Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.2s

Alternatives: 18

Speedup: 1.0×

• 35.6% 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: 67.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := \left(y - z\right) \cdot t\\ t_3 := z \cdot \left(x - t\right)\\ t_4 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -5.9 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+17}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-84}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-193}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-259}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-62}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+21}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x)))
        (t_2 (* (- y z) t))
        (t_3 (* z (- x t)))
        (t_4 (* x (+ z 1.0))))
   (if (<= y -5.9e+54)
     t_1
     (if (<= y -1.5e+17)
       t_3
       (if (<= y -5.2e-84)
         (+ x (* y t))
         (if (<= y -4.8e-111)
           t_2
           (if (<= y -7.8e-193)
             t_4
             (if (<= y 1.2e-259)
               t_3
               (if (<= y 8.6e-62) t_4 (if (<= y 2.3e+21) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = (y - z) * t;
	double t_3 = z * (x - t);
	double t_4 = x * (z + 1.0);
	double tmp;
	if (y <= -5.9e+54) {
		tmp = t_1;
	} else if (y <= -1.5e+17) {
		tmp = t_3;
	} else if (y <= -5.2e-84) {
		tmp = x + (y * t);
	} else if (y <= -4.8e-111) {
		tmp = t_2;
	} else if (y <= -7.8e-193) {
		tmp = t_4;
	} else if (y <= 1.2e-259) {
		tmp = t_3;
	} else if (y <= 8.6e-62) {
		tmp = t_4;
	} else if (y <= 2.3e+21) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = (y - z) * t
    t_3 = z * (x - t)
    t_4 = x * (z + 1.0d0)
    if (y <= (-5.9d+54)) then
        tmp = t_1
    else if (y <= (-1.5d+17)) then
        tmp = t_3
    else if (y <= (-5.2d-84)) then
        tmp = x + (y * t)
    else if (y <= (-4.8d-111)) then
        tmp = t_2
    else if (y <= (-7.8d-193)) then
        tmp = t_4
    else if (y <= 1.2d-259) then
        tmp = t_3
    else if (y <= 8.6d-62) then
        tmp = t_4
    else if (y <= 2.3d+21) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = (y - z) * t;
	double t_3 = z * (x - t);
	double t_4 = x * (z + 1.0);
	double tmp;
	if (y <= -5.9e+54) {
		tmp = t_1;
	} else if (y <= -1.5e+17) {
		tmp = t_3;
	} else if (y <= -5.2e-84) {
		tmp = x + (y * t);
	} else if (y <= -4.8e-111) {
		tmp = t_2;
	} else if (y <= -7.8e-193) {
		tmp = t_4;
	} else if (y <= 1.2e-259) {
		tmp = t_3;
	} else if (y <= 8.6e-62) {
		tmp = t_4;
	} else if (y <= 2.3e+21) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = (y - z) * t
	t_3 = z * (x - t)
	t_4 = x * (z + 1.0)
	tmp = 0
	if y <= -5.9e+54:
		tmp = t_1
	elif y <= -1.5e+17:
		tmp = t_3
	elif y <= -5.2e-84:
		tmp = x + (y * t)
	elif y <= -4.8e-111:
		tmp = t_2
	elif y <= -7.8e-193:
		tmp = t_4
	elif y <= 1.2e-259:
		tmp = t_3
	elif y <= 8.6e-62:
		tmp = t_4
	elif y <= 2.3e+21:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(Float64(y - z) * t)
	t_3 = Float64(z * Float64(x - t))
	t_4 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -5.9e+54)
		tmp = t_1;
	elseif (y <= -1.5e+17)
		tmp = t_3;
	elseif (y <= -5.2e-84)
		tmp = Float64(x + Float64(y * t));
	elseif (y <= -4.8e-111)
		tmp = t_2;
	elseif (y <= -7.8e-193)
		tmp = t_4;
	elseif (y <= 1.2e-259)
		tmp = t_3;
	elseif (y <= 8.6e-62)
		tmp = t_4;
	elseif (y <= 2.3e+21)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = (y - z) * t;
	t_3 = z * (x - t);
	t_4 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -5.9e+54)
		tmp = t_1;
	elseif (y <= -1.5e+17)
		tmp = t_3;
	elseif (y <= -5.2e-84)
		tmp = x + (y * t);
	elseif (y <= -4.8e-111)
		tmp = t_2;
	elseif (y <= -7.8e-193)
		tmp = t_4;
	elseif (y <= 1.2e-259)
		tmp = t_3;
	elseif (y <= 8.6e-62)
		tmp = t_4;
	elseif (y <= 2.3e+21)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.9e+54], t$95$1, If[LessEqual[y, -1.5e+17], t$95$3, If[LessEqual[y, -5.2e-84], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-111], t$95$2, If[LessEqual[y, -7.8e-193], t$95$4, If[LessEqual[y, 1.2e-259], t$95$3, If[LessEqual[y, 8.6e-62], t$95$4, If[LessEqual[y, 2.3e+21], t$95$2, t$95$1]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.8999999999999997e54 or 2.3e21 < 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 96.1%

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

      1. fma-def 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 y around inf 85.9%

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

      1. neg-mul-1 85.9%

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

      2. sub-neg 85.9%

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

   8. Simplified 85.9%

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

   if -5.8999999999999997e54 < y < -1.5e17 or -7.7999999999999997e-193 < y < 1.2e-259

   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 96.9%

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

      1. fma-def 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 z around inf 85.1%

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

      1. mul-1-neg 85.1%

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

      2. sub-neg 85.1%

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

   8. Simplified 85.1%

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

   if -1.5e17 < y < -5.2e-84

   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 87.7%

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

   4. Taylor expanded in y around inf 72.7%

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

      1. *-commutative 72.7%

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

   6. Simplified 72.7%

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

   if -5.2e-84 < y < -4.8000000000000001e-111 or 8.5999999999999993e-62 < y < 2.3e21

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate--r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. mul-1-neg 100.0%

