Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.5s

Alternatives: 16

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: 40.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+120}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+56}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -245:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-18}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+24}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* x (- y))))
   (if (<= y -1.1e+120)
     (* y t)
     (if (<= y -7.5e+91)
       t_2
       (if (<= y -3.8e+56)
         (* y t)
         (if (<= y -245.0)
           t_1
           (if (<= y -1.75e-18)
             (* z x)
             (if (<= y -3e-115)
               x
               (if (<= y 4.1e-126)
                 t_1
                 (if (<= y 7.1e-99)
                   x
                   (if (<= y 4.5e-24)
                     t_1
                     (if (<= y 2.5e+24) (* z x) t_2))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x * -y;
	double tmp;
	if (y <= -1.1e+120) {
		tmp = y * t;
	} else if (y <= -7.5e+91) {
		tmp = t_2;
	} else if (y <= -3.8e+56) {
		tmp = y * t;
	} else if (y <= -245.0) {
		tmp = t_1;
	} else if (y <= -1.75e-18) {
		tmp = z * x;
	} else if (y <= -3e-115) {
		tmp = x;
	} else if (y <= 4.1e-126) {
		tmp = t_1;
	} else if (y <= 7.1e-99) {
		tmp = x;
	} else if (y <= 4.5e-24) {
		tmp = t_1;
	} else if (y <= 2.5e+24) {
		tmp = z * x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * -t
    t_2 = x * -y
    if (y <= (-1.1d+120)) then
        tmp = y * t
    else if (y <= (-7.5d+91)) then
        tmp = t_2
    else if (y <= (-3.8d+56)) then
        tmp = y * t
    else if (y <= (-245.0d0)) then
        tmp = t_1
    else if (y <= (-1.75d-18)) then
        tmp = z * x
    else if (y <= (-3d-115)) then
        tmp = x
    else if (y <= 4.1d-126) then
        tmp = t_1
    else if (y <= 7.1d-99) then
        tmp = x
    else if (y <= 4.5d-24) then
        tmp = t_1
    else if (y <= 2.5d+24) then
        tmp = z * x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = x * -y;
	double tmp;
	if (y <= -1.1e+120) {
		tmp = y * t;
	} else if (y <= -7.5e+91) {
		tmp = t_2;
	} else if (y <= -3.8e+56) {
		tmp = y * t;
	} else if (y <= -245.0) {
		tmp = t_1;
	} else if (y <= -1.75e-18) {
		tmp = z * x;
	} else if (y <= -3e-115) {
		tmp = x;
	} else if (y <= 4.1e-126) {
		tmp = t_1;
	} else if (y <= 7.1e-99) {
		tmp = x;
	} else if (y <= 4.5e-24) {
		tmp = t_1;
	} else if (y <= 2.5e+24) {
		tmp = z * x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = x * -y
	tmp = 0
	if y <= -1.1e+120:
		tmp = y * t
	elif y <= -7.5e+91:
		tmp = t_2
	elif y <= -3.8e+56:
		tmp = y * t
	elif y <= -245.0:
		tmp = t_1
	elif y <= -1.75e-18:
		tmp = z * x
	elif y <= -3e-115:
		tmp = x
	elif y <= 4.1e-126:
		tmp = t_1
	elif y <= 7.1e-99:
		tmp = x
	elif y <= 4.5e-24:
		tmp = t_1
	elif y <= 2.5e+24:
		tmp = z * x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1.1e+120)
		tmp = Float64(y * t);
	elseif (y <= -7.5e+91)
		tmp = t_2;
	elseif (y <= -3.8e+56)
		tmp = Float64(y * t);
	elseif (y <= -245.0)
		tmp = t_1;
	elseif (y <= -1.75e-18)
		tmp = Float64(z * x);
	elseif (y <= -3e-115)
		tmp = x;
	elseif (y <= 4.1e-126)
		tmp = t_1;
	elseif (y <= 7.1e-99)
		tmp = x;
	elseif (y <= 4.5e-24)
		tmp = t_1;
	elseif (y <= 2.5e+24)
		tmp = Float64(z * x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = x * -y;
	tmp = 0.0;
	if (y <= -1.1e+120)
		tmp = y * t;
	elseif (y <= -7.5e+91)
		tmp = t_2;
	elseif (y <= -3.8e+56)
		tmp = y * t;
	elseif (y <= -245.0)
		tmp = t_1;
	elseif (y <= -1.75e-18)
		tmp = z * x;
	elseif (y <= -3e-115)
		tmp = x;
	elseif (y <= 4.1e-126)
		tmp = t_1;
	elseif (y <= 7.1e-99)
		tmp = x;
	elseif (y <= 4.5e-24)
		tmp = t_1;
	elseif (y <= 2.5e+24)
		tmp = z * x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.1e+120], N[(y * t), $MachinePrecision], If[LessEqual[y, -7.5e+91], t$95$2, If[LessEqual[y, -3.8e+56], N[(y * t), $MachinePrecision], If[LessEqual[y, -245.0], t$95$1, If[LessEqual[y, -1.75e-18], N[(z * x), $MachinePrecision], If[LessEqual[y, -3e-115], x, If[LessEqual[y, 4.1e-126], t$95$1, If[LessEqual[y, 7.1e-99], x, If[LessEqual[y, 4.5e-24], t$95$1, If[LessEqual[y, 2.5e+24], N[(z * x), $MachinePrecision], t$95$2]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.1000000000000001e120 or -7.50000000000000033e91 < y < -3.79999999999999996e56

   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 95.3%

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

      1. fma-def 95.3%

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

      2. +-commutative 95.3%

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

      3. mul-1-neg 95.3%

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

      4. neg-sub0 95.3%

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

      5. associate-+l- 95.3%

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

      6. associate--r+ 95.3%

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

      7. +-commutative 95.3%

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

      8. neg-sub0 95.3%

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

      9. distribute-rgt-neg-in 95.3%

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

      10. mul-1-neg 95.3%

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

      11. mul-1-neg 95.3%

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

      12. distribute-rgt-neg-in 95.3%

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

      13. neg-sub0 95.3%

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

      14. +-commutative 95.3%

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

      15. associate--r+ 95.3%

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

      16. associate-+l- 95.3%

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

      17. neg-sub0 95.3%

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

      18. mul-1-neg 95.3%

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

      19. +-commutative 95.3%

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

      20. mul-1-neg 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in z around 0 84.4%

