Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 11.0s

Alternatives: 17

Speedup: 1.0×

• 33.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.2× 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: 62.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := x \cdot \left(z + 1\right)\\ t_3 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-293}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-269}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (* x (+ z 1.0))) (t_3 (* x (- 1.0 y))))
   (if (<= t -9.6e-6)
     t_1
     (if (<= t -2.6e-75)
       t_3
       (if (<= t -6.1e-93)
         t_1
         (if (<= t -1.4e-209)
           t_2
           (if (<= t -2.1e-293)
             t_3
             (if (<= t 1.85e-269)
               t_2
               (if (<= t 7.5e-90) t_3 (if (<= t 3.1e-54) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = x * (z + 1.0);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (t <= -9.6e-6) {
		tmp = t_1;
	} else if (t <= -2.6e-75) {
		tmp = t_3;
	} else if (t <= -6.1e-93) {
		tmp = t_1;
	} else if (t <= -1.4e-209) {
		tmp = t_2;
	} else if (t <= -2.1e-293) {
		tmp = t_3;
	} else if (t <= 1.85e-269) {
		tmp = t_2;
	} else if (t <= 7.5e-90) {
		tmp = t_3;
	} else if (t <= 3.1e-54) {
		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) :: tmp
    t_1 = (y - z) * t
    t_2 = x * (z + 1.0d0)
    t_3 = x * (1.0d0 - y)
    if (t <= (-9.6d-6)) then
        tmp = t_1
    else if (t <= (-2.6d-75)) then
        tmp = t_3
    else if (t <= (-6.1d-93)) then
        tmp = t_1
    else if (t <= (-1.4d-209)) then
        tmp = t_2
    else if (t <= (-2.1d-293)) then
        tmp = t_3
    else if (t <= 1.85d-269) then
        tmp = t_2
    else if (t <= 7.5d-90) then
        tmp = t_3
    else if (t <= 3.1d-54) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = x * (z + 1.0);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (t <= -9.6e-6) {
		tmp = t_1;
	} else if (t <= -2.6e-75) {
		tmp = t_3;
	} else if (t <= -6.1e-93) {
		tmp = t_1;
	} else if (t <= -1.4e-209) {
		tmp = t_2;
	} else if (t <= -2.1e-293) {
		tmp = t_3;
	} else if (t <= 1.85e-269) {
		tmp = t_2;
	} else if (t <= 7.5e-90) {
		tmp = t_3;
	} else if (t <= 3.1e-54) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	t_2 = x * (z + 1.0)
	t_3 = x * (1.0 - y)
	tmp = 0
	if t <= -9.6e-6:
		tmp = t_1
	elif t <= -2.6e-75:
		tmp = t_3
	elif t <= -6.1e-93:
		tmp = t_1
	elif t <= -1.4e-209:
		tmp = t_2
	elif t <= -2.1e-293:
		tmp = t_3
	elif t <= 1.85e-269:
		tmp = t_2
	elif t <= 7.5e-90:
		tmp = t_3
	elif t <= 3.1e-54:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(x * Float64(z + 1.0))
	t_3 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (t <= -9.6e-6)
		tmp = t_1;
	elseif (t <= -2.6e-75)
		tmp = t_3;
	elseif (t <= -6.1e-93)
		tmp = t_1;
	elseif (t <= -1.4e-209)
		tmp = t_2;
	elseif (t <= -2.1e-293)
		tmp = t_3;
	elseif (t <= 1.85e-269)
		tmp = t_2;
	elseif (t <= 7.5e-90)
		tmp = t_3;
	elseif (t <= 3.1e-54)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	t_2 = x * (z + 1.0);
	t_3 = x * (1.0 - y);
	tmp = 0.0;
	if (t <= -9.6e-6)
		tmp = t_1;
	elseif (t <= -2.6e-75)
		tmp = t_3;
	elseif (t <= -6.1e-93)
		tmp = t_1;
	elseif (t <= -1.4e-209)
		tmp = t_2;
	elseif (t <= -2.1e-293)
		tmp = t_3;
	elseif (t <= 1.85e-269)
		tmp = t_2;
	elseif (t <= 7.5e-90)
		tmp = t_3;
	elseif (t <= 3.1e-54)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.6e-6], t$95$1, If[LessEqual[t, -2.6e-75], t$95$3, If[LessEqual[t, -6.1e-93], t$95$1, If[LessEqual[t, -1.4e-209], t$95$2, If[LessEqual[t, -2.1e-293], t$95$3, If[LessEqual[t, 1.85e-269], t$95$2, If[LessEqual[t, 7.5e-90], t$95$3, If[LessEqual[t, 3.1e-54], t$95$2, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.5999999999999996e-6 or -2.6e-75 < t < -6.09999999999999971e-93 or 3.10000000000000004e-54 < 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 88.5%

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

      1. +-commutative 88.5%

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

      2. mul-1-neg 88.5%

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

      3. neg-sub0 88.5%

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

      4. associate-+l- 88.5%

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

      5. associate--r+ 88.5%

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

      6. +-commutative 88.5%

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

      7. neg-sub0 88.5%

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

      8. distribute-rgt-neg-in 88.5%

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

      9. mul-1-neg 88.5%

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

      10. fma-def 94.2%

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

      11. mul-1-neg 94.2%

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

      12. distribute-rgt-neg-in 94.2%

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

      13. neg-sub0 94.2%

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

      14. +-commutative 94.2%

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

      15. associate--r+ 94.2%

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

      16. associate-+l- 94.2%

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

      17. neg-sub0 94.2%

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

      18. mul-1-neg 94.2%

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

      19. +-commutative 94.2%

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

      20. mul-1-neg 94.2%

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

   5. Simplified 94.2%

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

   6. Taylor expanded in t around inf 73.2%

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

   if -9.5999999999999996e-6 < t < -2.6e-75 or -1.40000000000000006e-209 < t < -2.10000000000000005e-293 or 1.84999999999999989e-269 < t < 7.4999999999999999e-90

