Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.4s

Alternatives: 14

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× 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: 52.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := y \cdot \left(-x\right)\\ \mathbf{if}\;y - z \leq -1 \cdot 10^{+224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq -5 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y - z \leq -0.05:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{+98} \lor \neg \left(y - z \leq 10^{+158}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (* y (- x))))
   (if (<= (- y z) -1e+224)
     t_1
     (if (<= (- y z) -5e+152)
       t_2
       (if (<= (- y z) -0.05)
         t_1
         (if (<= (- y z) 2e-13)
           x
           (if (or (<= (- y z) 4e+98) (not (<= (- y z) 1e+158))) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = y * -x;
	double tmp;
	if ((y - z) <= -1e+224) {
		tmp = t_1;
	} else if ((y - z) <= -5e+152) {
		tmp = t_2;
	} else if ((y - z) <= -0.05) {
		tmp = t_1;
	} else if ((y - z) <= 2e-13) {
		tmp = x;
	} else if (((y - z) <= 4e+98) || !((y - z) <= 1e+158)) {
		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 - z) * t
    t_2 = y * -x
    if ((y - z) <= (-1d+224)) then
        tmp = t_1
    else if ((y - z) <= (-5d+152)) then
        tmp = t_2
    else if ((y - z) <= (-0.05d0)) then
        tmp = t_1
    else if ((y - z) <= 2d-13) then
        tmp = x
    else if (((y - z) <= 4d+98) .or. (.not. ((y - z) <= 1d+158))) 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 - z) * t;
	double t_2 = y * -x;
	double tmp;
	if ((y - z) <= -1e+224) {
		tmp = t_1;
	} else if ((y - z) <= -5e+152) {
		tmp = t_2;
	} else if ((y - z) <= -0.05) {
		tmp = t_1;
	} else if ((y - z) <= 2e-13) {
		tmp = x;
	} else if (((y - z) <= 4e+98) || !((y - z) <= 1e+158)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	t_2 = y * -x
	tmp = 0
	if (y - z) <= -1e+224:
		tmp = t_1
	elif (y - z) <= -5e+152:
		tmp = t_2
	elif (y - z) <= -0.05:
		tmp = t_1
	elif (y - z) <= 2e-13:
		tmp = x
	elif ((y - z) <= 4e+98) or not ((y - z) <= 1e+158):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(y * Float64(-x))
	tmp = 0.0
	if (Float64(y - z) <= -1e+224)
		tmp = t_1;
	elseif (Float64(y - z) <= -5e+152)
		tmp = t_2;
	elseif (Float64(y - z) <= -0.05)
		tmp = t_1;
	elseif (Float64(y - z) <= 2e-13)
		tmp = x;
	elseif ((Float64(y - z) <= 4e+98) || !(Float64(y - z) <= 1e+158))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	t_2 = y * -x;
	tmp = 0.0;
	if ((y - z) <= -1e+224)
		tmp = t_1;
	elseif ((y - z) <= -5e+152)
		tmp = t_2;
	elseif ((y - z) <= -0.05)
		tmp = t_1;
	elseif ((y - z) <= 2e-13)
		tmp = x;
	elseif (((y - z) <= 4e+98) || ~(((y - z) <= 1e+158)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[N[(y - z), $MachinePrecision], -1e+224], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], -5e+152], t$95$2, If[LessEqual[N[(y - z), $MachinePrecision], -0.05], t$95$1, If[LessEqual[N[(y - z), $MachinePrecision], 2e-13], x, If[Or[LessEqual[N[(y - z), $MachinePrecision], 4e+98], N[Not[LessEqual[N[(y - z), $MachinePrecision], 1e+158]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 y z) < -9.9999999999999997e223 or -5e152 < (-.f64 y z) < -0.050000000000000003 or 2.0000000000000001e-13 < (-.f64 y z) < 3.99999999999999999e98 or 9.99999999999999953e157 < (-.f64 y z)

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 62.5%

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

   3. Taylor expanded in x around 0 62.5%

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

      1. *-commutative 62.5%

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

      2. fma-udef 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in t around inf 62.2%

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

   if -9.9999999999999997e223 < (-.f64 y z) < -5e152 or 3.99999999999999999e98 < (-.f64 y z) < 9.99999999999999953e157

