Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 34.0s

Alternatives: 13

Speedup: 1.0×

• 33.9% 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: 67.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+95}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* (- y z) t)))
   (if (<= y -6.8e+52)
     t_1
     (if (<= y -4.5e-23)
       t_2
       (if (<= y 5.8e-81) (* x (+ z 1.0)) (if (<= y 2.25e+95) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = (y - z) * t;
	double tmp;
	if (y <= -6.8e+52) {
		tmp = t_1;
	} else if (y <= -4.5e-23) {
		tmp = t_2;
	} else if (y <= 5.8e-81) {
		tmp = x * (z + 1.0);
	} else if (y <= 2.25e+95) {
		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 = (y - z) * t
    if (y <= (-6.8d+52)) then
        tmp = t_1
    else if (y <= (-4.5d-23)) then
        tmp = t_2
    else if (y <= 5.8d-81) then
        tmp = x * (z + 1.0d0)
    else if (y <= 2.25d+95) 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 = (y - z) * t;
	double tmp;
	if (y <= -6.8e+52) {
		tmp = t_1;
	} else if (y <= -4.5e-23) {
		tmp = t_2;
	} else if (y <= 5.8e-81) {
		tmp = x * (z + 1.0);
	} else if (y <= 2.25e+95) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = (y - z) * t
	tmp = 0
	if y <= -6.8e+52:
		tmp = t_1
	elif y <= -4.5e-23:
		tmp = t_2
	elif y <= 5.8e-81:
		tmp = x * (z + 1.0)
	elif y <= 2.25e+95:
		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(Float64(y - z) * t)
	tmp = 0.0
	if (y <= -6.8e+52)
		tmp = t_1;
	elseif (y <= -4.5e-23)
		tmp = t_2;
	elseif (y <= 5.8e-81)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 2.25e+95)
		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 = (y - z) * t;
	tmp = 0.0;
	if (y <= -6.8e+52)
		tmp = t_1;
	elseif (y <= -4.5e-23)
		tmp = t_2;
	elseif (y <= 5.8e-81)
		tmp = x * (z + 1.0);
	elseif (y <= 2.25e+95)
		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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -6.8e+52], t$95$1, If[LessEqual[y, -4.5e-23], t$95$2, If[LessEqual[y, 5.8e-81], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e+95], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.8e52 or 2.25000000000000008e95 < 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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right) \]

      2. --lowering--.f64 84.9%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 84.9%

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

   if -6.8e52 < y < -4.49999999999999975e-23 or 5.79999999999999978e-81 < y < 2.25000000000000008e95

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 65.1%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 65.1%

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

   if -4.49999999999999975e-23 < y < 5.79999999999999978e-81

   1. Initial program 100.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{y \cdot y - z \cdot z}{\color{blue}{y + z}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{y + z}{y \cdot y - z \cdot z}}}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{y + z}{y \cdot y - z \cdot z}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y + z}{y \cdot y - z \cdot z}\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y + z}}{y \cdot y - z \cdot z}\right)\right)\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{1}{\color{blue}{\frac{y \cdot y - z \cdot z}{y + z}}}\right)\right)\right) \]

      8. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{1}{y - \color{blue}{z}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(1, \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(y - z\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \left(y - z\right) + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-1 \cdot \left(y - z\right)\right), \color{blue}{1}\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\left(y - z\right)\right)\right), 1\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), 1\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\left(y + -1 \cdot z\right)\right)\right), 1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\left(-1 \cdot z + y\right)\right)\right), 1\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\mathsf{neg}\left(-1 \cdot z\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right), 1\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right), 1\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(y\right)\right)\right), 1\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(z - y\right), 1\right)\right) \]

      12. --lowering--.f64 61.3%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(z, y\right), 1\right)\right) \]

   7. Simplified 61.3%

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

   8. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + z\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 61.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \color{blue}{1}\right)\right) \]

