Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.9s

Alternatives: 13

Speedup: 1.0×

• 34.8% 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: 37.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{-205}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-273}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-303}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1100000000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= z -1.5e+31)
     (* z (- t))
     (if (<= z -4.2e-64)
       t_1
       (if (<= z -7.3e-205)
         (* y t)
         (if (<= z -9.5e-259)
           t_1
           (if (<= z -2.8e-273)
             x
             (if (<= z 1.45e-303)
               (* y t)
               (if (<= z 9.2e-234)
                 x
                 (if (<= z 6.5e-172)
                   t_1
                   (if (<= z 6.4e-105)
                     x
                     (if (<= z 1100000000000.0) (* y t) (* z x)))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (z <= -1.5e+31) {
		tmp = z * -t;
	} else if (z <= -4.2e-64) {
		tmp = t_1;
	} else if (z <= -7.3e-205) {
		tmp = y * t;
	} else if (z <= -9.5e-259) {
		tmp = t_1;
	} else if (z <= -2.8e-273) {
		tmp = x;
	} else if (z <= 1.45e-303) {
		tmp = y * t;
	} else if (z <= 9.2e-234) {
		tmp = x;
	} else if (z <= 6.5e-172) {
		tmp = t_1;
	} else if (z <= 6.4e-105) {
		tmp = x;
	} else if (z <= 1100000000000.0) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * -x
    if (z <= (-1.5d+31)) then
        tmp = z * -t
    else if (z <= (-4.2d-64)) then
        tmp = t_1
    else if (z <= (-7.3d-205)) then
        tmp = y * t
    else if (z <= (-9.5d-259)) then
        tmp = t_1
    else if (z <= (-2.8d-273)) then
        tmp = x
    else if (z <= 1.45d-303) then
        tmp = y * t
    else if (z <= 9.2d-234) then
        tmp = x
    else if (z <= 6.5d-172) then
        tmp = t_1
    else if (z <= 6.4d-105) then
        tmp = x
    else if (z <= 1100000000000.0d0) 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 t_1 = y * -x;
	double tmp;
	if (z <= -1.5e+31) {
		tmp = z * -t;
	} else if (z <= -4.2e-64) {
		tmp = t_1;
	} else if (z <= -7.3e-205) {
		tmp = y * t;
	} else if (z <= -9.5e-259) {
		tmp = t_1;
	} else if (z <= -2.8e-273) {
		tmp = x;
	} else if (z <= 1.45e-303) {
		tmp = y * t;
	} else if (z <= 9.2e-234) {
		tmp = x;
	} else if (z <= 6.5e-172) {
		tmp = t_1;
	} else if (z <= 6.4e-105) {
		tmp = x;
	} else if (z <= 1100000000000.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if z <= -1.5e+31:
		tmp = z * -t
	elif z <= -4.2e-64:
		tmp = t_1
	elif z <= -7.3e-205:
		tmp = y * t
	elif z <= -9.5e-259:
		tmp = t_1
	elif z <= -2.8e-273:
		tmp = x
	elif z <= 1.45e-303:
		tmp = y * t
	elif z <= 9.2e-234:
		tmp = x
	elif z <= 6.5e-172:
		tmp = t_1
	elif z <= 6.4e-105:
		tmp = x
	elif z <= 1100000000000.0:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (z <= -1.5e+31)
		tmp = Float64(z * Float64(-t));
	elseif (z <= -4.2e-64)
		tmp = t_1;
	elseif (z <= -7.3e-205)
		tmp = Float64(y * t);
	elseif (z <= -9.5e-259)
		tmp = t_1;
	elseif (z <= -2.8e-273)
		tmp = x;
	elseif (z <= 1.45e-303)
		tmp = Float64(y * t);
	elseif (z <= 9.2e-234)
		tmp = x;
	elseif (z <= 6.5e-172)
		tmp = t_1;
	elseif (z <= 6.4e-105)
		tmp = x;
	elseif (z <= 1100000000000.0)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (z <= -1.5e+31)
		tmp = z * -t;
	elseif (z <= -4.2e-64)
		tmp = t_1;
	elseif (z <= -7.3e-205)
		tmp = y * t;
	elseif (z <= -9.5e-259)
		tmp = t_1;
	elseif (z <= -2.8e-273)
		tmp = x;
	elseif (z <= 1.45e-303)
		tmp = y * t;
	elseif (z <= 9.2e-234)
		tmp = x;
	elseif (z <= 6.5e-172)
		tmp = t_1;
	elseif (z <= 6.4e-105)
		tmp = x;
	elseif (z <= 1100000000000.0)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[z, -1.5e+31], N[(z * (-t)), $MachinePrecision], If[LessEqual[z, -4.2e-64], t$95$1, If[LessEqual[z, -7.3e-205], N[(y * t), $MachinePrecision], If[LessEqual[z, -9.5e-259], t$95$1, If[LessEqual[z, -2.8e-273], x, If[LessEqual[z, 1.45e-303], N[(y * t), $MachinePrecision], If[LessEqual[z, 9.2e-234], x, If[LessEqual[z, 6.5e-172], t$95$1, If[LessEqual[z, 6.4e-105], x, If[LessEqual[z, 1100000000000.0], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.49999999999999995e31