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.1%

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

      1. *-commutative 78.1%

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

      2. mul-1-neg 78.1%

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

      3. unsub-neg 78.1%

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

      4. distribute-lft-out-- 78.1%

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

      5. *-rgt-identity 78.1%

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

   4. Simplified 78.1%

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

   5. Taylor expanded in y around inf 48.0%

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

      1. mul-1-neg 48.0%

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

      2. distribute-rgt-neg-in 48.0%

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

   7. Simplified 48.0%

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

   if -0.050000000000000003 < (-.f64 y z) < 2.0000000000000001e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 97.4%

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

   3. Taylor expanded in x around inf 75.5%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -1 \cdot 10^{+224}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq -5 \cdot 10^{+152}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y - z \leq -0.05:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y - z \leq 2 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;y - z \leq 4 \cdot 10^{+98} \lor \neg \left(y - z \leq 10^{+158}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{if}\;x \leq -4.9 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-5} \lor \neg \left(x \leq 1.85 \cdot 10^{+32}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (* x (- (+ z 1.0) y))))
   (if (<= x -4.9e-18)
     t_2
     (if (<= x -1.9e-92)
       t_1
       (if (<= x -4.8e-149)
         t_2
         (if (<= x 7.6e-39)
           t_1
           (if (or (<= x 6.5e-5) (not (<= x 1.85e+32)))
             t_2
             (- x (* z t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = x * ((z + 1.0) - y);
	double tmp;
	if (x <= -4.9e-18) {
		tmp = t_2;
	} else if (x <= -1.9e-92) {
		tmp = t_1;
	} else if (x <= -4.8e-149) {
		tmp = t_2;
	} else if (x <= 7.6e-39) {
		tmp = t_1;
	} else if ((x <= 6.5e-5) || !(x <= 1.85e+32)) {
		tmp = t_2;
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y - z) * t
    t_2 = x * ((z + 1.0d0) - y)
    if (x <= (-4.9d-18)) then
        tmp = t_2
    else if (x <= (-1.9d-92)) then
        tmp = t_1
    else if (x <= (-4.8d-149)) then
        tmp = t_2
    else if (x <= 7.6d-39) then
        tmp = t_1
    else if ((x <= 6.5d-5) .or. (.not. (x <= 1.85d+32))) then
        tmp = t_2
    else
        tmp = x - (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = x * ((z + 1.0) - y);
	double tmp;
	if (x <= -4.9e-18) {
		tmp = t_2;
	} else if (x <= -1.9e-92) {
		tmp = t_1;
	} else if (x <= -4.8e-149) {
		tmp = t_2;
	} else if (x <= 7.6e-39) {
		tmp = t_1;
	} else if ((x <= 6.5e-5) || !(x <= 1.85e+32)) {
		tmp = t_2;
	} else {
		tmp = x - (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	t_2 = x * ((z + 1.0) - y)
	tmp = 0
	if x <= -4.9e-18:
		tmp = t_2
	elif x <= -1.9e-92:
		tmp = t_1
	elif x <= -4.8e-149:
		tmp = t_2
	elif x <= 7.6e-39:
		tmp = t_1
	elif (x <= 6.5e-5) or not (x <= 1.85e+32):
		tmp = t_2
	else:
		tmp = x - (z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(x * Float64(Float64(z + 1.0) - y))
	tmp = 0.0
	if (x <= -4.9e-18)
		tmp = t_2;
	elseif (x <= -1.9e-92)
		tmp = t_1;
	elseif (x <= -4.8e-149)
		tmp = t_2;
	elseif (x <= 7.6e-39)
		tmp = t_1;
	elseif ((x <= 6.5e-5) || !(x <= 1.85e+32))
		tmp = t_2;
	else
		tmp = Float64(x - Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	t_2 = x * ((z + 1.0) - y);
	tmp = 0.0;
	if (x <= -4.9e-18)
		tmp = t_2;
	elseif (x <= -1.9e-92)
		tmp = t_1;
	elseif (x <= -4.8e-149)
		tmp = t_2;
	elseif (x <= 7.6e-39)
		tmp = t_1;
	elseif ((x <= 6.5e-5) || ~((x <= 1.85e+32)))
		tmp = t_2;
	else
		tmp = x - (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.9e-18], t$95$2, If[LessEqual[x, -1.9e-92], t$95$1, If[LessEqual[x, -4.8e-149], t$95$2, If[LessEqual[x, 7.6e-39], t$95$1, If[Or[LessEqual[x, 6.5e-5], N[Not[LessEqual[x, 1.85e+32]], $MachinePrecision]], t$95$2, N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.9000000000000001e-18 or -1.9e-92 < x < -4.8000000000000002e-149 or 7.6000000000000004e-39 < x < 6.49999999999999943e-5 or 1.85e32 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 87.4%

