Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.6s

Alternatives: 12

Speedup: 1.0×

• 35.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 54.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+18}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* (- y z) t)))
   (if (<= z -3.6e+115)
     t_2
     (if (<= z -4.3e+18)
       (* z x)
       (if (<= z -9.5e-56)
         t_1
         (if (<= z -2.1e-94) x (if (<= z 4.5e-44) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -3.6e+115) {
		tmp = t_2;
	} else if (z <= -4.3e+18) {
		tmp = z * x;
	} else if (z <= -9.5e-56) {
		tmp = t_1;
	} else if (z <= -2.1e-94) {
		tmp = x;
	} else if (z <= 4.5e-44) {
		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) :: tmp
    t_1 = y * (t - x)
    t_2 = (y - z) * t
    if (z <= (-3.6d+115)) then
        tmp = t_2
    else if (z <= (-4.3d+18)) then
        tmp = z * x
    else if (z <= (-9.5d-56)) then
        tmp = t_1
    else if (z <= (-2.1d-94)) then
        tmp = x
    else if (z <= 4.5d-44) 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 = y * (t - x);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -3.6e+115) {
		tmp = t_2;
	} else if (z <= -4.3e+18) {
		tmp = z * x;
	} else if (z <= -9.5e-56) {
		tmp = t_1;
	} else if (z <= -2.1e-94) {
		tmp = x;
	} else if (z <= 4.5e-44) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = (y - z) * t
	tmp = 0
	if z <= -3.6e+115:
		tmp = t_2
	elif z <= -4.3e+18:
		tmp = z * x
	elif z <= -9.5e-56:
		tmp = t_1
	elif z <= -2.1e-94:
		tmp = x
	elif z <= 4.5e-44:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (z <= -3.6e+115)
		tmp = t_2;
	elseif (z <= -4.3e+18)
		tmp = Float64(z * x);
	elseif (z <= -9.5e-56)
		tmp = t_1;
	elseif (z <= -2.1e-94)
		tmp = x;
	elseif (z <= 4.5e-44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = (y - z) * t;
	tmp = 0.0;
	if (z <= -3.6e+115)
		tmp = t_2;
	elseif (z <= -4.3e+18)
		tmp = z * x;
	elseif (z <= -9.5e-56)
		tmp = t_1;
	elseif (z <= -2.1e-94)
		tmp = x;
	elseif (z <= 4.5e-44)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -3.6e+115], t$95$2, If[LessEqual[z, -4.3e+18], N[(z * x), $MachinePrecision], If[LessEqual[z, -9.5e-56], t$95$1, If[LessEqual[z, -2.1e-94], x, If[LessEqual[z, 4.5e-44], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6000000000000001e115 or 4.4999999999999999e-44 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 94.4%

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

      1. +-commutative 94.4%

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

      2. fma-def 98.1%

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

      3. mul-1-neg 98.1%

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

      4. distribute-rgt-neg-in 98.1%

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

      5. +-commutative 98.1%

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

   4. Simplified 98.1%

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

   5. Taylor expanded in t around inf 63.3%

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

   if -3.6000000000000001e115 < z < -4.3e18

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 95.7%

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

      1. +-commutative 95.7%

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

      2. fma-def 100.0%

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

      3. mul-1-neg 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 81.9%

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

      1. +-commutative 81.9%

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

      2. mul-1-neg 81.9%

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

      3. sub-neg 81.9%

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

      4. *-commutative 81.9%

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

   7. Simplified 81.9%

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

   8. Taylor expanded in x around inf 78.8%

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

   if -4.3e18 < z < -9.4999999999999991e-56 or -2.1000000000000001e-94 < z < 4.4999999999999999e-44