   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 83.9%

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

      1. mul-1-neg 83.9%

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

      2. unsub-neg 83.9%

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

   5. Simplified 83.9%

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

   6. Taylor expanded in z around 0 64.6%

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

   if -6.09999999999999971e-93 < t < -1.40000000000000006e-209 or -2.10000000000000005e-293 < t < 1.84999999999999989e-269 or 7.4999999999999999e-90 < t < 3.10000000000000004e-54

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.7%

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

      1. mul-1-neg 86.7%

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

      2. unsub-neg 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in y around 0 76.5%

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

      1. +-commutative 76.5%

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

   8. Simplified 76.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{-6}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{-93}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-269}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-120}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-133}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-265}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -7.2e-94)
     t_1
     (if (<= t -9.6e-120)
       (* z x)
       (if (<= t -8.8e-133)
         (* y t)
         (if (<= t -3.7e-147)
           x
           (if (<= t 1.16e-265)
             (* z x)
             (if (<= t 3.3e-134) (* y (- x)) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -7.2e-94) {
		tmp = t_1;
	} else if (t <= -9.6e-120) {
		tmp = z * x;
	} else if (t <= -8.8e-133) {
		tmp = y * t;
	} else if (t <= -3.7e-147) {
		tmp = x;
	} else if (t <= 1.16e-265) {
		tmp = z * x;
	} else if (t <= 3.3e-134) {
		tmp = y * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-7.2d-94)) then
        tmp = t_1
    else if (t <= (-9.6d-120)) then
        tmp = z * x
    else if (t <= (-8.8d-133)) then
        tmp = y * t
    else if (t <= (-3.7d-147)) then
        tmp = x
    else if (t <= 1.16d-265) then
        tmp = z * x
    else if (t <= 3.3d-134) then
        tmp = y * -x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -7.2e-94) {
		tmp = t_1;
	} else if (t <= -9.6e-120) {
		tmp = z * x;
	} else if (t <= -8.8e-133) {
		tmp = y * t;
	} else if (t <= -3.7e-147) {
		tmp = x;
	} else if (t <= 1.16e-265) {
		tmp = z * x;
	} else if (t <= 3.3e-134) {
		tmp = y * -x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -7.2e-94:
		tmp = t_1
	elif t <= -9.6e-120:
		tmp = z * x
	elif t <= -8.8e-133:
		tmp = y * t
	elif t <= -3.7e-147:
		tmp = x
	elif t <= 1.16e-265:
		tmp = z * x
	elif t <= 3.3e-134:
		tmp = y * -x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -7.2e-94)
		tmp = t_1;
	elseif (t <= -9.6e-120)
		tmp = Float64(z * x);
	elseif (t <= -8.8e-133)
		tmp = Float64(y * t);
	elseif (t <= -3.7e-147)
		tmp = x;
	elseif (t <= 1.16e-265)
		tmp = Float64(z * x);
	elseif (t <= 3.3e-134)
		tmp = Float64(y * Float64(-x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -7.2e-94)
		tmp = t_1;
	elseif (t <= -9.6e-120)
		tmp = z * x;
	elseif (t <= -8.8e-133)
		tmp = y * t;
	elseif (t <= -3.7e-147)
		tmp = x;
	elseif (t <= 1.16e-265)
		tmp = z * x;
	elseif (t <= 3.3e-134)
		tmp = y * -x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -7.2e-94], t$95$1, If[LessEqual[t, -9.6e-120], N[(z * x), $MachinePrecision], If[LessEqual[t, -8.8e-133], N[(y * t), $MachinePrecision], If[LessEqual[t, -3.7e-147], x, If[LessEqual[t, 1.16e-265], N[(z * x), $MachinePrecision], If[LessEqual[t, 3.3e-134], N[(y * (-x)), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -7.2e-94 or 3.30000000000000019e-134 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 90.3%

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

      1. +-commutative 90.3%

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

      2. mul-1-neg 90.3%

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

      3. neg-sub0 90.3%

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

      4. associate-+l- 90.3%

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

      5. associate--r+ 90.3%

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

      6. +-commutative 90.3%

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

      7. neg-sub0 90.3%

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

      8. distribute-rgt-neg-in 90.3%

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

      9. mul-1-neg 90.3%

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

      10. fma-def 95.1%

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

      11. mul-1-neg 95.1%

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

      12. distribute-rgt-neg-in 95.1%

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

      13. neg-sub0 95.1%

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

      14. +-commutative 95.1%

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

      15. associate--r+ 95.1%

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

      16. associate-+l- 95.1%

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

      17. neg-sub0 95.1%

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

      18. mul-1-neg 95.1%

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

      19. +-commutative 95.1%

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

      20. mul-1-neg 95.1%

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

   5. Simplified 95.1%

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

   6. Taylor expanded in t around inf 65.0%

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

   if -7.2e-94 < t < -9.5999999999999998e-120 or -3.7000000000000002e-147 < t < 1.15999999999999998e-265

   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. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. neg-sub0 100.0%