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

      1. *-commutative 87.4%

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

      2. mul-1-neg 87.4%

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

      3. unsub-neg 87.4%

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

      4. distribute-lft-out-- 87.4%

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

      5. *-rgt-identity 87.4%

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

   4. Simplified 87.4%

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

   5. Taylor expanded in x around 0 87.4%

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

   if -4.9000000000000001e-18 < x < -1.9e-92 or -4.8000000000000002e-149 < x < 7.6000000000000004e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 91.5%

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

   3. Taylor expanded in x around 0 91.5%

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

      1. *-commutative 91.5%

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

      2. fma-udef 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in t around inf 85.7%

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

   if 6.49999999999999943e-5 < x < 1.85e32

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 96.6%

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

   3. Taylor expanded in y around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. mul-1-neg 76.8%

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

      3. unsub-neg 76.8%

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

      4. *-commutative 76.8%

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

   5. Simplified 76.8%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-92}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-149}:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-39}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-5} \lor \neg \left(x \leq 1.85 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot t\\ \end{array} \]

Alternative 4: 60.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+148} \lor \neg \left(x \leq 5.1 \cdot 10^{+156}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))) (t_2 (* (- y z) t)))
   (if (<= x -1.6e+21)
     t_1
     (if (<= x -4.5e-103)
       t_2
       (if (<= x -4.8e-149)
         t_1
         (if (<= x 3.8e+36)
           t_2
           (if (or (<= x 4.1e+148) (not (<= x 5.1e+156)))
             t_1
             (* y (- x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = (y - z) * t;
	double tmp;
	if (x <= -1.6e+21) {
		tmp = t_1;
	} else if (x <= -4.5e-103) {
		tmp = t_2;
	} else if (x <= -4.8e-149) {
		tmp = t_1;
	} else if (x <= 3.8e+36) {
		tmp = t_2;
	} else if ((x <= 4.1e+148) || !(x <= 5.1e+156)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    t_2 = (y - z) * t
    if (x <= (-1.6d+21)) then
        tmp = t_1
    else if (x <= (-4.5d-103)) then
        tmp = t_2
    else if (x <= (-4.8d-149)) then
        tmp = t_1
    else if (x <= 3.8d+36) then
        tmp = t_2
    else if ((x <= 4.1d+148) .or. (.not. (x <= 5.1d+156))) then
        tmp = t_1
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = (y - z) * t;
	double tmp;
	if (x <= -1.6e+21) {
		tmp = t_1;
	} else if (x <= -4.5e-103) {
		tmp = t_2;
	} else if (x <= -4.8e-149) {
		tmp = t_1;
	} else if (x <= 3.8e+36) {
		tmp = t_2;
	} else if ((x <= 4.1e+148) || !(x <= 5.1e+156)) {
		tmp = t_1;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	t_2 = (y - z) * t
	tmp = 0
	if x <= -1.6e+21:
		tmp = t_1
	elif x <= -4.5e-103:
		tmp = t_2
	elif x <= -4.8e-149:
		tmp = t_1
	elif x <= 3.8e+36:
		tmp = t_2
	elif (x <= 4.1e+148) or not (x <= 5.1e+156):
		tmp = t_1
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (x <= -1.6e+21)
		tmp = t_1;
	elseif (x <= -4.5e-103)
		tmp = t_2;
	elseif (x <= -4.8e-149)
		tmp = t_1;
	elseif (x <= 3.8e+36)
		tmp = t_2;
	elseif ((x <= 4.1e+148) || !(x <= 5.1e+156))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	t_2 = (y - z) * t;
	tmp = 0.0;
	if (x <= -1.6e+21)
		tmp = t_1;
	elseif (x <= -4.5e-103)
		tmp = t_2;
	elseif (x <= -4.8e-149)
		tmp = t_1;
	elseif (x <= 3.8e+36)
		tmp = t_2;
	elseif ((x <= 4.1e+148) || ~((x <= 5.1e+156)))
		tmp = t_1;
	else
		tmp = y * -x;
	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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[x, -1.6e+21], t$95$1, If[LessEqual[x, -4.5e-103], t$95$2, If[LessEqual[x, -4.8e-149], t$95$1, If[LessEqual[x, 3.8e+36], t$95$2, If[Or[LessEqual[x, 4.1e+148], N[Not[LessEqual[x, 5.1e+156]], $MachinePrecision]], t$95$1, N[(y * (-x)), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6e21 or -4.5e-103 < x < -4.8000000000000002e-149 or 3.80000000000000025e36 < x < 4.0999999999999998e148 or 5.10000000000000014e156 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around -inf 88.8%

