Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.4s

Alternatives: 14

Speedup: 1.0×

• 34.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y - z, t - x, x\right) \]
6. Add Preprocessing

Alternative 2: 38.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+121}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+78}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-272}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-7}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.5e+121)
   (* z x)
   (if (<= z -2.7e+78)
     (* y t)
     (if (<= z -1.0)
       (* z x)
       (if (<= z -2.5e-67)
         x
         (if (<= z -1.05e-272)
           (* y t)
           (if (<= z 6.4e-84) x (if (<= z 1.85e-7) (* y t) (* z x)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+121) {
		tmp = z * x;
	} else if (z <= -2.7e+78) {
		tmp = y * t;
	} else if (z <= -1.0) {
		tmp = z * x;
	} else if (z <= -2.5e-67) {
		tmp = x;
	} else if (z <= -1.05e-272) {
		tmp = y * t;
	} else if (z <= 6.4e-84) {
		tmp = x;
	} else if (z <= 1.85e-7) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.5d+121)) then
        tmp = z * x
    else if (z <= (-2.7d+78)) then
        tmp = y * t
    else if (z <= (-1.0d0)) then
        tmp = z * x
    else if (z <= (-2.5d-67)) then
        tmp = x
    else if (z <= (-1.05d-272)) then
        tmp = y * t
    else if (z <= 6.4d-84) then
        tmp = x
    else if (z <= 1.85d-7) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+121) {
		tmp = z * x;
	} else if (z <= -2.7e+78) {
		tmp = y * t;
	} else if (z <= -1.0) {
		tmp = z * x;
	} else if (z <= -2.5e-67) {
		tmp = x;
	} else if (z <= -1.05e-272) {
		tmp = y * t;
	} else if (z <= 6.4e-84) {
		tmp = x;
	} else if (z <= 1.85e-7) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.5e+121:
		tmp = z * x
	elif z <= -2.7e+78:
		tmp = y * t
	elif z <= -1.0:
		tmp = z * x
	elif z <= -2.5e-67:
		tmp = x
	elif z <= -1.05e-272:
		tmp = y * t
	elif z <= 6.4e-84:
		tmp = x
	elif z <= 1.85e-7:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.5e+121)
		tmp = Float64(z * x);
	elseif (z <= -2.7e+78)
		tmp = Float64(y * t);
	elseif (z <= -1.0)
		tmp = Float64(z * x);
	elseif (z <= -2.5e-67)
		tmp = x;
	elseif (z <= -1.05e-272)
		tmp = Float64(y * t);
	elseif (z <= 6.4e-84)
		tmp = x;
	elseif (z <= 1.85e-7)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.5e+121)
		tmp = z * x;
	elseif (z <= -2.7e+78)
		tmp = y * t;
	elseif (z <= -1.0)
		tmp = z * x;
	elseif (z <= -2.5e-67)
		tmp = x;
	elseif (z <= -1.05e-272)
		tmp = y * t;
	elseif (z <= 6.4e-84)
		tmp = x;
	elseif (z <= 1.85e-7)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.5e+121], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.7e+78], N[(y * t), $MachinePrecision], If[LessEqual[z, -1.0], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.5e-67], x, If[LessEqual[z, -1.05e-272], N[(y * t), $MachinePrecision], If[LessEqual[z, 6.4e-84], x, If[LessEqual[z, 1.85e-7], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000004e121 or -2.70000000000000004e78 < z < -1 or 1.85000000000000002e-7 < 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 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

   5. Simplified 78.5%

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

      1. sub-neg 78.5%

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

      2. distribute-lft-in 72.9%

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

   7. Applied egg-rr 72.9%

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

   8. Taylor expanded in x around -inf 51.7%

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

   9. Taylor expanded in z around inf 51.0%

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

       1. *-commutative 51.0%

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

   11. Simplified 51.0%

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

   if -2.50000000000000004e121 < z < -2.70000000000000004e78 or -2.4999999999999999e-67 < z < -1.04999999999999993e-272 or 6.3999999999999999e-84 < z < 1.85000000000000002e-7

   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 98.4%

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

      1. fma-def 98.4%

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

      2. +-commutative 98.4%

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

      3. mul-1-neg 98.4%

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

      4. neg-sub0 98.4%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 98.4%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 98.4%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 98.4%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 98.4%

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

      9. distribute-rgt-neg-in 98.4%

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

      10. mul-1-neg 98.4%

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

      11. mul-1-neg 98.4%

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

      12. distribute-rgt-neg-in 98.4%

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

      13. neg-sub0 98.4%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 98.4%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 98.4%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 98.4%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 98.4%

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

      18. mul-1-neg 98.4%

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

      19. +-commutative 98.4%

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

      20. mul-1-neg 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in t around inf 63.7%

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

   7. Taylor expanded in y around inf 44.4%

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

      1. *-commutative 44.4%

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

   9. Simplified 44.4%

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

   if -1 < z < -2.4999999999999999e-67 or -1.04999999999999993e-272 < z < 6.3999999999999999e-84

