Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 10.1s

Alternatives: 15

Speedup: 1.0×

• 35.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 68.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ t_3 := x \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-146}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-193}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 1.82:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))) (t_3 (* x (- 1.0 y))))
   (if (<= z -1.95e-22)
     t_2
     (if (<= z -1.2e-146)
       t_3
       (if (<= z -5.2e-260)
         t_1
         (if (<= z 1.75e-193) t_3 (if (<= z 1.82) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (z <= -1.95e-22) {
		tmp = t_2;
	} else if (z <= -1.2e-146) {
		tmp = t_3;
	} else if (z <= -5.2e-260) {
		tmp = t_1;
	} else if (z <= 1.75e-193) {
		tmp = t_3;
	} else if (z <= 1.82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (t - x)
    t_2 = z * (x - t)
    t_3 = x * (1.0d0 - y)
    if (z <= (-1.95d-22)) then
        tmp = t_2
    else if (z <= (-1.2d-146)) then
        tmp = t_3
    else if (z <= (-5.2d-260)) then
        tmp = t_1
    else if (z <= 1.75d-193) then
        tmp = t_3
    else if (z <= 1.82d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double t_3 = x * (1.0 - y);
	double tmp;
	if (z <= -1.95e-22) {
		tmp = t_2;
	} else if (z <= -1.2e-146) {
		tmp = t_3;
	} else if (z <= -5.2e-260) {
		tmp = t_1;
	} else if (z <= 1.75e-193) {
		tmp = t_3;
	} else if (z <= 1.82) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = z * (x - t)
	t_3 = x * (1.0 - y)
	tmp = 0
	if z <= -1.95e-22:
		tmp = t_2
	elif z <= -1.2e-146:
		tmp = t_3
	elif z <= -5.2e-260:
		tmp = t_1
	elif z <= 1.75e-193:
		tmp = t_3
	elif z <= 1.82:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(x - t))
	t_3 = Float64(x * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -1.95e-22)
		tmp = t_2;
	elseif (z <= -1.2e-146)
		tmp = t_3;
	elseif (z <= -5.2e-260)
		tmp = t_1;
	elseif (z <= 1.75e-193)
		tmp = t_3;
	elseif (z <= 1.82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = z * (x - t);
	t_3 = x * (1.0 - y);
	tmp = 0.0;
	if (z <= -1.95e-22)
		tmp = t_2;
	elseif (z <= -1.2e-146)
		tmp = t_3;
	elseif (z <= -5.2e-260)
		tmp = t_1;
	elseif (z <= 1.75e-193)
		tmp = t_3;
	elseif (z <= 1.82)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e-22], t$95$2, If[LessEqual[z, -1.2e-146], t$95$3, If[LessEqual[z, -5.2e-260], t$95$1, If[LessEqual[z, 1.75e-193], t$95$3, If[LessEqual[z, 1.82], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.94999999999999999e-22 or 1.82000000000000006 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 96.1%

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

      1. fma-define 98.4%

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

      2. +-commutative 98.4%

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

      3. mul-1-neg 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in z around inf 79.3%

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

      1. mul-1-neg 79.3%

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

      2. sub-neg 79.3%

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

   8. Simplified 79.3%

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

   if -1.94999999999999999e-22 < z < -1.2000000000000001e-146 or -5.19999999999999987e-260 < z < 1.75000000000000002e-193

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. unsub-neg 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in z around 0 79.7%

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

   if -1.2000000000000001e-146 < z < -5.19999999999999987e-260 or 1.75000000000000002e-193 < z < 1.82000000000000006

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 96.7%

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

      1. fma-define 98.3%

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

      2. +-commutative 98.3%

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

      3. mul-1-neg 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in y around inf 73.9%

