmp = x
    else if (z <= 4.8d-258) then
        tmp = y * t
    else if (z <= 3d-167) then
        tmp = x
    else if (z <= 1.9d+59) then
        tmp = y * t
    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 (z <= -9.5e+17) {
		tmp = z * x;
	} else if (z <= -3.9e-104) {
		tmp = y * t;
	} else if (z <= -1.05e-265) {
		tmp = x;
	} else if (z <= -5.8e-306) {
		tmp = y * -x;
	} else if (z <= 4.7e-298) {
		tmp = x;
	} else if (z <= 4.8e-258) {
		tmp = y * t;
	} else if (z <= 3e-167) {
		tmp = x;
	} else if (z <= 1.9e+59) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.5e+17:
		tmp = z * x
	elif z <= -3.9e-104:
		tmp = y * t
	elif z <= -1.05e-265:
		tmp = x
	elif z <= -5.8e-306:
		tmp = y * -x
	elif z <= 4.7e-298:
		tmp = x
	elif z <= 4.8e-258:
		tmp = y * t
	elif z <= 3e-167:
		tmp = x
	elif z <= 1.9e+59:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.5e+17)
		tmp = Float64(z * x);
	elseif (z <= -3.9e-104)
		tmp = Float64(y * t);
	elseif (z <= -1.05e-265)
		tmp = x;
	elseif (z <= -5.8e-306)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 4.7e-298)
		tmp = x;
	elseif (z <= 4.8e-258)
		tmp = Float64(y * t);
	elseif (z <= 3e-167)
		tmp = x;
	elseif (z <= 1.9e+59)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.5e+17)
		tmp = z * x;
	elseif (z <= -3.9e-104)
		tmp = y * t;
	elseif (z <= -1.05e-265)
		tmp = x;
	elseif (z <= -5.8e-306)
		tmp = y * -x;
	elseif (z <= 4.7e-298)
		tmp = x;
	elseif (z <= 4.8e-258)
		tmp = y * t;
	elseif (z <= 3e-167)
		tmp = x;
	elseif (z <= 1.9e+59)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.5e+17], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.9e-104], N[(y * t), $MachinePrecision], If[LessEqual[z, -1.05e-265], x, If[LessEqual[z, -5.8e-306], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 4.7e-298], x, If[LessEqual[z, 4.8e-258], N[(y * t), $MachinePrecision], If[LessEqual[z, 3e-167], x, If[LessEqual[z, 1.9e+59], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.5e17 or 1.9e59 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 57.8%

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

      1. mul-1-neg 57.8%

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

      2. distribute-rgt-neg-in 57.8%

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

      3. neg-sub0 57.8%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 57.8%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 57.8%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 57.8%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 57.8%

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

      8. remove-double-neg 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in y around 0 49.3%

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

      1. *-commutative 49.3%

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

   7. Simplified 49.3%

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

   8. Taylor expanded in z around inf 49.3%

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

      1. *-commutative 49.3%

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

   10. Simplified 49.3%

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

   if -9.5e17 < z < -3.9000000000000002e-104 or 4.70000000000000037e-298 < z < 4.8000000000000003e-258 or 2.9999999999999998e-167 < z < 1.9e59

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 85.3%

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

      1. *-commutative 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in x around -inf 83.9%

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

      1. +-commutative 83.9%

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

      2. mul-1-neg 83.9%

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

      3. unsub-neg 83.9%

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

      4. sub-neg 83.9%

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

      5. metadata-eval 83.9%

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

      6. +-commutative 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in t around inf 47.9%

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

   if -3.9000000000000002e-104 < z < -1.05000000000000002e-265 or -5.7999999999999998e-306 < z < 4.70000000000000037e-298 or 4.8000000000000003e-258 < z < 2.9999999999999998e-167

   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 53.5%

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

   if -1.05000000000000002e-265 < z < -5.7999999999999998e-306

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. distribute-rgt-neg-in 82.3%

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

      3. neg-sub0 82.3%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 82.3%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 82.3%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 82.3%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 82.3%