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 67.3%

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

   4. Taylor expanded in x around inf 41.3%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+121}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+78}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-272}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-7}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -7300:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-278}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 10^{-244}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 10^{+18}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* x (+ z 1.0))))
   (if (<= y -7300.0)
     t_1
     (if (<= y 2.05e-278)
       t_2
       (if (<= y 1e-244)
         (* z (- t))
         (if (<= y 1.4e-29) t_2 (if (<= y 1e+18) (* (- y z) t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -7300.0) {
		tmp = t_1;
	} else if (y <= 2.05e-278) {
		tmp = t_2;
	} else if (y <= 1e-244) {
		tmp = z * -t;
	} else if (y <= 1.4e-29) {
		tmp = t_2;
	} else if (y <= 1e+18) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = x * (z + 1.0d0)
    if (y <= (-7300.0d0)) then
        tmp = t_1
    else if (y <= 2.05d-278) then
        tmp = t_2
    else if (y <= 1d-244) then
        tmp = z * -t
    else if (y <= 1.4d-29) then
        tmp = t_2
    else if (y <= 1d+18) then
        tmp = (y - z) * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -7300.0) {
		tmp = t_1;
	} else if (y <= 2.05e-278) {
		tmp = t_2;
	} else if (y <= 1e-244) {
		tmp = z * -t;
	} else if (y <= 1.4e-29) {
		tmp = t_2;
	} else if (y <= 1e+18) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -7300.0:
		tmp = t_1
	elif y <= 2.05e-278:
		tmp = t_2
	elif y <= 1e-244:
		tmp = z * -t
	elif y <= 1.4e-29:
		tmp = t_2
	elif y <= 1e+18:
		tmp = (y - z) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -7300.0)
		tmp = t_1;
	elseif (y <= 2.05e-278)
		tmp = t_2;
	elseif (y <= 1e-244)
		tmp = Float64(z * Float64(-t));
	elseif (y <= 1.4e-29)
		tmp = t_2;
	elseif (y <= 1e+18)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -7300.0)
		tmp = t_1;
	elseif (y <= 2.05e-278)
		tmp = t_2;
	elseif (y <= 1e-244)
		tmp = z * -t;
	elseif (y <= 1.4e-29)
		tmp = t_2;
	elseif (y <= 1e+18)
		tmp = (y - z) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7300.0], t$95$1, If[LessEqual[y, 2.05e-278], t$95$2, If[LessEqual[y, 1e-244], N[(z * (-t)), $MachinePrecision], If[LessEqual[y, 1.4e-29], t$95$2, If[LessEqual[y, 1e+18], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7300 or 1e18 < 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 94.3%

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

      1. fma-def 97.6%

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

      2. +-commutative 97.6%

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

      3. mul-1-neg 97.6%

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

      4. neg-sub0 97.6%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 97.6%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 97.6%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 97.6%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 97.6%

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

      9. distribute-rgt-neg-in 97.6%

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

      10. mul-1-neg 97.6%

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

      11. mul-1-neg 97.6%

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

      12. distribute-rgt-neg-in 97.6%

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

      13. neg-sub0 97.6%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 97.6%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 97.6%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 97.6%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 97.6%

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

      18. mul-1-neg 97.6%

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

      19. +-commutative 97.6%

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

      20. mul-1-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in y around inf 83.7%

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

      1. neg-mul-1 83.7%

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

      2. sub-neg 83.7%

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

   8. Simplified 83.7%

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

   if -7300 < y < 2.05000000000000001e-278 or 9.9999999999999993e-245 < y < 1.4000000000000001e-29