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

      1. mul-1-neg 88.8%

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

      2. distribute-rgt-neg-in 88.8%

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

      3. +-commutative 88.8%

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

   4. Simplified 88.8%

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

   5. Taylor expanded in y around 0 64.8%

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

   if -1.6e21 < x < -4.5e-103 or -4.8000000000000002e-149 < x < 3.80000000000000025e36

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 85.9%

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

   3. Taylor expanded in x around 0 85.9%

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

      1. *-commutative 85.9%

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

      2. fma-udef 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in t around inf 75.6%

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

   if 4.0999999999999998e148 < x < 5.10000000000000014e156

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-lft-out-- 100.0%

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

      5. *-rgt-identity 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. distribute-rgt-neg-in 78.3%

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

   7. Simplified 78.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-103}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-149}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+36}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+148} \lor \neg \left(x \leq 5.1 \cdot 10^{+156}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 5: 37.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{+98}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+54}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -6.6e+284)
     t_1
     (if (<= z -1.08e+98)
       (* z x)
       (if (<= z -5.8e-34)
         t_1
         (if (<= z 8.5e-27) x (if (<= z 1.65e+54) (* y t) (* z x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -6.6e+284) {
		tmp = t_1;
	} else if (z <= -1.08e+98) {
		tmp = z * x;
	} else if (z <= -5.8e-34) {
		tmp = t_1;
	} else if (z <= 8.5e-27) {
		tmp = x;
	} else if (z <= 1.65e+54) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-6.6d+284)) then
        tmp = t_1
    else if (z <= (-1.08d+98)) then
        tmp = z * x
    else if (z <= (-5.8d-34)) then
        tmp = t_1
    else if (z <= 8.5d-27) then
        tmp = x
    else if (z <= 1.65d+54) 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 t_1 = z * -t;
	double tmp;
	if (z <= -6.6e+284) {
		tmp = t_1;
	} else if (z <= -1.08e+98) {
		tmp = z * x;
	} else if (z <= -5.8e-34) {
		tmp = t_1;
	} else if (z <= 8.5e-27) {
		tmp = x;
	} else if (z <= 1.65e+54) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -6.6e+284:
		tmp = t_1
	elif z <= -1.08e+98:
		tmp = z * x
	elif z <= -5.8e-34:
		tmp = t_1
	elif z <= 8.5e-27:
		tmp = x
	elif z <= 1.65e+54:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -6.6e+284)
		tmp = t_1;
	elseif (z <= -1.08e+98)
		tmp = Float64(z * x);
	elseif (z <= -5.8e-34)
		tmp = t_1;
	elseif (z <= 8.5e-27)
		tmp = x;
	elseif (z <= 1.65e+54)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -6.6e+284)
		tmp = t_1;
	elseif (z <= -1.08e+98)
		tmp = z * x;
	elseif (z <= -5.8e-34)
		tmp = t_1;
	elseif (z <= 8.5e-27)
		tmp = x;
	elseif (z <= 1.65e+54)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -6.6e+284], t$95$1, If[LessEqual[z, -1.08e+98], N[(z * x), $MachinePrecision], If[LessEqual[z, -5.8e-34], t$95$1, If[LessEqual[z, 8.5e-27], x, If[LessEqual[z, 1.65e+54], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5999999999999995e284 or -1.07999999999999997e98 < z < -5.8000000000000004e-34