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

      11. mul-1-neg 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. neg-sub0 100.0%

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

      14. +-commutative 100.0%

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

      15. associate--r+ 100.0%

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

      16. associate-+l- 100.0%

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

      17. neg-sub0 100.0%

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

      18. mul-1-neg 100.0%

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

      19. +-commutative 100.0%

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

      20. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 74.6%

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

   if -4.8000000000000001e-111 < y < -7.7999999999999997e-193 or 1.2e-259 < y < 8.5999999999999993e-62

   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 94.7%

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

      1. mul-1-neg 94.7%

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

      2. unsub-neg 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in x around inf 71.1%

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

      1. cancel-sign-sub-inv 71.1%

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

      2. metadata-eval 71.1%

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

      3. *-lft-identity 71.1%

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

   8. Simplified 71.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-84}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-111}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-259}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+21}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-110}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-275}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+15}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))) (t_2 (* y (- t x))) (t_3 (* (- y z) t)))
   (if (<= y -1.85e+55)
     t_2
     (if (<= y -3.6e-110)
       t_3
       (if (<= y -4.8e-191)
         t_1
         (if (<= y 1.3e-275)
           t_3
           (if (<= y 7.4e-61) t_1 (if (<= y 1.3e+15) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double t_3 = (y - z) * t;
	double tmp;
	if (y <= -1.85e+55) {
		tmp = t_2;
	} else if (y <= -3.6e-110) {
		tmp = t_3;
	} else if (y <= -4.8e-191) {
		tmp = t_1;
	} else if (y <= 1.3e-275) {
		tmp = t_3;
	} else if (y <= 7.4e-61) {
		tmp = t_1;
	} else if (y <= 1.3e+15) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    t_2 = y * (t - x)
    t_3 = (y - z) * t
    if (y <= (-1.85d+55)) then
        tmp = t_2
    else if (y <= (-3.6d-110)) then
        tmp = t_3
    else if (y <= (-4.8d-191)) then
        tmp = t_1
    else if (y <= 1.3d-275) then
        tmp = t_3
    else if (y <= 7.4d-61) then
        tmp = t_1
    else if (y <= 1.3d+15) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double t_3 = (y - z) * t;
	double tmp;
	if (y <= -1.85e+55) {
		tmp = t_2;
	} else if (y <= -3.6e-110) {
		tmp = t_3;
	} else if (y <= -4.8e-191) {
		tmp = t_1;
	} else if (y <= 1.3e-275) {
		tmp = t_3;
	} else if (y <= 7.4e-61) {
		tmp = t_1;
	} else if (y <= 1.3e+15) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	t_2 = y * (t - x)
	t_3 = (y - z) * t
	tmp = 0
	if y <= -1.85e+55:
		tmp = t_2
	elif y <= -3.6e-110:
		tmp = t_3
	elif y <= -4.8e-191:
		tmp = t_1
	elif y <= 1.3e-275:
		tmp = t_3
	elif y <= 7.4e-61:
		tmp = t_1
	elif y <= 1.3e+15:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (y <= -1.85e+55)
		tmp = t_2;
	elseif (y <= -3.6e-110)
		tmp = t_3;
	elseif (y <= -4.8e-191)
		tmp = t_1;
	elseif (y <= 1.3e-275)
		tmp = t_3;
	elseif (y <= 7.4e-61)
		tmp = t_1;
	elseif (y <= 1.3e+15)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	t_2 = y * (t - x);
	t_3 = (y - z) * t;
	tmp = 0.0;
	if (y <= -1.85e+55)
		tmp = t_2;
	elseif (y <= -3.6e-110)
		tmp = t_3;
	elseif (y <= -4.8e-191)
		tmp = t_1;
	elseif (y <= 1.3e-275)
		tmp = t_3;
	elseif (y <= 7.4e-61)
		tmp = t_1;
	elseif (y <= 1.3e+15)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -1.85e+55], t$95$2, If[LessEqual[y, -3.6e-110], t$95$3, If[LessEqual[y, -4.8e-191], t$95$1, If[LessEqual[y, 1.3e-275], t$95$3, If[LessEqual[y, 7.4e-61], t$95$1, If[LessEqual[y, 1.3e+15], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8500000000000001e55 or 1.3e15 < 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 96.1%

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

      1. fma-def 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 y around inf 85.9%

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

      1. neg-mul-1 85.9%

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

      2. sub-neg 85.9%

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

   8. Simplified 85.9%

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

   if -1.8500000000000001e55 < y < -3.59999999999999995e-110 or -4.7999999999999998e-191 < y < 1.29999999999999996e-275 or 7.3999999999999999e-61 < y < 1.3e15

   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 98.5%

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

      1. fma-def 98.5%

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

      2. +-commutative 98.5%

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

      3. mul-1-neg 98.5%

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

      4. neg-sub0 98.5%

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

      5. associate-+l- 98.5%

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

      6. associate--r+ 98.5%

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

      7. +-commutative 98.5%

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

      8. neg-sub0 98.5%

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

      9. distribute-rgt-neg-in 98.5%

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

      10. mul-1-neg 98.5%

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

      11. mul-1-neg 98.5%

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

      12. distribute-rgt-neg-in 98.5%

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

      13. neg-sub0 98.5%

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

      14. +-commutative 98.5%

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

      15. associate--r+ 98.5%

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

      16. associate-+l- 98.5%

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

      17. neg-sub0 98.5%

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

      18. mul-1-neg 98.5%

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

      19. +-commutative 98.5%

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

      20. mul-1-neg 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in t around inf 69.8%

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

   if -3.59999999999999995e-110 < y < -4.7999999999999998e-191 or 1.29999999999999996e-275 < y < 7.3999999999999999e-61