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

      8. remove-double-neg 82.3%

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

   4. Simplified 82.3%

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

   5. Taylor expanded in z around 0 82.3%

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

      1. *-rgt-identity 82.3%

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

      2. mul-1-neg 82.3%

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

      3. distribute-rgt-neg-out 82.3%

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

      4. distribute-lft-in 82.3%

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

      5. unsub-neg 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in y around inf 64.6%

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

      1. neg-mul-1 64.6%

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

      2. distribute-lft-neg-in 64.6%

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

      3. *-commutative 64.6%

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

   10. Simplified 64.6%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-104}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-265}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-258}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-167}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+59}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3: 51.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+136}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (* y (- t x))))
   (if (<= z -2.25e+136)
     (* z x)
     (if (<= z -2e-104)
       t_2
       (if (<= z 3.2e-298)
         t_1
         (if (<= z 1.06e-259)
           t_2
           (if (<= z 5e-166) t_1 (if (<= z 2.55e+119) t_2 (* z x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = y * (t - x);
	double tmp;
	if (z <= -2.25e+136) {
		tmp = z * x;
	} else if (z <= -2e-104) {
		tmp = t_2;
	} else if (z <= 3.2e-298) {
		tmp = t_1;
	} else if (z <= 1.06e-259) {
		tmp = t_2;
	} else if (z <= 5e-166) {
		tmp = t_1;
	} else if (z <= 2.55e+119) {
		tmp = t_2;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = y * (t - x)
    if (z <= (-2.25d+136)) then
        tmp = z * x
    else if (z <= (-2d-104)) then
        tmp = t_2
    else if (z <= 3.2d-298) then
        tmp = t_1
    else if (z <= 1.06d-259) then
        tmp = t_2
    else if (z <= 5d-166) then
        tmp = t_1
    else if (z <= 2.55d+119) then
        tmp = t_2
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = y * (t - x);
	double tmp;
	if (z <= -2.25e+136) {
		tmp = z * x;
	} else if (z <= -2e-104) {
		tmp = t_2;
	} else if (z <= 3.2e-298) {
		tmp = t_1;
	} else if (z <= 1.06e-259) {
		tmp = t_2;
	} else if (z <= 5e-166) {
		tmp = t_1;
	} else if (z <= 2.55e+119) {
		tmp = t_2;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = y * (t - x)
	tmp = 0
	if z <= -2.25e+136:
		tmp = z * x
	elif z <= -2e-104:
		tmp = t_2
	elif z <= 3.2e-298:
		tmp = t_1
	elif z <= 1.06e-259:
		tmp = t_2
	elif z <= 5e-166:
		tmp = t_1
	elif z <= 2.55e+119:
		tmp = t_2
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (z <= -2.25e+136)
		tmp = Float64(z * x);
	elseif (z <= -2e-104)
		tmp = t_2;
	elseif (z <= 3.2e-298)
		tmp = t_1;
	elseif (z <= 1.06e-259)
		tmp = t_2;
	elseif (z <= 5e-166)
		tmp = t_1;
	elseif (z <= 2.55e+119)
		tmp = t_2;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = y * (t - x);
	tmp = 0.0;
	if (z <= -2.25e+136)
		tmp = z * x;
	elseif (z <= -2e-104)
		tmp = t_2;
	elseif (z <= 3.2e-298)
		tmp = t_1;
	elseif (z <= 1.06e-259)
		tmp = t_2;
	elseif (z <= 5e-166)
		tmp = t_1;
	elseif (z <= 2.55e+119)
		tmp = t_2;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+136], N[(z * x), $MachinePrecision], If[LessEqual[z, -2e-104], t$95$2, If[LessEqual[z, 3.2e-298], t$95$1, If[LessEqual[z, 1.06e-259], t$95$2, If[LessEqual[z, 5e-166], t$95$1, If[LessEqual[z, 2.55e+119], t$95$2, N[(z * x), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.25e136 or 2.54999999999999992e119 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. distribute-rgt-neg-in 61.2%

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

      3. neg-sub0 61.2%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 61.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 61.2%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 61.2%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 61.2%