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 61.4%

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

   3. Taylor expanded in y around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

      3. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in x around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. *-commutative 54.7%

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

      3. distribute-rgt-neg-in 54.7%

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

   8. Simplified 54.7%

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

   if -1.49999999999999995e31 < z < -4.20000000000000023e-64 or -7.29999999999999992e-205 < z < -9.4999999999999995e-259 or 9.19999999999999961e-234 < z < 6.50000000000000012e-172

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. distribute-rgt-neg-in 75.2%

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

      3. neg-sub0 75.2%

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

      4. sub-neg 75.2%

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

      5. +-commutative 75.2%

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

      6. associate--r+ 75.2%

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

      7. neg-sub0 75.2%

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

      8. remove-double-neg 75.2%

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

   4. Simplified 75.2%

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

   5. Taylor expanded in z around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. *-rgt-identity 70.1%

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

      3. distribute-rgt-neg-out 70.1%

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

      4. distribute-lft-in 70.1%

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

      5. unsub-neg 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in y around inf 51.2%

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

      1. associate-*r* 51.2%

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

      2. neg-mul-1 51.2%

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

   10. Simplified 51.2%

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

   if -4.20000000000000023e-64 < z < -7.29999999999999992e-205 or -2.79999999999999985e-273 < z < 1.45000000000000007e-303 or 6.39999999999999962e-105 < z < 1.1e12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 90.4%

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

      1. *-commutative 90.4%

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

   4. Simplified 90.4%

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

   5. Taylor expanded in t around inf 73.4%

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

      1. *-commutative 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in x around 0 52.1%

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

   if -9.4999999999999995e-259 < z < -2.79999999999999985e-273 or 1.45000000000000007e-303 < z < 9.19999999999999961e-234 or 6.50000000000000012e-172 < z < 6.39999999999999962e-105

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 87.2%

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

   3. Taylor expanded in x around inf 65.6%

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

   if 1.1e12 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. distribute-rgt-neg-in 67.5%