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 86.8%

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

   3. Taylor expanded in z around inf 64.0%

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

      1. associate-*r* 64.0%

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

      2. neg-mul-1 64.0%

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

   5. Simplified 64.0%

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

   if -6.5999999999999995e284 < z < -1.07999999999999997e98 or 1.65e54 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 65.5%

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

      1. *-commutative 65.5%

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

      2. mul-1-neg 65.5%

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

      3. unsub-neg 65.5%

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

      4. distribute-lft-out-- 65.5%

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

      5. *-rgt-identity 65.5%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in z around inf 55.1%

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

   if -5.8000000000000004e-34 < z < 8.50000000000000033e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 72.6%

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

   3. Taylor expanded in x around inf 45.2%

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

   if 8.50000000000000033e-27 < z < 1.65e54

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.5%

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

   3. Taylor expanded in y around inf 45.0%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+284}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{+98}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+54}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 6: 55.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* (- y z) t)))
   (if (<= z -8.5e+97)
     t_1
     (if (<= z -4.5e-34)
       t_2
       (if (<= z 2.6e-27) x (if (<= z 3.8e+64) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -8.5e+97) {
		tmp = t_1;
	} else if (z <= -4.5e-34) {
		tmp = t_2;
	} else if (z <= 2.6e-27) {
		tmp = x;
	} else if (z <= 3.8e+64) {
		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 = (y - z) * t
    if (z <= (-8.5d+97)) then
        tmp = t_1
    else if (z <= (-4.5d-34)) then
        tmp = t_2
    else if (z <= 2.6d-27) then
        tmp = x
    else if (z <= 3.8d+64) 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 = (y - z) * t;
	double tmp;
	if (z <= -8.5e+97) {
		tmp = t_1;
	} else if (z <= -4.5e-34) {
		tmp = t_2;
	} else if (z <= 2.6e-27) {
		tmp = x;
	} else if (z <= 3.8e+64) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = (y - z) * t
	tmp = 0
	if z <= -8.5e+97:
		tmp = t_1
	elif z <= -4.5e-34:
		tmp = t_2
	elif z <= 2.6e-27:
		tmp = x
	elif z <= 3.8e+64:
		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(Float64(y - z) * t)
	tmp = 0.0
	if (z <= -8.5e+97)
		tmp = t_1;
	elseif (z <= -4.5e-34)
		tmp = t_2;
	elseif (z <= 2.6e-27)
		tmp = x;
	elseif (z <= 3.8e+64)
		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 = (y - z) * t;
	tmp = 0.0;
	if (z <= -8.5e+97)
		tmp = t_1;
	elseif (z <= -4.5e-34)
		tmp = t_2;
	elseif (z <= 2.6e-27)
		tmp = x;
	elseif (z <= 3.8e+64)
		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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -8.5e+97], t$95$1, If[LessEqual[z, -4.5e-34], t$95$2, If[LessEqual[z, 2.6e-27], x, If[LessEqual[z, 3.8e+64], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999993e97 or 3.8000000000000001e64 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.5%

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

      1. +-commutative 84.5%

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

      2. mul-1-neg 84.5%

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

      3. unsub-neg 84.5%

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

      4. *-commutative 84.5%

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

   4. Simplified 84.5%

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

   5. Taylor expanded in z around inf 84.5%

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

   if -8.4999999999999993e97 < z < -4.50000000000000042e-34 or 2.60000000000000017e-27 < z < 3.8000000000000001e64

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 81.2%

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

   3. Taylor expanded in x around 0 81.2%

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

      1. *-commutative 81.2%

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

      2. fma-udef 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in t around inf 76.7%

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

   if -4.50000000000000042e-34 < z < 2.60000000000000017e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 72.6%