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

      8. remove-double-neg 61.2%

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

   4. Simplified 61.2%

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

   5. Taylor expanded in y around 0 56.4%

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

      1. *-commutative 56.4%

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

   7. Simplified 56.4%

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

   8. Taylor expanded in z around inf 56.4%

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

      1. *-commutative 56.4%

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

   10. Simplified 56.4%

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

   if -2.25e136 < z < -1.99999999999999985e-104 or 3.19999999999999997e-298 < z < 1.06e-259 or 5e-166 < z < 2.54999999999999992e119

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 71.9%

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

      1. *-commutative 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in x around -inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. sub-neg 71.0%

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

      5. metadata-eval 71.0%

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

      6. +-commutative 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in y around inf 61.8%

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

   if -1.99999999999999985e-104 < z < 3.19999999999999997e-298 or 1.06e-259 < z < 5e-166

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 79.0%

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

      1. mul-1-neg 79.0%

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

      2. distribute-rgt-neg-in 79.0%

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

      3. neg-sub0 79.0%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 79.0%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 79.0%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 79.0%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 79.0%

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

      8. remove-double-neg 79.0%

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

   4. Simplified 79.0%

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

   5. Taylor expanded in z around 0 79.0%

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

      1. *-rgt-identity 79.0%

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

      2. mul-1-neg 79.0%

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

      3. distribute-rgt-neg-out 79.0%

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

      4. distribute-lft-in 79.0%

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

      5. unsub-neg 79.0%

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

   7. Simplified 79.0%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+136}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-104}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 4: 37.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -52000000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-103}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-258}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+56}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -52000000000.0)
   (* z x)
   (if (<= z -1.2e-103)
     (* y t)
     (if (<= z 1.25e-298)
       x
       (if (<= z 7.5e-258)
         (* y t)
         (if (<= z 1.25e-164) x (if (<= z 4.2e+56) (* y t) (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -52000000000.0) {
		tmp = z * x;
	} else if (z <= -1.2e-103) {
		tmp = y * t;
	} else if (z <= 1.25e-298) {
		tmp = x;
	} else if (z <= 7.5e-258) {
		tmp = y * t;
	} else if (z <= 1.25e-164) {
		tmp = x;
	} else if (z <= 4.2e+56) {
		tmp = y * t;
	} 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 (z <= (-52000000000.0d0)) then
        tmp = z * x
    else if (z <= (-1.2d-103)) then
        tmp = y * t
    else if (z <= 1.25d-298) then
        tmp = x
    else if (z <= 7.5d-258) then
        tmp = y * t
    else if (z <= 1.25d-164) then
        tmp = x
    else if (z <= 4.2d+56) then
        tmp = y * t
    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 (z <= -52000000000.0) {
		tmp = z * x;
	} else if (z <= -1.2e-103) {
		tmp = y * t;
	} else if (z <= 1.25e-298) {
		tmp = x;
	} else if (z <= 7.5e-258) {
		tmp = y * t;
	} else if (z <= 1.25e-164) {
		tmp = x;
	} else if (z <= 4.2e+56) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -52000000000.0:
		tmp = z * x
	elif z <= -1.2e-103:
		tmp = y * t
	elif z <= 1.25e-298:
		tmp = x
	elif z <= 7.5e-258:
		tmp = y * t
	elif z <= 1.25e-164:
		tmp = x
	elif z <= 4.2e+56:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -52000000000.0)
		tmp = Float64(z * x);
	elseif (z <= -1.2e-103)
		tmp = Float64(y * t);
	elseif (z <= 1.25e-298)
		tmp = x;
	elseif (z <= 7.5e-258)
		tmp = Float64(y * t);
	elseif (z <= 1.25e-164)
		tmp = x;
	elseif (z <= 4.2e+56)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -52000000000.0)
		tmp = z * x;
	elseif (z <= -1.2e-103)
		tmp = y * t;
	elseif (z <= 1.25e-298)
		tmp = x;
	elseif (z <= 7.5e-258)
		tmp = y * t;
	elseif (z <= 1.25e-164)
		tmp = x;
	elseif (z <= 4.2e+56)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -52000000000.0], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.2e-103], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.25e-298], x, If[LessEqual[z, 7.5e-258], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.25e-164], x, If[LessEqual[z, 4.2e+56], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2e10 or 4.20000000000000034e56 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 57.8%

