Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.9s

Alternatives: 12

Speedup: 1.0×

• 34.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 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. Add Preprocessing

Alternative 2: 46.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - y\right)\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{+26}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-173}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 3.65 \cdot 10^{+25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+190}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 y))) (t_2 (* z (- t))))
   (if (<= t -3.2e+94)
     t_2
     (if (<= t -6.1e+26)
       (* y t)
       (if (<= t -1.45e+18)
         t_2
         (if (<= t 1.55e-218)
           t_1
           (if (<= t 1.6e-173)
             (* x (+ z 1.0))
             (if (<= t 3.65e+25) t_1 (if (<= t 5.2e+190) t_2 (* y t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = z * -t;
	double tmp;
	if (t <= -3.2e+94) {
		tmp = t_2;
	} else if (t <= -6.1e+26) {
		tmp = y * t;
	} else if (t <= -1.45e+18) {
		tmp = t_2;
	} else if (t <= 1.55e-218) {
		tmp = t_1;
	} else if (t <= 1.6e-173) {
		tmp = x * (z + 1.0);
	} else if (t <= 3.65e+25) {
		tmp = t_1;
	} else if (t <= 5.2e+190) {
		tmp = t_2;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (1.0d0 - y)
    t_2 = z * -t
    if (t <= (-3.2d+94)) then
        tmp = t_2
    else if (t <= (-6.1d+26)) then
        tmp = y * t
    else if (t <= (-1.45d+18)) then
        tmp = t_2
    else if (t <= 1.55d-218) then
        tmp = t_1
    else if (t <= 1.6d-173) then
        tmp = x * (z + 1.0d0)
    else if (t <= 3.65d+25) then
        tmp = t_1
    else if (t <= 5.2d+190) then
        tmp = t_2
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - y);
	double t_2 = z * -t;
	double tmp;
	if (t <= -3.2e+94) {
		tmp = t_2;
	} else if (t <= -6.1e+26) {
		tmp = y * t;
	} else if (t <= -1.45e+18) {
		tmp = t_2;
	} else if (t <= 1.55e-218) {
		tmp = t_1;
	} else if (t <= 1.6e-173) {
		tmp = x * (z + 1.0);
	} else if (t <= 3.65e+25) {
		tmp = t_1;
	} else if (t <= 5.2e+190) {
		tmp = t_2;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - y)
	t_2 = z * -t
	tmp = 0
	if t <= -3.2e+94:
		tmp = t_2
	elif t <= -6.1e+26:
		tmp = y * t
	elif t <= -1.45e+18:
		tmp = t_2
	elif t <= 1.55e-218:
		tmp = t_1
	elif t <= 1.6e-173:
		tmp = x * (z + 1.0)
	elif t <= 3.65e+25:
		tmp = t_1
	elif t <= 5.2e+190:
		tmp = t_2
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - y))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (t <= -3.2e+94)
		tmp = t_2;
	elseif (t <= -6.1e+26)
		tmp = Float64(y * t);
	elseif (t <= -1.45e+18)
		tmp = t_2;
	elseif (t <= 1.55e-218)
		tmp = t_1;
	elseif (t <= 1.6e-173)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (t <= 3.65e+25)
		tmp = t_1;
	elseif (t <= 5.2e+190)
		tmp = t_2;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - y);
	t_2 = z * -t;
	tmp = 0.0;
	if (t <= -3.2e+94)
		tmp = t_2;
	elseif (t <= -6.1e+26)
		tmp = y * t;
	elseif (t <= -1.45e+18)
		tmp = t_2;
	elseif (t <= 1.55e-218)
		tmp = t_1;
	elseif (t <= 1.6e-173)
		tmp = x * (z + 1.0);
	elseif (t <= 3.65e+25)
		tmp = t_1;
	elseif (t <= 5.2e+190)
		tmp = t_2;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[t, -3.2e+94], t$95$2, If[LessEqual[t, -6.1e+26], N[(y * t), $MachinePrecision], If[LessEqual[t, -1.45e+18], t$95$2, If[LessEqual[t, 1.55e-218], t$95$1, If[LessEqual[t, 1.6e-173], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.65e+25], t$95$1, If[LessEqual[t, 5.2e+190], t$95$2, N[(y * t), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.20000000000000014e94 or -6.1000000000000003e26 < t < -1.45e18 or 3.6499999999999998e25 < t < 5.20000000000000022e190