   10. Simplified 61.3%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-23}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-81}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+95}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -0.052:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-86}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -0.052)
     t_1
     (if (<= z 7e-86) (+ x (* y t)) (if (<= z 1.55e+19) (* y (- t x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -0.052) {
		tmp = t_1;
	} else if (z <= 7e-86) {
		tmp = x + (y * t);
	} else if (z <= 1.55e+19) {
		tmp = y * (t - 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 = z * (x - t)
    if (z <= (-0.052d0)) then
        tmp = t_1
    else if (z <= 7d-86) then
        tmp = x + (y * t)
    else if (z <= 1.55d+19) then
        tmp = y * (t - 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 = z * (x - t);
	double tmp;
	if (z <= -0.052) {
		tmp = t_1;
	} else if (z <= 7e-86) {
		tmp = x + (y * t);
	} else if (z <= 1.55e+19) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -0.052:
		tmp = t_1
	elif z <= 7e-86:
		tmp = x + (y * t)
	elif z <= 1.55e+19:
		tmp = y * (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -0.052)
		tmp = t_1;
	elseif (z <= 7e-86)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 1.55e+19)
		tmp = Float64(y * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -0.052)
		tmp = t_1;
	elseif (z <= 7e-86)
		tmp = x + (y * t);
	elseif (z <= 1.55e+19)
		tmp = y * (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.052], t$95$1, If[LessEqual[z, 7e-86], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+19], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0519999999999999976 or 1.55e19 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 83.8%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 83.8%

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

   if -0.0519999999999999976 < z < 7.00000000000000041e-86

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 92.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 92.7%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{t}\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 69.5%

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

   if 7.00000000000000041e-86 < z < 1.55e19

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right) \]

      2. --lowering--.f64 64.7%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 64.7%

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

Alternative 4: 55.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y - z \leq -2 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y - z \leq 4.05 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= (- y z) -2e-18) t_1 (if (<= (- y z) 4.05e-47) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -2e-18) {
		tmp = t_1;
	} else if ((y - z) <= 4.05e-47) {
		tmp = 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 - z) * t
    if ((y - z) <= (-2d-18)) then
        tmp = t_1
    else if ((y - z) <= 4.05d-47) then
        tmp = 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 - z) * t;
	double tmp;
	if ((y - z) <= -2e-18) {
		tmp = t_1;
	} else if ((y - z) <= 4.05e-47) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if (y - z) <= -2e-18:
		tmp = t_1
	elif (y - z) <= 4.05e-47:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (Float64(y - z) <= -2e-18)
		tmp = t_1;
	elseif (Float64(y - z) <= 4.05e-47)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if ((y - z) <= -2e-18)
		tmp = t_1;
	elseif ((y - z) <= 4.05e-47)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(y - z), $MachinePrecision], -2e-18], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 4.05e-47], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -2.0000000000000001e-18 or 4.0500000000000002e-47 < (-.f64 y z)

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 52.6%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 52.6%

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

   if -2.0000000000000001e-18 < (-.f64 y z) < 4.0500000000000002e-47

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 81.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 81.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   7. Step-by-step derivation

   8. Simplified 73.2%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -2 \cdot 10^{-18}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq 4.05 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+20}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* z (- x t)))))
   (if (<= z -1.2e-14) t_1 (if (<= z 1.35e+20) (+ x (* y (- t x))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (z * (x - t));
	double tmp;
	if (z <= -1.2e-14) {
		tmp = t_1;
	} else if (z <= 1.35e+20) {
		tmp = x + (y * (t - 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 = x + (z * (x - t))
    if (z <= (-1.2d-14)) then
        tmp = t_1
    else if (z <= 1.35d+20) then
        tmp = x + (y * (t - 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 = x + (z * (x - t));
	double tmp;
	if (z <= -1.2e-14) {
		tmp = t_1;
	} else if (z <= 1.35e+20) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (z * (x - t))
	tmp = 0
	if z <= -1.2e-14:
		tmp = t_1
	elif z <= 1.35e+20:
		tmp = x + (y * (t - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(z * Float64(x - t)))
	tmp = 0.0
	if (z <= -1.2e-14)
		tmp = t_1;
	elseif (z <= 1.35e+20)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (z * (x - t));
	tmp = 0.0;
	if (z <= -1.2e-14)
		tmp = t_1;
	elseif (z <= 1.35e+20)
		tmp = x + (y * (t - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e-14], t$95$1, If[LessEqual[z, 1.35e+20], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e-14 or 1.35e20 < z