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

      1. mul-1-neg 57.8%

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

      2. distribute-rgt-neg-in 57.8%

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

      3. neg-sub0 57.8%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 57.8%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 57.8%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 57.8%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 57.8%

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

      8. remove-double-neg 57.8%

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

   4. Simplified 57.8%

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

   5. Taylor expanded in y around 0 49.3%

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

      1. *-commutative 49.3%

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

   7. Simplified 49.3%

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

   8. Taylor expanded in z around inf 49.3%

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

      1. *-commutative 49.3%

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

   10. Simplified 49.3%

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

   if -5.2e10 < z < -1.2000000000000001e-103 or 1.25000000000000005e-298 < z < 7.4999999999999998e-258 or 1.2499999999999999e-164 < z < 4.20000000000000034e56

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 85.3%

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

      1. *-commutative 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in x around -inf 83.9%

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

      1. +-commutative 83.9%

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

      2. mul-1-neg 83.9%

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

      3. unsub-neg 83.9%

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

      4. sub-neg 83.9%

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

      5. metadata-eval 83.9%

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

      6. +-commutative 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in t around inf 47.9%

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

   if -1.2000000000000001e-103 < z < 1.25000000000000005e-298 or 7.4999999999999998e-258 < z < 1.2499999999999999e-164

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 70.2%

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

   3. Taylor expanded in x around inf 48.3%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -52000000000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-103}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-298}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-258}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-164}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+56}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 5: 69.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + z \cdot x\\ \mathbf{if}\;y \leq -2 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-206}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 0.06:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (+ x (* z x))))
   (if (<= y -2e-24)
     t_1
     (if (<= y -3.8e-254)
       t_2
       (if (<= y 1.15e-206) (- x (* z t)) (if (<= y 0.06) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x + (z * x);
	double tmp;
	if (y <= -2e-24) {
		tmp = t_1;
	} else if (y <= -3.8e-254) {
		tmp = t_2;
	} else if (y <= 1.15e-206) {
		tmp = x - (z * t);
	} else if (y <= 0.06) {
		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 = x + (z * x)
    if (y <= (-2d-24)) then
        tmp = t_1
    else if (y <= (-3.8d-254)) then
        tmp = t_2
    else if (y <= 1.15d-206) then
        tmp = x - (z * t)
    else if (y <= 0.06d0) 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 = x + (z * x);
	double tmp;
	if (y <= -2e-24) {
		tmp = t_1;
	} else if (y <= -3.8e-254) {
		tmp = t_2;
	} else if (y <= 1.15e-206) {
		tmp = x - (z * t);
	} else if (y <= 0.06) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x + (z * x)
	tmp = 0
	if y <= -2e-24:
		tmp = t_1
	elif y <= -3.8e-254:
		tmp = t_2
	elif y <= 1.15e-206:
		tmp = x - (z * t)
	elif y <= 0.06:
		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(x + Float64(z * x))
	tmp = 0.0
	if (y <= -2e-24)
		tmp = t_1;
	elseif (y <= -3.8e-254)
		tmp = t_2;
	elseif (y <= 1.15e-206)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 0.06)
		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 = x + (z * x);
	tmp = 0.0;
	if (y <= -2e-24)
		tmp = t_1;
	elseif (y <= -3.8e-254)
		tmp = t_2;
	elseif (y <= 1.15e-206)
		tmp = x - (z * t);
	elseif (y <= 0.06)
		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[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e-24], t$95$1, If[LessEqual[y, -3.8e-254], t$95$2, If[LessEqual[y, 1.15e-206], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.06], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999985e-24 or 0.059999999999999998 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.1%

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

      1. *-commutative 79.1%

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

   4. Simplified 79.1%

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

   5. Taylor expanded in x around -inf 77.6%

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

      1. +-commutative 77.6%

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

      2. mul-1-neg 77.6%

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

      3. unsub-neg 77.6%

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

      4. sub-neg 77.6%

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

      5. metadata-eval 77.6%

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

      6. +-commutative 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in y around inf 76.9%