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 90.1%

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

   4. Taylor expanded in y around 0 58.8%

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

      1. associate-*r* 58.8%

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

      2. mul-1-neg 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in x around 0 55.6%

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

      1. associate-*r* 55.6%

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

      2. mul-1-neg 55.6%

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

   9. Simplified 55.6%

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

   if -3.20000000000000014e94 < t < -6.1000000000000003e26 or 5.20000000000000022e190 < t

   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 72.3%

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

      1. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around inf 72.2%

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

   7. Taylor expanded in t around inf 66.7%

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

      1. *-commutative 66.7%

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

   9. Simplified 66.7%

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

   if -1.45e18 < t < 1.54999999999999999e-218 or 1.6e-173 < t < 3.6499999999999998e25

   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 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in z around 0 59.9%

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

   if 1.54999999999999999e-218 < t < 1.6e-173

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 89.5%

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

      1. mul-1-neg 89.5%

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

      2. unsub-neg 89.5%

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

   5. Simplified 89.5%

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

   6. Taylor expanded in y around 0 87.6%

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

      1. +-commutative 87.6%

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

   8. Simplified 87.6%

      \[\leadsto \color{blue}{x \cdot \left(z + 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+94}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq -6.1 \cdot 10^{+26}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-173}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 3.65 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{+190}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 42.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{+93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+25}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq -0.00029:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+191}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))) (t_2 (* z (- t))))
   (if (<= t -2.7e+93)
     t_2
     (if (<= t -3.4e+25)
       (* y t)
       (if (<= t -0.00029)
         t_2
         (if (<= t -6e-95)
           t_1
           (if (<= t -7e-209)
             (* y (- x))
             (if (<= t 1.5e-34) t_1 (if (<= t 1.05e+191) t_2 (* y t))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = z * -t;
	double tmp;
	if (t <= -2.7e+93) {
		tmp = t_2;
	} else if (t <= -3.4e+25) {
		tmp = y * t;
	} else if (t <= -0.00029) {
		tmp = t_2;
	} else if (t <= -6e-95) {
		tmp = t_1;
	} else if (t <= -7e-209) {
		tmp = y * -x;
	} else if (t <= 1.5e-34) {
		tmp = t_1;
	} else if (t <= 1.05e+191) {
		tmp = t_2;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    t_2 = z * -t
    if (t <= (-2.7d+93)) then
        tmp = t_2
    else if (t <= (-3.4d+25)) then
        tmp = y * t
    else if (t <= (-0.00029d0)) then
        tmp = t_2
    else if (t <= (-6d-95)) then
        tmp = t_1
    else if (t <= (-7d-209)) then
        tmp = y * -x
    else if (t <= 1.5d-34) then
        tmp = t_1
    else if (t <= 1.05d+191) then
        tmp = t_2
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = z * -t;
	double tmp;
	if (t <= -2.7e+93) {
		tmp = t_2;
	} else if (t <= -3.4e+25) {
		tmp = y * t;
	} else if (t <= -0.00029) {
		tmp = t_2;
	} else if (t <= -6e-95) {
		tmp = t_1;
	} else if (t <= -7e-209) {
		tmp = y * -x;
	} else if (t <= 1.5e-34) {
		tmp = t_1;
	} else if (t <= 1.05e+191) {
		tmp = t_2;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	t_2 = z * -t
	tmp = 0
	if t <= -2.7e+93:
		tmp = t_2
	elif t <= -3.4e+25:
		tmp = y * t
	elif t <= -0.00029:
		tmp = t_2
	elif t <= -6e-95:
		tmp = t_1
	elif t <= -7e-209:
		tmp = y * -x
	elif t <= 1.5e-34:
		tmp = t_1
	elif t <= 1.05e+191:
		tmp = t_2
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (t <= -2.7e+93)
		tmp = t_2;
	elseif (t <= -3.4e+25)
		tmp = Float64(y * t);
	elseif (t <= -0.00029)
		tmp = t_2;
	elseif (t <= -6e-95)
		tmp = t_1;
	elseif (t <= -7e-209)
		tmp = Float64(y * Float64(-x));
	elseif (t <= 1.5e-34)
		tmp = t_1;
	elseif (t <= 1.05e+191)
		tmp = t_2;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	t_2 = z * -t;
	tmp = 0.0;
	if (t <= -2.7e+93)
		tmp = t_2;
	elseif (t <= -3.4e+25)
		tmp = y * t;
	elseif (t <= -0.00029)
		tmp = t_2;
	elseif (t <= -6e-95)
		tmp = t_1;
	elseif (t <= -7e-209)
		tmp = y * -x;
	elseif (t <= 1.5e-34)
		tmp = t_1;
	elseif (t <= 1.05e+191)
		tmp = t_2;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[t, -2.7e+93], t$95$2, If[LessEqual[t, -3.4e+25], N[(y * t), $MachinePrecision], If[LessEqual[t, -0.00029], t$95$2, If[LessEqual[t, -6e-95], t$95$1, If[LessEqual[t, -7e-209], N[(y * (-x)), $MachinePrecision], If[LessEqual[t, 1.5e-34], t$95$1, If[LessEqual[t, 1.05e+191], t$95$2, N[(y * t), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6999999999999999e93 or -3.39999999999999984e25 < t < -2.9e-4 or 1.5e-34 < t < 1.05e191