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

      1. fma-def 84.4%

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

   8. Simplified 84.4%

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

   9. Taylor expanded in t around inf 66.3%

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

       1. *-commutative 66.3%

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

   11. Simplified 66.3%

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

   if -1.1000000000000001e120 < y < -7.50000000000000033e91 or 2.50000000000000023e24 < 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 91.1%

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

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

   9. Taylor expanded in t around 0 58.5%

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

       1. associate-*r* 58.5%

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

       2. neg-mul-1 58.5%

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

       3. *-commutative 58.5%

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

   11. Simplified 58.5%

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

   if -3.79999999999999996e56 < y < -245 or -3.0000000000000002e-115 < y < 4.0999999999999997e-126 or 7.09999999999999994e-99 < y < 4.4999999999999997e-24

   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 95.9%

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

      1. fma-def 95.9%

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

      2. +-commutative 95.9%

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

      3. mul-1-neg 95.9%

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

      4. neg-sub0 95.9%

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

      5. associate-+l- 95.9%

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

      6. associate--r+ 95.9%

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

      7. +-commutative 95.9%

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

      8. neg-sub0 95.9%

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

      9. distribute-rgt-neg-in 95.9%

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

      10. mul-1-neg 95.9%

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

      11. mul-1-neg 95.9%

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

      12. distribute-rgt-neg-in 95.9%

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

      13. neg-sub0 95.9%

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

      14. +-commutative 95.9%

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

      15. associate--r+ 95.9%

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

      16. associate-+l- 95.9%

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

      17. neg-sub0 95.9%

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

      18. mul-1-neg 95.9%

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

      19. +-commutative 95.9%

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

      20. mul-1-neg 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in t around inf 57.5%

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

   7. Taylor expanded in y around 0 52.7%

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

      1. associate-*r* 52.7%

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

      2. mul-1-neg 52.7%

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

   9. Simplified 52.7%

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

   if -245 < y < -1.7499999999999999e-18 or 4.4999999999999997e-24 < y < 2.50000000000000023e24

   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 94.7%

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

      1. fma-def 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 69.0%

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

      1. mul-1-neg 69.0%

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

      2. sub-neg 69.0%

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

   8. Simplified 69.0%

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

   9. Taylor expanded in x around inf 59.2%

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

   if -1.7499999999999999e-18 < y < -3.0000000000000002e-115 or 4.0999999999999997e-126 < y < 7.09999999999999994e-99

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 71.4%

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

      1. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in y around 0 57.3%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+120}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+56}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -245:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-18}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-24}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+24}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -0.0019:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-171}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-293}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+122}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))) (t_3 (* x (- 1.0 y))))
   (if (<= z -0.0019)
     t_2
     (if (<= z -8e-171)
       t_3
       (if (<= z -3.2e-231)
         t_1
         (if (<= z 1.35e-293)
           t_3
           (if (<= z 1.05e-86)
             t_1
             (if (<= z 4.8e+122) (* (- y z) t) t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (z <= -0.0019) {
		tmp = t_2;
	} else if (z <= -8e-171) {
		tmp = t_3;
	} else if (z <= -3.2e-231) {
		tmp = t_1;
	} else if (z <= 1.35e-293) {
		tmp = t_3;
	} else if (z <= 1.05e-86) {
		tmp = t_1;
	} else if (z <= 4.8e+122) {
		tmp = (y - z) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * (x - t)
    t_3 = x * (1.0d0 - y)
    if (z <= (-0.0019d0)) then
        tmp = t_2
    else if (z <= (-8d-171)) then
        tmp = t_3
    else if (z <= (-3.2d-231)) then
        tmp = t_1
    else if (z <= 1.35d-293) then
        tmp = t_3
    else if (z <= 1.05d-86) then
        tmp = t_1
    else if (z <= 4.8d+122) then
        tmp = (y - z) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (z <= -0.0019) {
		tmp = t_2;
	} else if (z <= -8e-171) {
		tmp = t_3;
	} else if (z <= -3.2e-231) {
		tmp = t_1;
	} else if (z <= 1.35e-293) {
		tmp = t_3;
	} else if (z <= 1.05e-86) {
		tmp = t_1;
	} else if (z <= 4.8e+122) {
		tmp = (y - z) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * (x - t)
	t_3 = x * (1.0 - y)
	tmp = 0
	if z <= -0.0019:
		tmp = t_2
	elif z <= -8e-171:
		tmp = t_3
	elif z <= -3.2e-231:
		tmp = t_1
	elif z <= 1.35e-293:
		tmp = t_3
	elif z <= 1.05e-86:
		tmp = t_1
	elif z <= 4.8e+122:
		tmp = (y - z) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(x - t))
	t_3 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -0.0019)
		tmp = t_2;
	elseif (z <= -8e-171)
		tmp = t_3;
	elseif (z <= -3.2e-231)
		tmp = t_1;
	elseif (z <= 1.35e-293)
		tmp = t_3;
	elseif (z <= 1.05e-86)
		tmp = t_1;
	elseif (z <= 4.8e+122)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * (x - t);
	t_3 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -0.0019)
		tmp = t_2;
	elseif (z <= -8e-171)
		tmp = t_3;
	elseif (z <= -3.2e-231)
		tmp = t_1;
	elseif (z <= 1.35e-293)
		tmp = t_3;
	elseif (z <= 1.05e-86)
		tmp = t_1;
	elseif (z <= 4.8e+122)
		tmp = (y - z) * t;
	else
		tmp = t_2;
	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[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0019], t$95$2, If[LessEqual[z, -8e-171], t$95$3, If[LessEqual[z, -3.2e-231], t$95$1, If[LessEqual[z, 1.35e-293], t$95$3, If[LessEqual[z, 1.05e-86], t$95$1, If[LessEqual[z, 4.8e+122], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0019 or 4.8000000000000004e122 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.2%