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

      1. neg-mul-1 73.9%

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

      2. sub-neg 73.9%

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

   8. Simplified 73.9%

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

Alternative 3: 38.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-251}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+61}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -6.5e-23)
     t_1
     (if (<= z -6.2e-133)
       x
       (if (<= z -3.2e-251)
         (* y t)
         (if (<= z 1.4e-193) x (if (<= z 2.8e+61) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -6.5e-23) {
		tmp = t_1;
	} else if (z <= -6.2e-133) {
		tmp = x;
	} else if (z <= -3.2e-251) {
		tmp = y * t;
	} else if (z <= 1.4e-193) {
		tmp = x;
	} else if (z <= 2.8e+61) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (z <= (-6.5d-23)) then
        tmp = t_1
    else if (z <= (-6.2d-133)) then
        tmp = x
    else if (z <= (-3.2d-251)) then
        tmp = y * t
    else if (z <= 1.4d-193) then
        tmp = x
    else if (z <= 2.8d+61) then
        tmp = y * t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -6.5e-23) {
		tmp = t_1;
	} else if (z <= -6.2e-133) {
		tmp = x;
	} else if (z <= -3.2e-251) {
		tmp = y * t;
	} else if (z <= 1.4e-193) {
		tmp = x;
	} else if (z <= 2.8e+61) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if z <= -6.5e-23:
		tmp = t_1
	elif z <= -6.2e-133:
		tmp = x
	elif z <= -3.2e-251:
		tmp = y * t
	elif z <= 1.4e-193:
		tmp = x
	elif z <= 2.8e+61:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -6.5e-23)
		tmp = t_1;
	elseif (z <= -6.2e-133)
		tmp = x;
	elseif (z <= -3.2e-251)
		tmp = Float64(y * t);
	elseif (z <= 1.4e-193)
		tmp = x;
	elseif (z <= 2.8e+61)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (z <= -6.5e-23)
		tmp = t_1;
	elseif (z <= -6.2e-133)
		tmp = x;
	elseif (z <= -3.2e-251)
		tmp = y * t;
	elseif (z <= 1.4e-193)
		tmp = x;
	elseif (z <= 2.8e+61)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -6.5e-23], t$95$1, If[LessEqual[z, -6.2e-133], x, If[LessEqual[z, -3.2e-251], N[(y * t), $MachinePrecision], If[LessEqual[z, 1.4e-193], x, If[LessEqual[z, 2.8e+61], N[(y * t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e-23 or 2.8000000000000001e61 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.8%

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

      1. fma-define 98.3%

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

      2. +-commutative 98.3%

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

      3. mul-1-neg 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in t around inf 56.3%

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

   7. Taylor expanded in y around 0 48.9%

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

      1. mul-1-neg 48.9%

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

      2. *-commutative 48.9%

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

      3. distribute-rgt-neg-in 48.9%

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

   9. Simplified 48.9%

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

   if -6.5e-23 < z < -6.20000000000000032e-133 or -3.19999999999999982e-251 < z < 1.4000000000000001e-193

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 95.7%

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

      1. *-commutative 95.7%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in y around 0 47.5%

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

   if -6.20000000000000032e-133 < z < -3.19999999999999982e-251 or 1.4000000000000001e-193 < z < 2.8000000000000001e61

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.0%

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

      1. fma-define 98.4%

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

      2. +-commutative 98.4%

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

      3. mul-1-neg 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in y around inf 70.2%

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

      1. neg-mul-1 70.2%

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

      2. sub-neg 70.2%

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

   8. Simplified 70.2%

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

   9. Taylor expanded in t around inf 48.4%

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

Alternative 4: 38.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+16}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-251}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+64}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.05e+16)
   (* z x)
   (if (<= z -3.15e-133)
     x
     (if (<= z -3.1e-251)
       (* y t)
       (if (<= z 2e-193) x (if (<= z 7.8e+64) (* y t) (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.05e+16) {
		tmp = z * x;
	} else if (z <= -3.15e-133) {
		tmp = x;
	} else if (z <= -3.1e-251) {
		tmp = y * t;
	} else if (z <= 2e-193) {
		tmp = x;
	} else if (z <= 7.8e+64) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.05d+16)) then
        tmp = z * x
    else if (z <= (-3.15d-133)) then
        tmp = x
    else if (z <= (-3.1d-251)) then
        tmp = y * t
    else if (z <= 2d-193) then
        tmp = x
    else if (z <= 7.8d+64) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.05e+16) {
		tmp = z * x;
	} else if (z <= -3.15e-133) {
		tmp = x;
	} else if (z <= -3.1e-251) {
		tmp = y * t;
	} else if (z <= 2e-193) {
		tmp = x;
	} else if (z <= 7.8e+64) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.05e+16:
		tmp = z * x
	elif z <= -3.15e-133:
		tmp = x
	elif z <= -3.1e-251:
		tmp = y * t
	elif z <= 2e-193:
		tmp = x
	elif z <= 7.8e+64:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.05e+16)
		tmp = Float64(z * x);
	elseif (z <= -3.15e-133)
		tmp = x;
	elseif (z <= -3.1e-251)
		tmp = Float64(y * t);
	elseif (z <= 2e-193)
		tmp = x;
	elseif (z <= 7.8e+64)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.05e+16)
		tmp = z * x;
	elseif (z <= -3.15e-133)
		tmp = x;
	elseif (z <= -3.1e-251)
		tmp = y * t;
	elseif (z <= 2e-193)
		tmp = x;
	elseif (z <= 7.8e+64)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.05e+16], N[(z * x), $MachinePrecision], If[LessEqual[z, -3.15e-133], x, If[LessEqual[z, -3.1e-251], N[(y * t), $MachinePrecision], If[LessEqual[z, 2e-193], x, If[LessEqual[z, 7.8e+64], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.05e16 or 7.7999999999999996e64 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 53.3%