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

   3. Taylor expanded in x around inf 45.2%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-34}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+64}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 7: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* (- y z) t)))
   (if (<= z -8.5e+97)
     t_1
     (if (<= z -1e-33)
       t_2
       (if (<= z 2e-23) (* x (- 1.0 y)) (if (<= z 8.2e+69) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -8.5e+97) {
		tmp = t_1;
	} else if (z <= -1e-33) {
		tmp = t_2;
	} else if (z <= 2e-23) {
		tmp = x * (1.0 - y);
	} else if (z <= 8.2e+69) {
		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 = (y - z) * t
    if (z <= (-8.5d+97)) then
        tmp = t_1
    else if (z <= (-1d-33)) then
        tmp = t_2
    else if (z <= 2d-23) then
        tmp = x * (1.0d0 - y)
    else if (z <= 8.2d+69) 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 = (y - z) * t;
	double tmp;
	if (z <= -8.5e+97) {
		tmp = t_1;
	} else if (z <= -1e-33) {
		tmp = t_2;
	} else if (z <= 2e-23) {
		tmp = x * (1.0 - y);
	} else if (z <= 8.2e+69) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = (y - z) * t
	tmp = 0
	if z <= -8.5e+97:
		tmp = t_1
	elif z <= -1e-33:
		tmp = t_2
	elif z <= 2e-23:
		tmp = x * (1.0 - y)
	elif z <= 8.2e+69:
		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(Float64(y - z) * t)
	tmp = 0.0
	if (z <= -8.5e+97)
		tmp = t_1;
	elseif (z <= -1e-33)
		tmp = t_2;
	elseif (z <= 2e-23)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 8.2e+69)
		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 = (y - z) * t;
	tmp = 0.0;
	if (z <= -8.5e+97)
		tmp = t_1;
	elseif (z <= -1e-33)
		tmp = t_2;
	elseif (z <= 2e-23)
		tmp = x * (1.0 - y);
	elseif (z <= 8.2e+69)
		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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -8.5e+97], t$95$1, If[LessEqual[z, -1e-33], t$95$2, If[LessEqual[z, 2e-23], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+69], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999993e97 or 8.1999999999999998e69 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.5%

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

      1. +-commutative 84.5%

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

      2. mul-1-neg 84.5%

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

      3. unsub-neg 84.5%

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

      4. *-commutative 84.5%

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

   4. Simplified 84.5%

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

   5. Taylor expanded in z around inf 84.5%

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

   if -8.4999999999999993e97 < z < -1.0000000000000001e-33 or 1.99999999999999992e-23 < z < 8.1999999999999998e69

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 82.9%

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

   3. Taylor expanded in x around 0 82.9%

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

      1. *-commutative 82.9%

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

      2. fma-udef 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in t around inf 78.2%

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

   if -1.0000000000000001e-33 < z < 1.99999999999999992e-23

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. distribute-lft-out-- 71.9%

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

      5. *-rgt-identity 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in x around 0 71.9%

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

   6. Taylor expanded in z around 0 71.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-33}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+69}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 8: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-25}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* (- y z) t)))
   (if (<= z -8.5e+97)
     t_1
     (if (<= z -3e-34)
       t_2
       (if (<= z 6e-25) (- x (* y x)) (if (<= z 4.8e+69) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -8.5e+97) {
		tmp = t_1;
	} else if (z <= -3e-34) {
		tmp = t_2;
	} else if (z <= 6e-25) {
		tmp = x - (y * x);
	} else if (z <= 4.8e+69) {
		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 = (y - z) * t
    if (z <= (-8.5d+97)) then
        tmp = t_1
    else if (z <= (-3d-34)) then
        tmp = t_2
    else if (z <= 6d-25) then
        tmp = x - (y * x)
    else if (z <= 4.8d+69) 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 = (y - z) * t;
	double tmp;
	if (z <= -8.5e+97) {
		tmp = t_1;
	} else if (z <= -3e-34) {
		tmp = t_2;
	} else if (z <= 6e-25) {
		tmp = x - (y * x);
	} else if (z <= 4.8e+69) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = (y - z) * t
	tmp = 0
	if z <= -8.5e+97:
		tmp = t_1
	elif z <= -3e-34:
		tmp = t_2
	elif z <= 6e-25:
		tmp = x - (y * x)
	elif z <= 4.8e+69:
		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(Float64(y - z) * t)
	tmp = 0.0
	if (z <= -8.5e+97)
		tmp = t_1;
	elseif (z <= -3e-34)
		tmp = t_2;
	elseif (z <= 6e-25)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 4.8e+69)
		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 = (y - z) * t;
	tmp = 0.0;
	if (z <= -8.5e+97)
		tmp = t_1;
	elseif (z <= -3e-34)
		tmp = t_2;
	elseif (z <= 6e-25)
		tmp = x - (y * x);
	elseif (z <= 4.8e+69)
		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[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -8.5e+97], t$95$1, If[LessEqual[z, -3e-34], t$95$2, If[LessEqual[z, 6e-25], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+69], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999993e97 or 4.8000000000000003e69 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.5%