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

      1. fma-def 96.1%

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

      2. +-commutative 96.1%

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

      3. mul-1-neg 96.1%

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

      4. neg-sub0 96.1%

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

      5. associate-+l- 96.1%

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

      6. associate--r+ 96.1%

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

      7. +-commutative 96.1%

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

      8. neg-sub0 96.1%

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

      9. distribute-rgt-neg-in 96.1%

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

      10. mul-1-neg 96.1%

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

      11. mul-1-neg 96.1%

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

      12. distribute-rgt-neg-in 96.1%

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

      13. neg-sub0 96.1%

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

      14. +-commutative 96.1%

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

      15. associate--r+ 96.1%

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

      16. associate-+l- 96.1%

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

      17. neg-sub0 96.1%

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

      18. mul-1-neg 96.1%

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

      19. +-commutative 96.1%

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

      20. mul-1-neg 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in z around inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. sub-neg 87.1%

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

   8. Simplified 87.1%

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

   if -0.0019 < z < -7.9999999999999999e-171 or -3.20000000000000008e-231 < z < 1.35000000000000001e-293

   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 98.2%

      \[\leadsto \color{blue}{t \cdot \left(y - z\right) + x \cdot \left(1 + -1 \cdot \left(y - z\right)\right)} \]
   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 z around 0 94.8%

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

      1. fma-def 94.8%

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

   8. Simplified 94.8%

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

   9. Taylor expanded in t around 0 81.3%

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

   if -7.9999999999999999e-171 < z < -3.20000000000000008e-231 or 1.35000000000000001e-293 < z < 1.05e-86

   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 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 94.3%

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

      2. +-commutative 94.3%

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

      3. mul-1-neg 94.3%

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

      4. neg-sub0 94.3%

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

      5. associate-+l- 94.3%

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

      6. associate--r+ 94.3%

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

      7. +-commutative 94.3%

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

      8. neg-sub0 94.3%

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

      9. distribute-rgt-neg-in 94.3%

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

      10. mul-1-neg 94.3%

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

      11. mul-1-neg 94.3%

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

      12. distribute-rgt-neg-in 94.3%

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

      13. neg-sub0 94.3%

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

      14. +-commutative 94.3%

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

      15. associate--r+ 94.3%

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

      16. associate-+l- 94.3%

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

      17. neg-sub0 94.3%

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

      18. mul-1-neg 94.3%

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

      19. +-commutative 94.3%

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

      20. mul-1-neg 94.3%

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

   5. Simplified 94.3%

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

   6. Taylor expanded in y around inf 76.5%

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

      1. neg-mul-1 76.5%

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

      2. sub-neg 76.5%

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

   8. Simplified 76.5%

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

   if 1.05e-86 < z < 4.8000000000000004e122

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{t \cdot \left(y - z\right) + x \cdot \left(1 + -1 \cdot \left(y - z\right)\right)} \]
   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 64.7%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0019:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-171}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-231}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+122}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 54.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y - z \leq -5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{+234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{+291}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= (- y z) -5e-19)
     t_1
     (if (<= (- y z) 4e-26)
       x
       (if (<= (- y z) 2e+234)
         t_1
         (if (<= (- y z) 4e+291) (* x (- y)) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -5e-19) {
		tmp = t_1;
	} else if ((y - z) <= 4e-26) {
		tmp = x;
	} else if ((y - z) <= 2e+234) {
		tmp = t_1;
	} else if ((y - z) <= 4e+291) {
		tmp = x * -y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if ((y - z) <= (-5d-19)) then
        tmp = t_1
    else if ((y - z) <= 4d-26) then
        tmp = x
    else if ((y - z) <= 2d+234) then
        tmp = t_1
    else if ((y - z) <= 4d+291) then
        tmp = x * -y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if ((y - z) <= -5e-19) {
		tmp = t_1;
	} else if ((y - z) <= 4e-26) {
		tmp = x;
	} else if ((y - z) <= 2e+234) {
		tmp = t_1;
	} else if ((y - z) <= 4e+291) {
		tmp = x * -y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if (y - z) <= -5e-19:
		tmp = t_1
	elif (y - z) <= 4e-26:
		tmp = x
	elif (y - z) <= 2e+234:
		tmp = t_1
	elif (y - z) <= 4e+291:
		tmp = x * -y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (Float64(y - z) <= -5e-19)
		tmp = t_1;
	elseif (Float64(y - z) <= 4e-26)
		tmp = x;
	elseif (Float64(y - z) <= 2e+234)
		tmp = t_1;
	elseif (Float64(y - z) <= 4e+291)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if ((y - z) <= -5e-19)
		tmp = t_1;
	elseif ((y - z) <= 4e-26)
		tmp = x;
	elseif ((y - z) <= 2e+234)
		tmp = t_1;
	elseif ((y - z) <= 4e+291)
		tmp = x * -y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[(y - z), $MachinePrecision], -5e-19], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 4e-26], x, If[LessEqual[N[(y - z), $MachinePrecision], 2e+234], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 4e+291], N[(x * (-y)), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 y z) < -5.0000000000000004e-19 or 4.0000000000000002e-26 < (-.f64 y z) < 2.00000000000000004e234