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

      4. associate-+l- 100.0%

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

      5. associate--r+ 100.0%

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

      6. +-commutative 100.0%

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

      7. neg-sub0 100.0%

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

      8. distribute-rgt-neg-in 100.0%

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

      9. mul-1-neg 100.0%

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

      10. fma-def 100.0%

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

      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 62.5%

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

   7. Taylor expanded in t around 0 51.4%

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

   if -9.5999999999999998e-120 < t < -8.8000000000000003e-133

   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 76.3%

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

      1. *-commutative 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in t around inf 75.2%

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

      1. *-commutative 75.2%

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

   8. Simplified 75.2%

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

   9. Taylor expanded in x around 0 75.2%

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

       1. *-commutative 75.2%

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

   11. Simplified 75.2%

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

   if -8.8000000000000003e-133 < t < -3.7000000000000002e-147

   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 76.5%

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

      1. *-commutative 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in y around 0 76.5%

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

   if 1.15999999999999998e-265 < t < 3.30000000000000019e-134

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. associate--r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. neg-sub0 99.9%

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

      8. distribute-rgt-neg-in 99.9%

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

      9. mul-1-neg 99.9%

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

      10. fma-def 100.0%

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

      11. mul-1-neg 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. neg-sub0 100.0%

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

      14. +-commutative 100.0%

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

      15. associate--r+ 100.0%

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

      16. associate-+l- 100.0%

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

      17. neg-sub0 100.0%

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

      18. mul-1-neg 100.0%

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

      19. +-commutative 100.0%

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

      20. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 50.9%

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

      1. neg-mul-1 50.9%

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

      2. sub-neg 50.9%

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

   8. Simplified 50.9%

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

   9. Taylor expanded in t around 0 50.9%

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

       1. mul-1-neg 50.9%

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

       2. distribute-rgt-neg-in 50.9%

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

   11. Simplified 50.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-94}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-120}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-133}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{-265}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-134}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-129}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-197}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 58000000000:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 10^{+218}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -2.25e-61)
     t_1
     (if (<= z -4.8e-129)
       (* y (- x))
       (if (<= z -8.2e-197)
         (* y t)
         (if (<= z 9.5e-293)
           x
           (if (<= z 58000000000.0)
             (* y t)
             (if (<= z 1e+218) (* z x) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -2.25e-61) {
		tmp = t_1;
	} else if (z <= -4.8e-129) {
		tmp = y * -x;
	} else if (z <= -8.2e-197) {
		tmp = y * t;
	} else if (z <= 9.5e-293) {
		tmp = x;
	} else if (z <= 58000000000.0) {
		tmp = y * t;
	} else if (z <= 1e+218) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-2.25d-61)) then
        tmp = t_1
    else if (z <= (-4.8d-129)) then
        tmp = y * -x
    else if (z <= (-8.2d-197)) then
        tmp = y * t
    else if (z <= 9.5d-293) then
        tmp = x
    else if (z <= 58000000000.0d0) then
        tmp = y * t
    else if (z <= 1d+218) then
        tmp = z * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -2.25e-61) {
		tmp = t_1;
	} else if (z <= -4.8e-129) {
		tmp = y * -x;
	} else if (z <= -8.2e-197) {
		tmp = y * t;
	} else if (z <= 9.5e-293) {
		tmp = x;
	} else if (z <= 58000000000.0) {
		tmp = y * t;
	} else if (z <= 1e+218) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -2.25e-61:
		tmp = t_1
	elif z <= -4.8e-129:
		tmp = y * -x
	elif z <= -8.2e-197:
		tmp = y * t
	elif z <= 9.5e-293:
		tmp = x
	elif z <= 58000000000.0:
		tmp = y * t
	elif z <= 1e+218:
		tmp = z * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -2.25e-61)
		tmp = t_1;
	elseif (z <= -4.8e-129)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -8.2e-197)
		tmp = Float64(y * t);
	elseif (z <= 9.5e-293)
		tmp = x;
	elseif (z <= 58000000000.0)
		tmp = Float64(y * t);
	elseif (z <= 1e+218)
		tmp = Float64(z * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -2.25e-61)
		tmp = t_1;
	elseif (z <= -4.8e-129)
		tmp = y * -x;
	elseif (z <= -8.2e-197)
		tmp = y * t;
	elseif (z <= 9.5e-293)
		tmp = x;
	elseif (z <= 58000000000.0)
		tmp = y * t;
	elseif (z <= 1e+218)
		tmp = z * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -2.25e-61], t$95$1, If[LessEqual[z, -4.8e-129], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -8.2e-197], N[(y * t), $MachinePrecision], If[LessEqual[z, 9.5e-293], x, If[LessEqual[z, 58000000000.0], N[(y * t), $MachinePrecision], If[LessEqual[z, 1e+218], N[(z * x), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.25e-61 or 1.00000000000000008e218 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 86.3%

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

      1. mul-1-neg 86.3%

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

      2. unsub-neg 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in x around 0 51.9%

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

      1. associate-*r* 51.9%

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

      2. neg-mul-1 51.9%

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

   8. Simplified 51.9%

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

   if -2.25e-61 < z < -4.79999999999999977e-129

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.4%

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

      1. +-commutative 94.4%

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

      2. mul-1-neg 94.4%

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

      3. neg-sub0 94.4%

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

      4. associate-+l- 94.4%

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

      5. associate--r+ 94.4%

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

      6. +-commutative 94.4%

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

      7. neg-sub0 94.4%

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

      8. distribute-rgt-neg-in 94.4%

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

      9. mul-1-neg 94.4%

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

      10. fma-def 100.0%

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

      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 62.3%

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

      1. neg-mul-1 62.3%

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

      2. sub-neg 62.3%

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

   8. Simplified 62.3%

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

   9. Taylor expanded in t around 0 46.3%

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

       1. mul-1-neg 46.3%

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

       2. distribute-rgt-neg-in 46.3%

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

   11. Simplified 46.3%

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

   if -4.79999999999999977e-129 < z < -8.2e-197 or 9.50000000000000049e-293 < z < 5.8e10