   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 92.4%

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

      1. mul-1-neg 92.4%

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

      2. unsub-neg 92.4%

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

   5. Simplified 92.4%

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

      1. sub-neg 92.4%

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

      2. distribute-lft-in 88.8%

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

   7. Applied egg-rr 88.8%

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

   8. Taylor expanded in x around -inf 68.6%

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

   if 2.05000000000000001e-278 < y < 9.9999999999999993e-245

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. mul-1-neg 100.0%

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

      11. mul-1-neg 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 100.0%

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

      18. mul-1-neg 100.0%

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

      19. +-commutative 100.0%

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

      20. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 86.1%

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

   7. Taylor expanded in y around 0 86.1%

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

      1. associate-*r* 86.1%

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

      2. *-commutative 86.1%

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

      3. mul-1-neg 86.1%

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

   9. Simplified 86.1%

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

   if 1.4000000000000001e-29 < y < 1e18

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. mul-1-neg 100.0%

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

      11. mul-1-neg 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 100.0%

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

      18. mul-1-neg 100.0%

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

      19. +-commutative 100.0%

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

      20. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 73.1%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7300:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 10^{-244}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 10^{+18}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-102} \lor \neg \left(x \leq 1.5 \cdot 10^{-94} \lor \neg \left(x \leq 7.5 \cdot 10^{-30}\right) \land x \leq 8.5 \cdot 10^{+65}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.25e-102)
         (not (or (<= x 1.5e-94) (and (not (<= x 7.5e-30)) (<= x 8.5e+65)))))
   (* x (+ (- z y) 1.0))
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.25e-102) || !((x <= 1.5e-94) || (!(x <= 7.5e-30) && (x <= 8.5e+65)))) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2.25d-102)) .or. (.not. (x <= 1.5d-94) .or. (.not. (x <= 7.5d-30)) .and. (x <= 8.5d+65))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.25e-102) || !((x <= 1.5e-94) || (!(x <= 7.5e-30) && (x <= 8.5e+65)))) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.25e-102) or not ((x <= 1.5e-94) or (not (x <= 7.5e-30) and (x <= 8.5e+65))):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.25e-102) || !((x <= 1.5e-94) || (!(x <= 7.5e-30) && (x <= 8.5e+65))))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.25e-102) || ~(((x <= 1.5e-94) || (~((x <= 7.5e-30)) && (x <= 8.5e+65)))))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.25e-102], N[Not[Or[LessEqual[x, 1.5e-94], And[N[Not[LessEqual[x, 7.5e-30]], $MachinePrecision], LessEqual[x, 8.5e+65]]]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e-102 or 1.5000000000000001e-94 < x < 7.5000000000000006e-30 or 8.50000000000000075e65 < x

   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 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

   5. Simplified 81.2%

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

   if -2.25e-102 < x < 1.5000000000000001e-94 or 7.5000000000000006e-30 < x < 8.50000000000000075e65

   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 99.9%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. mul-1-neg 100.0%

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

      11. mul-1-neg 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 100.0%

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

      18. mul-1-neg 100.0%

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

      19. +-commutative 100.0%

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

      20. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 80.4%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-102} \lor \neg \left(x \leq 1.5 \cdot 10^{-94} \lor \neg \left(x \leq 7.5 \cdot 10^{-30}\right) \land x \leq 8.5 \cdot 10^{+65}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -51000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+18}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+67}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -51000000.0)
     t_1
     (if (<= y 3.6e+18)
       (- x (* z (- t x)))
       (if (<= y 2.1e+57)
         (* x (+ (- z y) 1.0))
         (if (<= y 6.6e+67) (* z (- x t)) (+ x t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -51000000.0) {
		tmp = t_1;
	} else if (y <= 3.6e+18) {
		tmp = x - (z * (t - x));
	} else if (y <= 2.1e+57) {
		tmp = x * ((z - y) + 1.0);
	} else if (y <= 6.6e+67) {
		tmp = z * (x - t);
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-51000000.0d0)) then
        tmp = t_1
    else if (y <= 3.6d+18) then
        tmp = x - (z * (t - x))
    else if (y <= 2.1d+57) then
        tmp = x * ((z - y) + 1.0d0)
    else if (y <= 6.6d+67) then
        tmp = z * (x - t)
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -51000000.0) {
		tmp = t_1;
	} else if (y <= 3.6e+18) {
		tmp = x - (z * (t - x));
	} else if (y <= 2.1e+57) {
		tmp = x * ((z - y) + 1.0);
	} else if (y <= 6.6e+67) {
		tmp = z * (x - t);
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -51000000.0:
		tmp = t_1
	elif y <= 3.6e+18:
		tmp = x - (z * (t - x))
	elif y <= 2.1e+57:
		tmp = x * ((z - y) + 1.0)
	elif y <= 6.6e+67:
		tmp = z * (x - t)
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -51000000.0)
		tmp = t_1;
	elseif (y <= 3.6e+18)
		tmp = Float64(x - Float64(z * Float64(t - x)));
	elseif (y <= 2.1e+57)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	elseif (y <= 6.6e+67)
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -51000000.0)
		tmp = t_1;
	elseif (y <= 3.6e+18)
		tmp = x - (z * (t - x));
	elseif (y <= 2.1e+57)
		tmp = x * ((z - y) + 1.0);
	elseif (y <= 6.6e+67)
		tmp = z * (x - t);
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -51000000.0], t$95$1, If[LessEqual[y, 3.6e+18], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+57], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+67], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.1e7

   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 94.6%

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

      1. fma-def 98.2%

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

      2. +-commutative 98.2%

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

      3. mul-1-neg 98.2%

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

      4. neg-sub0 98.2%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 98.2%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 98.2%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 98.2%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 98.2%

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

      9. distribute-rgt-neg-in 98.2%

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

      10. mul-1-neg 98.2%

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

      11. mul-1-neg 98.2%

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

      12. distribute-rgt-neg-in 98.2%

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

      13. neg-sub0 98.2%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 98.2%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 98.2%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 98.2%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 98.2%

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

      18. mul-1-neg 98.2%

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

      19. +-commutative 98.2%

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

      20. mul-1-neg 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in y around inf 89.7%