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

      3. neg-sub0 67.5%

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

      4. sub-neg 67.5%

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

      5. +-commutative 67.5%

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

      6. associate--r+ 67.5%

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

      7. neg-sub0 67.5%

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

      8. remove-double-neg 67.5%

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

   4. Simplified 67.5%

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

      1. sub-neg 67.5%

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

      2. distribute-rgt-in 63.0%

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

   6. Applied egg-rr 63.0%

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

      1. associate-+r+ 63.0%

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

      2. *-commutative 63.0%

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

      3. distribute-rgt-neg-out 63.0%

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

      4. unsub-neg 63.0%

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

      5. *-un-lft-identity 63.0%

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

      6. distribute-rgt-out 63.0%

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

   8. Applied egg-rr 63.0%

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

   9. Taylor expanded in z around inf 57.7%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-64}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -7.3 \cdot 10^{-205}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-259}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-273}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-303}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-234}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-172}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1100000000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 3: 55.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;y \leq -190:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-187}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-221}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 39000000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* y (- t x))) (t_3 (* x (- 1.0 y))))
   (if (<= y -190.0)
     t_2
     (if (<= y -5.2e-187)
       t_3
       (if (<= y 3.7e-301)
         t_1
         (if (<= y 1.36e-221)
           (* z x)
           (if (<= y 5.2e-124)
             x
             (if (<= y 9.2e-32) t_1 (if (<= y 39000000.0) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = y * (t - x);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (y <= -190.0) {
		tmp = t_2;
	} else if (y <= -5.2e-187) {
		tmp = t_3;
	} else if (y <= 3.7e-301) {
		tmp = t_1;
	} else if (y <= 1.36e-221) {
		tmp = z * x;
	} else if (y <= 5.2e-124) {
		tmp = x;
	} else if (y <= 9.2e-32) {
		tmp = t_1;
	} else if (y <= 39000000.0) {
		tmp = t_3;
	} 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 = z * -t
    t_2 = y * (t - x)
    t_3 = x * (1.0d0 - y)
    if (y <= (-190.0d0)) then
        tmp = t_2
    else if (y <= (-5.2d-187)) then
        tmp = t_3
    else if (y <= 3.7d-301) then
        tmp = t_1
    else if (y <= 1.36d-221) then
        tmp = z * x
    else if (y <= 5.2d-124) then
        tmp = x
    else if (y <= 9.2d-32) then
        tmp = t_1
    else if (y <= 39000000.0d0) then
        tmp = t_3
    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 = z * -t;
	double t_2 = y * (t - x);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (y <= -190.0) {
		tmp = t_2;
	} else if (y <= -5.2e-187) {
		tmp = t_3;
	} else if (y <= 3.7e-301) {
		tmp = t_1;
	} else if (y <= 1.36e-221) {
		tmp = z * x;
	} else if (y <= 5.2e-124) {
		tmp = x;
	} else if (y <= 9.2e-32) {
		tmp = t_1;
	} else if (y <= 39000000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = y * (t - x)
	t_3 = x * (1.0 - y)
	tmp = 0
	if y <= -190.0:
		tmp = t_2
	elif y <= -5.2e-187:
		tmp = t_3
	elif y <= 3.7e-301:
		tmp = t_1
	elif y <= 1.36e-221:
		tmp = z * x
	elif y <= 5.2e-124:
		tmp = x
	elif y <= 9.2e-32:
		tmp = t_1
	elif y <= 39000000.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (y <= -190.0)
		tmp = t_2;
	elseif (y <= -5.2e-187)
		tmp = t_3;
	elseif (y <= 3.7e-301)
		tmp = t_1;
	elseif (y <= 1.36e-221)
		tmp = Float64(z * x);
	elseif (y <= 5.2e-124)
		tmp = x;
	elseif (y <= 9.2e-32)
		tmp = t_1;
	elseif (y <= 39000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = y * (t - x);
	t_3 = x * (1.0 - y);
	tmp = 0.0;
	if (y <= -190.0)
		tmp = t_2;
	elseif (y <= -5.2e-187)
		tmp = t_3;
	elseif (y <= 3.7e-301)
		tmp = t_1;
	elseif (y <= 1.36e-221)
		tmp = z * x;
	elseif (y <= 5.2e-124)
		tmp = x;
	elseif (y <= 9.2e-32)
		tmp = t_1;
	elseif (y <= 39000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -190.0], t$95$2, If[LessEqual[y, -5.2e-187], t$95$3, If[LessEqual[y, 3.7e-301], t$95$1, If[LessEqual[y, 1.36e-221], N[(z * x), $MachinePrecision], If[LessEqual[y, 5.2e-124], x, If[LessEqual[y, 9.2e-32], t$95$1, If[LessEqual[y, 39000000.0], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -190 or 3.9e7 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.7%

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

      1. *-commutative 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in x around -inf 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

      4. *-commutative 78.5%

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

      5. sub-neg 78.5%

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

      6. metadata-eval 78.5%

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

      7. +-commutative 78.5%

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

   7. Simplified 78.5%

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

   8. Taylor expanded in y around inf 80.7%

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

   if -190 < y < -5.1999999999999999e-187 or 9.2000000000000002e-32 < y < 3.9e7

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. distribute-rgt-neg-in 79.3%

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

      3. neg-sub0 79.3%

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

      4. sub-neg 79.3%

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

      5. +-commutative 79.3%

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

      6. associate--r+ 79.3%

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

      7. neg-sub0 79.3%

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

      8. remove-double-neg 79.3%

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

   4. Simplified 79.3%

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

   5. Taylor expanded in z around 0 57.1%

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

      1. mul-1-neg 57.1%

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

      2. *-rgt-identity 57.1%

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

      3. distribute-rgt-neg-out 57.1%

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

      4. distribute-lft-in 57.1%

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

      5. unsub-neg 57.1%

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

   7. Simplified 57.1%

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

   if -5.1999999999999999e-187 < y < 3.6999999999999998e-301 or 5.1999999999999999e-124 < y < 9.2000000000000002e-32

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 90.2%

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

   3. Taylor expanded in y around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

      3. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in x around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. *-commutative 56.1%

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

      3. distribute-rgt-neg-in 56.1%

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

   8. Simplified 56.1%

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

   if 3.6999999999999998e-301 < y < 1.3600000000000001e-221

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. distribute-rgt-neg-in 79.2%