   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 96.7%

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

      1. mul-1-neg 96.7%

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

      2. unsub-neg 96.7%

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

   5. Simplified 96.7%

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

   6. Taylor expanded in x around inf 71.8%

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

      1. cancel-sign-sub-inv 71.8%

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

      2. metadata-eval 71.8%

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

      3. *-lft-identity 71.8%

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

   8. Simplified 71.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-110}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-191}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-275}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+15}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-111}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-207}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+24}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))) (t_2 (* y (- t x))) (t_3 (* (- y z) t)))
   (if (<= y -1.9e+56)
     t_2
     (if (<= y -5.2e-111)
       t_3
       (if (<= y -2e-207)
         t_1
         (if (<= y 2.95e-260)
           (* z (- x t))
           (if (<= y 5.2e-61) t_1 (if (<= y 2.5e+24) t_3 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double t_3 = (y - z) * t;
	double tmp;
	if (y <= -1.9e+56) {
		tmp = t_2;
	} else if (y <= -5.2e-111) {
		tmp = t_3;
	} else if (y <= -2e-207) {
		tmp = t_1;
	} else if (y <= 2.95e-260) {
		tmp = z * (x - t);
	} else if (y <= 5.2e-61) {
		tmp = t_1;
	} else if (y <= 2.5e+24) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    t_2 = y * (t - x)
    t_3 = (y - z) * t
    if (y <= (-1.9d+56)) then
        tmp = t_2
    else if (y <= (-5.2d-111)) then
        tmp = t_3
    else if (y <= (-2d-207)) then
        tmp = t_1
    else if (y <= 2.95d-260) then
        tmp = z * (x - t)
    else if (y <= 5.2d-61) then
        tmp = t_1
    else if (y <= 2.5d+24) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double t_3 = (y - z) * t;
	double tmp;
	if (y <= -1.9e+56) {
		tmp = t_2;
	} else if (y <= -5.2e-111) {
		tmp = t_3;
	} else if (y <= -2e-207) {
		tmp = t_1;
	} else if (y <= 2.95e-260) {
		tmp = z * (x - t);
	} else if (y <= 5.2e-61) {
		tmp = t_1;
	} else if (y <= 2.5e+24) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	t_2 = y * (t - x)
	t_3 = (y - z) * t
	tmp = 0
	if y <= -1.9e+56:
		tmp = t_2
	elif y <= -5.2e-111:
		tmp = t_3
	elif y <= -2e-207:
		tmp = t_1
	elif y <= 2.95e-260:
		tmp = z * (x - t)
	elif y <= 5.2e-61:
		tmp = t_1
	elif y <= 2.5e+24:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (y <= -1.9e+56)
		tmp = t_2;
	elseif (y <= -5.2e-111)
		tmp = t_3;
	elseif (y <= -2e-207)
		tmp = t_1;
	elseif (y <= 2.95e-260)
		tmp = Float64(z * Float64(x - t));
	elseif (y <= 5.2e-61)
		tmp = t_1;
	elseif (y <= 2.5e+24)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	t_2 = y * (t - x);
	t_3 = (y - z) * t;
	tmp = 0.0;
	if (y <= -1.9e+56)
		tmp = t_2;
	elseif (y <= -5.2e-111)
		tmp = t_3;
	elseif (y <= -2e-207)
		tmp = t_1;
	elseif (y <= 2.95e-260)
		tmp = z * (x - t);
	elseif (y <= 5.2e-61)
		tmp = t_1;
	elseif (y <= 2.5e+24)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -1.9e+56], t$95$2, If[LessEqual[y, -5.2e-111], t$95$3, If[LessEqual[y, -2e-207], t$95$1, If[LessEqual[y, 2.95e-260], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-61], t$95$1, If[LessEqual[y, 2.5e+24], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.89999999999999998e56 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 96.1%

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

      1. fma-def 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 y around inf 85.9%

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

      1. neg-mul-1 85.9%

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

      2. sub-neg 85.9%

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

   8. Simplified 85.9%

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

   if -1.89999999999999998e56 < y < -5.19999999999999965e-111 or 5.20000000000000021e-61 < 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 0 100.0%

      \[\leadsto \color{blue}{t \cdot \left(y - z\right) + x \cdot \left(1 + -1 \cdot \left(y - z\right)\right)} \]
   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 65.5%

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

   if -5.19999999999999965e-111 < y < -1.99999999999999985e-207 or 2.95e-260 < y < 5.20000000000000021e-61

   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 94.7%

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

      1. mul-1-neg 94.7%

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

      2. unsub-neg 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in x around inf 71.1%

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

      1. cancel-sign-sub-inv 71.1%

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

      2. metadata-eval 71.1%

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

      3. *-lft-identity 71.1%

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

   8. Simplified 71.1%

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

   if -1.99999999999999985e-207 < y < 2.95e-260

   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 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 96.0%

