Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.1s

Alternatives: 12

Speedup: 1.0×

• 34.9% 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: 60.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot x\\ t_2 := x \cdot \left(z + 1\right)\\ t_3 := \left(y - z\right) \cdot t\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+116}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+99}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+158}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* y x))) (t_2 (* x (+ z 1.0))) (t_3 (* (- y z) t)))
   (if (<= x -3.8e+137)
     t_1
     (if (<= x -8e+116)
       t_3
       (if (<= x -3.6e-16)
         t_1
         (if (<= x 3.6e-94)
           t_3
           (if (<= x 1.15e+42)
             t_2
             (if (<= x 8e+99) t_3 (if (<= x 9.5e+158) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y * x);
	double t_2 = x * (z + 1.0);
	double t_3 = (y - z) * t;
	double tmp;
	if (x <= -3.8e+137) {
		tmp = t_1;
	} else if (x <= -8e+116) {
		tmp = t_3;
	} else if (x <= -3.6e-16) {
		tmp = t_1;
	} else if (x <= 3.6e-94) {
		tmp = t_3;
	} else if (x <= 1.15e+42) {
		tmp = t_2;
	} else if (x <= 8e+99) {
		tmp = t_3;
	} else if (x <= 9.5e+158) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x - (y * x)
    t_2 = x * (z + 1.0d0)
    t_3 = (y - z) * t
    if (x <= (-3.8d+137)) then
        tmp = t_1
    else if (x <= (-8d+116)) then
        tmp = t_3
    else if (x <= (-3.6d-16)) then
        tmp = t_1
    else if (x <= 3.6d-94) then
        tmp = t_3
    else if (x <= 1.15d+42) then
        tmp = t_2
    else if (x <= 8d+99) then
        tmp = t_3
    else if (x <= 9.5d+158) 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 = x - (y * x);
	double t_2 = x * (z + 1.0);
	double t_3 = (y - z) * t;
	double tmp;
	if (x <= -3.8e+137) {
		tmp = t_1;
	} else if (x <= -8e+116) {
		tmp = t_3;
	} else if (x <= -3.6e-16) {
		tmp = t_1;
	} else if (x <= 3.6e-94) {
		tmp = t_3;
	} else if (x <= 1.15e+42) {
		tmp = t_2;
	} else if (x <= 8e+99) {
		tmp = t_3;
	} else if (x <= 9.5e+158) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y * x)
	t_2 = x * (z + 1.0)
	t_3 = (y - z) * t
	tmp = 0
	if x <= -3.8e+137:
		tmp = t_1
	elif x <= -8e+116:
		tmp = t_3
	elif x <= -3.6e-16:
		tmp = t_1
	elif x <= 3.6e-94:
		tmp = t_3
	elif x <= 1.15e+42:
		tmp = t_2
	elif x <= 8e+99:
		tmp = t_3
	elif x <= 9.5e+158:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y * x))
	t_2 = Float64(x * Float64(z + 1.0))
	t_3 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (x <= -3.8e+137)
		tmp = t_1;
	elseif (x <= -8e+116)
		tmp = t_3;
	elseif (x <= -3.6e-16)
		tmp = t_1;
	elseif (x <= 3.6e-94)
		tmp = t_3;
	elseif (x <= 1.15e+42)
		tmp = t_2;
	elseif (x <= 8e+99)
		tmp = t_3;
	elseif (x <= 9.5e+158)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y * x);
	t_2 = x * (z + 1.0);
	t_3 = (y - z) * t;
	tmp = 0.0;
	if (x <= -3.8e+137)
		tmp = t_1;
	elseif (x <= -8e+116)
		tmp = t_3;
	elseif (x <= -3.6e-16)
		tmp = t_1;
	elseif (x <= 3.6e-94)
		tmp = t_3;
	elseif (x <= 1.15e+42)
		tmp = t_2;
	elseif (x <= 8e+99)
		tmp = t_3;
	elseif (x <= 9.5e+158)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[x, -3.8e+137], t$95$1, If[LessEqual[x, -8e+116], t$95$3, If[LessEqual[x, -3.6e-16], t$95$1, If[LessEqual[x, 3.6e-94], t$95$3, If[LessEqual[x, 1.15e+42], t$95$2, If[LessEqual[x, 8e+99], t$95$3, If[LessEqual[x, 9.5e+158], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.79999999999999963e137 or -8.00000000000000012e116 < x < -3.59999999999999983e-16 or 9.49999999999999913e158 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 71.6%