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

      3. neg-sub0 79.2%

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

      4. sub-neg 79.2%

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

      5. +-commutative 79.2%

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

      6. associate--r+ 79.2%

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

      7. neg-sub0 79.2%

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

      8. remove-double-neg 79.2%

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

   4. Simplified 79.2%

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

      1. sub-neg 79.2%

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

      2. distribute-rgt-in 79.2%

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

   6. Applied egg-rr 79.2%

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

      1. associate-+r+ 79.2%

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

      2. *-commutative 79.2%

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

      3. distribute-rgt-neg-out 79.2%

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

      4. unsub-neg 79.2%

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

      5. *-un-lft-identity 79.2%

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

      6. distribute-rgt-out 79.2%

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

   8. Applied egg-rr 79.2%

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

   9. Taylor expanded in z around inf 53.7%

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

   if 1.3600000000000001e-221 < y < 5.1999999999999999e-124

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 86.3%

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

   3. Taylor expanded in x around inf 59.3%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -190:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-187}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-301}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-221}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-32}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 39000000:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 48.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-306}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.4:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 4.15 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))))
   (if (<= z -7.6e+32)
     (* z (- t))
     (if (<= z -1.55e-273)
       t_1
       (if (<= z -1.36e-306)
         (* y t)
         (if (<= z 1.95e-82)
           t_1
           (if (<= z 0.4) (* y t) (if (<= z 4.15e+24) t_1 (* z x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (z <= -7.6e+32) {
		tmp = z * -t;
	} else if (z <= -1.55e-273) {
		tmp = t_1;
	} else if (z <= -1.36e-306) {
		tmp = y * t;
	} else if (z <= 1.95e-82) {
		tmp = t_1;
	} else if (z <= 0.4) {
		tmp = y * t;
	} else if (z <= 4.15e+24) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    if (z <= (-7.6d+32)) then
        tmp = z * -t
    else if (z <= (-1.55d-273)) then
        tmp = t_1
    else if (z <= (-1.36d-306)) then
        tmp = y * t
    else if (z <= 1.95d-82) then
        tmp = t_1
    else if (z <= 0.4d0) then
        tmp = y * t
    else if (z <= 4.15d+24) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double tmp;
	if (z <= -7.6e+32) {
		tmp = z * -t;
	} else if (z <= -1.55e-273) {
		tmp = t_1;
	} else if (z <= -1.36e-306) {
		tmp = y * t;
	} else if (z <= 1.95e-82) {
		tmp = t_1;
	} else if (z <= 0.4) {
		tmp = y * t;
	} else if (z <= 4.15e+24) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	tmp = 0
	if z <= -7.6e+32:
		tmp = z * -t
	elif z <= -1.55e-273:
		tmp = t_1
	elif z <= -1.36e-306:
		tmp = y * t
	elif z <= 1.95e-82:
		tmp = t_1
	elif z <= 0.4:
		tmp = y * t
	elif z <= 4.15e+24:
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -7.6e+32)
		tmp = Float64(z * Float64(-t));
	elseif (z <= -1.55e-273)
		tmp = t_1;
	elseif (z <= -1.36e-306)
		tmp = Float64(y * t);
	elseif (z <= 1.95e-82)
		tmp = t_1;
	elseif (z <= 0.4)
		tmp = Float64(y * t);
	elseif (z <= 4.15e+24)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -7.6e+32)
		tmp = z * -t;
	elseif (z <= -1.55e-273)
		tmp = t_1;
	elseif (z <= -1.36e-306)
		tmp = y * t;
	elseif (z <= 1.95e-82)
		tmp = t_1;
	elseif (z <= 0.4)
		tmp = y * t;
	elseif (z <= 4.15e+24)
		tmp = t_1;
	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]}, If[LessEqual[z, -7.6e+32], N[(z * (-t)), $MachinePrecision], If[LessEqual[z, -1.55e-273], t$95$1, If[LessEqual[z, -1.36e-306], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.95e-82], t$95$1, If[LessEqual[z, 0.4], N[(y * t), $MachinePrecision], If[LessEqual[z, 4.15e+24], t$95$1, N[(z * x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.6000000000000006e32

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 61.4%

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

   3. Taylor expanded in y around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

      3. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   6. Taylor expanded in x around 0 54.7%

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

      1. mul-1-neg 54.7%

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

      2. *-commutative 54.7%

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

      3. distribute-rgt-neg-in 54.7%

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

   8. Simplified 54.7%

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

   if -7.6000000000000006e32 < z < -1.54999999999999994e-273 or -1.35999999999999996e-306 < z < 1.94999999999999987e-82 or 0.40000000000000002 < z < 4.1500000000000002e24

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-rgt-neg-in 72.3%

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

      3. neg-sub0 72.3%

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

      4. sub-neg 72.3%

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

      5. +-commutative 72.3%

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

      6. associate--r+ 72.3%

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

      7. neg-sub0 72.3%

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

      8. remove-double-neg 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in z around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. *-rgt-identity 69.7%

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

      3. distribute-rgt-neg-out 69.7%

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

      4. distribute-lft-in 69.7%

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

      5. unsub-neg 69.7%

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

   7. Simplified 69.7%

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

   if -1.54999999999999994e-273 < z < -1.35999999999999996e-306 or 1.94999999999999987e-82 < z < 0.40000000000000002

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 81.5%

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

      1. *-commutative 81.5%

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

   4. Simplified 81.5%

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

   5. Taylor expanded in t around inf 78.3%

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

      1. *-commutative 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in x around 0 59.2%

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

   if 4.1500000000000002e24 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 66.0%