   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 97.2%

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

      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 t around inf 59.7%

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

   if -5.0000000000000004e-19 < (-.f64 y z) < 4.0000000000000002e-26

   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 86.3%

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

      1. *-commutative 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 72.5%

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

   if 2.00000000000000004e234 < (-.f64 y z) < 3.9999999999999998e291

   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 87.5%

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

      1. fma-def 87.5%

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

      2. +-commutative 87.5%

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

      3. mul-1-neg 87.5%

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

      4. neg-sub0 87.5%

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

      5. associate-+l- 87.5%

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

      6. associate--r+ 87.5%

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

      7. +-commutative 87.5%

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

      8. neg-sub0 87.5%

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

      9. distribute-rgt-neg-in 87.5%

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

      10. mul-1-neg 87.5%

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

      11. mul-1-neg 87.5%

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

      12. distribute-rgt-neg-in 87.5%

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

      13. neg-sub0 87.5%

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

      14. +-commutative 87.5%

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

      15. associate--r+ 87.5%

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

      16. associate-+l- 87.5%

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

      17. neg-sub0 87.5%

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

      18. mul-1-neg 87.5%

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

      19. +-commutative 87.5%

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

      20. mul-1-neg 87.5%

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

   5. Simplified 87.5%

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

   6. Taylor expanded in y around inf 75.6%

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

      1. neg-mul-1 75.6%

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

      2. sub-neg 75.6%

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

   8. Simplified 75.6%

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

   9. Taylor expanded in t around 0 59.5%

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

       1. associate-*r* 59.5%

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

       2. neg-mul-1 59.5%

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

       3. *-commutative 59.5%

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

   11. Simplified 59.5%

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

   if 3.9999999999999998e291 < (-.f64 y z)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{t \cdot \left(y - z\right) + x \cdot \left(1 + -1 \cdot \left(y - z\right)\right)} \]
   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 80.8%

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

      1. mul-1-neg 80.8%

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

      2. sub-neg 80.8%

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

   8. Simplified 80.8%

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

   9. Taylor expanded in x around inf 80.8%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -5 \cdot 10^{-19}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{+234}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{+291}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -0.135:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-30}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-103}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -6.2e+31)
     t_1
     (if (<= y -0.135)
       (* (- y z) t)
       (if (<= y -1.55e-30)
         (+ x (* z x))
         (if (<= y 9e-103)
           (- x (* z t))
           (if (<= y 2.05e+24) (* z (- x t)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -6.2e+31) {
		tmp = t_1;
	} else if (y <= -0.135) {
		tmp = (y - z) * t;
	} else if (y <= -1.55e-30) {
		tmp = x + (z * x);
	} else if (y <= 9e-103) {
		tmp = x - (z * t);
	} else if (y <= 2.05e+24) {
		tmp = z * (x - 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 * (t - x)
    if (y <= (-6.2d+31)) then
        tmp = t_1
    else if (y <= (-0.135d0)) then
        tmp = (y - z) * t
    else if (y <= (-1.55d-30)) then
        tmp = x + (z * x)
    else if (y <= 9d-103) then
        tmp = x - (z * t)
    else if (y <= 2.05d+24) then
        tmp = z * (x - 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 tmp;
	if (y <= -6.2e+31) {
		tmp = t_1;
	} else if (y <= -0.135) {
		tmp = (y - z) * t;
	} else if (y <= -1.55e-30) {
		tmp = x + (z * x);
	} else if (y <= 9e-103) {
		tmp = x - (z * t);
	} else if (y <= 2.05e+24) {
		tmp = z * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -6.2e+31:
		tmp = t_1
	elif y <= -0.135:
		tmp = (y - z) * t
	elif y <= -1.55e-30:
		tmp = x + (z * x)
	elif y <= 9e-103:
		tmp = x - (z * t)
	elif y <= 2.05e+24:
		tmp = z * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -6.2e+31)
		tmp = t_1;
	elseif (y <= -0.135)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= -1.55e-30)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 9e-103)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 2.05e+24)
		tmp = Float64(z * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -6.2e+31)
		tmp = t_1;
	elseif (y <= -0.135)
		tmp = (y - z) * t;
	elseif (y <= -1.55e-30)
		tmp = x + (z * x);
	elseif (y <= 9e-103)
		tmp = x - (z * t);
	elseif (y <= 2.05e+24)
		tmp = z * (x - 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]}, If[LessEqual[y, -6.2e+31], t$95$1, If[LessEqual[y, -0.135], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, -1.55e-30], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-103], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e+24], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.2000000000000004e31 or 2.05e24 < 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 96.5%

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

      2. +-commutative 96.5%

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

      3. mul-1-neg 96.5%

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

      4. neg-sub0 96.5%

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

      5. associate-+l- 96.5%

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

      6. associate--r+ 96.5%

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

      7. +-commutative 96.5%

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

      8. neg-sub0 96.5%

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

      9. distribute-rgt-neg-in 96.5%

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

      10. mul-1-neg 96.5%

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

      11. mul-1-neg 96.5%

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

      12. distribute-rgt-neg-in 96.5%

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

      13. neg-sub0 96.5%

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

      14. +-commutative 96.5%

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

      15. associate--r+ 96.5%

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

      16. associate-+l- 96.5%

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

      17. neg-sub0 96.5%

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

      18. mul-1-neg 96.5%

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

      19. +-commutative 96.5%

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

      20. mul-1-neg 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in y around inf 88.9%

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

      1. neg-mul-1 88.9%

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

      2. sub-neg 88.9%

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

   8. Simplified 88.9%

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

   if -6.2000000000000004e31 < y < -0.13500000000000001

   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 83.1%

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

      1. fma-def 83.3%

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

      2. +-commutative 83.3%

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

      3. mul-1-neg 83.3%

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

      4. neg-sub0 83.3%

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

      5. associate-+l- 83.3%

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

      6. associate--r+ 83.3%

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

      7. +-commutative 83.3%

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

      8. neg-sub0 83.3%

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

      9. distribute-rgt-neg-in 83.3%

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

      10. mul-1-neg 83.3%

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

      11. mul-1-neg 83.3%

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

      12. distribute-rgt-neg-in 83.3%

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

      13. neg-sub0 83.3%

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

      14. +-commutative 83.3%

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

      15. associate--r+ 83.3%

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

      16. associate-+l- 83.3%

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

      17. neg-sub0 83.3%

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

      18. mul-1-neg 83.3%

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

      19. +-commutative 83.3%

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

      20. mul-1-neg 83.3%

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

   5. Simplified 83.3%

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

   6. Taylor expanded in t around inf 99.7%

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

   if -0.13500000000000001 < y < -1.54999999999999995e-30

   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 79.9%

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

      1. mul-1-neg 79.9%

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

      2. unsub-neg 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in t around 0 79.9%