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

      1. mul-1-neg 53.3%

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

      2. unsub-neg 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in z around inf 43.2%

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

   if -3.05e16 < z < -3.1500000000000001e-133 or -3.10000000000000003e-251 < z < 2.0000000000000001e-193

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.9%

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

      1. *-commutative 90.9%

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

   5. Simplified 90.9%

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

   6. Taylor expanded in y around 0 44.7%

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

   if -3.1500000000000001e-133 < z < -3.10000000000000003e-251 or 2.0000000000000001e-193 < z < 7.7999999999999996e64

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.0%

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

      1. fma-define 98.4%

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

      2. +-commutative 98.4%

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

      3. mul-1-neg 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in y around inf 70.2%

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

      1. neg-mul-1 70.2%

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

      2. sub-neg 70.2%

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

   8. Simplified 70.2%

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

   9. Taylor expanded in t around inf 48.4%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+16}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-251}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-193}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+64}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y - z \leq -7 \cdot 10^{-44} \lor \neg \left(y - z \leq 10^{-22}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (- y z) -7e-44) (not (<= (- y z) 1e-22))) (* (- y z) t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -7e-44) || !((y - z) <= 1e-22)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((y - z) <= (-7d-44)) .or. (.not. ((y - z) <= 1d-22))) then
        tmp = (y - z) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -7e-44) || !((y - z) <= 1e-22)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y - z) <= -7e-44) or not ((y - z) <= 1e-22):
		tmp = (y - z) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y - z) <= -7e-44) || !(Float64(y - z) <= 1e-22))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y - z) <= -7e-44) || ~(((y - z) <= 1e-22)))
		tmp = (y - z) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y - z), $MachinePrecision], -7e-44], N[Not[LessEqual[N[(y - z), $MachinePrecision], 1e-22]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -6.9999999999999995e-44 or 1e-22 < (-.f64 y z)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 96.6%

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

      1. fma-define 98.5%

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

      2. +-commutative 98.5%

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

      3. mul-1-neg 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in t around inf 54.3%

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

   if -6.9999999999999995e-44 < (-.f64 y z) < 1e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 92.1%

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

      1. *-commutative 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in y around 0 78.0%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -7 \cdot 10^{-44} \lor \neg \left(y - z \leq 10^{-22}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-22} \lor \neg \left(z \leq 0.0175\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.9e-22) (not (<= z 0.0175)))
   (+ x (* z (- x t)))
   (- x (* y (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e-22) || !(z <= 0.0175)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.9d-22)) .or. (.not. (z <= 0.0175d0))) then
        tmp = x + (z * (x - t))
    else
        tmp = x - (y * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.9e-22) || !(z <= 0.0175)) {
		tmp = x + (z * (x - t));
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.9e-22) or not (z <= 0.0175):
		tmp = x + (z * (x - t))
	else:
		tmp = x - (y * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.9e-22) || !(z <= 0.0175))
		tmp = Float64(x + Float64(z * Float64(x - t)));
	else
		tmp = Float64(x - Float64(y * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.9e-22) || ~((z <= 0.0175)))
		tmp = x + (z * (x - t));
	else
		tmp = x - (y * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.9e-22], N[Not[LessEqual[z, 0.0175]], $MachinePrecision]], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.90000000000000012e-22 or 0.017500000000000002 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