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \left(z \cdot \left(t - x\right)\right)\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\mathsf{neg}\left(z \cdot \left(t - x\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(t - x\right)\right)\right)}\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \left(-1 \cdot \color{blue}{\left(t - x\right)}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right)\right) \]

      9. distribute-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right)\right) \]

      10. unsub-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right)\right) \]

      11. remove-double-neg N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \left(x - t\right)\right)\right) \]

      12. --lowering--.f64 83.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 83.8%

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

   if -1.2e-14 < z < 1.35e20

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 90.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 90.4%

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

Alternative 6: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+20}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1100.0) t_1 (if (<= z 1.45e+20) (+ x (* y (- t x))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1100.0) {
		tmp = t_1;
	} else if (z <= 1.45e+20) {
		tmp = x + (y * (t - 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 = z * (x - t)
    if (z <= (-1100.0d0)) then
        tmp = t_1
    else if (z <= 1.45d+20) then
        tmp = x + (y * (t - 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 = z * (x - t);
	double tmp;
	if (z <= -1100.0) {
		tmp = t_1;
	} else if (z <= 1.45e+20) {
		tmp = x + (y * (t - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1100.0:
		tmp = t_1
	elif z <= 1.45e+20:
		tmp = x + (y * (t - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1100.0)
		tmp = t_1;
	elseif (z <= 1.45e+20)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1100.0)
		tmp = t_1;
	elseif (z <= 1.45e+20)
		tmp = x + (y * (t - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1100.0], t$95$1, If[LessEqual[z, 1.45e+20], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1100 or 1.45e20 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 83.8%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 83.8%

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

   if -1100 < z < 1.45e20

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 89.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 89.5%

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

Alternative 7: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 + \left(z - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -1.55e+71) t_1 (if (<= t 4.4e+38) (* x (+ 1.0 (- z y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -1.55e+71) {
		tmp = t_1;
	} else if (t <= 4.4e+38) {
		tmp = x * (1.0 + (z - y));
	} 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 - z) * t
    if (t <= (-1.55d+71)) then
        tmp = t_1
    else if (t <= 4.4d+38) then
        tmp = x * (1.0d0 + (z - y))
    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 - z) * t;
	double tmp;
	if (t <= -1.55e+71) {
		tmp = t_1;
	} else if (t <= 4.4e+38) {
		tmp = x * (1.0 + (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -1.55e+71:
		tmp = t_1
	elif t <= 4.4e+38:
		tmp = x * (1.0 + (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -1.55e+71)
		tmp = t_1;
	elseif (t <= 4.4e+38)
		tmp = Float64(x * Float64(1.0 + Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -1.55e+71)
		tmp = t_1;
	elseif (t <= 4.4e+38)
		tmp = x * (1.0 + (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -1.55e+71], t$95$1, If[LessEqual[t, 4.4e+38], N[(x * N[(1.0 + N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.55000000000000009e71 or 4.40000000000000013e38 < t

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 80.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 80.5%

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

   if -1.55000000000000009e71 < t < 4.40000000000000013e38

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(y - z\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      6. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      8. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \left(z - y\right)\right)\right) \]