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

      1. mul-1-neg 79.9%

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

      2. distribute-lft-neg-out 79.9%

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

      3. *-commutative 79.9%

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

   8. Simplified 79.9%

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

   if -1.54999999999999995e-30 < y < 9e-103

   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 96.2%

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

      1. mul-1-neg 96.2%

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

      2. unsub-neg 96.2%

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

   5. Simplified 96.2%

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

   6. Taylor expanded in t around inf 75.5%

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

      1. *-commutative 75.5%

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

   8. Simplified 75.5%

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

   if 9e-103 < y < 2.05e24

   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 96.2%

      \[\leadsto \color{blue}{t \cdot \left(y - z\right) + x \cdot \left(1 + -1 \cdot \left(y - z\right)\right)} \]
   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 69.9%

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

      1. mul-1-neg 69.9%

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

      2. sub-neg 69.9%

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

   8. Simplified 69.9%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -0.135:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-30}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-103}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-12}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-256}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+123}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.2e-12)
   (* z x)
   (if (<= z -1.5e-54)
     x
     (if (<= z -3.8e-256)
       (* y t)
       (if (<= z 1.45e-295) x (if (<= z 3.6e+123) (* y t) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e-12) {
		tmp = z * x;
	} else if (z <= -1.5e-54) {
		tmp = x;
	} else if (z <= -3.8e-256) {
		tmp = y * t;
	} else if (z <= 1.45e-295) {
		tmp = x;
	} else if (z <= 3.6e+123) {
		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 <= (-7.2d-12)) then
        tmp = z * x
    else if (z <= (-1.5d-54)) then
        tmp = x
    else if (z <= (-3.8d-256)) then
        tmp = y * t
    else if (z <= 1.45d-295) then
        tmp = x
    else if (z <= 3.6d+123) 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 <= -7.2e-12) {
		tmp = z * x;
	} else if (z <= -1.5e-54) {
		tmp = x;
	} else if (z <= -3.8e-256) {
		tmp = y * t;
	} else if (z <= 1.45e-295) {
		tmp = x;
	} else if (z <= 3.6e+123) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.2e-12:
		tmp = z * x
	elif z <= -1.5e-54:
		tmp = x
	elif z <= -3.8e-256:
		tmp = y * t
	elif z <= 1.45e-295:
		tmp = x
	elif z <= 3.6e+123:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.2e-12)
		tmp = Float64(z * x);
	elseif (z <= -1.5e-54)
		tmp = x;
	elseif (z <= -3.8e-256)
		tmp = Float64(y * t);
	elseif (z <= 1.45e-295)
		tmp = x;
	elseif (z <= 3.6e+123)
		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 <= -7.2e-12)
		tmp = z * x;
	elseif (z <= -1.5e-54)
		tmp = x;
	elseif (z <= -3.8e-256)
		tmp = y * t;
	elseif (z <= 1.45e-295)
		tmp = x;
	elseif (z <= 3.6e+123)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.2e-12], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.5e-54], x, If[LessEqual[z, -3.8e-256], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.45e-295], x, If[LessEqual[z, 3.6e+123], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2e-12 or 3.59999999999999998e123 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.3%

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

      1. fma-def 96.2%

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

      2. +-commutative 96.2%

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

      3. mul-1-neg 96.2%

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

      4. neg-sub0 96.2%

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

      5. associate-+l- 96.2%

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

      6. associate--r+ 96.2%

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

      7. +-commutative 96.2%

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

      8. neg-sub0 96.2%

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

      9. distribute-rgt-neg-in 96.2%

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

      10. mul-1-neg 96.2%

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

      11. mul-1-neg 96.2%

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

      12. distribute-rgt-neg-in 96.2%

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

      13. neg-sub0 96.2%

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

      14. +-commutative 96.2%

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

      15. associate--r+ 96.2%

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

      16. associate-+l- 96.2%

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

      17. neg-sub0 96.2%

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

      18. mul-1-neg 96.2%

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

      19. +-commutative 96.2%

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

      20. mul-1-neg 96.2%

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

   5. Simplified 96.2%

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

   6. Taylor expanded in z around inf 85.6%

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

      1. mul-1-neg 85.6%

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

      2. sub-neg 85.6%

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

   8. Simplified 85.6%

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

   9. Taylor expanded in x around inf 41.7%

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

   if -7.2e-12 < z < -1.50000000000000005e-54 or -3.79999999999999977e-256 < z < 1.45000000000000008e-295

   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 93.1%

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

      1. *-commutative 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in y around 0 58.5%

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

   if -1.50000000000000005e-54 < z < -3.79999999999999977e-256 or 1.45000000000000008e-295 < z < 3.59999999999999998e123

   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 96.7%

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

      1. fma-def 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 z around 0 81.1%

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

      1. fma-def 81.1%

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

   8. Simplified 81.1%

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

   9. Taylor expanded in t around inf 43.4%

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

       1. *-commutative 43.4%

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

   11. Simplified 43.4%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-12}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-256}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+123}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0116:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-237}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+122}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.0116)
   (* z x)
   (if (<= z -3.5e-120)
     (* x (- y))
     (if (<= z -2.45e-237)
       (* y t)
       (if (<= z 3.7e-295) x (if (<= z 7.8e+122) (* y t) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.0116) {
		tmp = z * x;
	} else if (z <= -3.5e-120) {
		tmp = x * -y;
	} else if (z <= -2.45e-237) {
		tmp = y * t;
	} else if (z <= 3.7e-295) {
		tmp = x;
	} else if (z <= 7.8e+122) {
		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 <= (-0.0116d0)) then
        tmp = z * x
    else if (z <= (-3.5d-120)) then
        tmp = x * -y
    else if (z <= (-2.45d-237)) then
        tmp = y * t
    else if (z <= 3.7d-295) then
        tmp = x
    else if (z <= 7.8d+122) 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 <= -0.0116) {
		tmp = z * x;
	} else if (z <= -3.5e-120) {
		tmp = x * -y;
	} else if (z <= -2.45e-237) {
		tmp = y * t;
	} else if (z <= 3.7e-295) {
		tmp = x;
	} else if (z <= 7.8e+122) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.0116:
		tmp = z * x
	elif z <= -3.5e-120:
		tmp = x * -y
	elif z <= -2.45e-237:
		tmp = y * t
	elif z <= 3.7e-295:
		tmp = x
	elif z <= 7.8e+122:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.0116)
		tmp = Float64(z * x);
	elseif (z <= -3.5e-120)
		tmp = Float64(x * Float64(-y));
	elseif (z <= -2.45e-237)
		tmp = Float64(y * t);
	elseif (z <= 3.7e-295)
		tmp = x;
	elseif (z <= 7.8e+122)
		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 <= -0.0116)
		tmp = z * x;
	elseif (z <= -3.5e-120)
		tmp = x * -y;
	elseif (z <= -2.45e-237)
		tmp = y * t;
	elseif (z <= 3.7e-295)
		tmp = x;
	elseif (z <= 7.8e+122)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.0116], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.5e-120], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, -2.45e-237], N[(y * t), $MachinePrecision], If[LessEqual[z, 3.7e-295], x, If[LessEqual[z, 7.8e+122], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0116 or 7.7999999999999999e122 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.2%

