Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.5s

Alternatives: 13

Speedup: 1.0×

• 34.5% 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: 38.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+255}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))))
   (if (<= y -1e+255)
     (* y t)
     (if (<= y -1.0)
       (* y (- x))
       (if (<= y -2.4e-146)
         x
         (if (<= y -1.12e-237)
           t_1
           (if (<= y -3.5e-280)
             x
             (if (<= y 2.5e-264) t_1 (if (<= y 4.8e-27) x (* y t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (y <= -1e+255) {
		tmp = y * t;
	} else if (y <= -1.0) {
		tmp = y * -x;
	} else if (y <= -2.4e-146) {
		tmp = x;
	} else if (y <= -1.12e-237) {
		tmp = t_1;
	} else if (y <= -3.5e-280) {
		tmp = x;
	} else if (y <= 2.5e-264) {
		tmp = t_1;
	} else if (y <= 4.8e-27) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -z
    if (y <= (-1d+255)) then
        tmp = y * t
    else if (y <= (-1.0d0)) then
        tmp = y * -x
    else if (y <= (-2.4d-146)) then
        tmp = x
    else if (y <= (-1.12d-237)) then
        tmp = t_1
    else if (y <= (-3.5d-280)) then
        tmp = x
    else if (y <= 2.5d-264) then
        tmp = t_1
    else if (y <= 4.8d-27) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double tmp;
	if (y <= -1e+255) {
		tmp = y * t;
	} else if (y <= -1.0) {
		tmp = y * -x;
	} else if (y <= -2.4e-146) {
		tmp = x;
	} else if (y <= -1.12e-237) {
		tmp = t_1;
	} else if (y <= -3.5e-280) {
		tmp = x;
	} else if (y <= 2.5e-264) {
		tmp = t_1;
	} else if (y <= 4.8e-27) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	tmp = 0
	if y <= -1e+255:
		tmp = y * t
	elif y <= -1.0:
		tmp = y * -x
	elif y <= -2.4e-146:
		tmp = x
	elif y <= -1.12e-237:
		tmp = t_1
	elif y <= -3.5e-280:
		tmp = x
	elif y <= 2.5e-264:
		tmp = t_1
	elif y <= 4.8e-27:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	tmp = 0.0
	if (y <= -1e+255)
		tmp = Float64(y * t);
	elseif (y <= -1.0)
		tmp = Float64(y * Float64(-x));
	elseif (y <= -2.4e-146)
		tmp = x;
	elseif (y <= -1.12e-237)
		tmp = t_1;
	elseif (y <= -3.5e-280)
		tmp = x;
	elseif (y <= 2.5e-264)
		tmp = t_1;
	elseif (y <= 4.8e-27)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	tmp = 0.0;
	if (y <= -1e+255)
		tmp = y * t;
	elseif (y <= -1.0)
		tmp = y * -x;
	elseif (y <= -2.4e-146)
		tmp = x;
	elseif (y <= -1.12e-237)
		tmp = t_1;
	elseif (y <= -3.5e-280)
		tmp = x;
	elseif (y <= 2.5e-264)
		tmp = t_1;
	elseif (y <= 4.8e-27)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, If[LessEqual[y, -1e+255], N[(y * t), $MachinePrecision], If[LessEqual[y, -1.0], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, -2.4e-146], x, If[LessEqual[y, -1.12e-237], t$95$1, If[LessEqual[y, -3.5e-280], x, If[LessEqual[y, 2.5e-264], t$95$1, If[LessEqual[y, 4.8e-27], x, N[(y * t), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.99999999999999988e254 or 4.80000000000000004e-27 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 55.8%

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

   3. Taylor expanded in y around inf 48.4%

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

   if -9.99999999999999988e254 < y < -1

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 71.7%

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

      3. associate-*r/ 66.1%

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

   3. Applied egg-rr 66.1%

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

      1. associate-/l* 71.5%

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

      2. difference-of-squares 80.9%

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

      3. associate-/r* 99.5%

         \[\leadsto x + \frac{t - x}{\color{blue}{\frac{\frac{y + z}{y + z}}{y - z}}} \]

      4. *-inverses 99.5%

         \[\leadsto x + \frac{t - x}{\frac{\color{blue}{1}}{y - z}} \]

   5. Simplified 99.5%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{1}{y - z}}} \]

   6. Taylor expanded in y around inf 81.6%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{1}{y}}} \]

   7. Taylor expanded in x around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. distribute-rgt1-in 53.0%

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

      3. mul-1-neg 53.0%

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

      4. cancel-sign-sub-inv 53.0%

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

   9. Simplified 53.0%

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

   10. Taylor expanded in y around inf 53.0%

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

       1. mul-1-neg 53.0%

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

       2. distribute-rgt-neg-out 53.0%

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

   12. Simplified 53.0%

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

   if -1 < y < -2.4000000000000002e-146 or -1.12000000000000002e-237 < y < -3.5000000000000001e-280 or 2.5e-264 < y < 4.80000000000000004e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.4%