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 86.4%

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

   4. Taylor expanded in y around 0 56.3%

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

      1. associate-*r* 56.3%

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

      2. mul-1-neg 56.3%

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

   6. Simplified 56.3%

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

   7. Taylor expanded in x around 0 51.6%

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

      1. associate-*r* 51.6%

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

      2. mul-1-neg 51.6%

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

   9. Simplified 51.6%

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

   if -2.6999999999999999e93 < t < -3.39999999999999984e25 or 1.05e191 < t

   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 72.3%

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

      1. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in y around inf 72.2%

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

   7. Taylor expanded in t around inf 66.7%

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

      1. *-commutative 66.7%

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

   9. Simplified 66.7%

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

   if -2.9e-4 < t < -6e-95 or -7.00000000000000004e-209 < t < 1.5e-34

   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 83.8%

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

      1. mul-1-neg 83.8%

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

      2. unsub-neg 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in y around 0 52.3%

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

      1. +-commutative 52.3%

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

   8. Simplified 52.3%

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

   if -6e-95 < t < -7.00000000000000004e-209

   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 69.4%

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

      1. mul-1-neg 69.4%

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

      2. unsub-neg 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in z around 0 65.3%

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

   7. Taylor expanded in y around inf 49.4%

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

      1. associate-*r* 49.4%

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

      2. neg-mul-1 49.4%

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

      3. *-commutative 49.4%

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

   9. Simplified 49.4%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+93}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+25}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;t \leq -0.00029:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-95}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+191}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := x \cdot \left(z + 1\right)\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-201}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-89}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 920000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))) (t_2 (* y (- t x))) (t_3 (* x (+ z 1.0))))
   (if (<= y -5.2e-11)
     t_2
     (if (<= y 1.05e-201)
       t_3
       (if (<= y 4.6e-138)
         t_1
         (if (<= y 3.1e-89) t_3 (if (<= y 920000000.0) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = y * (t - x);
	double t_3 = x * (z + 1.0);
	double tmp;
	if (y <= -5.2e-11) {
		tmp = t_2;
	} else if (y <= 1.05e-201) {
		tmp = t_3;
	} else if (y <= 4.6e-138) {
		tmp = t_1;
	} else if (y <= 3.1e-89) {
		tmp = t_3;
	} else if (y <= 920000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z * -t
    t_2 = y * (t - x)
    t_3 = x * (z + 1.0d0)
    if (y <= (-5.2d-11)) then
        tmp = t_2
    else if (y <= 1.05d-201) then
        tmp = t_3
    else if (y <= 4.6d-138) then
        tmp = t_1
    else if (y <= 3.1d-89) then
        tmp = t_3
    else if (y <= 920000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double t_2 = y * (t - x);
	double t_3 = x * (z + 1.0);
	double tmp;
	if (y <= -5.2e-11) {
		tmp = t_2;
	} else if (y <= 1.05e-201) {
		tmp = t_3;
	} else if (y <= 4.6e-138) {
		tmp = t_1;
	} else if (y <= 3.1e-89) {
		tmp = t_3;
	} else if (y <= 920000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	t_2 = y * (t - x)
	t_3 = x * (z + 1.0)
	tmp = 0
	if y <= -5.2e-11:
		tmp = t_2
	elif y <= 1.05e-201:
		tmp = t_3
	elif y <= 4.6e-138:
		tmp = t_1
	elif y <= 3.1e-89:
		tmp = t_3
	elif y <= 920000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(x * Float64(z + 1.0))
	tmp = 0.0
	if (y <= -5.2e-11)
		tmp = t_2;
	elseif (y <= 1.05e-201)
		tmp = t_3;
	elseif (y <= 4.6e-138)
		tmp = t_1;
	elseif (y <= 3.1e-89)
		tmp = t_3;
	elseif (y <= 920000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	t_2 = y * (t - x);
	t_3 = x * (z + 1.0);
	tmp = 0.0;
	if (y <= -5.2e-11)
		tmp = t_2;
	elseif (y <= 1.05e-201)
		tmp = t_3;
	elseif (y <= 4.6e-138)
		tmp = t_1;
	elseif (y <= 3.1e-89)
		tmp = t_3;
	elseif (y <= 920000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e-11], t$95$2, If[LessEqual[y, 1.05e-201], t$95$3, If[LessEqual[y, 4.6e-138], t$95$1, If[LessEqual[y, 3.1e-89], t$95$3, If[LessEqual[y, 920000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2000000000000001e-11 or 9.2e8 < 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 inf 87.7%

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

      1. +-commutative 87.7%

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

      2. *-commutative 87.7%

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

      3. *-commutative 87.7%

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

      4. associate-/l* 88.4%

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

      5. distribute-lft-out 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in y around inf 73.7%

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

   7. Taylor expanded in x around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. associate-*r* 76.3%

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

      3. neg-mul-1 76.3%

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

      4. distribute-rgt-out 79.2%

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

      5. unsub-neg 79.2%

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

   9. Simplified 79.2%

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

   if -5.2000000000000001e-11 < y < 1.05000000000000006e-201 or 4.5999999999999998e-138 < y < 3.09999999999999996e-89

   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 56.5%

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

      1. mul-1-neg 56.5%

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

      2. unsub-neg 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in y around 0 56.5%

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

      1. +-commutative 56.5%

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

   8. Simplified 56.5%

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

   if 1.05000000000000006e-201 < y < 4.5999999999999998e-138 or 3.09999999999999996e-89 < y < 9.2e8

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 93.1%

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

   4. Taylor expanded in y around 0 68.1%

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

      1. associate-*r* 68.1%

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

      2. mul-1-neg 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in x around 0 57.0%