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

      1. fma-def 96.1%

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

      2. +-commutative 96.1%

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

      3. mul-1-neg 96.1%

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

      4. neg-sub0 96.1%

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

      5. associate-+l- 96.1%

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

      6. associate--r+ 96.1%

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

      7. +-commutative 96.1%

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

      8. neg-sub0 96.1%

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

      9. distribute-rgt-neg-in 96.1%

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

      10. mul-1-neg 96.1%

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

      11. mul-1-neg 96.1%

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

      12. distribute-rgt-neg-in 96.1%

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

      13. neg-sub0 96.1%

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

      14. +-commutative 96.1%

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

      15. associate--r+ 96.1%

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

      16. associate-+l- 96.1%

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

      17. neg-sub0 96.1%

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

      18. mul-1-neg 96.1%

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

      19. +-commutative 96.1%

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

      20. mul-1-neg 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in z around inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. sub-neg 87.1%

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

   8. Simplified 87.1%

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

   9. Taylor expanded in x around inf 42.4%

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

   if -0.0116 < z < -3.5e-120

   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 95.7%

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

      1. fma-def 95.7%

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

      2. +-commutative 95.7%

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

      3. mul-1-neg 95.7%

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

      4. neg-sub0 95.7%

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

      5. associate-+l- 95.7%

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

      6. associate--r+ 95.7%

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

      7. +-commutative 95.7%

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

      8. neg-sub0 95.7%

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

      9. distribute-rgt-neg-in 95.7%

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

      10. mul-1-neg 95.7%

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

      11. mul-1-neg 95.7%

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

      12. distribute-rgt-neg-in 95.7%

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

      13. neg-sub0 95.7%

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

      14. +-commutative 95.7%

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

      15. associate--r+ 95.7%

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

      16. associate-+l- 95.7%

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

      17. neg-sub0 95.7%

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

      18. mul-1-neg 95.7%

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

      19. +-commutative 95.7%

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

      20. mul-1-neg 95.7%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in y around inf 60.0%

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

      1. neg-mul-1 60.0%

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

      2. sub-neg 60.0%

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

   8. Simplified 60.0%

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

   9. Taylor expanded in t around 0 47.3%

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

       1. associate-*r* 47.3%

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

       2. neg-mul-1 47.3%

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

       3. *-commutative 47.3%

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

   11. Simplified 47.3%

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

   if -3.5e-120 < z < -2.45e-237 or 3.6999999999999999e-295 < z < 7.7999999999999999e122

   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 97.2%

      \[\leadsto \color{blue}{t \cdot \left(y - z\right) + x \cdot \left(1 + -1 \cdot \left(y - z\right)\right)} \]
   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 z around 0 79.1%

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

      1. fma-def 79.1%

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

   8. Simplified 79.1%

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

   9. Taylor expanded in t around inf 45.2%

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

       1. *-commutative 45.2%

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

   11. Simplified 45.2%

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

   if -2.45e-237 < z < 3.6999999999999999e-295

   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 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 49.3%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0116:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-237}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-295}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+122}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -0.0116:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-99}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+122}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -0.0116)
     t_1
     (if (<= z 1e-99)
       (+ x (* y (- t x)))
       (if (<= z 4.8e+122) (+ x (* (- y z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -0.0116) {
		tmp = t_1;
	} else if (z <= 1e-99) {
		tmp = x + (y * (t - x));
	} else if (z <= 4.8e+122) {
		tmp = x + ((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) :: tmp
    t_1 = z * (x - t)
    if (z <= (-0.0116d0)) then
        tmp = t_1
    else if (z <= 1d-99) then
        tmp = x + (y * (t - x))
    else if (z <= 4.8d+122) then
        tmp = x + ((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 = z * (x - t);
	double tmp;
	if (z <= -0.0116) {
		tmp = t_1;
	} else if (z <= 1e-99) {
		tmp = x + (y * (t - x));
	} else if (z <= 4.8e+122) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -0.0116:
		tmp = t_1
	elif z <= 1e-99:
		tmp = x + (y * (t - x))
	elif z <= 4.8e+122:
		tmp = x + ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -0.0116)
		tmp = t_1;
	elseif (z <= 1e-99)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	elseif (z <= 4.8e+122)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -0.0116)
		tmp = t_1;
	elseif (z <= 1e-99)
		tmp = x + (y * (t - x));
	elseif (z <= 4.8e+122)
		tmp = x + ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0116], t$95$1, If[LessEqual[z, 1e-99], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+122], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0116 or 4.8000000000000004e122 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.2%

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

      1. fma-def 96.1%

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

      2. +-commutative 96.1%

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

      3. mul-1-neg 96.1%

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

      4. neg-sub0 96.1%

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

      5. associate-+l- 96.1%

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

      6. associate--r+ 96.1%

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

      7. +-commutative 96.1%

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

      8. neg-sub0 96.1%

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

      9. distribute-rgt-neg-in 96.1%

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

      10. mul-1-neg 96.1%

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

      11. mul-1-neg 96.1%

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

      12. distribute-rgt-neg-in 96.1%

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

      13. neg-sub0 96.1%

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

      14. +-commutative 96.1%

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

      15. associate--r+ 96.1%

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

      16. associate-+l- 96.1%

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

      17. neg-sub0 96.1%

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

      18. mul-1-neg 96.1%

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

      19. +-commutative 96.1%

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

      20. mul-1-neg 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in z around inf 87.1%