   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 89.9%

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

      1. *-commutative 89.9%

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

   5. Simplified 89.9%

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

   6. Taylor expanded in t around inf 70.4%

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

      1. *-commutative 70.4%

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

   8. Simplified 70.4%

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

   9. Taylor expanded in x around 0 49.7%

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

       1. *-commutative 49.7%

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

   11. Simplified 49.7%

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

   if -8.2e-197 < z < 9.50000000000000049e-293

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 51.6%

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

   if 5.8e10 < z < 1.00000000000000008e218

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 94.1%

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

      1. +-commutative 94.1%

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

      2. mul-1-neg 94.1%

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

      3. neg-sub0 94.1%

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

      4. associate-+l- 94.1%

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

      5. associate--r+ 94.1%

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

      6. +-commutative 94.1%

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

      7. neg-sub0 94.1%

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

      8. distribute-rgt-neg-in 94.1%

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

      9. mul-1-neg 94.1%

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

      10. fma-def 98.0%

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

      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 z around inf 82.6%

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

   7. Taylor expanded in t around 0 51.7%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-129}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-197}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 58000000000:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 10^{+218}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -0.00024:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-53}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 0.0126:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* x (+ z 1.0))))
   (if (<= y -0.00024)
     t_1
     (if (<= y 6e-131)
       t_2
       (if (<= y 7.5e-53) (* (- y z) t) (if (<= y 0.0126) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = x * (z + 1.0);
	double tmp;
	if (y <= -0.00024) {
		tmp = t_1;
	} else if (y <= 6e-131) {
		tmp = t_2;
	} else if (y <= 7.5e-53) {
		tmp = (y - z) * t;
	} else if (y <= 0.0126) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = x * (z + 1.0d0)
    if (y <= (-0.00024d0)) then
        tmp = t_1
    else if (y <= 6d-131) then
        tmp = t_2
    else if (y <= 7.5d-53) then
        tmp = (y - z) * t
    else if (y <= 0.0126d0) 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 = x * (z + 1.0);
	double tmp;
	if (y <= -0.00024) {
		tmp = t_1;
	} else if (y <= 6e-131) {
		tmp = t_2;
	} else if (y <= 7.5e-53) {
		tmp = (y - z) * t;
	} else if (y <= 0.0126) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = x * (z + 1.0)
	tmp = 0
	if y <= -0.00024:
		tmp = t_1
	elif y <= 6e-131:
		tmp = t_2
	elif y <= 7.5e-53:
		tmp = (y - z) * t
	elif y <= 0.0126:
		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(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -0.00024)
		tmp = t_1;
	elseif (y <= 6e-131)
		tmp = t_2;
	elseif (y <= 7.5e-53)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= 0.0126)
		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 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -0.00024)
		tmp = t_1;
	elseif (y <= 6e-131)
		tmp = t_2;
	elseif (y <= 7.5e-53)
		tmp = (y - z) * t;
	elseif (y <= 0.0126)
		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[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.00024], t$95$1, If[LessEqual[y, 6e-131], t$95$2, If[LessEqual[y, 7.5e-53], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 0.0126], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000006e-4 or 0.0126 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. mul-1-neg 93.4%

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

      3. neg-sub0 93.4%

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

      4. associate-+l- 93.4%

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

      5. associate--r+ 93.4%

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

      6. +-commutative 93.4%

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

      7. neg-sub0 93.4%

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

      8. distribute-rgt-neg-in 93.4%

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

      9. mul-1-neg 93.4%

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

      10. fma-def 97.1%

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

      11. mul-1-neg 97.1%

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

      12. distribute-rgt-neg-in 97.1%

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

      13. neg-sub0 97.1%

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

      14. +-commutative 97.1%

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

      15. associate--r+ 97.1%

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

      16. associate-+l- 97.1%

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

      17. neg-sub0 97.1%

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

      18. mul-1-neg 97.1%

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

      19. +-commutative 97.1%

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

      20. mul-1-neg 97.1%

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

   5. Simplified 97.1%

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

   6. Taylor expanded in y around inf 76.1%

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

      1. neg-mul-1 76.1%

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

      2. sub-neg 76.1%

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

   8. Simplified 76.1%

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

   if -2.40000000000000006e-4 < y < 5.99999999999999992e-131 or 7.5000000000000001e-53 < y < 0.0126

   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 65.5%

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

      1. mul-1-neg 65.5%

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

      2. unsub-neg 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in y around 0 64.6%

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

      1. +-commutative 64.6%

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

   8. Simplified 64.6%

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

   if 5.99999999999999992e-131 < y < 7.5000000000000001e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. associate--r+ 99.9%

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

      6. +-commutative 99.9%

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

      7. neg-sub0 99.9%

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

      8. distribute-rgt-neg-in 99.9%

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

      9. mul-1-neg 99.9%

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

      10. fma-def 100.0%

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

      11. mul-1-neg 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. neg-sub0 100.0%