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

   if -1.99999999999999985e-24 < y < -3.8000000000000001e-254 or 1.15e-206 < y < 0.059999999999999998

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. distribute-rgt-neg-in 70.5%

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

      3. neg-sub0 70.5%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 70.5%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 70.5%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 70.5%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 70.5%

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

      8. remove-double-neg 70.5%

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

   4. Simplified 70.5%

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

   5. Taylor expanded in y around 0 70.5%

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

      1. *-commutative 70.5%

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

   7. Simplified 70.5%

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

   if -3.8000000000000001e-254 < y < 1.15e-206

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 84.5%

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

   3. Taylor expanded in y around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

   5. Simplified 84.5%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-254}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-206}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 0.06:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 6: 58.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-145}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -5.5e-42)
     t_1
     (if (<= y -1e-145) (* z x) (if (<= y 3.6e-12) (+ x (* y t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -5.5e-42) {
		tmp = t_1;
	} else if (y <= -1e-145) {
		tmp = z * x;
	} else if (y <= 3.6e-12) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-5.5d-42)) then
        tmp = t_1
    else if (y <= (-1d-145)) then
        tmp = z * x
    else if (y <= 3.6d-12) then
        tmp = x + (y * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -5.5e-42) {
		tmp = t_1;
	} else if (y <= -1e-145) {
		tmp = z * x;
	} else if (y <= 3.6e-12) {
		tmp = x + (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -5.5e-42:
		tmp = t_1
	elif y <= -1e-145:
		tmp = z * x
	elif y <= 3.6e-12:
		tmp = x + (y * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -5.5e-42)
		tmp = t_1;
	elseif (y <= -1e-145)
		tmp = Float64(z * x);
	elseif (y <= 3.6e-12)
		tmp = Float64(x + Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -5.5e-42)
		tmp = t_1;
	elseif (y <= -1e-145)
		tmp = z * x;
	elseif (y <= 3.6e-12)
		tmp = x + (y * t);
	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]}, If[LessEqual[y, -5.5e-42], t$95$1, If[LessEqual[y, -1e-145], N[(z * x), $MachinePrecision], If[LessEqual[y, 3.6e-12], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5e-42 or 3.6e-12 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 77.0%

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

      1. *-commutative 77.0%

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

   4. Simplified 77.0%

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

   5. Taylor expanded in x around -inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

      4. sub-neg 75.6%

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

      5. metadata-eval 75.6%

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

      6. +-commutative 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in y around inf 74.0%

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

   if -5.5e-42 < y < -9.99999999999999915e-146

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. distribute-rgt-neg-in 74.1%

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

      3. neg-sub0 74.1%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 74.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 74.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 74.1%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 74.1%

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

      8. remove-double-neg 74.1%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in y around 0 74.1%

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

      1. *-commutative 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in z around inf 54.8%

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

      1. *-commutative 54.8%

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

   10. Simplified 54.8%

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

   if -9.99999999999999915e-146 < y < 3.6e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 74.7%

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

   3. Taylor expanded in z around 0 42.1%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-42}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-145}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-12}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 7: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -14 \lor \neg \left(y \leq 1.25 \cdot 10^{+28}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -14.0) (not (<= y 1.25e+28)))
   (* y (- t x))
   (+ x (* t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -14.0) || !(y <= 1.25e+28)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-14.0d0)) .or. (.not. (y <= 1.25d+28))) then
        tmp = y * (t - x)
    else
        tmp = x + (t * (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -14.0) || !(y <= 1.25e+28)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (t * (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -14.0) or not (y <= 1.25e+28):
		tmp = y * (t - x)
	else:
		tmp = x + (t * (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -14.0) || !(y <= 1.25e+28))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x + Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -14.0) || ~((y <= 1.25e+28)))
		tmp = y * (t - x);
	else
		tmp = x + (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -14.0], N[Not[LessEqual[y, 1.25e+28]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -14 or 1.24999999999999989e28 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.9%

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

      1. *-commutative 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in x around -inf 78.3%

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

      1. +-commutative 78.3%

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

      2. mul-1-neg 78.3%

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

      3. unsub-neg 78.3%

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

      4. sub-neg 78.3%

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

      5. metadata-eval 78.3%

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

      6. +-commutative 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in y around inf 78.8%