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

      1. neg-mul-1 89.7%

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

      2. sub-neg 89.7%

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

   8. Simplified 89.7%

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

   if -5.1e7 < y < 3.6e18

   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 90.8%

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

      1. mul-1-neg 90.8%

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

      2. unsub-neg 90.8%

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

   5. Simplified 90.8%

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

   if 3.6e18 < y < 2.09999999999999991e57

   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 72.0%

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

      1. mul-1-neg 72.0%

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

      2. unsub-neg 72.0%

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

   5. Simplified 72.0%

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

   if 2.09999999999999991e57 < y < 6.6000000000000006e67

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. mul-1-neg 100.0%

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

      11. mul-1-neg 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 100.0%

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

      18. mul-1-neg 100.0%

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

      19. +-commutative 100.0%

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

      20. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. sub-neg 100.0%

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

   8. Simplified 100.0%

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

   if 6.6000000000000006e67 < 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 90.1%

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

      1. *-commutative 90.1%

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

   5. Simplified 90.1%

      \[\leadsto x + \color{blue}{\left(t - x\right) \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -51000000:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+18}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+67}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+186}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+95} \lor \neg \left(x \leq 1.45 \cdot 10^{+110}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))))
   (if (<= x -3.5e+247)
     t_1
     (if (<= x -4.5e+186)
       (* y (- x))
       (if (or (<= x -1.8e+95) (not (<= x 1.45e+110))) t_1 (* (- y z) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double tmp;
	if (x <= -3.5e+247) {
		tmp = t_1;
	} else if (x <= -4.5e+186) {
		tmp = y * -x;
	} else if ((x <= -1.8e+95) || !(x <= 1.45e+110)) {
		tmp = t_1;
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    if (x <= (-3.5d+247)) then
        tmp = t_1
    else if (x <= (-4.5d+186)) then
        tmp = y * -x
    else if ((x <= (-1.8d+95)) .or. (.not. (x <= 1.45d+110))) then
        tmp = t_1
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double tmp;
	if (x <= -3.5e+247) {
		tmp = t_1;
	} else if (x <= -4.5e+186) {
		tmp = y * -x;
	} else if ((x <= -1.8e+95) || !(x <= 1.45e+110)) {
		tmp = t_1;
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	tmp = 0
	if x <= -3.5e+247:
		tmp = t_1
	elif x <= -4.5e+186:
		tmp = y * -x
	elif (x <= -1.8e+95) or not (x <= 1.45e+110):
		tmp = t_1
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (x <= -3.5e+247)
		tmp = t_1;
	elseif (x <= -4.5e+186)
		tmp = Float64(y * Float64(-x));
	elseif ((x <= -1.8e+95) || !(x <= 1.45e+110))
		tmp = t_1;
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	tmp = 0.0;
	if (x <= -3.5e+247)
		tmp = t_1;
	elseif (x <= -4.5e+186)
		tmp = y * -x;
	elseif ((x <= -1.8e+95) || ~((x <= 1.45e+110)))
		tmp = t_1;
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.5e+247], t$95$1, If[LessEqual[x, -4.5e+186], N[(y * (-x)), $MachinePrecision], If[Or[LessEqual[x, -1.8e+95], N[Not[LessEqual[x, 1.45e+110]], $MachinePrecision]], t$95$1, N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.5000000000000002e247 or -4.50000000000000045e186 < x < -1.79999999999999989e95 or 1.45e110 < x

   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 72.2%

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

      1. mul-1-neg 72.2%

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

      2. unsub-neg 72.2%

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

   5. Simplified 72.2%

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

      1. sub-neg 72.2%

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

      2. distribute-lft-in 65.6%

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

   7. Applied egg-rr 65.6%

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

   8. Taylor expanded in x around -inf 69.3%

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

   if -3.5000000000000002e247 < x < -4.50000000000000045e186

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. mul-1-neg 100.0%

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

      11. mul-1-neg 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 100.0%

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

      18. mul-1-neg 100.0%

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

      19. +-commutative 100.0%

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

      20. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 73.7%

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

      1. neg-mul-1 73.7%

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

      2. sub-neg 73.7%

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

   8. Simplified 73.7%

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

   9. Taylor expanded in t around 0 73.7%

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

       1. associate-*r* 73.7%

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

       2. mul-1-neg 73.7%

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

   11. Simplified 73.7%

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

   if -1.79999999999999989e95 < x < 1.45e110

   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 98.7%

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

      1. fma-def 98.7%

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

      2. +-commutative 98.7%

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

      3. mul-1-neg 98.7%

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

      4. neg-sub0 98.7%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 98.7%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 98.7%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 98.7%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 98.7%

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

      9. distribute-rgt-neg-in 98.7%

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

      10. mul-1-neg 98.7%

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

      11. mul-1-neg 98.7%

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

      12. distribute-rgt-neg-in 98.7%

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

      13. neg-sub0 98.7%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 98.7%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 98.7%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 98.7%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 98.7%

