Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.6s

Alternatives: 11

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 69.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -6 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-153}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-219}:\\ \;\;\;\;\mathsf{fma}\left(-t, z, x\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-112}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;y \leq 320000:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -6e+37)
     t_1
     (if (<= y -1.8e-153)
       (fma x z x)
       (if (<= y 2.8e-219)
         (fma (- t) z x)
         (if (<= y 5e-112)
           (fma x z x)
           (if (<= y 320000.0) (* (- y z) t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -6e+37) {
		tmp = t_1;
	} else if (y <= -1.8e-153) {
		tmp = fma(x, z, x);
	} else if (y <= 2.8e-219) {
		tmp = fma(-t, z, x);
	} else if (y <= 5e-112) {
		tmp = fma(x, z, x);
	} else if (y <= 320000.0) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -6e+37)
		tmp = t_1;
	elseif (y <= -1.8e-153)
		tmp = fma(x, z, x);
	elseif (y <= 2.8e-219)
		tmp = fma(Float64(-t), z, x);
	elseif (y <= 5e-112)
		tmp = fma(x, z, x);
	elseif (y <= 320000.0)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -6e+37], t$95$1, If[LessEqual[y, -1.8e-153], N[(x * z + x), $MachinePrecision], If[LessEqual[y, 2.8e-219], N[((-t) * z + x), $MachinePrecision], If[LessEqual[y, 5e-112], N[(x * z + x), $MachinePrecision], If[LessEqual[y, 320000.0], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.00000000000000043e37 or 3.2e5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.3

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

   5. Applied rewrites 83.3%

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

   if -6.00000000000000043e37 < y < -1.7999999999999999e-153 or 2.7999999999999999e-219 < y < 5.00000000000000044e-112

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 48.9%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 64.9%

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

   if -1.7999999999999999e-153 < y < 2.7999999999999999e-219

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 98.5

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

   5. Applied rewrites 98.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 87.5%

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

   if 5.00000000000000044e-112 < y < 3.2e5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 63.4

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

   5. Applied rewrites 63.4%

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

Alternative 3: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -6 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-258}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-220}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-112}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;y \leq 320000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (* (- t x) y)))
   (if (<= y -6e+37)
     t_2
     (if (<= y -3.35e-258)
       (fma x z x)
       (if (<= y 1.3e-220)
         t_1
         (if (<= y 5e-112) (fma x z x) (if (<= y 320000.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = (t - x) * y;
	double tmp;
	if (y <= -6e+37) {
		tmp = t_2;
	} else if (y <= -3.35e-258) {
		tmp = fma(x, z, x);
	} else if (y <= 1.3e-220) {
		tmp = t_1;
	} else if (y <= 5e-112) {
		tmp = fma(x, z, x);
	} else if (y <= 320000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -6e+37)
		tmp = t_2;
	elseif (y <= -3.35e-258)
		tmp = fma(x, z, x);
	elseif (y <= 1.3e-220)
		tmp = t_1;
	elseif (y <= 5e-112)
		tmp = fma(x, z, x);
	elseif (y <= 320000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -6e+37], t$95$2, If[LessEqual[y, -3.35e-258], N[(x * z + x), $MachinePrecision], If[LessEqual[y, 1.3e-220], t$95$1, If[LessEqual[y, 5e-112], N[(x * z + x), $MachinePrecision], If[LessEqual[y, 320000.0], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.00000000000000043e37 or 3.2e5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.3

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

   5. Applied rewrites 83.3%

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

   if -6.00000000000000043e37 < y < -3.3499999999999999e-258 or 1.3e-220 < y < 5.00000000000000044e-112

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 85.9

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

   5. Applied rewrites 85.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 56.8%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 66.2%

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

   if -3.3499999999999999e-258 < y < 1.3e-220 or 5.00000000000000044e-112 < y < 3.2e5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 64.3