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

      14. +-commutative 100.0%

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

      15. associate--r+ 100.0%

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

      16. associate-+l- 100.0%

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

      17. neg-sub0 100.0%

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

      18. mul-1-neg 100.0%

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

      19. +-commutative 100.0%

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

      20. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 64.2%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00024:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-53}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 0.0126:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -620000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-58}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 450000000000:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -620000000.0)
     t_1
     (if (<= z -1.35e-144)
       (* x (- 1.0 y))
       (if (<= z 7.5e-58)
         (+ x (* y t))
         (if (<= z 450000000000.0) (* y (- t x)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -620000000.0) {
		tmp = t_1;
	} else if (z <= -1.35e-144) {
		tmp = x * (1.0 - y);
	} else if (z <= 7.5e-58) {
		tmp = x + (y * t);
	} else if (z <= 450000000000.0) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-620000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.35d-144)) then
        tmp = x * (1.0d0 - y)
    else if (z <= 7.5d-58) then
        tmp = x + (y * t)
    else if (z <= 450000000000.0d0) then
        tmp = y * (t - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -620000000.0) {
		tmp = t_1;
	} else if (z <= -1.35e-144) {
		tmp = x * (1.0 - y);
	} else if (z <= 7.5e-58) {
		tmp = x + (y * t);
	} else if (z <= 450000000000.0) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -620000000.0:
		tmp = t_1
	elif z <= -1.35e-144:
		tmp = x * (1.0 - y)
	elif z <= 7.5e-58:
		tmp = x + (y * t)
	elif z <= 450000000000.0:
		tmp = y * (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -620000000.0)
		tmp = t_1;
	elseif (z <= -1.35e-144)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 7.5e-58)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 450000000000.0)
		tmp = Float64(y * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -620000000.0)
		tmp = t_1;
	elseif (z <= -1.35e-144)
		tmp = x * (1.0 - y);
	elseif (z <= 7.5e-58)
		tmp = x + (y * t);
	elseif (z <= 450000000000.0)
		tmp = y * (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -620000000.0], t$95$1, If[LessEqual[z, -1.35e-144], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-58], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 450000000000.0], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.2e8 or 4.5e11 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.3%

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

      1. +-commutative 91.3%

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

      2. mul-1-neg 91.3%

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

      3. neg-sub0 91.3%

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

      4. associate-+l- 91.3%

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

      5. associate--r+ 91.3%

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

      6. +-commutative 91.3%

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

      7. neg-sub0 91.3%

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

      8. distribute-rgt-neg-in 91.3%

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

      9. mul-1-neg 91.3%

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

      10. fma-def 94.5%

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

      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 z around inf 83.6%

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

      1. neg-mul-1 83.6%

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

      2. sub-neg 83.6%

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

   8. Simplified 83.6%

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

   if -6.2e8 < z < -1.34999999999999988e-144

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 72.4%

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

      1. mul-1-neg 72.4%

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

      2. unsub-neg 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in z around 0 69.5%

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

   if -1.34999999999999988e-144 < z < 7.50000000000000002e-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 94.8%

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

      1. *-commutative 94.8%

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

   5. Simplified 94.8%

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

   6. Taylor expanded in t around inf 76.6%

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

      1. *-commutative 76.6%

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

   8. Simplified 76.6%

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

   if 7.50000000000000002e-58 < z < 4.5e11

   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 95.5%

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

      1. +-commutative 95.5%

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

      2. mul-1-neg 95.5%

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

      3. neg-sub0 95.5%

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

      4. associate-+l- 95.5%

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

      5. associate--r+ 95.5%

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

      6. +-commutative 95.5%

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

      7. neg-sub0 95.5%

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

      8. distribute-rgt-neg-in 95.5%

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

      9. mul-1-neg 95.5%

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

      10. fma-def 100.0%

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

      11. mul-1-neg 100.0%

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

      12. distribute-rgt-neg-in 100.0%

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

      13. neg-sub0 100.0%

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

      14. +-commutative 100.0%

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

      15. associate--r+ 100.0%

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

      16. associate-+l- 100.0%

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

      17. neg-sub0 100.0%

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

      18. mul-1-neg 100.0%

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

      19. +-commutative 100.0%

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

      20. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 73.2%

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

      1. neg-mul-1 73.2%

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

      2. sub-neg 73.2%

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

   8. Simplified 73.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -620000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-58}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 450000000000:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -50000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 200000000000:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -50000000.0)
     t_1
     (if (<= z 3.2e-293)
       (* x (- 1.0 y))
       (if (<= z 200000000000.0) (* y (- t x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -50000000.0) {
		tmp = t_1;
	} else if (z <= 3.2e-293) {
		tmp = x * (1.0 - y);
	} else if (z <= 200000000000.0) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x - t)
    if (z <= (-50000000.0d0)) then
        tmp = t_1
    else if (z <= 3.2d-293) then
        tmp = x * (1.0d0 - y)
    else if (z <= 200000000000.0d0) then
        tmp = y * (t - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -50000000.0) {
		tmp = t_1;
	} else if (z <= 3.2e-293) {
		tmp = x * (1.0 - y);
	} else if (z <= 200000000000.0) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -50000000.0:
		tmp = t_1
	elif z <= 3.2e-293:
		tmp = x * (1.0 - y)
	elif z <= 200000000000.0:
		tmp = y * (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -50000000.0)
		tmp = t_1;
	elseif (z <= 3.2e-293)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 200000000000.0)
		tmp = Float64(y * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -50000000.0)
		tmp = t_1;
	elseif (z <= 3.2e-293)
		tmp = x * (1.0 - y);
	elseif (z <= 200000000000.0)
		tmp = y * (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -50000000.0], t$95$1, If[LessEqual[z, 3.2e-293], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 200000000000.0], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5e7 or 2e11 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.3%