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 97.4%

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

      1. +-commutative 97.4%

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

      2. fma-def 99.1%

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

      3. mul-1-neg 99.1%

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

      4. distribute-rgt-neg-in 99.1%

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

      5. +-commutative 99.1%

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

   4. Simplified 99.1%

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

   5. Taylor expanded in y around inf 65.0%

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

      1. mul-1-neg 65.0%

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

      2. sub-neg 65.0%

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

      3. *-commutative 65.0%

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

   7. Simplified 65.0%

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

   if -9.4999999999999991e-56 < z < -2.1000000000000001e-94

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 86.5%

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

   3. Taylor expanded in x around inf 64.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+115}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{+18}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 3: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -11200000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* (- y z) t))))
   (if (<= z -11200000000.0)
     t_1
     (if (<= z 4e-125)
       t_2
       (if (<= z 1.02e-69) (* y (- t x)) (if (<= z 1.6e+27) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (z <= -11200000000.0) {
		tmp = t_1;
	} else if (z <= 4e-125) {
		tmp = t_2;
	} else if (z <= 1.02e-69) {
		tmp = y * (t - x);
	} else if (z <= 1.6e+27) {
		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 = z * (x - t)
    t_2 = x + ((y - z) * t)
    if (z <= (-11200000000.0d0)) then
        tmp = t_1
    else if (z <= 4d-125) then
        tmp = t_2
    else if (z <= 1.02d-69) then
        tmp = y * (t - x)
    else if (z <= 1.6d+27) 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 = z * (x - t);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (z <= -11200000000.0) {
		tmp = t_1;
	} else if (z <= 4e-125) {
		tmp = t_2;
	} else if (z <= 1.02e-69) {
		tmp = y * (t - x);
	} else if (z <= 1.6e+27) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + ((y - z) * t)
	tmp = 0
	if z <= -11200000000.0:
		tmp = t_1
	elif z <= 4e-125:
		tmp = t_2
	elif z <= 1.02e-69:
		tmp = y * (t - x)
	elif z <= 1.6e+27:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (z <= -11200000000.0)
		tmp = t_1;
	elseif (z <= 4e-125)
		tmp = t_2;
	elseif (z <= 1.02e-69)
		tmp = Float64(y * Float64(t - x));
	elseif (z <= 1.6e+27)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x + ((y - z) * t);
	tmp = 0.0;
	if (z <= -11200000000.0)
		tmp = t_1;
	elseif (z <= 4e-125)
		tmp = t_2;
	elseif (z <= 1.02e-69)
		tmp = y * (t - x);
	elseif (z <= 1.6e+27)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -11200000000.0], t$95$1, If[LessEqual[z, 4e-125], t$95$2, If[LessEqual[z, 1.02e-69], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+27], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.12e10 or 1.60000000000000008e27 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 94.9%

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

      1. +-commutative 94.9%

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

      2. fma-def 98.3%

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

      3. mul-1-neg 98.3%

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

      4. distribute-rgt-neg-in 98.3%

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

      5. +-commutative 98.3%

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

   4. Simplified 98.3%

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

   5. Taylor expanded in z around inf 88.4%

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

      1. +-commutative 88.4%

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

      2. mul-1-neg 88.4%

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

      3. sub-neg 88.4%

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

      4. *-commutative 88.4%

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

   7. Simplified 88.4%

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

   if -1.12e10 < z < 4.00000000000000005e-125 or 1.02000000000000005e-69 < z < 1.60000000000000008e27

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 79.8%

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

   if 4.00000000000000005e-125 < z < 1.02000000000000005e-69

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. mul-1-neg 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. sub-neg 77.0%

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

      3. *-commutative 77.0%

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

   7. Simplified 77.0%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -11200000000:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-125}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 4: 39.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -z \cdot t\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-6}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.92 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+48}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+219}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t))))
   (if (<= z -1.2e+121)
     t_1
     (if (<= z -3.3e-6)
       (* z x)
       (if (<= z -1.92e-94)
         x
         (if (<= z 1.4e+48) (* y t) (if (<= z 2.25e+219) (* z x) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -(z * t);
	double tmp;
	if (z <= -1.2e+121) {
		tmp = t_1;
	} else if (z <= -3.3e-6) {
		tmp = z * x;
	} else if (z <= -1.92e-94) {
		tmp = x;
	} else if (z <= 1.4e+48) {
		tmp = y * t;
	} else if (z <= 2.25e+219) {
		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 <= (-1.2d+121)) then
        tmp = t_1
    else if (z <= (-3.3d-6)) then
        tmp = z * x
    else if (z <= (-1.92d-94)) then
        tmp = x
    else if (z <= 1.4d+48) then
        tmp = y * t
    else if (z <= 2.25d+219) 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 <= -1.2e+121) {
		tmp = t_1;
	} else if (z <= -3.3e-6) {
		tmp = z * x;
	} else if (z <= -1.92e-94) {
		tmp = x;
	} else if (z <= 1.4e+48) {
		tmp = y * t;
	} else if (z <= 2.25e+219) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -(z * t)
	tmp = 0
	if z <= -1.2e+121:
		tmp = t_1
	elif z <= -3.3e-6:
		tmp = z * x
	elif z <= -1.92e-94:
		tmp = x
	elif z <= 1.4e+48:
		tmp = y * t
	elif z <= 2.25e+219:
		tmp = z * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-Float64(z * t))
	tmp = 0.0
	if (z <= -1.2e+121)
		tmp = t_1;
	elseif (z <= -3.3e-6)
		tmp = Float64(z * x);
	elseif (z <= -1.92e-94)
		tmp = x;
	elseif (z <= 1.4e+48)
		tmp = Float64(y * t);
	elseif (z <= 2.25e+219)
		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 <= -1.2e+121)
		tmp = t_1;
	elseif (z <= -3.3e-6)
		tmp = z * x;
	elseif (z <= -1.92e-94)
		tmp = x;
	elseif (z <= 1.4e+48)
		tmp = y * t;
	elseif (z <= 2.25e+219)
		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, -1.2e+121], t$95$1, If[LessEqual[z, -3.3e-6], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.92e-94], x, If[LessEqual[z, 1.4e+48], N[(y * t), $MachinePrecision], If[LessEqual[z, 2.25e+219], N[(z * x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.2e121 or 2.25000000000000012e219 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 71.4%