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

      1. mul-1-neg 66.0%

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

      2. distribute-rgt-neg-in 66.0%

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

      3. neg-sub0 66.0%

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

      4. sub-neg 66.0%

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

      5. +-commutative 66.0%

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

      6. associate--r+ 66.0%

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

      7. neg-sub0 66.0%

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

      8. remove-double-neg 66.0%

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

   4. Simplified 66.0%

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

      1. sub-neg 66.0%

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

      2. distribute-rgt-in 61.3%

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

   6. Applied egg-rr 61.3%

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

      1. associate-+r+ 61.3%

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

      2. *-commutative 61.3%

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

      3. distribute-rgt-neg-out 61.3%

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

      4. unsub-neg 61.3%

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

      5. *-un-lft-identity 61.3%

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

      6. distribute-rgt-out 61.3%

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

   8. Applied egg-rr 61.3%

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

   9. Taylor expanded in z around inf 57.5%

      \[\leadsto \color{blue}{x \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-273}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-306}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 0.4:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 4.15 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 5: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -2 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-305}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-217}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (+ x (* (- y z) t))))
   (if (<= y -2e+36)
     t_1
     (if (<= y 2.15e-305)
       t_2
       (if (<= y 3.5e-217) (+ x (* z x)) (if (<= y 2.2e+59) 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 + ((y - z) * t);
	double tmp;
	if (y <= -2e+36) {
		tmp = t_1;
	} else if (y <= 2.15e-305) {
		tmp = t_2;
	} else if (y <= 3.5e-217) {
		tmp = x + (z * x);
	} else if (y <= 2.2e+59) {
		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 + ((y - z) * t)
    if (y <= (-2d+36)) then
        tmp = t_1
    else if (y <= 2.15d-305) then
        tmp = t_2
    else if (y <= 3.5d-217) then
        tmp = x + (z * x)
    else if (y <= 2.2d+59) 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 + ((y - z) * t);
	double tmp;
	if (y <= -2e+36) {
		tmp = t_1;
	} else if (y <= 2.15e-305) {
		tmp = t_2;
	} else if (y <= 3.5e-217) {
		tmp = x + (z * x);
	} else if (y <= 2.2e+59) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x + ((y - z) * t)
	tmp = 0
	if y <= -2e+36:
		tmp = t_1
	elif y <= 2.15e-305:
		tmp = t_2
	elif y <= 3.5e-217:
		tmp = x + (z * x)
	elif y <= 2.2e+59:
		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(Float64(y - z) * t))
	tmp = 0.0
	if (y <= -2e+36)
		tmp = t_1;
	elseif (y <= 2.15e-305)
		tmp = t_2;
	elseif (y <= 3.5e-217)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 2.2e+59)
		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 + ((y - z) * t);
	tmp = 0.0;
	if (y <= -2e+36)
		tmp = t_1;
	elseif (y <= 2.15e-305)
		tmp = t_2;
	elseif (y <= 3.5e-217)
		tmp = x + (z * x);
	elseif (y <= 2.2e+59)
		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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+36], t$95$1, If[LessEqual[y, 2.15e-305], t$95$2, If[LessEqual[y, 3.5e-217], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+59], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.00000000000000008e36 or 2.2e59 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.6%

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

      1. *-commutative 82.6%

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

   4. Simplified 82.6%

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

   5. Taylor expanded in x around -inf 80.2%

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

      1. +-commutative 80.2%

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

      2. mul-1-neg 80.2%

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

      3. unsub-neg 80.2%

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

      4. *-commutative 80.2%

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

      5. sub-neg 80.2%

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

      6. metadata-eval 80.2%

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

      7. +-commutative 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in y around inf 82.6%

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

   if -2.00000000000000008e36 < y < 2.1500000000000001e-305 or 3.5e-217 < y < 2.2e59

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 82.4%

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

   if 2.1500000000000001e-305 < y < 3.5e-217

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. distribute-rgt-neg-in 79.2%

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

      3. neg-sub0 79.2%

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

      4. sub-neg 79.2%

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

      5. +-commutative 79.2%

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

      6. associate--r+ 79.2%

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

      7. neg-sub0 79.2%

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

      8. remove-double-neg 79.2%

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

   4. Simplified 79.2%

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

   5. Taylor expanded in y around 0 79.2%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-305}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-217}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 6: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + z \cdot x\\ \mathbf{if}\;y \leq -1900000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-274}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.000118:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (+ x (* z x))))
   (if (<= y -1900000.0)
     t_1
     (if (<= y -7.5e-193)
       t_2
       (if (<= y -1.45e-274) (* z (- t)) (if (<= y 0.000118) 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 <= -1900000.0) {
		tmp = t_1;
	} else if (y <= -7.5e-193) {
		tmp = t_2;
	} else if (y <= -1.45e-274) {
		tmp = z * -t;
	} else if (y <= 0.000118) {
		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 <= (-1900000.0d0)) then
        tmp = t_1
    else if (y <= (-7.5d-193)) then
        tmp = t_2
    else if (y <= (-1.45d-274)) then
        tmp = z * -t
    else if (y <= 0.000118d0) 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 <= -1900000.0) {
		tmp = t_1;
	} else if (y <= -7.5e-193) {
		tmp = t_2;
	} else if (y <= -1.45e-274) {
		tmp = z * -t;
	} else if (y <= 0.000118) {
		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 <= -1900000.0:
		tmp = t_1
	elif y <= -7.5e-193:
		tmp = t_2
	elif y <= -1.45e-274:
		tmp = z * -t
	elif y <= 0.000118:
		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 <= -1900000.0)
		tmp = t_1;
	elseif (y <= -7.5e-193)
		tmp = t_2;
	elseif (y <= -1.45e-274)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 0.000118)
		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 <= -1900000.0)
		tmp = t_1;
	elseif (y <= -7.5e-193)
		tmp = t_2;
	elseif (y <= -1.45e-274)
		tmp = z * -t;
	elseif (y <= 0.000118)
		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, -1900000.0], t$95$1, If[LessEqual[y, -7.5e-193], t$95$2, If[LessEqual[y, -1.45e-274], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 0.000118], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9e6 or 1.18e-4 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.0%