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

   3. Taylor expanded in x around inf 44.5%

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

   if -2.4000000000000002e-146 < y < -1.12000000000000002e-237 or -3.5000000000000001e-280 < y < 2.5e-264

   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 z around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. *-commutative 59.4%

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

      3. distribute-rgt-neg-in 59.4%

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

   5. Simplified 59.4%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+255}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-146}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-237}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-264}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 3: 56.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))) (t_2 (* y (- t x))))
   (if (<= y -2.4e-47)
     t_2
     (if (<= y -7.5e-147)
       x
       (if (<= y -9e-238)
         t_1
         (if (<= y -1.28e-279)
           x
           (if (<= y 7.4e-264) t_1 (if (<= y 6e-27) x t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double t_2 = y * (t - x);
	double tmp;
	if (y <= -2.4e-47) {
		tmp = t_2;
	} else if (y <= -7.5e-147) {
		tmp = x;
	} else if (y <= -9e-238) {
		tmp = t_1;
	} else if (y <= -1.28e-279) {
		tmp = x;
	} else if (y <= 7.4e-264) {
		tmp = t_1;
	} else if (y <= 6e-27) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * -z
    t_2 = y * (t - x)
    if (y <= (-2.4d-47)) then
        tmp = t_2
    else if (y <= (-7.5d-147)) then
        tmp = x
    else if (y <= (-9d-238)) then
        tmp = t_1
    else if (y <= (-1.28d-279)) then
        tmp = x
    else if (y <= 7.4d-264) then
        tmp = t_1
    else if (y <= 6d-27) then
        tmp = x
    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 = t * -z;
	double t_2 = y * (t - x);
	double tmp;
	if (y <= -2.4e-47) {
		tmp = t_2;
	} else if (y <= -7.5e-147) {
		tmp = x;
	} else if (y <= -9e-238) {
		tmp = t_1;
	} else if (y <= -1.28e-279) {
		tmp = x;
	} else if (y <= 7.4e-264) {
		tmp = t_1;
	} else if (y <= 6e-27) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	t_2 = y * (t - x)
	tmp = 0
	if y <= -2.4e-47:
		tmp = t_2
	elif y <= -7.5e-147:
		tmp = x
	elif y <= -9e-238:
		tmp = t_1
	elif y <= -1.28e-279:
		tmp = x
	elif y <= 7.4e-264:
		tmp = t_1
	elif y <= 6e-27:
		tmp = x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	t_2 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -2.4e-47)
		tmp = t_2;
	elseif (y <= -7.5e-147)
		tmp = x;
	elseif (y <= -9e-238)
		tmp = t_1;
	elseif (y <= -1.28e-279)
		tmp = x;
	elseif (y <= 7.4e-264)
		tmp = t_1;
	elseif (y <= 6e-27)
		tmp = x;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	t_2 = y * (t - x);
	tmp = 0.0;
	if (y <= -2.4e-47)
		tmp = t_2;
	elseif (y <= -7.5e-147)
		tmp = x;
	elseif (y <= -9e-238)
		tmp = t_1;
	elseif (y <= -1.28e-279)
		tmp = x;
	elseif (y <= 7.4e-264)
		tmp = t_1;
	elseif (y <= 6e-27)
		tmp = x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.4e-47], t$95$2, If[LessEqual[y, -7.5e-147], x, If[LessEqual[y, -9e-238], t$95$1, If[LessEqual[y, -1.28e-279], x, If[LessEqual[y, 7.4e-264], t$95$1, If[LessEqual[y, 6e-27], x, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3999999999999999e-47 or 6.0000000000000002e-27 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. flip-- 70.1%

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

      3. associate-*r/ 62.7%

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

   3. Applied egg-rr 62.7%

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

      1. associate-/l* 70.0%

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

      2. difference-of-squares 79.7%

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

      3. associate-/r* 99.7%

         \[\leadsto x + \frac{t - x}{\color{blue}{\frac{\frac{y + z}{y + z}}{y - z}}} \]

      4. *-inverses 99.7%

         \[\leadsto x + \frac{t - x}{\frac{\color{blue}{1}}{y - z}} \]

   5. Simplified 99.7%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{1}{y - z}}} \]

   6. Taylor expanded in y around inf 81.6%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{1}{y}}} \]
   7. Step-by-step derivation