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

      18. mul-1-neg 98.7%

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

      19. +-commutative 98.7%

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

      20. mul-1-neg 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in t around inf 64.5%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+247}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+186}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+95} \lor \neg \left(x \leq 1.45 \cdot 10^{+110}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := y \cdot \left(-x\right)\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{-138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-230}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-212}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-31}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (* y (- x))))
   (if (<= t -5.4e-138)
     t_1
     (if (<= t 7.5e-230)
       t_2
       (if (<= t 5.2e-212) (* z x) (if (<= t 4e-31) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = y * -x;
	double tmp;
	if (t <= -5.4e-138) {
		tmp = t_1;
	} else if (t <= 7.5e-230) {
		tmp = t_2;
	} else if (t <= 5.2e-212) {
		tmp = z * x;
	} else if (t <= 4e-31) {
		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 - z) * t
    t_2 = y * -x
    if (t <= (-5.4d-138)) then
        tmp = t_1
    else if (t <= 7.5d-230) then
        tmp = t_2
    else if (t <= 5.2d-212) then
        tmp = z * x
    else if (t <= 4d-31) 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 - z) * t;
	double t_2 = y * -x;
	double tmp;
	if (t <= -5.4e-138) {
		tmp = t_1;
	} else if (t <= 7.5e-230) {
		tmp = t_2;
	} else if (t <= 5.2e-212) {
		tmp = z * x;
	} else if (t <= 4e-31) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	t_2 = y * -x
	tmp = 0
	if t <= -5.4e-138:
		tmp = t_1
	elif t <= 7.5e-230:
		tmp = t_2
	elif t <= 5.2e-212:
		tmp = z * x
	elif t <= 4e-31:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(y * Float64(-x))
	tmp = 0.0
	if (t <= -5.4e-138)
		tmp = t_1;
	elseif (t <= 7.5e-230)
		tmp = t_2;
	elseif (t <= 5.2e-212)
		tmp = Float64(z * x);
	elseif (t <= 4e-31)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	t_2 = y * -x;
	tmp = 0.0;
	if (t <= -5.4e-138)
		tmp = t_1;
	elseif (t <= 7.5e-230)
		tmp = t_2;
	elseif (t <= 5.2e-212)
		tmp = z * x;
	elseif (t <= 4e-31)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[t, -5.4e-138], t$95$1, If[LessEqual[t, 7.5e-230], t$95$2, If[LessEqual[t, 5.2e-212], N[(z * x), $MachinePrecision], If[LessEqual[t, 4e-31], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.40000000000000057e-138 or 4e-31 < 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 92.9%

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

      1. fma-def 96.8%

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

      2. +-commutative 96.8%

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

      3. mul-1-neg 96.8%

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

      4. neg-sub0 96.8%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 96.8%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 96.8%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 96.8%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 96.8%

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

      9. distribute-rgt-neg-in 96.8%

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

      10. mul-1-neg 96.8%

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

      11. mul-1-neg 96.8%

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

      12. distribute-rgt-neg-in 96.8%

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

      13. neg-sub0 96.8%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 96.8%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 96.8%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 96.8%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 96.8%

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

      18. mul-1-neg 96.8%

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

      19. +-commutative 96.8%

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

      20. mul-1-neg 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in t around inf 68.0%

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

   if -5.40000000000000057e-138 < t < 7.50000000000000006e-230 or 5.2e-212 < t < 4e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. mul-1-neg 100.0%

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

      11. mul-1-neg 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 100.0%

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

      18. mul-1-neg 100.0%

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

      19. +-commutative 100.0%

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

      20. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 50.0%

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

      1. neg-mul-1 50.0%

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

      2. sub-neg 50.0%

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

   8. Simplified 50.0%

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

   9. Taylor expanded in t around 0 43.1%

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

       1. associate-*r* 43.1%

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

       2. mul-1-neg 43.1%

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

   11. Simplified 43.1%

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

   if 7.50000000000000006e-230 < t < 5.2e-212

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-lft-in 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in x around -inf 100.0%