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

   if -14 < y < 1.24999999999999989e28

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 70.0%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -14 \lor \neg \left(y \leq 1.25 \cdot 10^{+28}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \end{array} \]

Alternative 8: 81.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-54} \lor \neg \left(t \leq 1.15 \cdot 10^{-48}\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.5e-54) (not (<= t 1.15e-48)))
   (+ x (* t (- y z)))
   (+ x (* x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.5e-54) || !(t <= 1.15e-48)) {
		tmp = x + (t * (y - z));
	} 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 <= (-1.5d-54)) .or. (.not. (t <= 1.15d-48))) then
        tmp = x + (t * (y - z))
    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 <= -1.5e-54) || !(t <= 1.15e-48)) {
		tmp = x + (t * (y - z));
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.5e-54) or not (t <= 1.15e-48):
		tmp = x + (t * (y - z))
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.5e-54) || !(t <= 1.15e-48))
		tmp = Float64(x + Float64(t * Float64(y - z)));
	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 <= -1.5e-54) || ~((t <= 1.15e-48)))
		tmp = x + (t * (y - z));
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.5e-54], N[Not[LessEqual[t, 1.15e-48]], $MachinePrecision]], N[(x + N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.50000000000000005e-54 or 1.15e-48 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 87.3%

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

   if -1.50000000000000005e-54 < t < 1.15e-48

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. distribute-rgt-neg-in 84.1%

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

      3. neg-sub0 84.1%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 84.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 84.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 84.1%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 84.1%

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

      8. remove-double-neg 84.1%

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

   4. Simplified 84.1%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-54} \lor \neg \left(t \leq 1.15 \cdot 10^{-48}\right):\\ \;\;\;\;x + t \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 9: 84.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \lor \neg \left(z \leq 3.2 \cdot 10^{+54}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.4) (not (<= z 3.2e+54)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4) || !(z <= 3.2e+54)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.4d0)) .or. (.not. (z <= 3.2d+54))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4) || !(z <= 3.2e+54)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.4) or not (z <= 3.2e+54):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.4) || !(z <= 3.2e+54))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.4) || ~((z <= 3.2e+54)))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.4], N[Not[LessEqual[z, 3.2e+54]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.39999999999999991 or 3.2e54 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. unsub-neg 85.1%

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

   4. Simplified 85.1%

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

   if -3.39999999999999991 < z < 3.2e54

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 90.7%

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

      1. *-commutative 90.7%

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

   4. Simplified 90.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \lor \neg \left(z \leq 3.2 \cdot 10^{+54}\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 10: 49.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -220 \lor \neg \left(z \leq 5.4 \cdot 10^{+118}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -220.0) (not (<= z 5.4e+118))) (* z x) (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -220.0) || !(z <= 5.4e+118)) {
		tmp = z * x;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-220.0d0)) .or. (.not. (z <= 5.4d+118))) then
        tmp = z * x
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -220.0) || !(z <= 5.4e+118)) {
		tmp = z * x;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -220.0) or not (z <= 5.4e+118):
		tmp = z * x
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -220.0) || !(z <= 5.4e+118))
		tmp = Float64(z * x);
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -220.0) || ~((z <= 5.4e+118)))
		tmp = z * x;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -220.0], N[Not[LessEqual[z, 5.4e+118]], $MachinePrecision]], N[(z * x), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -220 or 5.4e118 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 58.9%

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

      1. mul-1-neg 58.9%

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

      2. distribute-rgt-neg-in 58.9%

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

      3. neg-sub0 58.9%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 58.9%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 58.9%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 58.9%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 58.9%

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

      8. remove-double-neg 58.9%

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

   4. Simplified 58.9%

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

   5. Taylor expanded in y around 0 51.3%

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

      1. *-commutative 51.3%

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

   7. Simplified 51.3%

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

   8. Taylor expanded in z around inf 51.3%

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

      1. *-commutative 51.3%

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

   10. Simplified 51.3%

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

   if -220 < z < 5.4e118

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-rgt-neg-in 60.4%

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

      3. neg-sub0 60.4%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 60.4%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 60.4%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 60.4%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 60.4%