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

      2. +-commutative 96.0%

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

      3. mul-1-neg 96.0%

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

      4. neg-sub0 96.0%

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

      5. associate-+l- 96.0%

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

      6. associate--r+ 96.0%

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

      7. +-commutative 96.0%

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

      8. neg-sub0 96.0%

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

      9. distribute-rgt-neg-in 96.0%

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

      10. mul-1-neg 96.0%

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

      11. mul-1-neg 96.0%

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

      12. distribute-rgt-neg-in 96.0%

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

      13. neg-sub0 96.0%

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

      14. +-commutative 96.0%

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

      15. associate--r+ 96.0%

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

      16. associate-+l- 96.0%

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

      17. neg-sub0 96.0%

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

      18. mul-1-neg 96.0%

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

      19. +-commutative 96.0%

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

      20. mul-1-neg 96.0%

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

   5. Simplified 96.0%

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

   6. Taylor expanded in z around inf 84.1%

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

      1. mul-1-neg 84.1%

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

      2. sub-neg 84.1%

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

   8. Simplified 84.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-111}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+24}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -56000000000000:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-32}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-291}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-206}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+57}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -56000000000000.0)
   (* t (- z))
   (if (<= z -4.1e-32)
     (* y (- x))
     (if (<= z 4.5e-291)
       (* y t)
       (if (<= z 9.5e-206) x (if (<= z 3.05e+57) (* y t) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -56000000000000.0) {
		tmp = t * -z;
	} else if (z <= -4.1e-32) {
		tmp = y * -x;
	} else if (z <= 4.5e-291) {
		tmp = y * t;
	} else if (z <= 9.5e-206) {
		tmp = x;
	} else if (z <= 3.05e+57) {
		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 <= (-56000000000000.0d0)) then
        tmp = t * -z
    else if (z <= (-4.1d-32)) then
        tmp = y * -x
    else if (z <= 4.5d-291) then
        tmp = y * t
    else if (z <= 9.5d-206) then
        tmp = x
    else if (z <= 3.05d+57) 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 <= -56000000000000.0) {
		tmp = t * -z;
	} else if (z <= -4.1e-32) {
		tmp = y * -x;
	} else if (z <= 4.5e-291) {
		tmp = y * t;
	} else if (z <= 9.5e-206) {
		tmp = x;
	} else if (z <= 3.05e+57) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -56000000000000.0:
		tmp = t * -z
	elif z <= -4.1e-32:
		tmp = y * -x
	elif z <= 4.5e-291:
		tmp = y * t
	elif z <= 9.5e-206:
		tmp = x
	elif z <= 3.05e+57:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -56000000000000.0)
		tmp = Float64(t * Float64(-z));
	elseif (z <= -4.1e-32)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 4.5e-291)
		tmp = Float64(y * t);
	elseif (z <= 9.5e-206)
		tmp = x;
	elseif (z <= 3.05e+57)
		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 <= -56000000000000.0)
		tmp = t * -z;
	elseif (z <= -4.1e-32)
		tmp = y * -x;
	elseif (z <= 4.5e-291)
		tmp = y * t;
	elseif (z <= 9.5e-206)
		tmp = x;
	elseif (z <= 3.05e+57)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -56000000000000.0], N[(t * (-z)), $MachinePrecision], If[LessEqual[z, -4.1e-32], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 4.5e-291], N[(y * t), $MachinePrecision], If[LessEqual[z, 9.5e-206], x, If[LessEqual[z, 3.05e+57], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.6e13

   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 73.3%

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

      1. mul-1-neg 73.3%

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

      2. unsub-neg 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in t around inf 50.9%

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

      1. *-commutative 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in x around 0 51.0%

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

       1. mul-1-neg 51.0%

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

       2. distribute-rgt-neg-out 51.0%

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

   11. Simplified 51.0%

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

   if -5.6e13 < z < -4.09999999999999975e-32

   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 y around inf 69.2%

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

      1. neg-mul-1 69.2%

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

      2. sub-neg 69.2%

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

   8. Simplified 69.2%

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

   9. Taylor expanded in t around 0 50.2%

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

       1. mul-1-neg 50.2%

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

       2. distribute-rgt-neg-in 50.2%

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

   11. Simplified 50.2%

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

   if -4.09999999999999975e-32 < z < 4.49999999999999974e-291 or 9.49999999999999979e-206 < z < 3.04999999999999988e57

   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 96.6%

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

      1. fma-def 97.4%

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

      2. +-commutative 97.4%

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

      3. mul-1-neg 97.4%

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

      4. neg-sub0 97.4%

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

      5. associate-+l- 97.4%

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

      6. associate--r+ 97.4%

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

      7. +-commutative 97.4%

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

      8. neg-sub0 97.4%

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

      9. distribute-rgt-neg-in 97.4%

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

      10. mul-1-neg 97.4%

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

      11. mul-1-neg 97.4%

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

      12. distribute-rgt-neg-in 97.4%

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

      13. neg-sub0 97.4%

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

      14. +-commutative 97.4%

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

      15. associate--r+ 97.4%

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

      16. associate-+l- 97.4%

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

      17. neg-sub0 97.4%

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

      18. mul-1-neg 97.4%

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

      19. +-commutative 97.4%

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

      20. mul-1-neg 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in y around inf 66.0%

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

      1. neg-mul-1 66.0%

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

      2. sub-neg 66.0%

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

   8. Simplified 66.0%

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

   9. Taylor expanded in t around inf 48.5%

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

       1. *-commutative 48.5%

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

   11. Simplified 48.5%

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

   if 4.49999999999999974e-291 < z < 9.49999999999999979e-206

   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 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 72.8%

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

   if 3.04999999999999988e57 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.6%

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

      1. mul-1-neg 75.6%

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

      2. unsub-neg 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x around inf 47.7%

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

      1. cancel-sign-sub-inv 47.7%

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

      2. metadata-eval 47.7%

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

      3. *-lft-identity 47.7%

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

   8. Simplified 47.7%

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

   9. Taylor expanded in z around inf 47.7%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -56000000000000:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-32}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-291}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-206}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+57}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-20} \lor \neg \left(x \leq 1.05 \cdot 10^{-110} \lor \neg \left(x \leq 1.9 \cdot 10^{-45}\right) \land x \leq 8.2 \cdot 10^{+47}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.4e-20)
         (not (or (<= x 1.05e-110) (and (not (<= x 1.9e-45)) (<= x 8.2e+47)))))
   (* x (- 1.0 y))
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.4e-20) || !((x <= 1.05e-110) || (!(x <= 1.9e-45) && (x <= 8.2e+47)))) {
		tmp = x * (1.0 - y);
	} 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 <= (-8.4d-20)) .or. (.not. (x <= 1.05d-110) .or. (.not. (x <= 1.9d-45)) .and. (x <= 8.2d+47))) then
        tmp = x * (1.0d0 - y)
    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 <= -8.4e-20) || !((x <= 1.05e-110) || (!(x <= 1.9e-45) && (x <= 8.2e+47)))) {
		tmp = x * (1.0 - y);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.4e-20) or not ((x <= 1.05e-110) or (not (x <= 1.9e-45) and (x <= 8.2e+47))):
		tmp = x * (1.0 - y)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.4e-20) || !((x <= 1.05e-110) || (!(x <= 1.9e-45) && (x <= 8.2e+47))))
		tmp = Float64(x * Float64(1.0 - y));
	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 <= -8.4e-20) || ~(((x <= 1.05e-110) || (~((x <= 1.9e-45)) && (x <= 8.2e+47)))))
		tmp = x * (1.0 - y);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.4e-20], N[Not[Or[LessEqual[x, 1.05e-110], And[N[Not[LessEqual[x, 1.9e-45]], $MachinePrecision], LessEqual[x, 8.2e+47]]]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.3999999999999996e-20 or 1.05000000000000001e-110 < x < 1.89999999999999999e-45 or 8.2000000000000002e47 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 73.3%