      1. +-commutative 81.6%

         \[\leadsto \color{blue}{\frac{t - x}{\frac{1}{y}} + x} \]

      2. div-sub 76.9%

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

      3. div-inv 76.9%

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

      4. remove-double-div 77.0%

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

      5. *-commutative 77.0%

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

      6. div-inv 77.0%

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

      7. remove-double-div 77.1%

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

      8. *-commutative 77.1%

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

      9. associate-+l- 77.1%

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

      10. *-commutative 77.1%

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

      11. add-sqr-sqrt 33.7%

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

      12. sqrt-unprod 45.3%

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

      13. sqr-neg 45.3%

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

      14. sqrt-unprod 23.8%

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

      15. add-sqr-sqrt 42.5%

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

      16. *-un-lft-identity 42.5%

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

      17. distribute-rgt-out-- 42.5%

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

      18. add-sqr-sqrt 23.8%

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

      19. sqrt-unprod 45.3%

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

      20. sqr-neg 45.3%

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

      21. sqrt-unprod 33.7%

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

      22. add-sqr-sqrt 77.1%

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

   8. Applied egg-rr 77.1%

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

   9. Taylor expanded in y around inf 80.0%

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

   if -2.3999999999999999e-47 < y < -7.50000000000000047e-147 or -8.99999999999999992e-238 < y < -1.28e-279 or 7.39999999999999991e-264 < y < 6.0000000000000002e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 75.0%

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

   3. Taylor expanded in x around inf 47.9%

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

   if -7.50000000000000047e-147 < y < -8.99999999999999992e-238 or -1.28e-279 < y < 7.39999999999999991e-264

   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 z around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. *-commutative 59.4%

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

      3. distribute-rgt-neg-in 59.4%

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

   5. Simplified 59.4%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-264}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 4: 59.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-z\right)\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := x + y \cdot t\\ \mathbf{if}\;y \leq -1.4:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.76 \cdot 10^{-147}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4200000000000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- z))) (t_2 (* y (- t x))) (t_3 (+ x (* y t))))
   (if (<= y -1.4)
     t_2
     (if (<= y -1.76e-147)
       t_3
       (if (<= y -9.5e-238)
         t_1
         (if (<= y -3.35e-279)
           x
           (if (<= y 1.65e-264) t_1 (if (<= y 4200000000000.0) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * -z;
	double t_2 = y * (t - x);
	double t_3 = x + (y * t);
	double tmp;
	if (y <= -1.4) {
		tmp = t_2;
	} else if (y <= -1.76e-147) {
		tmp = t_3;
	} else if (y <= -9.5e-238) {
		tmp = t_1;
	} else if (y <= -3.35e-279) {
		tmp = x;
	} else if (y <= 1.65e-264) {
		tmp = t_1;
	} else if (y <= 4200000000000.0) {
		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 = t * -z
    t_2 = y * (t - x)
    t_3 = x + (y * t)
    if (y <= (-1.4d0)) then
        tmp = t_2
    else if (y <= (-1.76d-147)) then
        tmp = t_3
    else if (y <= (-9.5d-238)) then
        tmp = t_1
    else if (y <= (-3.35d-279)) then
        tmp = x
    else if (y <= 1.65d-264) then
        tmp = t_1
    else if (y <= 4200000000000.0d0) 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 = t * -z;
	double t_2 = y * (t - x);
	double t_3 = x + (y * t);
	double tmp;
	if (y <= -1.4) {
		tmp = t_2;
	} else if (y <= -1.76e-147) {
		tmp = t_3;
	} else if (y <= -9.5e-238) {
		tmp = t_1;
	} else if (y <= -3.35e-279) {
		tmp = x;
	} else if (y <= 1.65e-264) {
		tmp = t_1;
	} else if (y <= 4200000000000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * -z
	t_2 = y * (t - x)
	t_3 = x + (y * t)
	tmp = 0
	if y <= -1.4:
		tmp = t_2
	elif y <= -1.76e-147:
		tmp = t_3
	elif y <= -9.5e-238:
		tmp = t_1
	elif y <= -3.35e-279:
		tmp = x
	elif y <= 1.65e-264:
		tmp = t_1
	elif y <= 4200000000000.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(-z))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(x + Float64(y * t))
	tmp = 0.0
	if (y <= -1.4)
		tmp = t_2;
	elseif (y <= -1.76e-147)
		tmp = t_3;
	elseif (y <= -9.5e-238)
		tmp = t_1;
	elseif (y <= -3.35e-279)
		tmp = x;
	elseif (y <= 1.65e-264)
		tmp = t_1;
	elseif (y <= 4200000000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * -z;
	t_2 = y * (t - x);
	t_3 = x + (y * t);
	tmp = 0.0;
	if (y <= -1.4)
		tmp = t_2;
	elseif (y <= -1.76e-147)
		tmp = t_3;
	elseif (y <= -9.5e-238)
		tmp = t_1;
	elseif (y <= -3.35e-279)
		tmp = x;
	elseif (y <= 1.65e-264)
		tmp = t_1;
	elseif (y <= 4200000000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4], t$95$2, If[LessEqual[y, -1.76e-147], t$95$3, If[LessEqual[y, -9.5e-238], t$95$1, If[LessEqual[y, -3.35e-279], x, If[LessEqual[y, 1.65e-264], t$95$1, If[LessEqual[y, 4200000000000.0], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3999999999999999 or 4.2e12 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. flip-- 67.2%