      9. --lowering--.f64 79.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 79.7%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{+71}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 + \left(z - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -980000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -980000.0) t_1 (if (<= z 2.8e+19) (* y (- t x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -980000.0) {
		tmp = t_1;
	} else if (z <= 2.8e+19) {
		tmp = y * (t - 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 = z * (x - t)
    if (z <= (-980000.0d0)) then
        tmp = t_1
    else if (z <= 2.8d+19) then
        tmp = y * (t - 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 = z * (x - t);
	double tmp;
	if (z <= -980000.0) {
		tmp = t_1;
	} else if (z <= 2.8e+19) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -980000.0:
		tmp = t_1
	elif z <= 2.8e+19:
		tmp = y * (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -980000.0)
		tmp = t_1;
	elseif (z <= 2.8e+19)
		tmp = Float64(y * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -980000.0)
		tmp = t_1;
	elseif (z <= 2.8e+19)
		tmp = y * (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -980000.0], t$95$1, If[LessEqual[z, 2.8e+19], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.8e5 or 2.8e19 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 83.8%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 83.8%

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

   if -9.8e5 < z < 2.8e19

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right) \]

      2. --lowering--.f64 60.3%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right) \]

   5. Simplified 60.3%

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

Alternative 9: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -4.8e+70) t_1 (if (<= t 2.55e+38) (* x (- 1.0 y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -4.8e+70) {
		tmp = t_1;
	} else if (t <= 2.55e+38) {
		tmp = x * (1.0 - y);
	} 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 - z) * t
    if (t <= (-4.8d+70)) then
        tmp = t_1
    else if (t <= 2.55d+38) then
        tmp = x * (1.0d0 - y)
    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 - z) * t;
	double tmp;
	if (t <= -4.8e+70) {
		tmp = t_1;
	} else if (t <= 2.55e+38) {
		tmp = x * (1.0 - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -4.8e+70:
		tmp = t_1
	elif t <= 2.55e+38:
		tmp = x * (1.0 - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -4.8e+70)
		tmp = t_1;
	elseif (t <= 2.55e+38)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -4.8e+70)
		tmp = t_1;
	elseif (t <= 2.55e+38)
		tmp = x * (1.0 - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.8e+70], t$95$1, If[LessEqual[t, 2.55e+38], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999974e70 or 2.5500000000000001e38 < t

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 80.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 80.5%

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

   if -4.79999999999999974e70 < t < 2.5500000000000001e38

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 64.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 64.1%

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

   6. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot y\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{y}\right)\right) \]

      4. --lowering--.f64 53.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{y}\right)\right) \]

   8. Simplified 53.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -4.8e+70) t_1 (if (<= t 1.45e+39) (* x (+ z 1.0)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -4.8e+70) {
		tmp = t_1;
	} else if (t <= 1.45e+39) {
		tmp = x * (z + 1.0);
	} 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 - z) * t
    if (t <= (-4.8d+70)) then
        tmp = t_1
    else if (t <= 1.45d+39) then
        tmp = x * (z + 1.0d0)
    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 - z) * t;
	double tmp;
	if (t <= -4.8e+70) {
		tmp = t_1;
	} else if (t <= 1.45e+39) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -4.8e+70:
		tmp = t_1
	elif t <= 1.45e+39:
		tmp = x * (z + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -4.8e+70)
		tmp = t_1;
	elseif (t <= 1.45e+39)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -4.8e+70)
		tmp = t_1;
	elseif (t <= 1.45e+39)
		tmp = x * (z + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -4.8e+70], t$95$1, If[LessEqual[t, 1.45e+39], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999974e70 or 1.45000000000000015e39 < t

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 80.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 80.5%

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

   if -4.79999999999999974e70 < t < 1.45000000000000015e39

   1. Initial program 100.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

      2. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{y \cdot y - z \cdot z}{\color{blue}{y + z}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(t - x\right) \cdot \frac{1}{\color{blue}{\frac{y + z}{y \cdot y - z \cdot z}}}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t - x}{\color{blue}{\frac{y + z}{y \cdot y - z \cdot z}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(t - x\right), \color{blue}{\left(\frac{y + z}{y \cdot y - z \cdot z}\right)}\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{\color{blue}{y + z}}{y \cdot y - z \cdot z}\right)\right)\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{1}{\color{blue}{\frac{y \cdot y - z \cdot z}{y + z}}}\right)\right)\right) \]