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

      1. +-commutative 91.3%

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

      2. mul-1-neg 91.3%

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

      3. neg-sub0 91.3%

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

      4. associate-+l- 91.3%

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

      5. associate--r+ 91.3%

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

      6. +-commutative 91.3%

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

      7. neg-sub0 91.3%

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

      8. distribute-rgt-neg-in 91.3%

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

      9. mul-1-neg 91.3%

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

      10. fma-def 94.5%

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

      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 z around inf 83.6%

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

      1. neg-mul-1 83.6%

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

      2. sub-neg 83.6%

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

   8. Simplified 83.6%

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

   if -5e7 < z < 3.20000000000000005e-293

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. unsub-neg 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in z around 0 68.6%

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

   if 3.20000000000000005e-293 < z < 2e11

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.3%

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

      1. +-commutative 95.3%

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

      2. mul-1-neg 95.3%

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

      3. neg-sub0 95.3%

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

      4. associate-+l- 95.3%

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

      5. associate--r+ 95.3%

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

      6. +-commutative 95.3%

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

      7. neg-sub0 95.3%

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

      8. distribute-rgt-neg-in 95.3%

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

      9. mul-1-neg 95.3%

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

      10. fma-def 100.0%

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

      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 68.3%

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

      1. neg-mul-1 68.3%

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

      2. sub-neg 68.3%

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

   8. Simplified 68.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -50000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 200000000000:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -70000000000000 \lor \neg \left(t \leq 1.7 \cdot 10^{+46}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -70000000000000.0) (not (<= t 1.7e+46)))
   (* (- y z) t)
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -70000000000000.0) || !(t <= 1.7e+46)) {
		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 <= (-70000000000000.0d0)) .or. (.not. (t <= 1.7d+46))) 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 <= -70000000000000.0) || !(t <= 1.7e+46)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -70000000000000.0) or not (t <= 1.7e+46):
		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 <= -70000000000000.0) || !(t <= 1.7e+46))
		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 <= -70000000000000.0) || ~((t <= 1.7e+46)))
		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, -70000000000000.0], N[Not[LessEqual[t, 1.7e+46]], $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 < -7e13 or 1.6999999999999999e46 < 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 85.9%

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

      1. +-commutative 85.9%

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

      2. mul-1-neg 85.9%

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

      3. neg-sub0 85.9%

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

      4. associate-+l- 85.9%

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

      5. associate--r+ 85.9%

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

      6. +-commutative 85.9%

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

      7. neg-sub0 85.9%

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

      8. distribute-rgt-neg-in 85.9%

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

      9. mul-1-neg 85.9%

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

      10. fma-def 92.9%

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

      11. mul-1-neg 92.9%

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

      12. distribute-rgt-neg-in 92.9%

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

      13. neg-sub0 92.9%

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

      14. +-commutative 92.9%

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

      15. associate--r+ 92.9%

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

      16. associate-+l- 92.9%

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

      17. neg-sub0 92.9%

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

      18. mul-1-neg 92.9%

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

      19. +-commutative 92.9%

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

      20. mul-1-neg 92.9%

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

   5. Simplified 92.9%

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

   6. Taylor expanded in t around inf 77.8%

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

   if -7e13 < t < 1.6999999999999999e46

   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 78.9%

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

      1. mul-1-neg 78.9%

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

      2. unsub-neg 78.9%

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

   5. Simplified 78.9%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -70000000000000 \lor \neg \left(t \leq 1.7 \cdot 10^{+46}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+16} \lor \neg \left(t \leq 6.8 \cdot 10^{-13}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.35e+16) (not (<= t 6.8e-13)))
   (+ x (* (- y z) t))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.35e+16) || !(t <= 6.8e-13)) {
		tmp = x + ((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 <= (-1.35d+16)) .or. (.not. (t <= 6.8d-13))) then
        tmp = x + ((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 <= -1.35e+16) || !(t <= 6.8e-13)) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.35e+16) or not (t <= 6.8e-13):
		tmp = x + ((y - z) * t)
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.35e+16) || !(t <= 6.8e-13))
		tmp = Float64(x + 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 <= -1.35e+16) || ~((t <= 6.8e-13)))
		tmp = x + ((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, -1.35e+16], N[Not[LessEqual[t, 6.8e-13]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e16 or 6.80000000000000031e-13 < 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 85.3%

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

   if -1.35e16 < t < 6.80000000000000031e-13

   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 80.3%

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

      1. mul-1-neg 80.3%

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

      2. unsub-neg 80.3%

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

   5. Simplified 80.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+16} \lor \neg \left(t \leq 6.8 \cdot 10^{-13}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -165000000000 \lor \neg \left(z \leq 480000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -165000000000.0) (not (<= z 480000000000.0)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -165000000000.0) || !(z <= 480000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - 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 <= (-165000000000.0d0)) .or. (.not. (z <= 480000000000.0d0))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -165000000000.0) || !(z <= 480000000000.0)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -165000000000.0) or not (z <= 480000000000.0):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -165000000000.0) || !(z <= 480000000000.0))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -165000000000.0) || ~((z <= 480000000000.0)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -165000000000.0], N[Not[LessEqual[z, 480000000000.0]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e11 or 4.8e11 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.3%