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

   3. Taylor expanded in t around 0 66.8%

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

      1. mul-1-neg 66.8%

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

      2. unsub-neg 66.8%

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

      3. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   if -3.79999999999999963e137 < x < -8.00000000000000012e116 or -3.59999999999999983e-16 < x < 3.6e-94 or 1.15e42 < x < 7.9999999999999997e99

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 88.3%

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

   3. Taylor expanded in y around 0 86.8%

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

   4. Taylor expanded in t around inf 82.2%

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

      1. neg-mul-1 82.2%

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

      2. +-commutative 82.2%

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

      3. unsub-neg 82.2%

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

   6. Simplified 82.2%

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

   if 3.6e-94 < x < 1.15e42 or 7.9999999999999997e99 < x < 9.49999999999999913e158

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. *-commutative 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in x around -inf 65.4%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+137}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+116}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-94}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+99}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \]

Alternative 3: 38.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{-8}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-51}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-303}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -7e-8)
     (* y t)
     (if (<= y -4e-51)
       (* z x)
       (if (<= y -6.2e-86)
         t_1
         (if (<= y 1.22e-303) x (if (<= y 1.5e-50) t_1 (* y t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -7e-8) {
		tmp = y * t;
	} else if (y <= -4e-51) {
		tmp = z * x;
	} else if (y <= -6.2e-86) {
		tmp = t_1;
	} else if (y <= 1.22e-303) {
		tmp = x;
	} else if (y <= 1.5e-50) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (y <= (-7d-8)) then
        tmp = y * t
    else if (y <= (-4d-51)) then
        tmp = z * x
    else if (y <= (-6.2d-86)) then
        tmp = t_1
    else if (y <= 1.22d-303) then
        tmp = x
    else if (y <= 1.5d-50) then
        tmp = t_1
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -7e-8) {
		tmp = y * t;
	} else if (y <= -4e-51) {
		tmp = z * x;
	} else if (y <= -6.2e-86) {
		tmp = t_1;
	} else if (y <= 1.22e-303) {
		tmp = x;
	} else if (y <= 1.5e-50) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -7e-8:
		tmp = y * t
	elif y <= -4e-51:
		tmp = z * x
	elif y <= -6.2e-86:
		tmp = t_1
	elif y <= 1.22e-303:
		tmp = x
	elif y <= 1.5e-50:
		tmp = t_1
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -7e-8)
		tmp = Float64(y * t);
	elseif (y <= -4e-51)
		tmp = Float64(z * x);
	elseif (y <= -6.2e-86)
		tmp = t_1;
	elseif (y <= 1.22e-303)
		tmp = x;
	elseif (y <= 1.5e-50)
		tmp = t_1;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (y <= -7e-8)
		tmp = y * t;
	elseif (y <= -4e-51)
		tmp = z * x;
	elseif (y <= -6.2e-86)
		tmp = t_1;
	elseif (y <= 1.22e-303)
		tmp = x;
	elseif (y <= 1.5e-50)
		tmp = t_1;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -7e-8], N[(y * t), $MachinePrecision], If[LessEqual[y, -4e-51], N[(z * x), $MachinePrecision], If[LessEqual[y, -6.2e-86], t$95$1, If[LessEqual[y, 1.22e-303], x, If[LessEqual[y, 1.5e-50], t$95$1, N[(y * t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.00000000000000048e-8 or 1.49999999999999995e-50 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 60.7%

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

   3. Taylor expanded in z around 0 45.9%

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

   4. Taylor expanded in y around inf 43.7%

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

   if -7.00000000000000048e-8 < y < -4e-51

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.7%

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

      1. +-commutative 98.7%

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

      2. mul-1-neg 98.7%

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

      3. unsub-neg 98.7%

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

      4. *-commutative 98.7%

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

   4. Simplified 98.7%

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

   5. Taylor expanded in x around -inf 78.1%

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

   6. Taylor expanded in z around inf 58.1%

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

   if -4e-51 < y < -6.19999999999999977e-86 or 1.2200000000000001e-303 < y < 1.49999999999999995e-50