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

      3. associate-*r/ 58.7%

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

   3. Applied egg-rr 58.7%

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

      1. associate-/l* 67.1%

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

      2. difference-of-squares 78.2%

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

      3. associate-/r* 99.7%

         \[\leadsto x + \frac{t - x}{\color{blue}{\frac{\frac{y + z}{y + z}}{y - z}}} \]

      4. *-inverses 99.7%

         \[\leadsto x + \frac{t - x}{\frac{\color{blue}{1}}{y - z}} \]

   5. Simplified 99.7%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{1}{y - z}}} \]

   6. Taylor expanded in y around inf 84.8%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{1}{y}}} \]
   7. Step-by-step derivation

      1. +-commutative 84.8%

         \[\leadsto \color{blue}{\frac{t - x}{\frac{1}{y}} + x} \]

      2. div-sub 79.4%

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

      3. div-inv 79.5%

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

      4. remove-double-div 79.5%

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

      5. *-commutative 79.5%

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

      6. div-inv 79.6%

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

      7. remove-double-div 79.7%

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

      8. *-commutative 79.7%

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

      9. associate-+l- 79.7%

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

      10. *-commutative 79.7%

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

      11. add-sqr-sqrt 35.4%

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

      12. sqrt-unprod 43.6%

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

      13. sqr-neg 43.6%

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

      14. sqrt-unprod 22.1%

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

      15. add-sqr-sqrt 40.3%

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

      16. *-un-lft-identity 40.3%

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

      17. distribute-rgt-out-- 40.3%

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

      18. add-sqr-sqrt 22.1%

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

      19. sqrt-unprod 43.6%

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

      20. sqr-neg 43.6%

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

      21. sqrt-unprod 35.4%

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

      22. add-sqr-sqrt 79.7%

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

   8. Applied egg-rr 79.7%

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

   9. Taylor expanded in y around inf 85.0%

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

   if -1.3999999999999999 < y < -1.76000000000000014e-147 or 1.65000000000000006e-264 < y < 4.2e12

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.9%

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

   3. Taylor expanded in z around 0 52.7%

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

   if -1.76000000000000014e-147 < y < -9.50000000000000059e-238 or -3.35000000000000018e-279 < y < 1.65000000000000006e-264

   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 z around inf 59.4%

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

      1. mul-1-neg 59.4%

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

      2. *-commutative 59.4%

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

      3. distribute-rgt-neg-in 59.4%

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

   5. Simplified 59.4%

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

   if -9.50000000000000059e-238 < y < -3.35000000000000018e-279

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 73.4%

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

   3. Taylor expanded in x around inf 73.4%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.76 \cdot 10^{-147}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-279}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-264}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 4200000000000:\\ \;\;\;\;x + y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 5: 76.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -225000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-96}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (+ x (* (- y z) t))))
   (if (<= y -225000000.0)
     t_1
     (if (<= y 5.4e-144)
       t_2
       (if (<= y 3.3e-96) (+ x (* z x)) (if (<= y 9e+34) 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 <= -225000000.0) {
		tmp = t_1;
	} else if (y <= 5.4e-144) {
		tmp = t_2;
	} else if (y <= 3.3e-96) {
		tmp = x + (z * x);
	} else if (y <= 9e+34) {
		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 <= (-225000000.0d0)) then
        tmp = t_1
    else if (y <= 5.4d-144) then
        tmp = t_2
    else if (y <= 3.3d-96) then
        tmp = x + (z * x)
    else if (y <= 9d+34) 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 <= -225000000.0) {
		tmp = t_1;
	} else if (y <= 5.4e-144) {
		tmp = t_2;
	} else if (y <= 3.3e-96) {
		tmp = x + (z * x);
	} else if (y <= 9e+34) {
		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 <= -225000000.0:
		tmp = t_1
	elif y <= 5.4e-144:
		tmp = t_2
	elif y <= 3.3e-96:
		tmp = x + (z * x)
	elif y <= 9e+34:
		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 <= -225000000.0)
		tmp = t_1;
	elseif (y <= 5.4e-144)
		tmp = t_2;
	elseif (y <= 3.3e-96)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 9e+34)
		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 <= -225000000.0)
		tmp = t_1;
	elseif (y <= 5.4e-144)
		tmp = t_2;
	elseif (y <= 3.3e-96)
		tmp = x + (z * x);
	elseif (y <= 9e+34)
		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, -225000000.0], t$95$1, If[LessEqual[y, 5.4e-144], t$95$2, If[LessEqual[y, 3.3e-96], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+34], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25e8 or 9.0000000000000001e34 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 67.0%