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

      1. +-commutative 91.3%

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

      2. mul-1-neg 91.3%

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

      3. neg-sub0 91.3%

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

      4. associate-+l- 91.3%

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

      5. associate--r+ 91.3%

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

      6. +-commutative 91.3%

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

      7. neg-sub0 91.3%

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

      8. distribute-rgt-neg-in 91.3%

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

      9. mul-1-neg 91.3%

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

      10. fma-def 94.5%

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

      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 z around inf 83.6%

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

      1. neg-mul-1 83.6%

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

      2. sub-neg 83.6%

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

   8. Simplified 83.6%

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

   if -1.65e11 < z < 4.8e11

   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 88.8%

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

      1. *-commutative 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -165000000000 \lor \neg \left(z \leq 480000000000\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-61} \lor \neg \left(z \leq 115000000000\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4e-61) (not (<= z 115000000000.0)))
   (+ x (* z (- x t)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e-61) || !(z <= 115000000000.0)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - 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 <= (-4d-61)) .or. (.not. (z <= 115000000000.0d0))) then
        tmp = x + (z * (x - t))
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e-61) || !(z <= 115000000000.0)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4e-61) or not (z <= 115000000000.0):
		tmp = x + (z * (x - t))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4e-61) || !(z <= 115000000000.0))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4e-61) || ~((z <= 115000000000.0)))
		tmp = x + (z * (x - t));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4e-61], N[Not[LessEqual[z, 115000000000.0]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0000000000000002e-61 or 1.15e11 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 82.6%

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

      1. mul-1-neg 82.6%

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

      2. unsub-neg 82.6%

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

   5. Simplified 82.6%

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

   if -4.0000000000000002e-61 < z < 1.15e11

   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 91.9%

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

      1. *-commutative 91.9%

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

   5. Simplified 91.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-61} \lor \neg \left(z \leq 115000000000\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 62000000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e+19)
   (* z x)
   (if (<= z 9.5e-293) x (if (<= z 62000000000.0) (* y t) (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+19) {
		tmp = z * x;
	} else if (z <= 9.5e-293) {
		tmp = x;
	} else if (z <= 62000000000.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.3d+19)) then
        tmp = z * x
    else if (z <= 9.5d-293) then
        tmp = x
    else if (z <= 62000000000.0d0) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+19) {
		tmp = z * x;
	} else if (z <= 9.5e-293) {
		tmp = x;
	} else if (z <= 62000000000.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e+19:
		tmp = z * x
	elif z <= 9.5e-293:
		tmp = x
	elif z <= 62000000000.0:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e+19)
		tmp = Float64(z * x);
	elseif (z <= 9.5e-293)
		tmp = x;
	elseif (z <= 62000000000.0)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.3e+19)
		tmp = z * x;
	elseif (z <= 9.5e-293)
		tmp = x;
	elseif (z <= 62000000000.0)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e+19], N[(z * x), $MachinePrecision], If[LessEqual[z, 9.5e-293], x, If[LessEqual[z, 62000000000.0], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e19 or 6.2e10 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.2%

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

      1. +-commutative 91.2%

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

      2. mul-1-neg 91.2%

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

      3. neg-sub0 91.2%

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

      4. associate-+l- 91.2%

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

      5. associate--r+ 91.2%

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

      6. +-commutative 91.2%

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

      7. neg-sub0 91.2%

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

      8. distribute-rgt-neg-in 91.2%

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

      9. mul-1-neg 91.2%

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

      10. fma-def 94.4%

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

      11. mul-1-neg 94.4%

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

      12. distribute-rgt-neg-in 94.4%

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

      13. neg-sub0 94.4%

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

      14. +-commutative 94.4%

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

      15. associate--r+ 94.4%

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

      16. associate-+l- 94.4%

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

      17. neg-sub0 94.4%

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

      18. mul-1-neg 94.4%

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

      19. +-commutative 94.4%

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

      20. mul-1-neg 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in z around inf 85.2%

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

   7. Taylor expanded in t around 0 46.9%

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

   if -2.3e19 < z < 9.50000000000000049e-293

   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 87.3%

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

      1. *-commutative 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in y around 0 37.6%

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

   if 9.50000000000000049e-293 < z < 6.2e10

   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 87.7%

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

      1. *-commutative 87.7%

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

   5. Simplified 87.7%

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

   6. Taylor expanded in t around inf 67.0%

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

      1. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   9. Taylor expanded in x around 0 48.6%

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

       1. *-commutative 48.6%

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

   11. Simplified 48.6%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+19}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-293}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 62000000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+65}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-129}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 800000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.1e+65)
   (* z x)
   (if (<= z -8.8e-129) (* y (- x)) (if (<= z 800000000.0) (* y t) (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.1e+65) {
		tmp = z * x;
	} else if (z <= -8.8e-129) {
		tmp = y * -x;
	} else if (z <= 800000000.0) {
		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 <= (-4.1d+65)) then
        tmp = z * x
    else if (z <= (-8.8d-129)) then
        tmp = y * -x
    else if (z <= 800000000.0d0) 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 <= -4.1e+65) {
		tmp = z * x;
	} else if (z <= -8.8e-129) {
		tmp = y * -x;
	} else if (z <= 800000000.0) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.1e+65:
		tmp = z * x
	elif z <= -8.8e-129:
		tmp = y * -x
	elif z <= 800000000.0:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.1e+65)
		tmp = Float64(z * x);
	elseif (z <= -8.8e-129)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 800000000.0)
		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 <= -4.1e+65)
		tmp = z * x;
	elseif (z <= -8.8e-129)
		tmp = y * -x;
	elseif (z <= 800000000.0)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.1e+65], N[(z * x), $MachinePrecision], If[LessEqual[z, -8.8e-129], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 800000000.0], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1000000000000001e65 or 8e8 < z