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

      1. *-commutative 82.0%

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

   4. Simplified 82.0%

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

   5. Taylor expanded in x around -inf 79.8%

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

      1. +-commutative 79.8%

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

      2. mul-1-neg 79.8%

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

      3. unsub-neg 79.8%

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

      4. *-commutative 79.8%

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

      5. sub-neg 79.8%

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

      6. metadata-eval 79.8%

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

      7. +-commutative 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in y around inf 81.5%

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

   if -1.9e6 < y < -7.4999999999999998e-193 or -1.44999999999999988e-274 < y < 1.18e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 69.6%

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

      1. mul-1-neg 69.6%

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

      2. distribute-rgt-neg-in 69.6%

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

      3. neg-sub0 69.6%

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

      4. sub-neg 69.6%

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

      5. +-commutative 69.6%

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

      6. associate--r+ 69.6%

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

      7. neg-sub0 69.6%

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

      8. remove-double-neg 69.6%

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

   4. Simplified 69.6%

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

   5. Taylor expanded in y around 0 68.3%

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

   if -7.4999999999999998e-193 < y < -1.44999999999999988e-274

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf 89.4%

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

   3. Taylor expanded in y around 0 74.9%

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

      1. mul-1-neg 74.9%

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

      2. unsub-neg 74.9%

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

      3. *-commutative 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in x around 0 63.1%

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

      1. mul-1-neg 63.1%

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

      2. *-commutative 63.1%

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

      3. distribute-rgt-neg-in 63.1%

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

   8. Simplified 63.1%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1900000:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-193}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-274}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.000118:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 7: 71.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x - z \cdot t\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{-302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-186}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (- x (* z t))))
   (if (<= y -1.32e+16)
     t_1
     (if (<= y 1.14e-302)
       t_2
       (if (<= y 5.3e-186) (+ x (* z x)) (if (<= y 1.65e-6) 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 * t);
	double tmp;
	if (y <= -1.32e+16) {
		tmp = t_1;
	} else if (y <= 1.14e-302) {
		tmp = t_2;
	} else if (y <= 5.3e-186) {
		tmp = x + (z * x);
	} else if (y <= 1.65e-6) {
		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 * t)
    if (y <= (-1.32d+16)) then
        tmp = t_1
    else if (y <= 1.14d-302) then
        tmp = t_2
    else if (y <= 5.3d-186) then
        tmp = x + (z * x)
    else if (y <= 1.65d-6) 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 * t);
	double tmp;
	if (y <= -1.32e+16) {
		tmp = t_1;
	} else if (y <= 1.14e-302) {
		tmp = t_2;
	} else if (y <= 5.3e-186) {
		tmp = x + (z * x);
	} else if (y <= 1.65e-6) {
		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 * t)
	tmp = 0
	if y <= -1.32e+16:
		tmp = t_1
	elif y <= 1.14e-302:
		tmp = t_2
	elif y <= 5.3e-186:
		tmp = x + (z * x)
	elif y <= 1.65e-6:
		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 * t))
	tmp = 0.0
	if (y <= -1.32e+16)
		tmp = t_1;
	elseif (y <= 1.14e-302)
		tmp = t_2;
	elseif (y <= 5.3e-186)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 1.65e-6)
		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 * t);
	tmp = 0.0;
	if (y <= -1.32e+16)
		tmp = t_1;
	elseif (y <= 1.14e-302)
		tmp = t_2;
	elseif (y <= 5.3e-186)
		tmp = x + (z * x);
	elseif (y <= 1.65e-6)
		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 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.32e+16], t$95$1, If[LessEqual[y, 1.14e-302], t$95$2, If[LessEqual[y, 5.3e-186], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-6], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.32e16 or 1.65000000000000008e-6 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.5%

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

      1. *-commutative 82.5%

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

   4. Simplified 82.5%

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

   5. Taylor expanded in x around -inf 80.3%

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

      1. +-commutative 80.3%

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

      2. mul-1-neg 80.3%

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

      3. unsub-neg 80.3%

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

      4. *-commutative 80.3%

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

      5. sub-neg 80.3%

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

      6. metadata-eval 80.3%

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

      7. +-commutative 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in y around inf 82.0%

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

   if -1.32e16 < y < 1.13999999999999996e-302 or 5.30000000000000022e-186 < y < 1.65000000000000008e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 82.0%

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

   3. Taylor expanded in y around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. unsub-neg 73.8%

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

      3. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   if 1.13999999999999996e-302 < y < 5.30000000000000022e-186