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

      1. associate-*r* 57.0%

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

      2. mul-1-neg 57.0%

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

   9. Simplified 57.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-201}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-138}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 920000000:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := x - z \cdot t\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-196}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-252}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 900000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (- x (* z t))))
   (if (<= y -2.2e-11)
     t_1
     (if (<= y -1.55e-196)
       t_2
       (if (<= y -4e-252) (* z (- x t)) (if (<= y 900000000.0) 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 * t);
	double tmp;
	if (y <= -2.2e-11) {
		tmp = t_1;
	} else if (y <= -1.55e-196) {
		tmp = t_2;
	} else if (y <= -4e-252) {
		tmp = z * (x - t);
	} else if (y <= 900000000.0) {
		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 * t)
    if (y <= (-2.2d-11)) then
        tmp = t_1
    else if (y <= (-1.55d-196)) then
        tmp = t_2
    else if (y <= (-4d-252)) then
        tmp = z * (x - t)
    else if (y <= 900000000.0d0) 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 * t);
	double tmp;
	if (y <= -2.2e-11) {
		tmp = t_1;
	} else if (y <= -1.55e-196) {
		tmp = t_2;
	} else if (y <= -4e-252) {
		tmp = z * (x - t);
	} else if (y <= 900000000.0) {
		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 * t)
	tmp = 0
	if y <= -2.2e-11:
		tmp = t_1
	elif y <= -1.55e-196:
		tmp = t_2
	elif y <= -4e-252:
		tmp = z * (x - t)
	elif y <= 900000000.0:
		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 * t))
	tmp = 0.0
	if (y <= -2.2e-11)
		tmp = t_1;
	elseif (y <= -1.55e-196)
		tmp = t_2;
	elseif (y <= -4e-252)
		tmp = Float64(z * Float64(x - t));
	elseif (y <= 900000000.0)
		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 * t);
	tmp = 0.0;
	if (y <= -2.2e-11)
		tmp = t_1;
	elseif (y <= -1.55e-196)
		tmp = t_2;
	elseif (y <= -4e-252)
		tmp = z * (x - t);
	elseif (y <= 900000000.0)
		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 * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e-11], t$95$1, If[LessEqual[y, -1.55e-196], t$95$2, If[LessEqual[y, -4e-252], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 900000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2000000000000002e-11 or 9e8 < 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 inf 87.8%

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

      1. +-commutative 87.8%

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

      2. *-commutative 87.8%

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

      3. *-commutative 87.8%

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

      4. associate-/l* 88.5%

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

      5. distribute-lft-out 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in y around inf 73.2%

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

   7. Taylor expanded in x around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-*r* 75.8%

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

      3. neg-mul-1 75.8%

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

      4. distribute-rgt-out 78.7%

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

      5. unsub-neg 78.7%