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

   3. Taylor expanded in z around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. *-commutative 68.1%

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

      3. distribute-rgt-neg-in 68.1%

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

   5. Simplified 68.1%

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

   if -1.2e121 < z < -3.30000000000000017e-6 or 1.40000000000000006e48 < z < 2.25000000000000012e219

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 95.5%

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

      1. +-commutative 95.5%

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

      2. fma-def 100.0%

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

      3. mul-1-neg 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 82.0%

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

      1. +-commutative 82.0%

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

      2. mul-1-neg 82.0%

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

      3. sub-neg 82.0%

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

      4. *-commutative 82.0%

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

   7. Simplified 82.0%

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

   8. Taylor expanded in x around inf 57.6%

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

   if -3.30000000000000017e-6 < z < -1.92e-94

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 71.1%

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

   3. Taylor expanded in x around inf 49.6%

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

   if -1.92e-94 < z < 1.40000000000000006e48

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 77.6%

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

   3. Taylor expanded in y around inf 46.6%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+121}:\\ \;\;\;\;-z \cdot t\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-6}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.92 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+48}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+219}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;-z \cdot t\\ \end{array} \]

Alternative 5: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-6} \lor \neg \left(z \leq 1.05 \cdot 10^{+28}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.3e-6) (not (<= z 1.05e+28)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3e-6) || !(z <= 1.05e+28)) {
		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 <= (-3.3d-6)) .or. (.not. (z <= 1.05d+28))) 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 <= -3.3e-6) || !(z <= 1.05e+28)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.3e-6) or not (z <= 1.05e+28):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.3e-6) || !(z <= 1.05e+28))
		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 <= -3.3e-6) || ~((z <= 1.05e+28)))
		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, -3.3e-6], N[Not[LessEqual[z, 1.05e+28]], $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 < -3.30000000000000017e-6 or 1.04999999999999995e28 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 95.1%

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

      1. +-commutative 95.1%

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

      2. fma-def 98.4%

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

      3. mul-1-neg 98.4%

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

      4. distribute-rgt-neg-in 98.4%

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

      5. +-commutative 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in z around inf 87.3%

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

      1. +-commutative 87.3%

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

      2. mul-1-neg 87.3%

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

      3. sub-neg 87.3%

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

      4. *-commutative 87.3%

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

   7. Simplified 87.3%

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

   if -3.30000000000000017e-6 < z < 1.04999999999999995e28

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around 0 93.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-6} \lor \neg \left(z \leq 1.05 \cdot 10^{+28}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 6: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e-14)
   (- x (* z (- t x)))
   (if (<= z 6.5e+26) (+ x (* y (- t x))) (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e-14) {
		tmp = x - (z * (t - x));
	} else if (z <= 6.5e+26) {
		tmp = x + (y * (t - x));
	} else {
		tmp = z * (x - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.05d-14)) then
        tmp = x - (z * (t - x))
    else if (z <= 6.5d+26) then
        tmp = x + (y * (t - x))
    else
        tmp = z * (x - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e-14) {
		tmp = x - (z * (t - x));
	} else if (z <= 6.5e+26) {
		tmp = x + (y * (t - x));
	} else {
		tmp = z * (x - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e-14:
		tmp = x - (z * (t - x))
	elif z <= 6.5e+26:
		tmp = x + (y * (t - x))
	else:
		tmp = z * (x - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e-14)
		tmp = Float64(x - Float64(z * Float64(t - x)));
	elseif (z <= 6.5e+26)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(z * Float64(x - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.05e-14)
		tmp = x - (z * (t - x));
	elseif (z <= 6.5e+26)
		tmp = x + (y * (t - x));
	else
		tmp = z * (x - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e-14], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+26], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0499999999999999e-14