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 75.4%

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

   3. Taylor expanded in y around 0 75.4%

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

   4. Taylor expanded in z around inf 52.8%

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

      1. associate-*r* 52.8%

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

      2. neg-mul-1 52.8%

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

   6. Simplified 52.8%

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

   if -6.19999999999999977e-86 < y < 1.2200000000000001e-303

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.6%

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

   3. Taylor expanded in x around inf 49.0%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-8}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-51}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-86}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-303}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 4: 37.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-9}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-61}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-84}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-194}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-77}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e-9)
   (* y t)
   (if (<= y -1.42e-61)
     (* z x)
     (if (<= y -8e-84)
       (* y t)
       (if (<= y 1.55e-194) x (if (<= y 6.5e-77) (* z x) (* y t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e-9) {
		tmp = y * t;
	} else if (y <= -1.42e-61) {
		tmp = z * x;
	} else if (y <= -8e-84) {
		tmp = y * t;
	} else if (y <= 1.55e-194) {
		tmp = x;
	} else if (y <= 6.5e-77) {
		tmp = z * 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 <= (-1.15d-9)) then
        tmp = y * t
    else if (y <= (-1.42d-61)) then
        tmp = z * x
    else if (y <= (-8d-84)) then
        tmp = y * t
    else if (y <= 1.55d-194) then
        tmp = x
    else if (y <= 6.5d-77) then
        tmp = z * 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 <= -1.15e-9) {
		tmp = y * t;
	} else if (y <= -1.42e-61) {
		tmp = z * x;
	} else if (y <= -8e-84) {
		tmp = y * t;
	} else if (y <= 1.55e-194) {
		tmp = x;
	} else if (y <= 6.5e-77) {
		tmp = z * x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e-9:
		tmp = y * t
	elif y <= -1.42e-61:
		tmp = z * x
	elif y <= -8e-84:
		tmp = y * t
	elif y <= 1.55e-194:
		tmp = x
	elif y <= 6.5e-77:
		tmp = z * x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e-9)
		tmp = Float64(y * t);
	elseif (y <= -1.42e-61)
		tmp = Float64(z * x);
	elseif (y <= -8e-84)
		tmp = Float64(y * t);
	elseif (y <= 1.55e-194)
		tmp = x;
	elseif (y <= 6.5e-77)
		tmp = Float64(z * x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e-9)
		tmp = y * t;
	elseif (y <= -1.42e-61)
		tmp = z * x;
	elseif (y <= -8e-84)
		tmp = y * t;
	elseif (y <= 1.55e-194)
		tmp = x;
	elseif (y <= 6.5e-77)
		tmp = z * x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e-9], N[(y * t), $MachinePrecision], If[LessEqual[y, -1.42e-61], N[(z * x), $MachinePrecision], If[LessEqual[y, -8e-84], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.55e-194], x, If[LessEqual[y, 6.5e-77], N[(z * x), $MachinePrecision], N[(y * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15e-9 or -1.42e-61 < y < -8.0000000000000003e-84 or 6.4999999999999999e-77 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 62.1%

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

   3. Taylor expanded in z around 0 45.1%

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

   4. Taylor expanded in y around inf 43.1%

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

   if -1.15e-9 < y < -1.42e-61 or 1.55000000000000005e-194 < y < 6.4999999999999999e-77