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

      3. associate-*r/ 58.9%

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

   3. Applied egg-rr 58.9%

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

      1. associate-/l* 66.8%

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

      2. difference-of-squares 78.3%

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

      3. associate-/r* 99.7%

         \[\leadsto x + \frac{t - x}{\color{blue}{\frac{\frac{y + z}{y + z}}{y - z}}} \]

      4. *-inverses 99.7%

         \[\leadsto x + \frac{t - x}{\frac{\color{blue}{1}}{y - z}} \]

   5. Simplified 99.7%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{1}{y - z}}} \]

   6. Taylor expanded in y around inf 86.6%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{1}{y}}} \]
   7. Step-by-step derivation

      1. +-commutative 86.6%

         \[\leadsto \color{blue}{\frac{t - x}{\frac{1}{y}} + x} \]

      2. div-sub 81.1%

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

      3. div-inv 81.1%

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

      4. remove-double-div 81.2%

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

      5. *-commutative 81.2%

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

      6. div-inv 81.3%

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

      7. remove-double-div 81.3%

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

      8. *-commutative 81.3%

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

      9. associate-+l- 81.3%

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

      10. *-commutative 81.3%

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

      11. add-sqr-sqrt 35.7%

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

      12. sqrt-unprod 44.1%

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

      13. sqr-neg 44.1%

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

      14. sqrt-unprod 22.8%

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

      15. add-sqr-sqrt 41.4%

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

      16. *-un-lft-identity 41.4%

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

      17. distribute-rgt-out-- 41.4%

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

      18. add-sqr-sqrt 22.8%

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

      19. sqrt-unprod 44.1%

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

      20. sqr-neg 44.1%

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

      21. sqrt-unprod 35.7%

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

      22. add-sqr-sqrt 81.3%

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

   8. Applied egg-rr 81.3%

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

   9. Taylor expanded in y around inf 86.8%

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

   if -2.25e8 < y < 5.3999999999999995e-144 or 3.2999999999999999e-96 < y < 9.0000000000000001e34

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.2%

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

   if 5.3999999999999995e-144 < y < 3.2999999999999999e-96

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in t around 0 89.0%

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

      1. mul-1-neg 89.0%

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

      2. distribute-lft-neg-out 89.0%

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

      3. *-commutative 89.0%

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

   7. Simplified 89.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -225000000:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-144}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-96}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+34}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 6: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot t\\ t_2 := x + y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-96}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) t))) (t_2 (+ x (* y (- t x)))))
   (if (<= y -9.2e-10)
     t_2
     (if (<= y 4.6e-144)
       t_1
       (if (<= y 1.55e-96) (+ x (* z x)) (if (<= y 9.5e+34) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double t_2 = x + (y * (t - x));
	double tmp;
	if (y <= -9.2e-10) {
		tmp = t_2;
	} else if (y <= 4.6e-144) {
		tmp = t_1;
	} else if (y <= 1.55e-96) {
		tmp = x + (z * x);
	} else if (y <= 9.5e+34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) * t)
    t_2 = x + (y * (t - x))
    if (y <= (-9.2d-10)) then
        tmp = t_2
    else if (y <= 4.6d-144) then
        tmp = t_1
    else if (y <= 1.55d-96) then
        tmp = x + (z * x)
    else if (y <= 9.5d+34) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - z) * t);
	double t_2 = x + (y * (t - x));
	double tmp;
	if (y <= -9.2e-10) {
		tmp = t_2;
	} else if (y <= 4.6e-144) {
		tmp = t_1;
	} else if (y <= 1.55e-96) {
		tmp = x + (z * x);
	} else if (y <= 9.5e+34) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - z) * t)
	t_2 = x + (y * (t - x))
	tmp = 0
	if y <= -9.2e-10:
		tmp = t_2
	elif y <= 4.6e-144:
		tmp = t_1
	elif y <= 1.55e-96:
		tmp = x + (z * x)
	elif y <= 9.5e+34:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - z) * t))
	t_2 = Float64(x + Float64(y * Float64(t - x)))
	tmp = 0.0
	if (y <= -9.2e-10)
		tmp = t_2;
	elseif (y <= 4.6e-144)
		tmp = t_1;
	elseif (y <= 1.55e-96)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 9.5e+34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - z) * t);
	t_2 = x + (y * (t - x));
	tmp = 0.0;
	if (y <= -9.2e-10)
		tmp = t_2;
	elseif (y <= 4.6e-144)
		tmp = t_1;
	elseif (y <= 1.55e-96)
		tmp = x + (z * x);
	elseif (y <= 9.5e+34)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e-10], t$95$2, If[LessEqual[y, 4.6e-144], t$95$1, If[LessEqual[y, 1.55e-96], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+34], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.20000000000000028e-10 or 9.4999999999999999e34 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 86.5%