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

      1. +-commutative 84.5%

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

      2. mul-1-neg 84.5%

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

      3. unsub-neg 84.5%

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

      4. *-commutative 84.5%

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

   4. Simplified 84.5%

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

   5. Taylor expanded in z around inf 84.5%

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

   if -8.4999999999999993e97 < z < -3e-34 or 5.9999999999999995e-25 < z < 4.8000000000000003e69

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 82.9%

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

   3. Taylor expanded in x around 0 82.9%

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

      1. *-commutative 82.9%

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

      2. fma-udef 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in t around inf 78.2%

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

   if -3e-34 < z < 5.9999999999999995e-25

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 71.9%

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

      1. *-commutative 71.9%

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

      2. mul-1-neg 71.9%

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

      3. unsub-neg 71.9%

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

      4. distribute-lft-out-- 71.9%

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

      5. *-rgt-identity 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in y around inf 71.9%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-34}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-25}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+69}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 9: 36.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -57000000000:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+55}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e+103)
   (* z x)
   (if (<= z -57000000000.0)
     (* y t)
     (if (<= z 5.2e-27) x (if (<= z 4e+55) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+103) {
		tmp = z * x;
	} else if (z <= -57000000000.0) {
		tmp = y * t;
	} else if (z <= 5.2e-27) {
		tmp = x;
	} else if (z <= 4e+55) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.3d+103)) then
        tmp = z * x
    else if (z <= (-57000000000.0d0)) then
        tmp = y * t
    else if (z <= 5.2d-27) then
        tmp = x
    else if (z <= 4d+55) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e+103) {
		tmp = z * x;
	} else if (z <= -57000000000.0) {
		tmp = y * t;
	} else if (z <= 5.2e-27) {
		tmp = x;
	} else if (z <= 4e+55) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.3e+103:
		tmp = z * x
	elif z <= -57000000000.0:
		tmp = y * t
	elif z <= 5.2e-27:
		tmp = x
	elif z <= 4e+55:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e+103)
		tmp = Float64(z * x);
	elseif (z <= -57000000000.0)
		tmp = Float64(y * t);
	elseif (z <= 5.2e-27)
		tmp = x;
	elseif (z <= 4e+55)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.3e+103)
		tmp = z * x;
	elseif (z <= -57000000000.0)
		tmp = y * t;
	elseif (z <= 5.2e-27)
		tmp = x;
	elseif (z <= 4e+55)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e+103], N[(z * x), $MachinePrecision], If[LessEqual[z, -57000000000.0], N[(y * t), $MachinePrecision], If[LessEqual[z, 5.2e-27], x, If[LessEqual[z, 4e+55], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.30000000000000008e103 or 4.00000000000000004e55 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 60.8%

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

      1. *-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. distribute-lft-out-- 60.8%

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

      5. *-rgt-identity 60.8%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in z around inf 51.7%

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

   if -2.30000000000000008e103 < z < -5.7e10 or 5.20000000000000034e-27 < z < 4.00000000000000004e55

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 78.3%

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

   3. Taylor expanded in y around inf 41.7%

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

   if -5.7e10 < z < 5.20000000000000034e-27

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 73.4%

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

   3. Taylor expanded in x around inf 42.7%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+103}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -57000000000:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+55}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 10: 81.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6700000000000 \lor \neg \left(x \leq 2.35 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6700000000000.0) (not (<= x 2.35e+55)))
   (* x (- (+ z 1.0) y))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6700000000000.0) || !(x <= 2.35e+55)) {
		tmp = x * ((z + 1.0) - y);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-6700000000000.0d0)) .or. (.not. (x <= 2.35d+55))) then
        tmp = x * ((z + 1.0d0) - y)
    else
        tmp = x + ((y - z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6700000000000.0) || !(x <= 2.35e+55)) {
		tmp = x * ((z + 1.0) - y);
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6700000000000.0) or not (x <= 2.35e+55):
		tmp = x * ((z + 1.0) - y)
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6700000000000.0) || !(x <= 2.35e+55))
		tmp = Float64(x * Float64(Float64(z + 1.0) - y));
	else
		tmp = Float64(x + Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6700000000000.0) || ~((x <= 2.35e+55)))
		tmp = x * ((z + 1.0) - y);
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6700000000000.0], N[Not[LessEqual[x, 2.35e+55]], $MachinePrecision]], N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.7e12 or 2.35e55 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 90.0%