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.1%

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

      1. +-commutative 96.1%

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

      2. mul-1-neg 96.1%

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

      3. unsub-neg 96.1%

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

      4. *-commutative 96.1%

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

   4. Simplified 96.1%

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

   5. Taylor expanded in x around -inf 52.5%

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

   6. Taylor expanded in z around inf 42.1%

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

   if -8.0000000000000003e-84 < y < 1.55000000000000005e-194

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.4%

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

   3. Taylor expanded in x around inf 42.5%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-9}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-61}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-84}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-194}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-77}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 5: 71.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot x\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+99}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* y x))))
   (if (<= x -1.9e+138)
     t_1
     (if (<= x 2.4e+99)
       (+ x (* (- y z) t))
       (if (<= x 1.52e+158) (* x (+ z 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y * x);
	double tmp;
	if (x <= -1.9e+138) {
		tmp = t_1;
	} else if (x <= 2.4e+99) {
		tmp = x + ((y - z) * t);
	} else if (x <= 1.52e+158) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * x)
    if (x <= (-1.9d+138)) then
        tmp = t_1
    else if (x <= 2.4d+99) then
        tmp = x + ((y - z) * t)
    else if (x <= 1.52d+158) then
        tmp = x * (z + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y * x);
	double tmp;
	if (x <= -1.9e+138) {
		tmp = t_1;
	} else if (x <= 2.4e+99) {
		tmp = x + ((y - z) * t);
	} else if (x <= 1.52e+158) {
		tmp = x * (z + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y * x)
	tmp = 0
	if x <= -1.9e+138:
		tmp = t_1
	elif x <= 2.4e+99:
		tmp = x + ((y - z) * t)
	elif x <= 1.52e+158:
		tmp = x * (z + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y * x))
	tmp = 0.0
	if (x <= -1.9e+138)
		tmp = t_1;
	elseif (x <= 2.4e+99)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	elseif (x <= 1.52e+158)
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y * x);
	tmp = 0.0;
	if (x <= -1.9e+138)
		tmp = t_1;
	elseif (x <= 2.4e+99)
		tmp = x + ((y - z) * t);
	elseif (x <= 1.52e+158)
		tmp = x * (z + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e+138], t$95$1, If[LessEqual[x, 2.4e+99], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.52e+158], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.90000000000000006e138 or 1.52e158 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 73.7%

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

   3. Taylor expanded in t around 0 72.1%

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

      1. mul-1-neg 72.1%

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

      2. unsub-neg 72.1%

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

      3. *-commutative 72.1%

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

   5. Simplified 72.1%

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

   if -1.90000000000000006e138 < x < 2.4000000000000001e99

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.1%

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

   if 2.4000000000000001e99 < x < 1.52e158

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.3%

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

      1. +-commutative 77.3%

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

      2. mul-1-neg 77.3%

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

      3. unsub-neg 77.3%

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

      4. *-commutative 77.3%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in x around -inf 65.6%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+138}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+99}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \]

Alternative 6: 73.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+206} \lor \neg \left(y \leq 4 \cdot 10^{-17}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e+206) (not (<= y 4e-17)))
   (+ x (* y (- t x)))
   (+ x (* (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e+206) || !(y <= 4e-17)) {
		tmp = x + (y * (t - x));
	} 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 ((y <= (-1.15d+206)) .or. (.not. (y <= 4d-17))) then
        tmp = x + (y * (t - x))
    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 ((y <= -1.15e+206) || !(y <= 4e-17)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + ((y - z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e+206) or not (y <= 4e-17):
		tmp = x + (y * (t - x))
	else:
		tmp = x + ((y - z) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e+206) || !(y <= 4e-17))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	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 ((y <= -1.15e+206) || ~((y <= 4e-17)))
		tmp = x + (y * (t - x));
	else
		tmp = x + ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.15e+206], N[Not[LessEqual[y, 4e-17]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000008e206 or 4.00000000000000029e-17 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 83.1%

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

   if -1.15000000000000008e206 < y < 4.00000000000000029e-17

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.5%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+206} \lor \neg \left(y \leq 4 \cdot 10^{-17}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \end{array} \]

Alternative 7: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -200 \lor \neg \left(z \leq 1.85 \cdot 10^{-13}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -200.0) (not (<= z 1.85e-13)))
   (- x (* z (- t x)))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -200.0) || !(z <= 1.85e-13)) {
		tmp = x - (z * (t - x));
	} 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 <= (-200.0d0)) .or. (.not. (z <= 1.85d-13))) then
        tmp = x - (z * (t - x))
    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 <= -200.0) || !(z <= 1.85e-13)) {
		tmp = x - (z * (t - x));
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -200.0) or not (z <= 1.85e-13):
		tmp = x - (z * (t - x))
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -200.0) || !(z <= 1.85e-13))
		tmp = Float64(x - Float64(z * Float64(t - x)));
	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 <= -200.0) || ~((z <= 1.85e-13)))
		tmp = x - (z * (t - x));
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -200.0], N[Not[LessEqual[z, 1.85e-13]], $MachinePrecision]], N[(x - N[(z * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -200 or 1.84999999999999994e-13 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.1%