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

   5. Applied rewrites 64.3%

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

Alternative 4: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ t_2 := \left(x - t\right) \cdot z\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-27}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-117}:\\ \;\;\;\;\mathsf{fma}\left(-t, z, x\right)\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)) (t_2 (* (- x t) z)))
   (if (<= y -8.5e+66)
     t_1
     (if (<= y -5.4e-27)
       t_2
       (if (<= y 2.45e-117) (fma (- t) z x) (if (<= y 7.4e+24) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double t_2 = (x - t) * z;
	double tmp;
	if (y <= -8.5e+66) {
		tmp = t_1;
	} else if (y <= -5.4e-27) {
		tmp = t_2;
	} else if (y <= 2.45e-117) {
		tmp = fma(-t, z, x);
	} else if (y <= 7.4e+24) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	t_2 = Float64(Float64(x - t) * z)
	tmp = 0.0
	if (y <= -8.5e+66)
		tmp = t_1;
	elseif (y <= -5.4e-27)
		tmp = t_2;
	elseif (y <= 2.45e-117)
		tmp = fma(Float64(-t), z, x);
	elseif (y <= 7.4e+24)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[y, -8.5e+66], t$95$1, If[LessEqual[y, -5.4e-27], t$95$2, If[LessEqual[y, 2.45e-117], N[((-t) * z + x), $MachinePrecision], If[LessEqual[y, 7.4e+24], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5000000000000004e66 or 7.39999999999999998e24 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 88.7

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

   5. Applied rewrites 88.7%

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

   if -8.5000000000000004e66 < y < -5.39999999999999978e-27 or 2.4499999999999999e-117 < y < 7.39999999999999998e24

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. distribute-lft-in N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-neg-in N/A

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

      8. unsub-neg N/A

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

      9. remove-double-neg N/A

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

      10. lower--.f64 63.2

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

   7. Applied rewrites 63.2%

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

   if -5.39999999999999978e-27 < y < 2.4499999999999999e-117

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 92.0

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

   5. Applied rewrites 92.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 72.8%

      \[\leadsto \mathsf{fma}\left(-t, z, x\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+66}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-27}:\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-117}:\\ \;\;\;\;\mathsf{fma}\left(-t, z, x\right)\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+24}:\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -6 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-258}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-220}:\\ \;\;\;\;\left(-z\right) \cdot t\\ \mathbf{elif}\;y \leq 212000000:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -6e+37)
     t_1
     (if (<= y -3.35e-258)
       (fma x z x)
       (if (<= y 1.3e-220)
         (* (- z) t)
         (if (<= y 212000000.0) (fma x z x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -6e+37) {
		tmp = t_1;
	} else if (y <= -3.35e-258) {
		tmp = fma(x, z, x);
	} else if (y <= 1.3e-220) {
		tmp = -z * t;
	} else if (y <= 212000000.0) {
		tmp = fma(x, z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -6e+37)
		tmp = t_1;
	elseif (y <= -3.35e-258)
		tmp = fma(x, z, x);
	elseif (y <= 1.3e-220)
		tmp = Float64(Float64(-z) * t);
	elseif (y <= 212000000.0)
		tmp = fma(x, z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -6e+37], t$95$1, If[LessEqual[y, -3.35e-258], N[(x * z + x), $MachinePrecision], If[LessEqual[y, 1.3e-220], N[((-z) * t), $MachinePrecision], If[LessEqual[y, 212000000.0], N[(x * z + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.00000000000000043e37 or 2.12e8 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 84.0

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

   5. Applied rewrites 84.0%

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

   if -6.00000000000000043e37 < y < -3.3499999999999999e-258 or 1.3e-220 < y < 2.12e8

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 82.4

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

   5. Applied rewrites 82.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 53.1%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 61.2%

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

   if -3.3499999999999999e-258 < y < 1.3e-220

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 64.9

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.5%

      \[\leadsto \left(-z\right) \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 46.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-x\right) \cdot y\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-258}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-220}:\\ \;\;\;\;\left(-z\right) \cdot t\\ \mathbf{elif}\;y \leq 6100000000:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x) y)))
   (if (<= y -1.4e+67)
     t_1
     (if (<= y -3.35e-258)
       (fma x z x)
       (if (<= y 1.3e-220)
         (* (- z) t)
         (if (<= y 6100000000.0) (fma x z x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x * y;
	double tmp;
	if (y <= -1.4e+67) {
		tmp = t_1;
	} else if (y <= -3.35e-258) {
		tmp = fma(x, z, x);
	} else if (y <= 1.3e-220) {
		tmp = -z * t;
	} else if (y <= 6100000000.0) {
		tmp = fma(x, z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) * y)
	tmp = 0.0
	if (y <= -1.4e+67)
		tmp = t_1;
	elseif (y <= -3.35e-258)
		tmp = fma(x, z, x);
	elseif (y <= 1.3e-220)
		tmp = Float64(Float64(-z) * t);
	elseif (y <= 6100000000.0)
		tmp = fma(x, z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) * y), $MachinePrecision]}, If[LessEqual[y, -1.4e+67], t$95$1, If[LessEqual[y, -3.35e-258], N[(x * z + x), $MachinePrecision], If[LessEqual[y, 1.3e-220], N[((-z) * t), $MachinePrecision], If[LessEqual[y, 6100000000.0], N[(x * z + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3999999999999999e67 or 6.1e9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 87.9