      8. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \left(\frac{1}{y - \color{blue}{z}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(1, \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, x\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -1 \cdot \left(y - z\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \left(y - z\right) + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-1 \cdot \left(y - z\right)\right), \color{blue}{1}\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\left(y - z\right)\right)\right), 1\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), 1\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\left(y + -1 \cdot z\right)\right)\right), 1\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\mathsf{neg}\left(\left(-1 \cdot z + y\right)\right)\right), 1\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\mathsf{neg}\left(-1 \cdot z\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right), 1\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \left(\mathsf{neg}\left(y\right)\right)\right), 1\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(z + \left(\mathsf{neg}\left(y\right)\right)\right), 1\right)\right) \]

      11. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(z - y\right), 1\right)\right) \]

      12. --lowering--.f64 79.7%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(z, y\right), 1\right)\right) \]

   7. Simplified 79.7%

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

   8. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + z\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 50.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \color{blue}{1}\right)\right) \]

   10. Simplified 50.0%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+70}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+79}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1000.0) (* x z) (if (<= z 1.06e+79) (* y t) (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1000.0) {
		tmp = x * z;
	} else if (z <= 1.06e+79) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1000.0d0)) then
        tmp = x * z
    else if (z <= 1.06d+79) then
        tmp = y * t
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1000.0) {
		tmp = x * z;
	} else if (z <= 1.06e+79) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1000.0:
		tmp = x * z
	elif z <= 1.06e+79:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1000.0)
		tmp = Float64(x * z);
	elseif (z <= 1.06e+79)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1000.0)
		tmp = x * z;
	elseif (z <= 1.06e+79)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1000.0], N[(x * z), $MachinePrecision], If[LessEqual[z, 1.06e+79], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e3 or 1.05999999999999992e79 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(t - x\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)\right)\right)\right) \]

      8. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) - \color{blue}{t}\right)\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x - t\right)\right) \]

      11. --lowering--.f64 85.4%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 85.4%

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

   6. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{x}\right) \]
   7. Step-by-step derivation

   8. Simplified 44.1%

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

   if -1e3 < z < 1.05999999999999992e79

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 47.0%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 47.0%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 34.8%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{t}\right) \]

   8. Simplified 34.8%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1000:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+79}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0003:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 4.05 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.0003) (* y t) (if (<= y 4.05e-47) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.0003) {
		tmp = y * t;
	} else if (y <= 4.05e-47) {
		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 <= (-0.0003d0)) then
        tmp = y * t
    else if (y <= 4.05d-47) 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 <= -0.0003) {
		tmp = y * t;
	} else if (y <= 4.05e-47) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.0003:
		tmp = y * t
	elif y <= 4.05e-47:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.0003)
		tmp = Float64(y * t);
	elseif (y <= 4.05e-47)
		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 <= -0.0003)
		tmp = y * t;
	elseif (y <= 4.05e-47)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.0003], N[(y * t), $MachinePrecision], If[LessEqual[y, 4.05e-47], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999974e-4 or 4.0500000000000002e-47 < y

   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. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(y - z\right)}\right) \]

      2. --lowering--.f64 51.7%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 51.7%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 40.6%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{t}\right) \]

   8. Simplified 40.6%

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

   if -2.99999999999999974e-4 < y < 4.0500000000000002e-47

   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(t - x\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right)\right) \]

      3. --lowering--.f64 39.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 39.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   7. Step-by-step derivation

   8. Simplified 34.3%

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

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. 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. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(t - x\right)\right)}\right) \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(t - x\right)}\right)\right) \]

   3. --lowering--.f64 58.9%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, \color{blue}{x}\right)\right)\right) \]

5. Simplified 58.9%

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

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{x} \]
7. Step-by-step derivation

8. Simplified 17.9%

   \[\leadsto \color{blue}{x} \]
9. Add Preprocessing

Developer Target 1: 96.5% 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 2024161 
(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))))