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

      1. +-commutative 81.1%

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

      2. mul-1-neg 81.1%

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

      3. unsub-neg 81.1%

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

      4. *-commutative 81.1%

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

   4. Simplified 81.1%

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

   if -200 < z < 1.84999999999999994e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 93.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -200 \lor \neg \left(z \leq 1.85 \cdot 10^{-13}\right):\\ \;\;\;\;x - z \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 8: 55.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-59} \lor \neg \left(t \leq 2.4 \cdot 10^{-125}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.5e-59) (not (<= t 2.4e-125))) (* (- y z) t) (* z x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.5e-59) || !(t <= 2.4e-125)) {
		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 ((t <= (-1.5d-59)) .or. (.not. (t <= 2.4d-125))) 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 ((t <= -1.5e-59) || !(t <= 2.4e-125)) {
		tmp = (y - z) * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.5e-59) or not (t <= 2.4e-125):
		tmp = (y - z) * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.5e-59) || !(t <= 2.4e-125))
		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 ((t <= -1.5e-59) || ~((t <= 2.4e-125)))
		tmp = (y - z) * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.5e-59], N[Not[LessEqual[t, 2.4e-125]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5e-59 or 2.4000000000000001e-125 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.9%

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

   3. Taylor expanded in y around 0 80.4%

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

   4. Taylor expanded in t around inf 72.3%

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

      1. neg-mul-1 72.3%

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

      2. +-commutative 72.3%

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

      3. unsub-neg 72.3%

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

   6. Simplified 72.3%

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

   if -1.5e-59 < t < 2.4000000000000001e-125

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 65.4%

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

      1. +-commutative 65.4%

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

      2. mul-1-neg 65.4%

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

      3. unsub-neg 65.4%

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

      4. *-commutative 65.4%

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

   4. Simplified 65.4%

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

   5. Taylor expanded in x around -inf 58.6%

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

   6. Taylor expanded in z around inf 38.0%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-59} \lor \neg \left(t \leq 2.4 \cdot 10^{-125}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 9: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-59} \lor \neg \left(t \leq 1.8 \cdot 10^{-124}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.8e-59) (not (<= t 1.8e-124))) (* (- y z) t) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e-59) || !(t <= 1.8e-124)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.8d-59)) .or. (.not. (t <= 1.8d-124))) then
        tmp = (y - z) * t
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.8e-59) || !(t <= 1.8e-124)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.8e-59) or not (t <= 1.8e-124):
		tmp = (y - z) * t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.8e-59) || !(t <= 1.8e-124))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.8e-59) || ~((t <= 1.8e-124)))
		tmp = (y - z) * t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.8e-59], N[Not[LessEqual[t, 1.8e-124]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.79999999999999981e-59 or 1.80000000000000005e-124 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 83.9%

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

   3. Taylor expanded in y around 0 80.4%

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

   4. Taylor expanded in t around inf 72.3%

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

      1. neg-mul-1 72.3%

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

      2. +-commutative 72.3%

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

      3. unsub-neg 72.3%

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

   6. Simplified 72.3%

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

   if -2.79999999999999981e-59 < t < 1.80000000000000005e-124

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 65.4%

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

      1. +-commutative 65.4%

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

      2. mul-1-neg 65.4%

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

      3. unsub-neg 65.4%

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

      4. *-commutative 65.4%

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

   4. Simplified 65.4%

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

   5. Taylor expanded in x around -inf 58.6%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-59} \lor \neg \left(t \leq 1.8 \cdot 10^{-124}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

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: 36.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-83}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.1e-83) (* y t) (if (<= y 2.4e-102) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e-83) {
		tmp = y * t;
	} else if (y <= 2.4e-102) {
		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 <= (-1.1d-83)) then
        tmp = y * t
    else if (y <= 2.4d-102) 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 <= -1.1e-83) {
		tmp = y * t;
	} else if (y <= 2.4e-102) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.1e-83:
		tmp = y * t
	elif y <= 2.4e-102:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.1e-83)
		tmp = Float64(y * t);
	elseif (y <= 2.4e-102)
		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 <= -1.1e-83)
		tmp = y * t;
	elseif (y <= 2.4e-102)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.1e-83], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.4e-102], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000004e-83 or 2.4e-102 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 61.5%

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

   3. Taylor expanded in z around 0 42.7%

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

   4. Taylor expanded in y around inf 39.7%

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

   if -1.10000000000000004e-83 < y < 2.4e-102

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.0%

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

   3. Taylor expanded in x around inf 36.6%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-83}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-102}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 12: 18.0% 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 67.6%

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

3. Taylor expanded in x around inf 16.8%

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

4. Final simplification 16.8%

   \[\leadsto x \]

Developer target: 96.7% 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 2023199 
(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))))