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

   if -9.20000000000000028e-10 < y < 4.6e-144 or 1.55e-96 < y < 9.4999999999999999e34

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.6%

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

   if 4.6e-144 < y < 1.55e-96

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in t around 0 89.0%

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

      1. mul-1-neg 89.0%

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

      2. distribute-lft-neg-out 89.0%

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

      3. *-commutative 89.0%

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

   7. Simplified 89.0%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-144}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-96}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+34}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 7: 70.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-144}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-27}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -2.9e-10)
     t_1
     (if (<= y 5.4e-144)
       (- x (* z t))
       (if (<= y 3.2e-27) (+ x (* z x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -2.9e-10) {
		tmp = t_1;
	} else if (y <= 5.4e-144) {
		tmp = x - (z * t);
	} else if (y <= 3.2e-27) {
		tmp = x + (z * x);
	} 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 <= (-2.9d-10)) then
        tmp = t_1
    else if (y <= 5.4d-144) then
        tmp = x - (z * t)
    else if (y <= 3.2d-27) then
        tmp = x + (z * x)
    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 <= -2.9e-10) {
		tmp = t_1;
	} else if (y <= 5.4e-144) {
		tmp = x - (z * t);
	} else if (y <= 3.2e-27) {
		tmp = x + (z * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -2.9e-10:
		tmp = t_1
	elif y <= 5.4e-144:
		tmp = x - (z * t)
	elif y <= 3.2e-27:
		tmp = x + (z * x)
	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 <= -2.9e-10)
		tmp = t_1;
	elseif (y <= 5.4e-144)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 3.2e-27)
		tmp = Float64(x + Float64(z * x));
	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 <= -2.9e-10)
		tmp = t_1;
	elseif (y <= 5.4e-144)
		tmp = x - (z * t);
	elseif (y <= 3.2e-27)
		tmp = x + (z * x);
	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, -2.9e-10], t$95$1, If[LessEqual[y, 5.4e-144], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-27], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.89999999999999981e-10 or 3.19999999999999991e-27 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. flip-- 69.5%

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

      3. associate-*r/ 61.8%

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

   3. Applied egg-rr 61.8%

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

      1. associate-/l* 69.4%

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

      2. difference-of-squares 79.5%

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

      3. associate-/r* 99.7%

         \[\leadsto x + \frac{t - x}{\color{blue}{\frac{\frac{y + z}{y + z}}{y - z}}} \]

      4. *-inverses 99.7%

         \[\leadsto x + \frac{t - x}{\frac{\color{blue}{1}}{y - z}} \]

   5. Simplified 99.7%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{1}{y - z}}} \]

   6. Taylor expanded in y around inf 82.8%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{1}{y}}} \]
   7. Step-by-step derivation

      1. +-commutative 82.8%

         \[\leadsto \color{blue}{\frac{t - x}{\frac{1}{y}} + x} \]