   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 90.9%

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

      1. +-commutative 90.9%

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

      2. mul-1-neg 90.9%

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

      3. neg-sub0 90.9%

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

      4. associate-+l- 90.9%

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

      5. associate--r+ 90.9%

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

      6. +-commutative 90.9%

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

      7. neg-sub0 90.9%

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

      8. distribute-rgt-neg-in 90.9%

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

      9. mul-1-neg 90.9%

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

      10. fma-def 94.2%

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

      11. mul-1-neg 94.2%

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

      12. distribute-rgt-neg-in 94.2%

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

      13. neg-sub0 94.2%

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

      14. +-commutative 94.2%

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

      15. associate--r+ 94.2%

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

      16. associate-+l- 94.2%

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

      17. neg-sub0 94.2%

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

      18. mul-1-neg 94.2%

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

      19. +-commutative 94.2%

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

      20. mul-1-neg 94.2%

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

   5. Simplified 94.2%

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

   6. Taylor expanded in z around inf 86.9%

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

   7. Taylor expanded in t around 0 47.9%

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

   if -4.1000000000000001e65 < z < -8.80000000000000012e-129

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. mul-1-neg 97.3%

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

      3. neg-sub0 97.3%

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

      4. associate-+l- 97.3%

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

      5. associate--r+ 97.3%

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

      6. +-commutative 97.3%

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

      7. neg-sub0 97.3%

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

      8. distribute-rgt-neg-in 97.3%

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

      9. mul-1-neg 97.3%

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

      10. fma-def 100.0%

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

      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 47.1%

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

      1. neg-mul-1 47.1%

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

      2. sub-neg 47.1%

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

   8. Simplified 47.1%

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

   9. Taylor expanded in t around 0 39.2%

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

       1. mul-1-neg 39.2%

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

       2. distribute-rgt-neg-in 39.2%

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

   11. Simplified 39.2%

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

   if -8.80000000000000012e-129 < z < 8e8

   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 92.2%

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

      1. *-commutative 92.2%

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

   5. Simplified 92.2%

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

   6. Taylor expanded in t around inf 72.0%

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

      1. *-commutative 72.0%

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

   8. Simplified 72.0%

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

   9. Taylor expanded in x around 0 45.1%

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

       1. *-commutative 45.1%

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

   11. Simplified 45.1%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+65}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-129}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 800000000:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-93} \lor \neg \left(t \leq 1.3 \cdot 10^{-55}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.5e-93) (not (<= t 1.3e-55))) (* (- y z) t) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.5e-93) || !(t <= 1.3e-55)) {
		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 <= (-6.5d-93)) .or. (.not. (t <= 1.3d-55))) 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 <= -6.5e-93) || !(t <= 1.3e-55)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.5e-93) or not (t <= 1.3e-55):
		tmp = (y - z) * t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.5e-93) || !(t <= 1.3e-55))
		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 <= -6.5e-93) || ~((t <= 1.3e-55)))
		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, -6.5e-93], N[Not[LessEqual[t, 1.3e-55]], $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 < -6.5e-93 or 1.2999999999999999e-55 < 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 89.4%

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

      1. +-commutative 89.4%

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

      2. mul-1-neg 89.4%

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

      3. neg-sub0 89.4%

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

      4. associate-+l- 89.4%

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

      5. associate--r+ 89.4%

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

      6. +-commutative 89.4%

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

      7. neg-sub0 89.4%

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

      8. distribute-rgt-neg-in 89.4%

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

      9. mul-1-neg 89.4%

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

      10. fma-def 94.7%

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

      11. mul-1-neg 94.7%

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

      12. distribute-rgt-neg-in 94.7%

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

      13. neg-sub0 94.7%

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

      14. +-commutative 94.7%

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

      15. associate--r+ 94.7%

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

      16. associate-+l- 94.7%

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

      17. neg-sub0 94.7%

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

      18. mul-1-neg 94.7%

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

      19. +-commutative 94.7%

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

      20. mul-1-neg 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in t around inf 68.8%

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

   if -6.5e-93 < t < 1.2999999999999999e-55

   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 85.2%

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

      1. mul-1-neg 85.2%

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

      2. unsub-neg 85.2%

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

   5. Simplified 85.2%

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

   6. Taylor expanded in y around 0 59.5%

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

      1. +-commutative 59.5%

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

   8. Simplified 59.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-93} \lor \neg \left(t \leq 1.3 \cdot 10^{-55}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 16: 37.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+19} \lor \neg \left(z \leq 0.0106\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.3e+19) (not (<= z 0.0106))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.3e+19) || !(z <= 0.0106)) {
		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 <= (-2.3d+19)) .or. (.not. (z <= 0.0106d0))) 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 <= -2.3e+19) || !(z <= 0.0106)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.3e+19) or not (z <= 0.0106):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.3e+19) || !(z <= 0.0106))
		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 <= -2.3e+19) || ~((z <= 0.0106)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.3e+19], N[Not[LessEqual[z, 0.0106]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e19 or 0.0106 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.4%

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

      1. +-commutative 91.4%

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

      2. mul-1-neg 91.4%

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

      3. neg-sub0 91.4%

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

      4. associate-+l- 91.4%

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

      5. associate--r+ 91.4%

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

      6. +-commutative 91.4%

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

      7. neg-sub0 91.4%

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

      8. distribute-rgt-neg-in 91.4%

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

      9. mul-1-neg 91.4%

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

      10. fma-def 94.5%

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

      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 z around inf 85.5%

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

   7. Taylor expanded in t around 0 45.9%

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

   if -2.3e19 < z < 0.0106

   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 87.2%

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

      1. *-commutative 87.2%

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

   5. Simplified 87.2%

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

   6. Taylor expanded in y around 0 30.5%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+19} \lor \neg \left(z \leq 0.0106\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 18.2% accurate, 17.0× 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 59.3%

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

   1. *-commutative 59.3%

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

5. Simplified 59.3%

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

6. Taylor expanded in y around 0 16.8%

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

7. Final simplification 16.8%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 96.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024011 
(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))))