   5. Simplified 81.2%

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

   if -1.90000000000000012e-22 < z < 0.017500000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-22} \lor \neg \left(z \leq 0.0175\right):\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-22} \lor \neg \left(z \leq 1.95\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.95e-22) (not (<= z 1.95)))
   (* z (- x t))
   (- x (* y (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-22) || !(z <= 1.95)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.95d-22)) .or. (.not. (z <= 1.95d0))) then
        tmp = z * (x - t)
    else
        tmp = x - (y * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-22) || !(z <= 1.95)) {
		tmp = z * (x - t);
	} else {
		tmp = x - (y * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.95e-22) or not (z <= 1.95):
		tmp = z * (x - t)
	else:
		tmp = x - (y * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.95e-22) || !(z <= 1.95))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x - Float64(y * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.95e-22) || ~((z <= 1.95)))
		tmp = z * (x - t);
	else
		tmp = x - (y * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.95e-22], N[Not[LessEqual[z, 1.95]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999999e-22 or 1.94999999999999996 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 96.1%

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

      1. fma-define 98.4%

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

      2. +-commutative 98.4%

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

      3. mul-1-neg 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in z around inf 79.3%

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

      1. mul-1-neg 79.3%

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

      2. sub-neg 79.3%

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

   8. Simplified 79.3%

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

   if -1.94999999999999999e-22 < z < 1.94999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-22} \lor \neg \left(z \leq 1.95\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-19} \lor \neg \left(x \leq 6.4 \cdot 10^{-125}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.2e-19) (not (<= x 6.4e-125)))
   (* x (+ (- z y) 1.0))
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.2e-19) || !(x <= 6.4e-125)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (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 <= (-1.2d-19)) .or. (.not. (x <= 6.4d-125))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = (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 <= -1.2e-19) || !(x <= 6.4e-125)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.2e-19) or not (x <= 6.4e-125):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.2e-19) || !(x <= 6.4e-125))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.2e-19) || ~((x <= 6.4e-125)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.2e-19], N[Not[LessEqual[x, 6.4e-125]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.20000000000000011e-19 or 6.3999999999999997e-125 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.3%

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

      1. mul-1-neg 78.3%

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

      2. unsub-neg 78.3%

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

   5. Simplified 78.3%

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

   if -1.20000000000000011e-19 < x < 6.3999999999999997e-125

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.9%

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

      1. fma-define 99.9%

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

      2. +-commutative 99.9%

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

      3. mul-1-neg 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in t around inf 78.0%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-19} \lor \neg \left(x \leq 6.4 \cdot 10^{-125}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-22} \lor \neg \left(z \leq 3.5 \cdot 10^{-7}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.95e-22) (not (<= z 3.5e-7))) (* z (- x t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-22) || !(z <= 3.5e-7)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (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 ((z <= (-1.95d-22)) .or. (.not. (z <= 3.5d-7))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-22) || !(z <= 3.5e-7)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.95e-22) or not (z <= 3.5e-7):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.95e-22) || !(z <= 3.5e-7))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.95e-22) || ~((z <= 3.5e-7)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.95e-22], N[Not[LessEqual[z, 3.5e-7]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999999e-22 or 3.49999999999999984e-7 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.4%

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

      1. fma-define 98.4%

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

      2. +-commutative 98.4%

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

      3. mul-1-neg 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in z around inf 78.7%

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

      1. mul-1-neg 78.7%

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

      2. sub-neg 78.7%

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

   8. Simplified 78.7%

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

   if -1.94999999999999999e-22 < z < 3.49999999999999984e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 95.4%

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

      1. *-commutative 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in t around inf 68.7%

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

      1. *-commutative 68.7%

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

   8. Simplified 68.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-22} \lor \neg \left(z \leq 3.5 \cdot 10^{-7}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-44} \lor \neg \left(y \leq 3.7 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e-44) (not (<= y 3.7e-31))) (* y (- t x)) (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e-44) || !(y <= 3.7e-31)) {
		tmp = y * (t - x);
	} 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 ((y <= (-7.5d-44)) .or. (.not. (y <= 3.7d-31))) then
        tmp = y * (t - x)
    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 ((y <= -7.5e-44) || !(y <= 3.7e-31)) {
		tmp = y * (t - x);
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e-44) or not (y <= 3.7e-31):
		tmp = y * (t - x)
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e-44) || !(y <= 3.7e-31))
		tmp = Float64(y * Float64(t - x));
	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 ((y <= -7.5e-44) || ~((y <= 3.7e-31)))
		tmp = y * (t - x);
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e-44], N[Not[LessEqual[y, 3.7e-31]], $MachinePrecision]], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.50000000000000008e-44 or 3.6999999999999998e-31 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.9%