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

      1. mul-1-neg 87.1%

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

      2. sub-neg 87.1%

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

   8. Simplified 87.1%

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

   if -0.0116 < z < 1e-99

   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 96.5%

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

      1. *-commutative 96.5%

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

   5. Simplified 96.5%

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

   if 1e-99 < z < 4.8000000000000004e122

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 71.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0116:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 10^{-99}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+122}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-100}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -5.2e+31)
     t_1
     (if (<= y 5.4e-100)
       (- x (* z t))
       (if (<= y 3.25e+24) (* z (- x t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -5.2e+31) {
		tmp = t_1;
	} else if (y <= 5.4e-100) {
		tmp = x - (z * t);
	} else if (y <= 3.25e+24) {
		tmp = z * (x - 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 * (t - x)
    if (y <= (-5.2d+31)) then
        tmp = t_1
    else if (y <= 5.4d-100) then
        tmp = x - (z * t)
    else if (y <= 3.25d+24) then
        tmp = z * (x - 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 tmp;
	if (y <= -5.2e+31) {
		tmp = t_1;
	} else if (y <= 5.4e-100) {
		tmp = x - (z * t);
	} else if (y <= 3.25e+24) {
		tmp = z * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -5.2e+31:
		tmp = t_1
	elif y <= 5.4e-100:
		tmp = x - (z * t)
	elif y <= 3.25e+24:
		tmp = z * (x - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -5.2e+31)
		tmp = t_1;
	elseif (y <= 5.4e-100)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 3.25e+24)
		tmp = Float64(z * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -5.2e+31)
		tmp = t_1;
	elseif (y <= 5.4e-100)
		tmp = x - (z * t);
	elseif (y <= 3.25e+24)
		tmp = z * (x - 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]}, If[LessEqual[y, -5.2e+31], t$95$1, If[LessEqual[y, 5.4e-100], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.25e+24], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2e31 or 3.2499999999999998e24 < 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 96.5%

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

      2. +-commutative 96.5%

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

      3. mul-1-neg 96.5%

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

      4. neg-sub0 96.5%

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

      5. associate-+l- 96.5%

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

      6. associate--r+ 96.5%

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

      7. +-commutative 96.5%

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

      8. neg-sub0 96.5%

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

      9. distribute-rgt-neg-in 96.5%

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

      10. mul-1-neg 96.5%

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

      11. mul-1-neg 96.5%

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

      12. distribute-rgt-neg-in 96.5%

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

      13. neg-sub0 96.5%

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

      14. +-commutative 96.5%

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

      15. associate--r+ 96.5%

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

      16. associate-+l- 96.5%

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

      17. neg-sub0 96.5%

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

      18. mul-1-neg 96.5%

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

      19. +-commutative 96.5%

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

      20. mul-1-neg 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in y around inf 88.9%

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

      1. neg-mul-1 88.9%

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

      2. sub-neg 88.9%

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

   8. Simplified 88.9%

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

   if -5.2e31 < y < 5.40000000000000031e-100

   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 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in t around inf 73.0%

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

      1. *-commutative 73.0%

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

   8. Simplified 73.0%

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

   if 5.40000000000000031e-100 < y < 3.2499999999999998e24

   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 96.2%

      \[\leadsto \color{blue}{t \cdot \left(y - z\right) + x \cdot \left(1 + -1 \cdot \left(y - z\right)\right)} \]
   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 69.9%

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

      1. mul-1-neg 69.9%

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

      2. sub-neg 69.9%

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

   8. Simplified 69.9%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-100}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-8} \lor \neg \left(x \leq 2.8 \cdot 10^{+79}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3e-8) (not (<= x 2.8e+79)))
   (* x (+ (- z y) 1.0))
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3e-8) || !(x <= 2.8e+79)) {
		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 <= (-3d-8)) .or. (.not. (x <= 2.8d+79))) 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 <= -3e-8) || !(x <= 2.8e+79)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3e-8) or not (x <= 2.8e+79):
		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 <= -3e-8) || !(x <= 2.8e+79))
		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 <= -3e-8) || ~((x <= 2.8e+79)))
		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, -3e-8], N[Not[LessEqual[x, 2.8e+79]], $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 < -2.99999999999999973e-8 or 2.8000000000000001e79 < 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 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   if -2.99999999999999973e-8 < x < 2.8000000000000001e79

   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 76.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-8} \lor \neg \left(x \leq 2.8 \cdot 10^{+79}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 80.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+67} \lor \neg \left(x \leq 5.8 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.65e+67) (not (<= x 5.8e+80)))
   (* x (+ (- z y) 1.0))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.65e+67) || !(x <= 5.8e+80)) {
		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 <= (-2.65d+67)) .or. (.not. (x <= 5.8d+80))) 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 <= -2.65e+67) || !(x <= 5.8e+80)) {
		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 <= -2.65e+67) or not (x <= 5.8e+80):
		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 <= -2.65e+67) || !(x <= 5.8e+80))
		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 <= -2.65e+67) || ~((x <= 5.8e+80)))
		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, -2.65e+67], N[Not[LessEqual[x, 5.8e+80]], $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 < -2.65e67 or 5.79999999999999971e80 < 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 89.1%

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

      1. mul-1-neg 89.1%

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

      2. unsub-neg 89.1%

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

   5. Simplified 89.1%

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

   if -2.65e67 < x < 5.79999999999999971e80

   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 84.1%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+67} \lor \neg \left(x \leq 5.8 \cdot 10^{+80}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+24}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -2.05e+32)
     t_1
     (if (<= y 2.05e+24) (- x (* z (- t x))) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -2.05e+32) {
		tmp = t_1;
	} else if (y <= 2.05e+24) {
		tmp = x - (z * (t - x));
	} 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 <= (-2.05d+32)) then
        tmp = t_1
    else if (y <= 2.05d+24) then
        tmp = x - (z * (t - x))
    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 <= -2.05e+32) {
		tmp = t_1;
	} else if (y <= 2.05e+24) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -2.05e+32:
		tmp = t_1
	elif y <= 2.05e+24:
		tmp = x - (z * (t - x))
	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 <= -2.05e+32)
		tmp = t_1;
	elseif (y <= 2.05e+24)
		tmp = Float64(x - Float64(z * Float64(t - x)));
	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 <= -2.05e+32)
		tmp = t_1;
	elseif (y <= 2.05e+24)
		tmp = x - (z * (t - x));
	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, -2.05e+32], t$95$1, If[LessEqual[y, 2.05e+24], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0499999999999999e32