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

   9. Taylor expanded in z around inf 86.2%

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

       1. *-commutative 86.2%

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

   11. Simplified 86.2%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-138}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-230}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-212}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5200:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-192}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))))
   (if (<= y -1.8e+86)
     t_1
     (if (<= y -5200.0)
       (* y t)
       (if (<= y -1.5e-192) (* z x) (if (<= y 6e+19) (* z (- t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -1.8e+86) {
		tmp = t_1;
	} else if (y <= -5200.0) {
		tmp = y * t;
	} else if (y <= -1.5e-192) {
		tmp = z * x;
	} else if (y <= 6e+19) {
		tmp = z * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -x
    if (y <= (-1.8d+86)) then
        tmp = t_1
    else if (y <= (-5200.0d0)) then
        tmp = y * t
    else if (y <= (-1.5d-192)) then
        tmp = z * x
    else if (y <= 6d+19) then
        tmp = z * -t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double tmp;
	if (y <= -1.8e+86) {
		tmp = t_1;
	} else if (y <= -5200.0) {
		tmp = y * t;
	} else if (y <= -1.5e-192) {
		tmp = z * x;
	} else if (y <= 6e+19) {
		tmp = z * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	tmp = 0
	if y <= -1.8e+86:
		tmp = t_1
	elif y <= -5200.0:
		tmp = y * t
	elif y <= -1.5e-192:
		tmp = z * x
	elif y <= 6e+19:
		tmp = z * -t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -1.8e+86)
		tmp = t_1;
	elseif (y <= -5200.0)
		tmp = Float64(y * t);
	elseif (y <= -1.5e-192)
		tmp = Float64(z * x);
	elseif (y <= 6e+19)
		tmp = Float64(z * Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	tmp = 0.0;
	if (y <= -1.8e+86)
		tmp = t_1;
	elseif (y <= -5200.0)
		tmp = y * t;
	elseif (y <= -1.5e-192)
		tmp = z * x;
	elseif (y <= 6e+19)
		tmp = z * -t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.8e+86], t$95$1, If[LessEqual[y, -5200.0], N[(y * t), $MachinePrecision], If[LessEqual[y, -1.5e-192], N[(z * x), $MachinePrecision], If[LessEqual[y, 6e+19], N[(z * (-t)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.80000000000000003e86 or 6e19 < 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 93.6%

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

      1. fma-def 97.2%

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

      2. +-commutative 97.2%

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

      3. mul-1-neg 97.2%

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

      4. neg-sub0 97.2%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 97.2%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 97.2%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 97.2%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 97.2%

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

      9. distribute-rgt-neg-in 97.2%

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

      10. mul-1-neg 97.2%

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

      11. mul-1-neg 97.2%

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

      12. distribute-rgt-neg-in 97.2%

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

      13. neg-sub0 97.2%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 97.2%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 97.2%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 97.2%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 97.2%

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

      18. mul-1-neg 97.2%

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

      19. +-commutative 97.2%

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

      20. mul-1-neg 97.2%

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

   5. Simplified 97.2%

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

   6. Taylor expanded in y around inf 83.3%

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

      1. neg-mul-1 83.3%

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

      2. sub-neg 83.3%

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

   8. Simplified 83.3%

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

   9. Taylor expanded in t around 0 52.8%

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

       1. associate-*r* 52.8%

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

       2. mul-1-neg 52.8%

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

   11. Simplified 52.8%

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

   if -1.80000000000000003e86 < y < -5200

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. mul-1-neg 100.0%

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

      11. mul-1-neg 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 100.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 100.0%

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

      18. mul-1-neg 100.0%

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

      19. +-commutative 100.0%

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

      20. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 78.9%

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

   7. Taylor expanded in y around inf 71.7%

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

      1. *-commutative 71.7%

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

   9. Simplified 71.7%

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

   if -5200 < y < -1.5e-192

   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 86.2%

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

      1. mul-1-neg 86.2%

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

      2. unsub-neg 86.2%

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

   5. Simplified 86.2%

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

      1. sub-neg 86.2%

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

      2. distribute-lft-in 80.5%

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

   7. Applied egg-rr 80.5%

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

   8. Taylor expanded in x around -inf 72.9%

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

   9. Taylor expanded in z around inf 55.6%

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

       1. *-commutative 55.6%

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

   11. Simplified 55.6%

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

   if -1.5e-192 < y < 6e19

   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 97.9%

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

      1. fma-def 99.0%

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

      2. +-commutative 99.0%

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

      3. mul-1-neg 99.0%

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

      4. neg-sub0 99.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 99.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 99.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 99.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 99.0%

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

      9. distribute-rgt-neg-in 99.0%

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

      10. mul-1-neg 99.0%

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

      11. mul-1-neg 99.0%

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

      12. distribute-rgt-neg-in 99.0%

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

      13. neg-sub0 99.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 99.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 99.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 99.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 99.0%

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

      18. mul-1-neg 99.0%

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

      19. +-commutative 99.0%

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

      20. mul-1-neg 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in t around inf 49.0%