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

   9. Simplified 78.7%

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

   if -2.2000000000000002e-11 < y < -1.54999999999999996e-196 or -3.99999999999999977e-252 < y < 9e8

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 84.3%

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

   4. Taylor expanded in y around 0 70.2%

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

      1. associate-*r* 70.2%

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

      2. mul-1-neg 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in x around 0 70.2%

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

      1. mul-1-neg 70.2%

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

      2. sub-neg 70.2%

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

   9. Simplified 70.2%

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

   if -1.54999999999999996e-196 < y < -3.99999999999999977e-252

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 92.1%

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

      1. *-commutative 92.1%

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

   8. Simplified 92.1%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-196}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-252}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 900000000:\\ \;\;\;\;x - z \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-258}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 880000000000:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))))
   (if (<= y -7.5e-11)
     t_1
     (if (<= y 5.7e-258)
       t_2
       (if (<= y 2.65e-207)
         (* x (+ z 1.0))
         (if (<= y 880000000000.0) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double tmp;
	if (y <= -7.5e-11) {
		tmp = t_1;
	} else if (y <= 5.7e-258) {
		tmp = t_2;
	} else if (y <= 2.65e-207) {
		tmp = x * (z + 1.0);
	} else if (y <= 880000000000.0) {
		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 = z * (x - t)
    if (y <= (-7.5d-11)) then
        tmp = t_1
    else if (y <= 5.7d-258) then
        tmp = t_2
    else if (y <= 2.65d-207) then
        tmp = x * (z + 1.0d0)
    else if (y <= 880000000000.0d0) 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 = z * (x - t);
	double tmp;
	if (y <= -7.5e-11) {
		tmp = t_1;
	} else if (y <= 5.7e-258) {
		tmp = t_2;
	} else if (y <= 2.65e-207) {
		tmp = x * (z + 1.0);
	} else if (y <= 880000000000.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * (x - t)
	tmp = 0
	if y <= -7.5e-11:
		tmp = t_1
	elif y <= 5.7e-258:
		tmp = t_2
	elif y <= 2.65e-207:
		tmp = x * (z + 1.0)
	elif y <= 880000000000.0:
		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(z * Float64(x - t))
	tmp = 0.0
	if (y <= -7.5e-11)
		tmp = t_1;
	elseif (y <= 5.7e-258)
		tmp = t_2;
	elseif (y <= 2.65e-207)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 880000000000.0)
		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 = z * (x - t);
	tmp = 0.0;
	if (y <= -7.5e-11)
		tmp = t_1;
	elseif (y <= 5.7e-258)
		tmp = t_2;
	elseif (y <= 2.65e-207)
		tmp = x * (z + 1.0);
	elseif (y <= 880000000000.0)
		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[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e-11], t$95$1, If[LessEqual[y, 5.7e-258], t$95$2, If[LessEqual[y, 2.65e-207], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 880000000000.0], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5e-11 or 8.8e11 < 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 inf 87.7%