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

      1. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   6. Taylor expanded in x around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. sub-neg 63.5%

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

   8. Simplified 63.5%

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

   if -8.3999999999999996e-20 < x < 1.05000000000000001e-110 or 1.89999999999999999e-45 < x < 8.2000000000000002e47

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

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

      5. associate-+l- 100.0%

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

      6. associate--r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. neg-sub0 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. mul-1-neg 100.0%

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

      11. mul-1-neg 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. neg-sub0 100.0%

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

      14. +-commutative 100.0%

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

      15. associate--r+ 100.0%

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

      16. associate-+l- 100.0%

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

      17. neg-sub0 100.0%

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

      18. mul-1-neg 100.0%

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

      19. +-commutative 100.0%

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

      20. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 80.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-20} \lor \neg \left(x \leq 1.05 \cdot 10^{-110} \lor \neg \left(x \leq 1.9 \cdot 10^{-45}\right) \land x \leq 8.2 \cdot 10^{+47}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1850000000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-96}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq 55000000000000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -6.2e+54)
     t_1
     (if (<= y -1850000000000.0)
       (* z (- x t))
       (if (<= y -4e-96)
         (+ x (* y t))
         (if (<= y 55000000000000.0) (- x (* z 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+54) {
		tmp = t_1;
	} else if (y <= -1850000000000.0) {
		tmp = z * (x - t);
	} else if (y <= -4e-96) {
		tmp = x + (y * t);
	} else if (y <= 55000000000000.0) {
		tmp = x - (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-6.2d+54)) then
        tmp = t_1
    else if (y <= (-1850000000000.0d0)) then
        tmp = z * (x - t)
    else if (y <= (-4d-96)) then
        tmp = x + (y * t)
    else if (y <= 55000000000000.0d0) then
        tmp = x - (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -6.2e+54) {
		tmp = t_1;
	} else if (y <= -1850000000000.0) {
		tmp = z * (x - t);
	} else if (y <= -4e-96) {
		tmp = x + (y * t);
	} else if (y <= 55000000000000.0) {
		tmp = x - (z * 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+54:
		tmp = t_1
	elif y <= -1850000000000.0:
		tmp = z * (x - t)
	elif y <= -4e-96:
		tmp = x + (y * t)
	elif y <= 55000000000000.0:
		tmp = x - (z * 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+54)
		tmp = t_1;
	elseif (y <= -1850000000000.0)
		tmp = Float64(z * Float64(x - t));
	elseif (y <= -4e-96)
		tmp = Float64(x + Float64(y * t));
	elseif (y <= 55000000000000.0)
		tmp = Float64(x - Float64(z * 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+54)
		tmp = t_1;
	elseif (y <= -1850000000000.0)
		tmp = z * (x - t);
	elseif (y <= -4e-96)
		tmp = x + (y * t);
	elseif (y <= 55000000000000.0)
		tmp = x - (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+54], t$95$1, If[LessEqual[y, -1850000000000.0], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4e-96], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 55000000000000.0], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.1999999999999999e54 or 5.5e13 < 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 96.1%

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

      1. fma-def 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 y around inf 85.9%

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

      1. neg-mul-1 85.9%

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

      2. sub-neg 85.9%

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

   8. Simplified 85.9%

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

   if -6.1999999999999999e54 < y < -1.85e12

   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 88.2%

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

      1. mul-1-neg 88.2%

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

      2. sub-neg 88.2%

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

   8. Simplified 88.2%

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

   if -1.85e12 < y < -3.9999999999999996e-96

   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 89.3%

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

   4. Taylor expanded in y around inf 72.2%

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

      1. *-commutative 72.2%

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

   6. Simplified 72.2%

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

   if -3.9999999999999996e-96 < y < 5.5e13

   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 92.4%

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

      1. mul-1-neg 92.4%

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

      2. unsub-neg 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in t around inf 74.1%

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

      1. *-commutative 74.1%

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

   8. Simplified 74.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1850000000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-96}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;y \leq 55000000000000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-293}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-205}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+56}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.16e+61)
   (* t (- z))
   (if (<= z 2.6e-293)
     (* y t)
     (if (<= z 1.6e-205) x (if (<= z 8.5e+56) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.16e+61) {
		tmp = t * -z;
	} else if (z <= 2.6e-293) {
		tmp = y * t;
	} else if (z <= 1.6e-205) {
		tmp = x;
	} else if (z <= 8.5e+56) {
		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 <= (-1.16d+61)) then
        tmp = t * -z
    else if (z <= 2.6d-293) then
        tmp = y * t
    else if (z <= 1.6d-205) then
        tmp = x
    else if (z <= 8.5d+56) 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 <= -1.16e+61) {
		tmp = t * -z;
	} else if (z <= 2.6e-293) {
		tmp = y * t;
	} else if (z <= 1.6e-205) {
		tmp = x;
	} else if (z <= 8.5e+56) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.16e+61:
		tmp = t * -z
	elif z <= 2.6e-293:
		tmp = y * t
	elif z <= 1.6e-205:
		tmp = x
	elif z <= 8.5e+56:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.16e+61)
		tmp = Float64(t * Float64(-z));
	elseif (z <= 2.6e-293)
		tmp = Float64(y * t);
	elseif (z <= 1.6e-205)
		tmp = x;
	elseif (z <= 8.5e+56)
		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 <= -1.16e+61)
		tmp = t * -z;
	elseif (z <= 2.6e-293)
		tmp = y * t;
	elseif (z <= 1.6e-205)
		tmp = x;
	elseif (z <= 8.5e+56)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.16e+61], N[(t * (-z)), $MachinePrecision], If[LessEqual[z, 2.6e-293], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.6e-205], x, If[LessEqual[z, 8.5e+56], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.16e61