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

      1. *-commutative 90.0%

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

      2. mul-1-neg 90.0%

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

      3. unsub-neg 90.0%

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

      4. distribute-lft-out-- 90.0%

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

      5. *-rgt-identity 90.0%

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

   4. Simplified 90.0%

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

   5. Taylor expanded in x around 0 90.0%

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

   if -6.7e12 < x < 2.35e55

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 87.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6700000000000 \lor \neg \left(x \leq 2.35 \cdot 10^{+55}\right):\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 11: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -185000000000:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+60}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -185000000000.0)
   (* x (- (+ z 1.0) y))
   (if (<= x 1.45e+60) (+ x (* (- y z) t)) (+ x (* x (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -185000000000.0) {
		tmp = x * ((z + 1.0) - y);
	} else if (x <= 1.45e+60) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-185000000000.0d0)) then
        tmp = x * ((z + 1.0d0) - y)
    else if (x <= 1.45d+60) then
        tmp = x + ((y - z) * t)
    else
        tmp = x + (x * (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -185000000000.0) {
		tmp = x * ((z + 1.0) - y);
	} else if (x <= 1.45e+60) {
		tmp = x + ((y - z) * t);
	} else {
		tmp = x + (x * (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -185000000000.0:
		tmp = x * ((z + 1.0) - y)
	elif x <= 1.45e+60:
		tmp = x + ((y - z) * t)
	else:
		tmp = x + (x * (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -185000000000.0)
		tmp = Float64(x * Float64(Float64(z + 1.0) - y));
	elseif (x <= 1.45e+60)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	else
		tmp = Float64(x + Float64(x * Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -185000000000.0)
		tmp = x * ((z + 1.0) - y);
	elseif (x <= 1.45e+60)
		tmp = x + ((y - z) * t);
	else
		tmp = x + (x * (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -185000000000.0], N[(x * N[(N[(z + 1.0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.45e+60], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.85e11

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 90.1%

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

      1. *-commutative 90.1%

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

      2. mul-1-neg 90.1%

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

      3. unsub-neg 90.1%

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

      4. distribute-lft-out-- 90.1%

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

      5. *-rgt-identity 90.1%

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

   4. Simplified 90.1%

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

   5. Taylor expanded in x around 0 90.1%

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

   if -1.85e11 < x < 1.45e60

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 87.3%

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

   if 1.45e60 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 89.9%

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

      1. *-commutative 89.9%

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

      2. mul-1-neg 89.9%

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

      3. unsub-neg 89.9%

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

      4. distribute-lft-out-- 90.0%

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

      5. *-rgt-identity 90.0%

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

   4. Simplified 90.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -185000000000:\\ \;\;\;\;x \cdot \left(\left(z + 1\right) - y\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+60}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z - y\right)\\ \end{array} \]

Alternative 12: 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. Final simplification 100.0%

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

Alternative 13: 37.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+23}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.5e+23) (* y t) (if (<= y 9e-6) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.5e+23) {
		tmp = y * t;
	} else if (y <= 9e-6) {
		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 <= (-4.5d+23)) then
        tmp = y * t
    else if (y <= 9d-6) 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 <= -4.5e+23) {
		tmp = y * t;
	} else if (y <= 9e-6) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.5e+23:
		tmp = y * t
	elif y <= 9e-6:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.5e+23)
		tmp = Float64(y * t);
	elseif (y <= 9e-6)
		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 <= -4.5e+23)
		tmp = y * t;
	elseif (y <= 9e-6)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.5e+23], N[(y * t), $MachinePrecision], If[LessEqual[y, 9e-6], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.49999999999999979e23 or 9.00000000000000023e-6 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 50.8%

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

   3. Taylor expanded in y around inf 38.6%

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

   if -4.49999999999999979e23 < y < 9.00000000000000023e-6

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 76.9%

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

   3. Taylor expanded in x around inf 40.2%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+23}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 14: 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. Taylor expanded in t around inf 64.4%

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

3. Taylor expanded in x around inf 22.3%

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

4. Final simplification 22.3%

   \[\leadsto x \]

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 2023196 
(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))))