   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 91.2%

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

      1. fma-def 96.5%

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

      2. +-commutative 96.5%

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

      3. mul-1-neg 96.5%

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

      4. neg-sub0 96.5%

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

      5. associate-+l- 96.5%

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

      6. associate--r+ 96.5%

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

      7. +-commutative 96.5%

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

      8. neg-sub0 96.5%

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

      9. distribute-rgt-neg-in 96.5%

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

      10. mul-1-neg 96.5%

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

      11. mul-1-neg 96.5%

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

      12. distribute-rgt-neg-in 96.5%

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

      13. neg-sub0 96.5%

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

      14. +-commutative 96.5%

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

      15. associate--r+ 96.5%

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

      16. associate-+l- 96.5%

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

      17. neg-sub0 96.5%

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

      18. mul-1-neg 96.5%

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

      19. +-commutative 96.5%

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

      20. mul-1-neg 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in y around inf 86.5%

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

      1. neg-mul-1 86.5%

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

      2. sub-neg 86.5%

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

   8. Simplified 86.5%

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

   if -2.0499999999999999e32 < y < 2.05e24

   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 90.4%

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

      1. mul-1-neg 90.4%

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

      2. unsub-neg 90.4%

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

   5. Simplified 90.4%

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

   if 2.05e24 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 91.4%

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

      1. *-commutative 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+24}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+27} \lor \neg \left(t \leq 3 \cdot 10^{+38}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.4e+27) (not (<= t 3e+38))) (* (- y z) t) (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.4e+27) || !(t <= 3e+38)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	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 ((t <= (-4.4d+27)) .or. (.not. (t <= 3d+38))) then
        tmp = (y - z) * t
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.4e+27) || !(t <= 3e+38)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.4e+27) or not (t <= 3e+38):
		tmp = (y - z) * t
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.4e+27) || !(t <= 3e+38))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.4e+27) || ~((t <= 3e+38)))
		tmp = (y - z) * t;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.4e+27], N[Not[LessEqual[t, 3e+38]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3999999999999997e27 or 3.0000000000000001e38 < 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 90.2%

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

      1. fma-def 94.0%

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

      2. +-commutative 94.0%

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

      3. mul-1-neg 94.0%

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

      4. neg-sub0 94.0%

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

      5. associate-+l- 94.0%

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

      6. associate--r+ 94.0%

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

      7. +-commutative 94.0%

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

      8. neg-sub0 94.0%

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

      9. distribute-rgt-neg-in 94.0%

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

      10. mul-1-neg 94.0%

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

      11. mul-1-neg 94.0%

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

      12. distribute-rgt-neg-in 94.0%

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

      13. neg-sub0 94.0%

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

      14. +-commutative 94.0%

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

      15. associate--r+ 94.0%

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

      16. associate-+l- 94.0%

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

      17. neg-sub0 94.0%

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

      18. mul-1-neg 94.0%

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

      19. +-commutative 94.0%

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

      20. mul-1-neg 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in t around inf 78.6%

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

   if -4.3999999999999997e27 < t < 3.0000000000000001e38

   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 0 65.9%

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

      1. fma-def 65.9%

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

   8. Simplified 65.9%

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

   9. Taylor expanded in t around 0 56.3%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+27} \lor \neg \left(t \leq 3 \cdot 10^{+38}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 36.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-12} \lor \neg \left(z \leq 0.038\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.2e-12) (not (<= z 0.038))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-12) || !(z <= 0.038)) {
		tmp = z * x;
	} 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 ((z <= (-7.2d-12)) .or. (.not. (z <= 0.038d0))) then
        tmp = z * x
    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 ((z <= -7.2e-12) || !(z <= 0.038)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.2e-12) or not (z <= 0.038):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.2e-12) || !(z <= 0.038))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.2e-12) || ~((z <= 0.038)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.2e-12], N[Not[LessEqual[z, 0.038]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e-12 or 0.0379999999999999991 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 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 96.9%

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

      2. +-commutative 96.9%

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

      3. mul-1-neg 96.9%

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

      4. neg-sub0 96.9%

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

      5. associate-+l- 96.9%

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

      6. associate--r+ 96.9%

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

      7. +-commutative 96.9%

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

      8. neg-sub0 96.9%

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

      9. distribute-rgt-neg-in 96.9%

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

      10. mul-1-neg 96.9%

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

      11. mul-1-neg 96.9%

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

      12. distribute-rgt-neg-in 96.9%

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

      13. neg-sub0 96.9%

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

      14. +-commutative 96.9%

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

      15. associate--r+ 96.9%

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

      16. associate-+l- 96.9%

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

      17. neg-sub0 96.9%

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

      18. mul-1-neg 96.9%

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

      19. +-commutative 96.9%

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

      20. mul-1-neg 96.9%

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

   5. Simplified 96.9%

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

   6. Taylor expanded in z around inf 78.2%

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

      1. mul-1-neg 78.2%

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

      2. sub-neg 78.2%

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

   8. Simplified 78.2%

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

   9. Taylor expanded in x around inf 38.4%

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

   if -7.2e-12 < z < 0.0379999999999999991

   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 92.8%

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

      1. *-commutative 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in y around 0 31.1%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-12} \lor \neg \left(z \leq 0.038\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 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 16: 18.1% 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 y around inf 60.4%

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

   1. *-commutative 60.4%

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

5. Simplified 60.4%

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

6. Taylor expanded in y around 0 16.9%

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

7. Final simplification 16.9%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 96.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024018 
(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))))