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

      1. fma-define 97.9%

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

      2. +-commutative 97.9%

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

      3. mul-1-neg 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in y around inf 70.9%

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

      1. neg-mul-1 70.9%

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

      2. sub-neg 70.9%

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

   8. Simplified 70.9%

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

   if -7.50000000000000008e-44 < y < 3.6999999999999998e-31

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 66.0%

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

      1. mul-1-neg 66.0%

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

      2. unsub-neg 66.0%

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

   5. Simplified 66.0%

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

   6. Taylor expanded in y around 0 66.0%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-44} \lor \neg \left(y \leq 3.7 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+99} \lor \neg \left(x \leq 4.4 \cdot 10^{+57}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.15e+99) (not (<= x 4.4e+57))) (* x (+ z 1.0)) (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.15e+99) || !(x <= 4.4e+57)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (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 <= (-2.15d+99)) .or. (.not. (x <= 4.4d+57))) then
        tmp = x * (z + 1.0d0)
    else
        tmp = (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 <= -2.15e+99) || !(x <= 4.4e+57)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.15e+99) or not (x <= 4.4e+57):
		tmp = x * (z + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.15e+99) || !(x <= 4.4e+57))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.15e+99) || ~((x <= 4.4e+57)))
		tmp = x * (z + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.15e+99], N[Not[LessEqual[x, 4.4e+57]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1500000000000001e99 or 4.4000000000000001e57 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. unsub-neg 89.7%

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

   5. Simplified 89.7%

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

   6. Taylor expanded in y around 0 66.2%

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

   if -2.1500000000000001e99 < x < 4.4000000000000001e57

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.3%

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

      1. fma-define 99.3%

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

      2. +-commutative 99.3%

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

      3. mul-1-neg 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in t around inf 65.7%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+99} \lor \neg \left(x \leq 4.4 \cdot 10^{+57}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+72}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9.5e+99)
   (* x (+ z 1.0))
   (if (<= x 6.2e+72) (* (- y z) t) (* x (- 1.0 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e+99) {
		tmp = x * (z + 1.0);
	} else if (x <= 6.2e+72) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - 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 <= (-9.5d+99)) then
        tmp = x * (z + 1.0d0)
    else if (x <= 6.2d+72) then
        tmp = (y - z) * t
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e+99) {
		tmp = x * (z + 1.0);
	} else if (x <= 6.2e+72) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.5e+99:
		tmp = x * (z + 1.0)
	elif x <= 6.2e+72:
		tmp = (y - z) * t
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9.5e+99)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (x <= 6.2e+72)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9.5e+99)
		tmp = x * (z + 1.0);
	elseif (x <= 6.2e+72)
		tmp = (y - z) * t;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.5e+99], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+72], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.49999999999999908e99

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 93.6%

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

      1. mul-1-neg 93.6%

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

      2. unsub-neg 93.6%

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

   5. Simplified 93.6%

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

   6. Taylor expanded in y around 0 71.4%

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

   if -9.49999999999999908e99 < x < 6.19999999999999977e72

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.3%

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

      1. fma-define 99.3%

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

      2. +-commutative 99.3%

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

      3. mul-1-neg 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in t around inf 65.5%

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

   if 6.19999999999999977e72 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 87.8%

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

      1. mul-1-neg 87.8%

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

      2. unsub-neg 87.8%

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

   5. Simplified 87.8%

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

   6. Taylor expanded in z around 0 65.5%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+99}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+72}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+16} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.05e+16) (not (<= z 1.0))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.05e+16) || !(z <= 1.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.05d+16)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.05e+16) || !(z <= 1.0)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.05e+16) or not (z <= 1.0):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.05e+16) || !(z <= 1.0))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.05e+16) || ~((z <= 1.0)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.05e+16], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.05e16 or 1 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 52.2%

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

      1. mul-1-neg 52.2%

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

      2. unsub-neg 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in z around inf 41.6%

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

   if -3.05e16 < z < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 92.8%

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

      1. *-commutative 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in y around 0 33.8%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+16} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 15: 17.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 61.6%

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

   1. *-commutative 61.6%

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

5. Simplified 61.6%

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

6. Taylor expanded in y around 0 18.7%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Developer Target 1: 96.2% 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 2024137 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

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