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in y around 0 85.8%

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

      1. +-commutative 85.8%

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

      2. mul-1-neg 85.8%

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

      3. unsub-neg 85.8%

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

      4. *-commutative 85.8%

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

   4. Simplified 85.8%

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

   if -1.0499999999999999e-14 < z < 6.50000000000000022e26

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in z around 0 93.3%

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

   if 6.50000000000000022e26 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 91.2%

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

      1. +-commutative 91.2%

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

      2. fma-def 96.5%

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

      3. mul-1-neg 96.5%

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

      4. distribute-rgt-neg-in 96.5%

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

      5. +-commutative 96.5%

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

   4. Simplified 96.5%

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

   5. Taylor expanded in z around inf 89.7%

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

      1. +-commutative 89.7%

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

      2. mul-1-neg 89.7%

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

      3. sub-neg 89.7%

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

      4. *-commutative 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-14}:\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 7: 38.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-6}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+49}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.3e-6)
   (* z x)
   (if (<= z -1.75e-94) x (if (<= z 1.85e+49) (* y t) (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.3e-6) {
		tmp = z * x;
	} else if (z <= -1.75e-94) {
		tmp = x;
	} else if (z <= 1.85e+49) {
		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 <= (-3.3d-6)) then
        tmp = z * x
    else if (z <= (-1.75d-94)) then
        tmp = x
    else if (z <= 1.85d+49) 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 <= -3.3e-6) {
		tmp = z * x;
	} else if (z <= -1.75e-94) {
		tmp = x;
	} else if (z <= 1.85e+49) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.3e-6:
		tmp = z * x
	elif z <= -1.75e-94:
		tmp = x
	elif z <= 1.85e+49:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.3e-6)
		tmp = Float64(z * x);
	elseif (z <= -1.75e-94)
		tmp = x;
	elseif (z <= 1.85e+49)
		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 <= -3.3e-6)
		tmp = z * x;
	elseif (z <= -1.75e-94)
		tmp = x;
	elseif (z <= 1.85e+49)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.3e-6], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.75e-94], x, If[LessEqual[z, 1.85e+49], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000017e-6 or 1.85000000000000009e49 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 95.0%

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

      1. +-commutative 95.0%

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

      2. fma-def 98.3%

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

      3. mul-1-neg 98.3%

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

      4. distribute-rgt-neg-in 98.3%

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

      5. +-commutative 98.3%

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

   4. Simplified 98.3%

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

   5. Taylor expanded in z around inf 87.6%

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

      1. +-commutative 87.6%

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

      2. mul-1-neg 87.6%

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

      3. sub-neg 87.6%

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

      4. *-commutative 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in x around inf 49.0%

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

   if -3.30000000000000017e-6 < z < -1.74999999999999999e-94

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 71.1%

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

   3. Taylor expanded in x around inf 49.6%

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

   if -1.74999999999999999e-94 < z < 1.85000000000000009e49

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 77.6%

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

   3. Taylor expanded in y around inf 46.6%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-6}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+49}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 8: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-6} \lor \neg \left(z \leq 6.2 \cdot 10^{+27}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e-6) (not (<= z 6.2e+27))) (* z (- x t)) (* y (- t x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-6) || !(z <= 6.2e+27)) {
		tmp = z * (x - t);
	} else {
		tmp = 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 <= (-2d-6)) .or. (.not. (z <= 6.2d+27))) then
        tmp = z * (x - t)
    else
        tmp = 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 <= -2e-6) || !(z <= 6.2e+27)) {
		tmp = z * (x - t);
	} else {
		tmp = y * (t - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2e-6) or not (z <= 6.2e+27):
		tmp = z * (x - t)
	else:
		tmp = y * (t - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e-6) || !(z <= 6.2e+27))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(y * Float64(t - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2e-6) || ~((z <= 6.2e+27)))
		tmp = z * (x - t);
	else
		tmp = y * (t - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e-6], N[Not[LessEqual[z, 6.2e+27]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.99999999999999991e-6 or 6.19999999999999992e27 < z