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

      1. +-commutative 87.7%

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

      2. *-commutative 87.7%

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

      3. *-commutative 87.7%

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

      4. associate-/l* 88.4%

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

      5. distribute-lft-out 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in y around inf 73.7%

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

   7. Taylor expanded in x around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. associate-*r* 76.3%

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

      3. neg-mul-1 76.3%

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

      4. distribute-rgt-out 79.2%

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

      5. unsub-neg 79.2%

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

   9. Simplified 79.2%

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

   if -7.5e-11 < y < 5.7000000000000002e-258 or 2.65e-207 < y < 8.8e11

   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 86.8%

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

      1. mul-1-neg 86.8%

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

      2. unsub-neg 86.8%

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

   5. Simplified 86.8%

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

   6. Taylor expanded in z around inf 63.2%

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

      1. *-commutative 63.2%

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

   8. Simplified 63.2%

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

   if 5.7000000000000002e-258 < y < 2.65e-207

   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 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

   5. Simplified 80.5%

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

   6. Taylor expanded in y around 0 80.5%

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

      1. +-commutative 80.5%

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

   8. Simplified 80.5%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-258}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 880000000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+15}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -2.1e-96)
     t_1
     (if (<= z -2.6e-296)
       (* y t)
       (if (<= z 2.4e-280) x (if (<= z 2.15e+15) (* y t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -2.1e-96) {
		tmp = t_1;
	} else if (z <= -2.6e-296) {
		tmp = y * t;
	} else if (z <= 2.4e-280) {
		tmp = x;
	} else if (z <= 2.15e+15) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-2.1d-96)) then
        tmp = t_1
    else if (z <= (-2.6d-296)) then
        tmp = y * t
    else if (z <= 2.4d-280) then
        tmp = x
    else if (z <= 2.15d+15) then
        tmp = y * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -2.1e-96) {
		tmp = t_1;
	} else if (z <= -2.6e-296) {
		tmp = y * t;
	} else if (z <= 2.4e-280) {
		tmp = x;
	} else if (z <= 2.15e+15) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -2.1e-96:
		tmp = t_1
	elif z <= -2.6e-296:
		tmp = y * t
	elif z <= 2.4e-280:
		tmp = x
	elif z <= 2.15e+15:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -2.1e-96)
		tmp = t_1;
	elseif (z <= -2.6e-296)
		tmp = Float64(y * t);
	elseif (z <= 2.4e-280)
		tmp = x;
	elseif (z <= 2.15e+15)
		tmp = Float64(y * t);
	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 <= -2.1e-96)
		tmp = t_1;
	elseif (z <= -2.6e-296)
		tmp = y * t;
	elseif (z <= 2.4e-280)
		tmp = x;
	elseif (z <= 2.15e+15)
		tmp = y * t;
	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, -2.1e-96], t$95$1, If[LessEqual[z, -2.6e-296], N[(y * t), $MachinePrecision], If[LessEqual[z, 2.4e-280], x, If[LessEqual[z, 2.15e+15], N[(y * t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.10000000000000001e-96 or 2.15e15 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 61.9%

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

   4. Taylor expanded in y around 0 48.0%

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

      1. associate-*r* 48.0%

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

      2. mul-1-neg 48.0%

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

   6. Simplified 48.0%

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

   7. Taylor expanded in x around 0 45.0%

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

      1. associate-*r* 45.0%

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

      2. mul-1-neg 45.0%

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

   9. Simplified 45.0%

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

   if -2.10000000000000001e-96 < z < -2.6000000000000001e-296 or 2.3999999999999998e-280 < z < 2.15e15