   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 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in t around inf 54.0%

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

      1. *-commutative 54.0%

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

   8. Simplified 54.0%

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

   9. Taylor expanded in x around 0 53.9%

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

       1. mul-1-neg 53.9%

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

       2. distribute-rgt-neg-out 53.9%

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

   11. Simplified 53.9%

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

   if -1.16e61 < z < 2.5999999999999998e-293 or 1.60000000000000005e-205 < z < 8.4999999999999998e56

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.3%

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

      1. fma-def 98.0%

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

      2. +-commutative 98.0%

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

      3. mul-1-neg 98.0%

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

      4. neg-sub0 98.0%

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

      5. associate-+l- 98.0%

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

      6. associate--r+ 98.0%

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

      7. +-commutative 98.0%

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

      8. neg-sub0 98.0%

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

      9. distribute-rgt-neg-in 98.0%

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

      10. mul-1-neg 98.0%

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

      11. mul-1-neg 98.0%

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

      12. distribute-rgt-neg-in 98.0%

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

      13. neg-sub0 98.0%

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

      14. +-commutative 98.0%

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

      15. associate--r+ 98.0%

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

      16. associate-+l- 98.0%

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

      17. neg-sub0 98.0%

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

      18. mul-1-neg 98.0%

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

      19. +-commutative 98.0%

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

      20. mul-1-neg 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in y around inf 66.2%

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

      1. neg-mul-1 66.2%

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

      2. sub-neg 66.2%

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

   8. Simplified 66.2%

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

   9. Taylor expanded in t around inf 44.7%

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

       1. *-commutative 44.7%

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

   11. Simplified 44.7%

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

   if 2.5999999999999998e-293 < z < 1.60000000000000005e-205

   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 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 72.8%

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

   if 8.4999999999999998e56 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.6%

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

      1. mul-1-neg 75.6%

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

      2. unsub-neg 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x around inf 47.7%

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

      1. cancel-sign-sub-inv 47.7%

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

      2. metadata-eval 47.7%

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

      3. *-lft-identity 47.7%

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

   8. Simplified 47.7%

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

   9. Taylor expanded in z around inf 47.7%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-293}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-205}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+56}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \left(z - y\right)\\ \mathbf{if}\;t \leq -0.78:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-58}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq 200:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* t (- z y)))))
   (if (<= t -0.78)
     t_1
     (if (<= t -2.6e-58)
       (- x (* y (- x t)))
       (if (<= t 200.0) (* x (+ (- z y) 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (t * (z - y));
	double tmp;
	if (t <= -0.78) {
		tmp = t_1;
	} else if (t <= -2.6e-58) {
		tmp = x - (y * (x - t));
	} else if (t <= 200.0) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (t * (z - y))
    if (t <= (-0.78d0)) then
        tmp = t_1
    else if (t <= (-2.6d-58)) then
        tmp = x - (y * (x - t))
    else if (t <= 200.0d0) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (t * (z - y));
	double tmp;
	if (t <= -0.78) {
		tmp = t_1;
	} else if (t <= -2.6e-58) {
		tmp = x - (y * (x - t));
	} else if (t <= 200.0) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (t * (z - y))
	tmp = 0
	if t <= -0.78:
		tmp = t_1
	elif t <= -2.6e-58:
		tmp = x - (y * (x - t))
	elif t <= 200.0:
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(t * Float64(z - y)))
	tmp = 0.0
	if (t <= -0.78)
		tmp = t_1;
	elseif (t <= -2.6e-58)
		tmp = Float64(x - Float64(y * Float64(x - t)));
	elseif (t <= 200.0)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (t * (z - y));
	tmp = 0.0;
	if (t <= -0.78)
		tmp = t_1;
	elseif (t <= -2.6e-58)
		tmp = x - (y * (x - t));
	elseif (t <= 200.0)
		tmp = x * ((z - y) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.78], t$95$1, If[LessEqual[t, -2.6e-58], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 200.0], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.78000000000000003 or 200 < t

   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 91.7%

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

   if -0.78000000000000003 < t < -2.60000000000000007e-58

   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 98.9%

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

      1. *-commutative 98.9%

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

   5. Simplified 98.9%

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

   if -2.60000000000000007e-58 < t < 200

   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 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

   5. Simplified 77.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.78:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-58}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \mathbf{elif}\;t \leq 200:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+86}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -1.15e+57)
     t_1
     (if (<= y -2.6e-110)
       (- x (* t (- z y)))
       (if (<= y 1.85e+86) (+ x (* 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 <= -1.15e+57) {
		tmp = t_1;
	} else if (y <= -2.6e-110) {
		tmp = x - (t * (z - y));
	} else if (y <= 1.85e+86) {
		tmp = x + (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 <= (-1.15d+57)) then
        tmp = t_1
    else if (y <= (-2.6d-110)) then
        tmp = x - (t * (z - y))
    else if (y <= 1.85d+86) then
        tmp = x + (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 <= -1.15e+57) {
		tmp = t_1;
	} else if (y <= -2.6e-110) {
		tmp = x - (t * (z - y));
	} else if (y <= 1.85e+86) {
		tmp = x + (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 <= -1.15e+57:
		tmp = t_1
	elif y <= -2.6e-110:
		tmp = x - (t * (z - y))
	elif y <= 1.85e+86:
		tmp = x + (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 <= -1.15e+57)
		tmp = t_1;
	elseif (y <= -2.6e-110)
		tmp = Float64(x - Float64(t * Float64(z - y)));
	elseif (y <= 1.85e+86)
		tmp = Float64(x + 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 <= -1.15e+57)
		tmp = t_1;
	elseif (y <= -2.6e-110)
		tmp = x - (t * (z - y));
	elseif (y <= 1.85e+86)
		tmp = x + (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, -1.15e+57], t$95$1, If[LessEqual[y, -2.6e-110], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+86], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1499999999999999e57 or 1.84999999999999996e86 < 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 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 96.6%