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 95.1%

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

      1. +-commutative 95.1%

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

      2. fma-def 98.4%

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

      3. mul-1-neg 98.4%

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

      4. distribute-rgt-neg-in 98.4%

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

      5. +-commutative 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in z around inf 87.3%

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

      1. +-commutative 87.3%

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

      2. mul-1-neg 87.3%

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

      3. sub-neg 87.3%

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

      4. *-commutative 87.3%

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

   7. Simplified 87.3%

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

   if -1.99999999999999991e-6 < z < 6.19999999999999992e27

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 96.9%

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

      1. +-commutative 96.9%

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

      2. fma-def 99.2%

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

      3. mul-1-neg 99.2%

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

      4. distribute-rgt-neg-in 99.2%

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

      5. +-commutative 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around inf 63.6%

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

      1. mul-1-neg 63.6%

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

      2. sub-neg 63.6%

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

      3. *-commutative 63.6%

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

   7. Simplified 63.6%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-6} \lor \neg \left(z \leq 6.2 \cdot 10^{+27}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 9: 55.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+92}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{+158}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1e+92) (* z x) (if (<= x 8.4e+158) (* (- y z) t) (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1e+92) {
		tmp = z * x;
	} else if (x <= 8.4e+158) {
		tmp = (y - z) * 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 (x <= (-1d+92)) then
        tmp = z * x
    else if (x <= 8.4d+158) then
        tmp = (y - z) * 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 (x <= -1e+92) {
		tmp = z * x;
	} else if (x <= 8.4e+158) {
		tmp = (y - z) * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1e+92:
		tmp = z * x
	elif x <= 8.4e+158:
		tmp = (y - z) * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1e+92)
		tmp = Float64(z * x);
	elseif (x <= 8.4e+158)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1e+92)
		tmp = z * x;
	elseif (x <= 8.4e+158)
		tmp = (y - z) * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1e+92], N[(z * x), $MachinePrecision], If[LessEqual[x, 8.4e+158], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1e92 or 8.3999999999999996e158 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 90.5%

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

      1. +-commutative 90.5%

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

      2. fma-def 97.6%

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

      3. mul-1-neg 97.6%

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

      4. distribute-rgt-neg-in 97.6%

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

      5. +-commutative 97.6%

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

   4. Simplified 97.6%

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

   5. Taylor expanded in z around inf 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. sub-neg 54.8%

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

      4. *-commutative 54.8%

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

   7. Simplified 54.8%

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

   8. Taylor expanded in x around inf 50.3%

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

   if -1e92 < x < 8.3999999999999996e158

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in x around -inf 98.8%

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

      1. +-commutative 98.8%

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

      2. fma-def 99.4%

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

      3. mul-1-neg 99.4%

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

      4. distribute-rgt-neg-in 99.4%

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

      5. +-commutative 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in t around inf 64.9%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+92}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{+158}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 10: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (x - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]

2. Final simplification 100.0%

   \[\leadsto x - \left(y - z\right) \cdot \left(x - t\right) \]

Alternative 11: 34.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-189}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.02 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.05e-189) (* y t) (if (<= y 2.02e-75) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.05e-189) {
		tmp = y * t;
	} else if (y <= 2.02e-75) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.05d-189)) then
        tmp = y * t
    else if (y <= 2.02d-75) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.05e-189) {
		tmp = y * t;
	} else if (y <= 2.02e-75) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.05e-189:
		tmp = y * t
	elif y <= 2.02e-75:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.05e-189)
		tmp = Float64(y * t);
	elseif (y <= 2.02e-75)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.05e-189)
		tmp = y * t;
	elseif (y <= 2.02e-75)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.05e-189], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.02e-75], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.05000000000000015e-189 or 2.0200000000000001e-75 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 58.5%

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

   3. Taylor expanded in y around inf 39.1%

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

   if -2.05000000000000015e-189 < y < 2.0200000000000001e-75

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]

   2. Taylor expanded in t around inf 76.0%

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

   3. Taylor expanded in x around inf 42.1%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-189}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.02 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 12: 17.4% 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. Taylor expanded in t around inf 63.9%

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

3. Taylor expanded in x around inf 17.2%

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

4. Final simplification 17.2%

   \[\leadsto x \]

Developer target: 96.3% 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 2023257 
(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))))