      2. div-sub 77.9%

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

      3. div-inv 77.9%

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

      4. remove-double-div 78.0%

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

      5. *-commutative 78.0%

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

      6. div-inv 78.1%

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

      7. remove-double-div 78.1%

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

      8. *-commutative 78.1%

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

      9. associate-+l- 78.1%

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

      10. *-commutative 78.1%

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

      11. add-sqr-sqrt 35.1%

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

      12. sqrt-unprod 45.1%

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

      13. sqr-neg 45.1%

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

      14. sqrt-unprod 22.7%

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

      15. add-sqr-sqrt 42.1%

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

      16. *-un-lft-identity 42.1%

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

      17. distribute-rgt-out-- 42.1%

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

      18. add-sqr-sqrt 22.7%

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

      19. sqrt-unprod 45.1%

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

      20. sqr-neg 45.1%

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

      21. sqrt-unprod 35.1%

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

      22. add-sqr-sqrt 78.1%

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

   8. Applied egg-rr 78.1%

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

   9. Taylor expanded in y around inf 81.8%

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

   if -2.89999999999999981e-10 < y < 5.3999999999999995e-144

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.2%

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

      1. +-commutative 95.2%

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

      2. mul-1-neg 95.2%

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

      3. unsub-neg 95.2%

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

      4. *-commutative 95.2%

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

   4. Simplified 95.2%

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

   5. Taylor expanded in t around inf 76.3%

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

      1. *-commutative 76.3%

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

   7. Simplified 76.3%

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

   if 5.3999999999999995e-144 < y < 3.19999999999999991e-27

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 90.3%

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

      1. +-commutative 90.3%

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

      2. mul-1-neg 90.3%

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

      3. unsub-neg 90.3%

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

      4. *-commutative 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in t around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. distribute-lft-neg-out 74.8%

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

      3. *-commutative 74.8%

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

   7. Simplified 74.8%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-144}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-27}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 8: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-43} \lor \neg \left(y \leq 1.45 \cdot 10^{+34}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.6e-43) (not (<= y 1.45e+34)))
   (+ x (* y (- t x)))
   (- x (* z (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e-43) || !(y <= 1.45e+34)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x - (z * (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 ((y <= (-1.6d-43)) .or. (.not. (y <= 1.45d+34))) then
        tmp = x + (y * (t - x))
    else
        tmp = x - (z * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e-43) || !(y <= 1.45e+34)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x - (z * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.6e-43) or not (y <= 1.45e+34):
		tmp = x + (y * (t - x))
	else:
		tmp = x - (z * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.6e-43) || !(y <= 1.45e+34))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x - Float64(z * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.6e-43) || ~((y <= 1.45e+34)))
		tmp = x + (y * (t - x));
	else
		tmp = x - (z * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.6e-43], N[Not[LessEqual[y, 1.45e+34]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999992e-43 or 1.4500000000000001e34 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 85.7%

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

   if -1.59999999999999992e-43 < y < 1.4500000000000001e34

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 92.0%

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

      1. +-commutative 92.0%

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

      2. mul-1-neg 92.0%

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

      3. unsub-neg 92.0%

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

      4. *-commutative 92.0%

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

   4. Simplified 92.0%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-43} \lor \neg \left(y \leq 1.45 \cdot 10^{+34}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \end{array} \]

Alternative 9: 37.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.7 \cdot 10^{+254}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.7e+254)
   (* y t)
   (if (<= y -1.0) (* y (- x)) (if (<= y 4.4e-27) x (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.7e+254) {
		tmp = y * t;
	} else if (y <= -1.0) {
		tmp = y * -x;
	} else if (y <= 4.4e-27) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8.7d+254)) then
        tmp = y * t
    else if (y <= (-1.0d0)) then
        tmp = y * -x
    else if (y <= 4.4d-27) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.7e+254) {
		tmp = y * t;
	} else if (y <= -1.0) {
		tmp = y * -x;
	} else if (y <= 4.4e-27) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.7e+254:
		tmp = y * t
	elif y <= -1.0:
		tmp = y * -x
	elif y <= 4.4e-27:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.7e+254)
		tmp = Float64(y * t);
	elseif (y <= -1.0)
		tmp = Float64(y * Float64(-x));
	elseif (y <= 4.4e-27)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.7e+254)
		tmp = y * t;
	elseif (y <= -1.0)
		tmp = y * -x;
	elseif (y <= 4.4e-27)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.7e+254], N[(y * t), $MachinePrecision], If[LessEqual[y, -1.0], N[(y * (-x)), $MachinePrecision], If[LessEqual[y, 4.4e-27], x, N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.69999999999999984e254 or 4.39999999999999974e-27 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 55.8%

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

   3. Taylor expanded in y around inf 48.4%

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

   if -8.69999999999999984e254 < y < -1

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. flip-- 71.7%

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

      3. associate-*r/ 66.1%

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

   3. Applied egg-rr 66.1%

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

      1. associate-/l* 71.5%

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

      2. difference-of-squares 80.9%

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

      3. associate-/r* 99.5%

         \[\leadsto x + \frac{t - x}{\color{blue}{\frac{\frac{y + z}{y + z}}{y - z}}} \]

      4. *-inverses 99.5%

         \[\leadsto x + \frac{t - x}{\frac{\color{blue}{1}}{y - z}} \]

   5. Simplified 99.5%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{1}{y - z}}} \]

   6. Taylor expanded in y around inf 81.6%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{1}{y}}} \]

   7. Taylor expanded in x around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. distribute-rgt1-in 53.0%

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

      3. mul-1-neg 53.0%

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

      4. cancel-sign-sub-inv 53.0%

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

   9. Simplified 53.0%

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

   10. Taylor expanded in y around inf 53.0%

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

       1. mul-1-neg 53.0%

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

       2. distribute-rgt-neg-out 53.0%

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

   12. Simplified 53.0%

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

   if -1 < y < 4.39999999999999974e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.9%