   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 89.3%

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

      1. *-commutative 89.3%

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

   5. Simplified 89.3%

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

   6. Taylor expanded in y around inf 85.7%

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

   7. Taylor expanded in t around inf 45.1%

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

      1. *-commutative 45.1%

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

   9. Simplified 45.1%

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

   if -2.6000000000000001e-296 < z < 2.3999999999999998e-280

   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 88.7%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-96}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-296}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-280}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+15}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1150000000000 \lor \neg \left(t \leq 0.00255\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1150000000000.0) (not (<= t 0.00255)))
   (+ x (* (- y z) t))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1150000000000.0) || !(t <= 0.00255)) {
		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 <= (-1150000000000.0d0)) .or. (.not. (t <= 0.00255d0))) 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 <= -1150000000000.0) || !(t <= 0.00255)) {
		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 <= -1150000000000.0) or not (t <= 0.00255):
		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 <= -1150000000000.0) || !(t <= 0.00255))
		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 <= -1150000000000.0) || ~((t <= 0.00255)))
		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, -1150000000000.0], N[Not[LessEqual[t, 0.00255]], $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 < -1.15e12 or 0.0025500000000000002 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 91.5%

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

   if -1.15e12 < t < 0.0025500000000000002

   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 79.6%

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

      1. mul-1-neg 79.6%

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

      2. unsub-neg 79.6%

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

   5. Simplified 79.6%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1150000000000 \lor \neg \left(t \leq 0.00255\right):\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+21} \lor \neg \left(t \leq 0.00125\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.2e+21) (not (<= t 0.00125))) (* y t) (* y (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.2e+21) || !(t <= 0.00125)) {
		tmp = y * t;
	} else {
		tmp = y * -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 ((t <= (-1.2d+21)) .or. (.not. (t <= 0.00125d0))) then
        tmp = y * t
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.2e+21) || !(t <= 0.00125)) {
		tmp = y * t;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.2e+21) or not (t <= 0.00125):
		tmp = y * t
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.2e+21) || !(t <= 0.00125))
		tmp = Float64(y * t);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.2e+21) || ~((t <= 0.00125)))
		tmp = y * t;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.2e+21], N[Not[LessEqual[t, 0.00125]], $MachinePrecision]], N[(y * t), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e21 or 0.00125000000000000003 < t

   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 55.9%

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

      1. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in y around inf 57.3%

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

   7. Taylor expanded in t around inf 47.0%

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

      1. *-commutative 47.0%

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

   9. Simplified 47.0%

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

   if -1.2e21 < t < 0.00125000000000000003

   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 79.0%

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

      1. mul-1-neg 79.0%

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

      2. unsub-neg 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in z around 0 57.8%

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

   7. Taylor expanded in y around inf 38.4%

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

      1. associate-*r* 38.4%

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

      2. neg-mul-1 38.4%

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

      3. *-commutative 38.4%

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

   9. Simplified 38.4%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+21} \lor \neg \left(t \leq 0.00125\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-11} \lor \neg \left(y \leq 9 \cdot 10^{-173}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e-11) (not (<= y 9e-173))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e-11) || !(y <= 9e-173)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.8d-11)) .or. (.not. (y <= 9d-173))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e-11) || !(y <= 9e-173)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e-11) or not (y <= 9e-173):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e-11) || !(y <= 9e-173))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.8e-11) || ~((y <= 9e-173)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e-11], N[Not[LessEqual[y, 9e-173]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999998e-11 or 9.00000000000000037e-173 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 71.2%

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

      1. *-commutative 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in y around inf 71.7%

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

   7. Taylor expanded in t around inf 39.0%

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

      1. *-commutative 39.0%

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

   9. Simplified 39.0%

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

   if -3.7999999999999998e-11 < y < 9.00000000000000037e-173

   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 39.1%

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

      1. *-commutative 39.1%

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

   5. Simplified 39.1%

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

   6. Taylor expanded in y around 0 34.7%

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

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-11} \lor \neg \left(y \leq 9 \cdot 10^{-173}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 12: 18.5% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 61.0%

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

   1. *-commutative 61.0%

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

5. Simplified 61.0%

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

6. Taylor expanded in y around 0 14.4%

   \[\leadsto \color{blue}{x} \]
7. 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 2024108 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

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