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

      2. +-commutative 96.6%

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

      3. mul-1-neg 96.6%

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

      4. neg-sub0 96.6%

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

      5. associate-+l- 96.6%

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

      6. associate--r+ 96.6%

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

      7. +-commutative 96.6%

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

      8. neg-sub0 96.6%

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

      9. distribute-rgt-neg-in 96.6%

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

      10. mul-1-neg 96.6%

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

      11. mul-1-neg 96.6%

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

      12. distribute-rgt-neg-in 96.6%

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

      13. neg-sub0 96.6%

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

      14. +-commutative 96.6%

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

      15. associate--r+ 96.6%

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

      16. associate-+l- 96.6%

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

      17. neg-sub0 96.6%

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

      18. mul-1-neg 96.6%

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

      19. +-commutative 96.6%

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

      20. mul-1-neg 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in y around inf 90.1%

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

      1. neg-mul-1 90.1%

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

      2. sub-neg 90.1%

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

   8. Simplified 90.1%

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

   if -1.1499999999999999e57 < y < -2.5999999999999999e-110

   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 87.1%

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

   if -2.5999999999999999e-110 < y < 1.84999999999999996e86

   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 88.5%

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

      1. mul-1-neg 88.5%

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

      2. unsub-neg 88.5%

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

   5. Simplified 88.5%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-110}:\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+86}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y - z \leq -1 \cdot 10^{-60} \lor \neg \left(y - z \leq 10^{-13}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (- y z) -1e-60) (not (<= (- y z) 1e-13))) (* (- y z) t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -1e-60) || !((y - z) <= 1e-13)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((y - z) <= (-1d-60)) .or. (.not. ((y - z) <= 1d-13))) then
        tmp = (y - z) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -1e-60) || !((y - z) <= 1e-13)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y - z) <= -1e-60) or not ((y - z) <= 1e-13):
		tmp = (y - z) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y - z) <= -1e-60) || !(Float64(y - z) <= 1e-13))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y - z) <= -1e-60) || ~(((y - z) <= 1e-13)))
		tmp = (y - z) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y - z), $MachinePrecision], -1e-60], N[Not[LessEqual[N[(y - z), $MachinePrecision], 1e-13]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -9.9999999999999997e-61 or 1e-13 < (-.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 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 96.6%

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

      2. +-commutative 96.6%

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

      3. mul-1-neg 96.6%

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

      4. neg-sub0 96.6%

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

      5. associate-+l- 96.6%

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

      6. associate--r+ 96.6%

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

      7. +-commutative 96.6%

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

      8. neg-sub0 96.6%

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

      9. distribute-rgt-neg-in 96.6%

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

      10. mul-1-neg 96.6%

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

      11. mul-1-neg 96.6%

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

      12. distribute-rgt-neg-in 96.6%

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

      13. neg-sub0 96.6%

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

      14. +-commutative 96.6%

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

      15. associate--r+ 96.6%

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

      16. associate-+l- 96.6%

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

      17. neg-sub0 96.6%

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

      18. mul-1-neg 96.6%

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

      19. +-commutative 96.6%

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

      20. mul-1-neg 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in t around inf 61.6%

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

   if -9.9999999999999997e-61 < (-.f64 y z) < 1e-13

   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 89.5%

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

      1. *-commutative 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in y around 0 70.1%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -1 \cdot 10^{-60} \lor \neg \left(y - z \leq 10^{-13}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.15 \lor \neg \left(t \leq 25500\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.15) (not (<= t 25500.0)))
   (* (- y z) t)
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.15) || !(t <= 25500.0)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	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 <= (-0.15d0)) .or. (.not. (t <= 25500.0d0))) then
        tmp = (y - z) * t
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.15) || !(t <= 25500.0)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -0.15) or not (t <= 25500.0):
		tmp = (y - z) * t
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -0.15) || !(t <= 25500.0))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -0.15) || ~((t <= 25500.0)))
		tmp = (y - z) * t;
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -0.15], N[Not[LessEqual[t, 25500.0]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.149999999999999994 or 25500 < 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 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 94.5%

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

      2. +-commutative 94.5%

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

      3. mul-1-neg 94.5%

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

      4. neg-sub0 94.5%

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

      5. associate-+l- 94.5%

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

      6. associate--r+ 94.5%

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

      7. +-commutative 94.5%

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

      8. neg-sub0 94.5%

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

      9. distribute-rgt-neg-in 94.5%

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

      10. mul-1-neg 94.5%

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

      11. mul-1-neg 94.5%

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

      12. distribute-rgt-neg-in 94.5%

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

      13. neg-sub0 94.5%

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

      14. +-commutative 94.5%

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

      15. associate--r+ 94.5%

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

      16. associate-+l- 94.5%

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

      17. neg-sub0 94.5%

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

      18. mul-1-neg 94.5%

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

      19. +-commutative 94.5%

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

      20. mul-1-neg 94.5%

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

   5. Simplified 94.5%

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

   6. Taylor expanded in t around inf 86.1%

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

   if -0.149999999999999994 < t < 25500

   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 76.2%

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

      1. mul-1-neg 76.2%

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

      2. unsub-neg 76.2%

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

   5. Simplified 76.2%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.15 \lor \neg \left(t \leq 25500\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.095 \lor \neg \left(t \leq 115\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.095) (not (<= t 115.0)))
   (- x (* t (- z y)))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.095) || !(t <= 115.0)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	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 <= (-0.095d0)) .or. (.not. (t <= 115.0d0))) then
        tmp = x - (t * (z - y))
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.095) || !(t <= 115.0)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -0.095) or not (t <= 115.0):
		tmp = x - (t * (z - y))
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -0.095) || !(t <= 115.0))
		tmp = Float64(x - Float64(t * Float64(z - y)));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -0.095) || ~((t <= 115.0)))
		tmp = x - (t * (z - y));
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -0.095], N[Not[LessEqual[t, 115.0]], $MachinePrecision]], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.095000000000000001 or 115 < t