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 57.1%

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

   if -1.3999999999999999e67 < y < -3.3499999999999999e-258 or 1.3e-220 < y < 6.1e9

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 81.5

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

   5. Applied rewrites 81.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 52.4%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 59.4%

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

   if -3.3499999999999999e-258 < y < 1.3e-220

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 64.9

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 62.5%

      \[\leadsto \left(-z\right) \cdot t \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 83.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+66} \lor \neg \left(y \leq 3600000000\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.5e+66) (not (<= y 3600000000.0)))
   (* (- t x) y)
   (fma (- x t) z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.5e+66) || !(y <= 3600000000.0)) {
		tmp = (t - x) * y;
	} else {
		tmp = fma((x - t), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.5e+66) || !(y <= 3600000000.0))
		tmp = Float64(Float64(t - x) * y);
	else
		tmp = fma(Float64(x - t), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.5e+66], N[Not[LessEqual[y, 3600000000.0]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], N[(N[(x - t), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5000000000000004e66 or 3.6e9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 87.9

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

   5. Applied rewrites 87.9%

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

   if -8.5000000000000004e66 < y < 3.6e9

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 84.9

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

   5. Applied rewrites 84.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+66} \lor \neg \left(y \leq 3600000000\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.205 \lor \neg \left(z \leq 11600000000\right):\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.205) (not (<= z 11600000000.0)))
   (* (- x t) z)
   (fma (- t x) y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.205) || !(z <= 11600000000.0)) {
		tmp = (x - t) * z;
	} else {
		tmp = fma((t - x), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.205) || !(z <= 11600000000.0))
		tmp = Float64(Float64(x - t) * z);
	else
		tmp = fma(Float64(t - x), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.205], N[Not[LessEqual[z, 11600000000.0]], $MachinePrecision]], N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.204999999999999988 or 1.16e10 < z

   1. Initial program 99.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift--.f64 N/A

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

      6. sub-neg N/A

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

      7. distribute-lft-in N/A

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

      8. associate-+l+ N/A

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

      9. *-commutative N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-neg.f64 98.3

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

   4. Applied rewrites 98.3%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-neg-in N/A

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

      8. unsub-neg N/A

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

      9. remove-double-neg N/A

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

      10. lower--.f64 81.1

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

   7. Applied rewrites 81.1%

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

   if -0.204999999999999988 < z < 1.16e10

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 85.4

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

   5. Applied rewrites 85.4%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.205 \lor \neg \left(z \leq 11600000000\right):\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+67} \lor \neg \left(y \leq 6100000000\right):\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e+67) (not (<= y 6100000000.0))) (* (- x) y) (fma x z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e+67) || !(y <= 6100000000.0)) {
		tmp = -x * y;
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.4e+67) || !(y <= 6100000000.0))
		tmp = Float64(Float64(-x) * y);
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.4e+67], N[Not[LessEqual[y, 6100000000.0]], $MachinePrecision]], N[((-x) * y), $MachinePrecision], N[(x * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3999999999999999e67 or 6.1e9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 87.9

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 57.1%

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

   if -1.3999999999999999e67 < y < 6.1e9

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 84.9

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

   5. Applied rewrites 84.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 60.2%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 54.9%

       \[\leadsto \mathsf{fma}\left(x, \color{blue}{z}, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+67} \lor \neg \left(y \leq 6100000000\right):\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-45} \lor \neg \left(x \leq 9 \cdot 10^{-239}\right):\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6.5e-45) (not (<= x 9e-239))) (fma x z x) (* y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.5e-45) || !(x <= 9e-239)) {
		tmp = fma(x, z, x);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6.5e-45) || !(x <= 9e-239))
		tmp = fma(x, z, x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6.5e-45], N[Not[LessEqual[x, 9e-239]], $MachinePrecision]], N[(x * z + x), $MachinePrecision], N[(y * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.4999999999999995e-45 or 9.00000000000000026e-239 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. lower--.f64 66.1

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

   5. Applied rewrites 66.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 39.3%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 52.7%

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

   if -6.4999999999999995e-45 < x < 9.00000000000000026e-239

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 49.9

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

   5. Applied rewrites 49.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 42.5%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-45} \lor \neg \left(x \leq 9 \cdot 10^{-239}\right):\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 27.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ y \cdot t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return y * 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 = y * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 42.9

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

5. Applied rewrites 42.9%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 21.9%

   \[\leadsto y \cdot \color{blue}{t} \]
9. Add Preprocessing

Developer Target 1: 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 2024318 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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