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. distribute-rgt-neg-in 78.6%

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

      3. neg-sub0 78.6%

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

      4. sub-neg 78.6%

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

      5. +-commutative 78.6%

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

      6. associate--r+ 78.6%

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

      7. neg-sub0 78.6%

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

      8. remove-double-neg 78.6%

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

   4. Simplified 78.6%

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

   5. Taylor expanded in y around 0 78.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 1.14 \cdot 10^{-302}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-186}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-6}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 8: 38.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-303}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 23000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.5)
   (* z x)
   (if (<= z 1.25e-303)
     (* y t)
     (if (<= z 6.8e-107) x (if (<= z 23000000.0) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5) {
		tmp = z * x;
	} else if (z <= 1.25e-303) {
		tmp = y * t;
	} else if (z <= 6.8e-107) {
		tmp = x;
	} else if (z <= 23000000.0) {
		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 <= (-4.5d0)) then
        tmp = z * x
    else if (z <= 1.25d-303) then
        tmp = y * t
    else if (z <= 6.8d-107) then
        tmp = x
    else if (z <= 23000000.0d0) 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 <= -4.5) {
		tmp = z * x;
	} else if (z <= 1.25e-303) {
		tmp = y * t;
	} else if (z <= 6.8e-107) {
		tmp = x;
	} else if (z <= 23000000.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.5:
		tmp = z * x
	elif z <= 1.25e-303:
		tmp = y * t
	elif z <= 6.8e-107:
		tmp = x
	elif z <= 23000000.0:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.5)
		tmp = Float64(z * x);
	elseif (z <= 1.25e-303)
		tmp = Float64(y * t);
	elseif (z <= 6.8e-107)
		tmp = x;
	elseif (z <= 23000000.0)
		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 <= -4.5)
		tmp = z * x;
	elseif (z <= 1.25e-303)
		tmp = y * t;
	elseif (z <= 6.8e-107)
		tmp = x;
	elseif (z <= 23000000.0)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.5], N[(z * x), $MachinePrecision], If[LessEqual[z, 1.25e-303], N[(y * t), $MachinePrecision], If[LessEqual[z, 6.8e-107], x, If[LessEqual[z, 23000000.0], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5 or 2.3e7 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 60.7%

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

      1. mul-1-neg 60.7%

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

      2. distribute-rgt-neg-in 60.7%

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

      3. neg-sub0 60.7%

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

      4. sub-neg 60.7%

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

      5. +-commutative 60.7%

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

      6. associate--r+ 60.7%

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

      7. neg-sub0 60.7%

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

      8. remove-double-neg 60.7%

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

   4. Simplified 60.7%

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

      1. sub-neg 60.7%

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

      2. distribute-rgt-in 57.5%

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

   6. Applied egg-rr 57.5%

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

      1. associate-+r+ 57.5%

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

      2. *-commutative 57.5%

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

      3. distribute-rgt-neg-out 57.5%

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

      4. unsub-neg 57.5%

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

      5. *-un-lft-identity 57.5%

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

      6. distribute-rgt-out 57.5%

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

   8. Applied egg-rr 57.5%

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

   9. Taylor expanded in z around inf 48.5%

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

   if -4.5 < z < 1.25e-303 or 6.79999999999999989e-107 < z < 2.3e7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 92.6%

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

      1. *-commutative 92.6%

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

   4. Simplified 92.6%

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

   5. Taylor expanded in t around inf 70.6%

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

      1. *-commutative 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in x around 0 45.6%

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

   if 1.25e-303 < z < 6.79999999999999989e-107

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 73.8%

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

   3. Taylor expanded in x around inf 47.6%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-303}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-107}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 23000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 9: 38.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -115:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-303}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 17000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -115.0)
   (* z (- t))
   (if (<= z 1.35e-303)
     (* y t)
     (if (<= z 5e-116) x (if (<= z 17000000.0) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -115.0) {
		tmp = z * -t;
	} else if (z <= 1.35e-303) {
		tmp = y * t;
	} else if (z <= 5e-116) {
		tmp = x;
	} else if (z <= 17000000.0) {
		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 <= (-115.0d0)) then
        tmp = z * -t
    else if (z <= 1.35d-303) then
        tmp = y * t
    else if (z <= 5d-116) then
        tmp = x
    else if (z <= 17000000.0d0) 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 <= -115.0) {
		tmp = z * -t;
	} else if (z <= 1.35e-303) {
		tmp = y * t;
	} else if (z <= 5e-116) {
		tmp = x;
	} else if (z <= 17000000.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -115.0:
		tmp = z * -t
	elif z <= 1.35e-303:
		tmp = y * t
	elif z <= 5e-116:
		tmp = x
	elif z <= 17000000.0:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -115.0)
		tmp = Float64(z * Float64(-t));
	elseif (z <= 1.35e-303)
		tmp = Float64(y * t);
	elseif (z <= 5e-116)
		tmp = x;
	elseif (z <= 17000000.0)
		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 <= -115.0)
		tmp = z * -t;
	elseif (z <= 1.35e-303)
		tmp = y * t;
	elseif (z <= 5e-116)
		tmp = x;
	elseif (z <= 17000000.0)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -115.0], N[(z * (-t)), $MachinePrecision], If[LessEqual[z, 1.35e-303], N[(y * t), $MachinePrecision], If[LessEqual[z, 5e-116], x, If[LessEqual[z, 17000000.0], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -115