   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 91.7%

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

   if -0.095000000000000001 < t < 115

   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 76.0%

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

      1. mul-1-neg 76.0%

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

      2. unsub-neg 76.0%

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

   5. Simplified 76.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.095 \lor \neg \left(t \leq 115\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-54} \lor \neg \left(t \leq 5600000\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.65e-54) (not (<= t 5600000.0)))
   (* (- y z) t)
   (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e-54) || !(t <= 5600000.0)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	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 <= (-1.65d-54)) .or. (.not. (t <= 5600000.0d0))) then
        tmp = (y - z) * t
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e-54) || !(t <= 5600000.0)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.65e-54) or not (t <= 5600000.0):
		tmp = (y - z) * t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.65e-54) || !(t <= 5600000.0))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.65e-54) || ~((t <= 5600000.0)))
		tmp = (y - z) * t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.65e-54], N[Not[LessEqual[t, 5600000.0]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.64999999999999996e-54 or 5.6e6 < 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 93.6%

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

      1. fma-def 95.0%

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

      2. +-commutative 95.0%

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

      3. mul-1-neg 95.0%

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

      4. neg-sub0 95.0%

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

      5. associate-+l- 95.0%

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

      6. associate--r+ 95.0%

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

      7. +-commutative 95.0%

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

      8. neg-sub0 95.0%

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

      9. distribute-rgt-neg-in 95.0%

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

      10. mul-1-neg 95.0%

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

      11. mul-1-neg 95.0%

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

      12. distribute-rgt-neg-in 95.0%

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

      13. neg-sub0 95.0%

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

      14. +-commutative 95.0%

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

      15. associate--r+ 95.0%

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

      16. associate-+l- 95.0%

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

      17. neg-sub0 95.0%

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

      18. mul-1-neg 95.0%

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

      19. +-commutative 95.0%

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

      20. mul-1-neg 95.0%

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

   5. Simplified 95.0%

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

   6. Taylor expanded in t around inf 82.4%

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

   if -1.64999999999999996e-54 < t < 5.6e6

   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 64.0%

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

      1. mul-1-neg 64.0%

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

      2. unsub-neg 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in x around inf 52.4%

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

      1. cancel-sign-sub-inv 52.4%

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

      2. metadata-eval 52.4%

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

      3. *-lft-identity 52.4%

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

   8. Simplified 52.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{-54} \lor \neg \left(t \leq 5600000\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{-9} \lor \neg \left(z \leq 1.38 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.45e-9) (not (<= z 1.38e+29))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.45e-9) || !(z <= 1.38e+29)) {
		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 <= (-3.45d-9)) .or. (.not. (z <= 1.38d+29))) 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 <= -3.45e-9) || !(z <= 1.38e+29)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.45e-9) or not (z <= 1.38e+29):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.45e-9) || !(z <= 1.38e+29))
		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 <= -3.45e-9) || ~((z <= 1.38e+29)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.45e-9], N[Not[LessEqual[z, 1.38e+29]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.44999999999999987e-9 or 1.38e29 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.8%

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

      1. mul-1-neg 69.8%

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

      2. unsub-neg 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in x around inf 32.3%

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

      1. cancel-sign-sub-inv 32.3%

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

      2. metadata-eval 32.3%

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

      3. *-lft-identity 32.3%

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

   8. Simplified 32.3%

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

   9. Taylor expanded in z around inf 31.5%

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

   if -3.44999999999999987e-9 < z < 1.38e29

   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 92.4%

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

      1. *-commutative 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in y around 0 30.3%

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

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{-9} \lor \neg \left(z \leq 1.38 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-110} \lor \neg \left(y \leq 2.35 \cdot 10^{-23}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.1e-110) (not (<= y 2.35e-23))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-110) || !(y <= 2.35e-23)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.1d-110)) .or. (.not. (y <= 2.35d-23))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-110) || !(y <= 2.35e-23)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.1e-110) or not (y <= 2.35e-23):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.1e-110) || !(y <= 2.35e-23))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.1e-110) || ~((y <= 2.35e-23)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.1e-110], N[Not[LessEqual[y, 2.35e-23]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.10000000000000002e-110 or 2.35e-23 < 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 97.1%

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

      1. fma-def 97.6%

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

      2. +-commutative 97.6%

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

      3. mul-1-neg 97.6%

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

      4. neg-sub0 97.6%

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

      5. associate-+l- 97.6%

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

      6. associate--r+ 97.6%

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

      7. +-commutative 97.6%

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

      8. neg-sub0 97.6%

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

      9. distribute-rgt-neg-in 97.6%

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

      10. mul-1-neg 97.6%

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

      11. mul-1-neg 97.6%

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

      12. distribute-rgt-neg-in 97.6%

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

      13. neg-sub0 97.6%

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

      14. +-commutative 97.6%

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

      15. associate--r+ 97.6%

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

      16. associate-+l- 97.6%

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

      17. neg-sub0 97.6%

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

      18. mul-1-neg 97.6%

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

      19. +-commutative 97.6%

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

      20. mul-1-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in y around inf 74.1%

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

      1. neg-mul-1 74.1%

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

      2. sub-neg 74.1%

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

   8. Simplified 74.1%

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

   9. Taylor expanded in t around inf 47.9%

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

       1. *-commutative 47.9%

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

   11. Simplified 47.9%

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

   if -2.10000000000000002e-110 < y < 2.35e-23

   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 42.3%

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

      1. *-commutative 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in y around 0 37.8%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-110} \lor \neg \left(y \leq 2.35 \cdot 10^{-23}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 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 18: 17.6% 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 67.1%

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

   1. *-commutative 67.1%

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

5. Simplified 67.1%

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

6. Taylor expanded in y around 0 17.1%

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

7. Final simplification 17.1%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 96.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024027 
(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))))