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

   7. Taylor expanded in y around 0 41.9%

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

      1. associate-*r* 41.9%

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

      2. *-commutative 41.9%

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

      3. mul-1-neg 41.9%

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

   9. Simplified 41.9%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -5200:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-192}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5200:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-194}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5200.0)
   (* y t)
   (if (<= y -3.3e-194) (* z x) (if (<= y 5.5e+97) (* z (- t)) (* y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5200.0) {
		tmp = y * t;
	} else if (y <= -3.3e-194) {
		tmp = z * x;
	} else if (y <= 5.5e+97) {
		tmp = z * -t;
	} 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 <= (-5200.0d0)) then
        tmp = y * t
    else if (y <= (-3.3d-194)) then
        tmp = z * x
    else if (y <= 5.5d+97) then
        tmp = z * -t
    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 <= -5200.0) {
		tmp = y * t;
	} else if (y <= -3.3e-194) {
		tmp = z * x;
	} else if (y <= 5.5e+97) {
		tmp = z * -t;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5200.0:
		tmp = y * t
	elif y <= -3.3e-194:
		tmp = z * x
	elif y <= 5.5e+97:
		tmp = z * -t
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5200.0)
		tmp = Float64(y * t);
	elseif (y <= -3.3e-194)
		tmp = Float64(z * x);
	elseif (y <= 5.5e+97)
		tmp = Float64(z * Float64(-t));
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5200.0)
		tmp = y * t;
	elseif (y <= -3.3e-194)
		tmp = z * x;
	elseif (y <= 5.5e+97)
		tmp = z * -t;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5200.0], N[(y * t), $MachinePrecision], If[LessEqual[y, -3.3e-194], N[(z * x), $MachinePrecision], If[LessEqual[y, 5.5e+97], N[(z * (-t)), $MachinePrecision], N[(y * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5200 or 5.50000000000000021e97 < 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 93.0%

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

      1. fma-def 97.0%

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

      2. +-commutative 97.0%

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

      3. mul-1-neg 97.0%

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

      4. neg-sub0 97.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 97.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 97.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 97.0%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 97.0%

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

      9. distribute-rgt-neg-in 97.0%

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

      10. mul-1-neg 97.0%

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

      11. mul-1-neg 97.0%

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

      12. distribute-rgt-neg-in 97.0%

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

      13. neg-sub0 97.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 97.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 97.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 97.0%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 97.0%

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

      18. mul-1-neg 97.0%

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

      19. +-commutative 97.0%

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

      20. mul-1-neg 97.0%

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

   5. Simplified 97.0%

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

   6. Taylor expanded in t around inf 48.9%

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

   7. Taylor expanded in y around inf 44.0%

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

      1. *-commutative 44.0%

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

   9. Simplified 44.0%

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

   if -5200 < y < -3.2999999999999999e-194

   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 86.2%

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

      1. mul-1-neg 86.2%

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

      2. unsub-neg 86.2%

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

   5. Simplified 86.2%

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

      1. sub-neg 86.2%

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

      2. distribute-lft-in 80.5%

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

   7. Applied egg-rr 80.5%

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

   8. Taylor expanded in x around -inf 72.9%

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

   9. Taylor expanded in z around inf 55.6%

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

       1. *-commutative 55.6%

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

   11. Simplified 55.6%

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

   if -3.2999999999999999e-194 < y < 5.50000000000000021e97

   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 98.3%

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

      1. fma-def 99.2%

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

      2. +-commutative 99.2%

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

      3. mul-1-neg 99.2%

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

      4. neg-sub0 99.2%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 99.2%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 99.2%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 99.2%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 99.2%

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

      9. distribute-rgt-neg-in 99.2%

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

      10. mul-1-neg 99.2%

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

      11. mul-1-neg 99.2%

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

      12. distribute-rgt-neg-in 99.2%

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

      13. neg-sub0 99.2%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 99.2%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 99.2%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 99.2%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 99.2%

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

      18. mul-1-neg 99.2%

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

      19. +-commutative 99.2%

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

      20. mul-1-neg 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in t around inf 49.2%

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

   7. Taylor expanded in y around 0 40.0%

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

      1. associate-*r* 40.0%

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

      2. *-commutative 40.0%

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

      3. mul-1-neg 40.0%

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

   9. Simplified 40.0%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5200:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-194}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.000205 \lor \neg \left(x \leq 2.7 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.000205) (not (<= x 2.7e+66)))
   (* x (+ (- z y) 1.0))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.000205) || !(x <= 2.7e+66)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-0.000205d0)) .or. (.not. (x <= 2.7d+66))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.000205) || !(x <= 2.7e+66)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -0.000205) or not (x <= 2.7e+66):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.000205) || !(x <= 2.7e+66))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -0.000205) || ~((x <= 2.7e+66)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.000205], N[Not[LessEqual[x, 2.7e+66]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.05e-4 or 2.7e66 < x

   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 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

   5. Simplified 86.6%

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

   if -2.05e-4 < x < 2.7e66

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 79.3%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.000205 \lor \neg \left(x \leq 2.7 \cdot 10^{+66}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -122000000 \lor \neg \left(y \leq 6.6 \cdot 10^{+67}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -122000000.0) (not (<= y 6.6e+67)))
   (* y (- t x))
   (* z (- x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -122000000.0) || !(y <= 6.6e+67)) {
		tmp = y * (t - x);
	} else {
		tmp = z * (x - 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 <= (-122000000.0d0)) .or. (.not. (y <= 6.6d+67))) then
        tmp = y * (t - x)
    else
        tmp = z * (x - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -122000000.0) || !(y <= 6.6e+67)) {
		tmp = y * (t - x);
	} else {
		tmp = z * (x - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -122000000.0) or not (y <= 6.6e+67):
		tmp = y * (t - x)
	else:
		tmp = z * (x - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -122000000.0) || !(y <= 6.6e+67))
		tmp = Float64(y * Float64(t - x));
	else
		tmp = Float64(z * Float64(x - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -122000000.0) || ~((y <= 6.6e+67)))
		tmp = y * (t - x);
	else
		tmp = z * (x - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -122000000.0], N[Not[LessEqual[y, 6.6e+67]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.22e8 or 6.6000000000000006e67 < 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 93.3%