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

   3. Taylor expanded in x around inf 38.3%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.7 \cdot 10^{+254}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 10: 71.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-10} \lor \neg \left(y \leq 1.6 \cdot 10^{-27}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3e-10) (not (<= y 1.6e-27))) (* y (- t x)) (- x (* z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e-10) || !(y <= 1.6e-27)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3d-10)) .or. (.not. (y <= 1.6d-27))) then
        tmp = y * (t - x)
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e-10) || !(y <= 1.6e-27)) {
		tmp = y * (t - x);
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3e-10) or not (y <= 1.6e-27):
		tmp = y * (t - x)
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3e-10) || !(y <= 1.6e-27))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3e-10) || ~((y <= 1.6e-27)))
		tmp = y * (t - x);
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3e-10], N[Not[LessEqual[y, 1.6e-27]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e-10 or 1.59999999999999995e-27 < y

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. flip-- 69.5%

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

      3. associate-*r/ 61.8%

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

   3. Applied egg-rr 61.8%

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

      1. associate-/l* 69.4%

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

      2. difference-of-squares 79.5%

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

      3. associate-/r* 99.7%

         \[\leadsto x + \frac{t - x}{\color{blue}{\frac{\frac{y + z}{y + z}}{y - z}}} \]

      4. *-inverses 99.7%

         \[\leadsto x + \frac{t - x}{\frac{\color{blue}{1}}{y - z}} \]

   5. Simplified 99.7%

      \[\leadsto x + \color{blue}{\frac{t - x}{\frac{1}{y - z}}} \]

   6. Taylor expanded in y around inf 82.8%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{1}{y}}} \]
   7. Step-by-step derivation

      1. +-commutative 82.8%

         \[\leadsto \color{blue}{\frac{t - x}{\frac{1}{y}} + x} \]

      2. div-sub 77.9%

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

      3. div-inv 77.9%

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

      4. remove-double-div 78.0%

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

      5. *-commutative 78.0%

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

      6. div-inv 78.1%

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

      7. remove-double-div 78.1%

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

      8. *-commutative 78.1%

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

      9. associate-+l- 78.1%

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

      10. *-commutative 78.1%

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

      11. add-sqr-sqrt 35.1%

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

      12. sqrt-unprod 45.1%

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

      13. sqr-neg 45.1%

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

      14. sqrt-unprod 22.7%

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

      15. add-sqr-sqrt 42.1%

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

      16. *-un-lft-identity 42.1%

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

      17. distribute-rgt-out-- 42.1%

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

      18. add-sqr-sqrt 22.7%

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

      19. sqrt-unprod 45.1%

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

      20. sqr-neg 45.1%

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

      21. sqrt-unprod 35.1%

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

      22. add-sqr-sqrt 78.1%

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

   8. Applied egg-rr 78.1%

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

   9. Taylor expanded in y around inf 81.8%

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

   if -3e-10 < y < 1.59999999999999995e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.0%

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

      1. +-commutative 94.0%

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

      2. mul-1-neg 94.0%

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

      3. unsub-neg 94.0%

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

      4. *-commutative 94.0%

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

   4. Simplified 94.0%

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

   5. Taylor expanded in t around inf 71.3%

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

      1. *-commutative 71.3%

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

   7. Simplified 71.3%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-10} \lor \neg \left(y \leq 1.6 \cdot 10^{-27}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (x - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 12: 37.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-47}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e-47) (* y t) (if (<= y 1.1e-27) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e-47) {
		tmp = y * t;
	} else if (y <= 1.1e-27) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4d-47)) then
        tmp = y * t
    else if (y <= 1.1d-27) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e-47) {
		tmp = y * t;
	} else if (y <= 1.1e-27) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4e-47:
		tmp = y * t
	elif y <= 1.1e-27:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4e-47)
		tmp = Float64(y * t);
	elseif (y <= 1.1e-27)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4e-47)
		tmp = y * t;
	elseif (y <= 1.1e-27)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4e-47], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.1e-27], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9999999999999999e-47 or 1.09999999999999993e-27 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 49.9%

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

   3. Taylor expanded in y around inf 41.3%

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

   if -3.9999999999999999e-47 < y < 1.09999999999999993e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.0%

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

   3. Taylor expanded in x around inf 40.2%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-47}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 13: 17.7% 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 60.8%

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

3. Taylor expanded in x around inf 19.1%

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

4. Final simplification 19.1%

   \[\leadsto x \]

Developer target: 96.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023224 
(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))))