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

      8. remove-double-neg 60.4%

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

   4. Simplified 60.4%

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

   5. Taylor expanded in z around 0 57.7%

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

      1. *-rgt-identity 57.7%

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

      2. mul-1-neg 57.7%

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

      3. distribute-rgt-neg-out 57.7%

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

      4. distribute-lft-in 57.7%

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

      5. unsub-neg 57.7%

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

   7. Simplified 57.7%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -220 \lor \neg \left(z \leq 5.4 \cdot 10^{+118}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 11: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-18} \lor \neg \left(y \leq 0.0012\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.4e-18) (not (<= y 0.0012))) (* y (- t x)) (+ x (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e-18) || !(y <= 0.0012)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (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 ((y <= (-2.4d-18)) .or. (.not. (y <= 0.0012d0))) then
        tmp = y * (t - x)
    else
        tmp = x + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e-18) || !(y <= 0.0012)) {
		tmp = y * (t - x);
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.4e-18) or not (y <= 0.0012):
		tmp = y * (t - x)
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.4e-18) || !(y <= 0.0012))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.4e-18) || ~((y <= 0.0012)))
		tmp = y * (t - x);
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.4e-18], N[Not[LessEqual[y, 0.0012]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999994e-18 or 0.00119999999999999989 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.1%

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

      1. *-commutative 79.1%

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

   4. Simplified 79.1%

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

   5. Taylor expanded in x around -inf 77.6%

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

      1. +-commutative 77.6%

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

      2. mul-1-neg 77.6%

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

      3. unsub-neg 77.6%

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

      4. sub-neg 77.6%

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

      5. metadata-eval 77.6%

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

      6. +-commutative 77.6%

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

   7. Simplified 77.6%

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

   8. Taylor expanded in y around inf 76.9%

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

   if -2.39999999999999994e-18 < y < 0.00119999999999999989

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. distribute-rgt-neg-in 65.1%

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

      3. neg-sub0 65.1%

         \[\leadsto x + x \cdot \color{blue}{\left(0 - \left(y - z\right)\right)} \]

      4. sub-neg 65.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(y + \left(-z\right)\right)}\right) \]

      5. +-commutative 65.1%

         \[\leadsto x + x \cdot \left(0 - \color{blue}{\left(\left(-z\right) + y\right)}\right) \]

      6. associate--r+ 65.1%

         \[\leadsto x + x \cdot \color{blue}{\left(\left(0 - \left(-z\right)\right) - y\right)} \]

      7. neg-sub0 65.1%

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

      8. remove-double-neg 65.1%

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

   4. Simplified 65.1%

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

   5. Taylor expanded in y around 0 65.1%

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

      1. *-commutative 65.1%

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

   7. Simplified 65.1%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-18} \lor \neg \left(y \leq 0.0012\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]

Alternative 12: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 13: 37.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-39} \lor \neg \left(y \leq 3.1 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.2e-39) (not (<= y 3.1e-12))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e-39) || !(y <= 3.1e-12)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.2d-39)) .or. (.not. (y <= 3.1d-12))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e-39) || !(y <= 3.1e-12)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.2e-39) or not (y <= 3.1e-12):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.2e-39) || !(y <= 3.1e-12))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.2e-39) || ~((y <= 3.1e-12)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.2e-39], N[Not[LessEqual[y, 3.1e-12]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.1999999999999998e-39 or 3.1000000000000001e-12 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 77.0%

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

      1. *-commutative 77.0%

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

   4. Simplified 77.0%

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

   5. Taylor expanded in x around -inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

      4. sub-neg 75.6%

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

      5. metadata-eval 75.6%

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

      6. +-commutative 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in t around inf 40.7%

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

   if -3.1999999999999998e-39 < y < 3.1000000000000001e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 69.9%

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

   3. Taylor expanded in x around inf 35.9%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-39} \lor \neg \left(y \leq 3.1 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 17.9% 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 61.2%

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

3. Taylor expanded in x around inf 18.4%

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

4. Final simplification 18.4%

   \[\leadsto x \]

Developer target: 96.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023334 
(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))))