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

      1. fma-def 97.1%

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

      2. +-commutative 97.1%

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

      3. mul-1-neg 97.1%

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

      4. neg-sub0 97.1%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 97.1%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 97.1%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 97.1%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 97.1%

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

      9. distribute-rgt-neg-in 97.1%

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

      10. mul-1-neg 97.1%

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

      11. mul-1-neg 97.1%

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

      12. distribute-rgt-neg-in 97.1%

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

      13. neg-sub0 97.1%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 97.1%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 97.1%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 97.1%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 97.1%

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

      18. mul-1-neg 97.1%

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

      19. +-commutative 97.1%

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

      20. mul-1-neg 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in y around inf 89.9%

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

      1. neg-mul-1 89.9%

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

      2. sub-neg 89.9%

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

   8. Simplified 89.9%

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

   if -1.22e8 < y < 6.6000000000000006e67

   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 97.3%

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

      1. fma-def 98.7%

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

      2. +-commutative 98.7%

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

      3. mul-1-neg 98.7%

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

      4. neg-sub0 98.7%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 98.7%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 98.7%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 98.7%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 98.7%

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

      9. distribute-rgt-neg-in 98.7%

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

      10. mul-1-neg 98.7%

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

      11. mul-1-neg 98.7%

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

      12. distribute-rgt-neg-in 98.7%

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

      13. neg-sub0 98.7%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 98.7%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 98.7%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 98.7%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 98.7%

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

      18. mul-1-neg 98.7%

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

      19. +-commutative 98.7%

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

      20. mul-1-neg 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in z around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. sub-neg 63.5%

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

   8. Simplified 63.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -122000000 \lor \neg \left(y \leq 6.6 \cdot 10^{+67}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-44} \lor \neg \left(y \leq 1.65 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.1e-44) (not (<= y 1.65e-32))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-44) || !(y <= 1.65e-32)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.1d-44)) .or. (.not. (y <= 1.65d-32))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-44) || !(y <= 1.65e-32)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.1e-44) or not (y <= 1.65e-32):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.1e-44) || !(y <= 1.65e-32))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.1e-44) || ~((y <= 1.65e-32)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.1e-44], N[Not[LessEqual[y, 1.65e-32]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000001e-44 or 1.65000000000000013e-32 < 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 94.6%

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

      1. fma-def 97.3%

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

      2. +-commutative 97.3%

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

      3. mul-1-neg 97.3%

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

      4. neg-sub0 97.3%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(\color{blue}{\left(0 - \left(y - z\right)\right)} + 1\right)\right) \]

      5. associate-+l- 97.3%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(\left(y - z\right) - 1\right)\right)}\right) \]

      6. associate--r+ 97.3%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(y - \left(z + 1\right)\right)}\right)\right) \]

      7. +-commutative 97.3%

         \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(1 + z\right)}\right)\right)\right) \]

      8. neg-sub0 97.3%

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

      9. distribute-rgt-neg-in 97.3%

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

      10. mul-1-neg 97.3%

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

      11. mul-1-neg 97.3%

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

      12. distribute-rgt-neg-in 97.3%

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

      13. neg-sub0 97.3%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(0 - \left(y - \left(1 + z\right)\right)\right)}\right) \]

      14. +-commutative 97.3%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \left(y - \color{blue}{\left(z + 1\right)}\right)\right)\right) \]

      15. associate--r+ 97.3%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \left(0 - \color{blue}{\left(\left(y - z\right) - 1\right)}\right)\right) \]

      16. associate-+l- 97.3%

          \[\leadsto \mathsf{fma}\left(t, y - z, x \cdot \color{blue}{\left(\left(0 - \left(y - z\right)\right) + 1\right)}\right) \]

      17. neg-sub0 97.3%

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

      18. mul-1-neg 97.3%

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

      19. +-commutative 97.3%

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

      20. mul-1-neg 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in t around inf 51.1%

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

   7. Taylor expanded in y around inf 37.0%

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

      1. *-commutative 37.0%

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

   9. Simplified 37.0%

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

   if -2.10000000000000001e-44 < y < 1.65000000000000013e-32

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 71.8%

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

   4. Taylor expanded in x around inf 33.8%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-44} \lor \neg \left(y \leq 1.65 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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. Final simplification 100.0%

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

Alternative 14: 18.3% 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 t around inf 60.3%

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

4. Taylor expanded in x around inf 16.0%

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

5. Final simplification 16.0%

   \[\leadsto x \]
6. Add Preprocessing

Developer target: 96.6% 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 2024031 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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