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 56.1%

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

   3. Taylor expanded in y around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. unsub-neg 49.6%

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

      3. *-commutative 49.6%

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

   5. Simplified 49.6%

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

   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. mul-1-neg 50.1%

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

      2. *-commutative 50.1%

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

      3. distribute-rgt-neg-in 50.1%

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

   8. Simplified 50.1%

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

   if -115 < z < 1.34999999999999993e-303 or 5.0000000000000003e-116 < z < 1.7e7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 92.7%

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

      1. *-commutative 92.7%

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

   4. Simplified 92.7%

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

   5. Taylor expanded in t around inf 69.9%

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

      1. *-commutative 69.9%

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

   7. Simplified 69.9%

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

   8. Taylor expanded in x around 0 45.1%

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

   if 1.34999999999999993e-303 < z < 5.0000000000000003e-116

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 73.8%

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

   3. Taylor expanded in x around inf 47.6%

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

   if 1.7e7 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. distribute-rgt-neg-in 67.5%

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

      3. neg-sub0 67.5%

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

      4. sub-neg 67.5%

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

      5. +-commutative 67.5%

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

      6. associate--r+ 67.5%

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

      7. neg-sub0 67.5%

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

      8. remove-double-neg 67.5%

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

   4. Simplified 67.5%

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

      1. sub-neg 67.5%

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

      2. distribute-rgt-in 63.0%

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

   6. Applied egg-rr 63.0%

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

      1. associate-+r+ 63.0%

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

      2. *-commutative 63.0%

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

      3. distribute-rgt-neg-out 63.0%

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

      4. unsub-neg 63.0%

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

      5. *-un-lft-identity 63.0%

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

      6. distribute-rgt-out 63.0%

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

   8. Applied egg-rr 63.0%

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

   9. Taylor expanded in z around inf 57.7%

      \[\leadsto \color{blue}{x \cdot z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -115:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-303}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 17000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 10: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-46} \lor \neg \left(x \leq 2.1 \cdot 10^{+42}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.7e-46) (not (<= x 2.1e+42)))
   (+ x (* x (- z y)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e-46) || !(x <= 2.1e+42)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.7d-46)) .or. (.not. (x <= 2.1d+42))) then
        tmp = x + (x * (z - y))
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e-46) || !(x <= 2.1e+42)) {
		tmp = x + (x * (z - y));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.7e-46) or not (x <= 2.1e+42):
		tmp = x + (x * (z - y))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.7e-46) || !(x <= 2.1e+42))
		tmp = Float64(x + Float64(x * Float64(z - y)));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.7e-46) || ~((x <= 2.1e+42)))
		tmp = x + (x * (z - y));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.7e-46], N[Not[LessEqual[x, 2.1e+42]], $MachinePrecision]], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999998e-46 or 2.09999999999999995e42 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 87.1%

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

      1. mul-1-neg 87.1%

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

      2. distribute-rgt-neg-in 87.1%

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

      3. neg-sub0 87.1%

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

      4. sub-neg 87.1%

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

      5. +-commutative 87.1%

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

      6. associate--r+ 87.1%

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

      7. neg-sub0 87.1%

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

      8. remove-double-neg 87.1%

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

   4. Simplified 87.1%

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

   if -1.69999999999999998e-46 < x < 2.09999999999999995e42

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 84.4%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-46} \lor \neg \left(x \leq 2.1 \cdot 10^{+42}\right):\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

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: 37.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \lor \neg \left(y \leq 6.4 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.4) (not (<= y 6.4e-8))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.4) || !(y <= 6.4e-8)) {
		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 <= (-3.4d0)) .or. (.not. (y <= 6.4d-8))) 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 <= -3.4) || !(y <= 6.4e-8)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.4) or not (y <= 6.4e-8):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.4) || !(y <= 6.4e-8))
		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 <= -3.4) || ~((y <= 6.4e-8)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.4], N[Not[LessEqual[y, 6.4e-8]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999991 or 6.4000000000000004e-8 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.9%

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

      1. *-commutative 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in t around inf 44.6%

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

      1. *-commutative 44.6%

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

   7. Simplified 44.6%

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

   8. Taylor expanded in x around 0 43.9%

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

   if -3.39999999999999991 < y < 6.4000000000000004e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.4%

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

   3. Taylor expanded in x around inf 38.2%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \lor \neg \left(y \leq 6.4 \cdot 10^{-8}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 18.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in t around inf 63.7%

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

3. Taylor expanded in x around inf 19.2%

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

4. Final simplification 19.2%

   \[\leadsto x \]

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 2023309 
(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))))