Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.0s

Alternatives: 14

Speedup: 1.0×

• 34.7% 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, 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 2: 71.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := y \cdot \left(t - x\right)\\ \mathbf{if}\;z \leq -1.66 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-227}:\\ \;\;\;\;\mathsf{fma}\left(y, -x, x\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* y (- t x))))
   (if (<= z -1.66e+44)
     t_1
     (if (<= z -7e-58)
       t_2
       (if (<= z -7.8e-227)
         (fma y (- x) x)
         (if (<= z 1.35e-6) (fma y t x) (if (<= z 4.7e+61) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = y * (t - x);
	double tmp;
	if (z <= -1.66e+44) {
		tmp = t_1;
	} else if (z <= -7e-58) {
		tmp = t_2;
	} else if (z <= -7.8e-227) {
		tmp = fma(y, -x, x);
	} else if (z <= 1.35e-6) {
		tmp = fma(y, t, x);
	} else if (z <= 4.7e+61) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (z <= -1.66e+44)
		tmp = t_1;
	elseif (z <= -7e-58)
		tmp = t_2;
	elseif (z <= -7.8e-227)
		tmp = fma(y, Float64(-x), x);
	elseif (z <= 1.35e-6)
		tmp = fma(y, t, x);
	elseif (z <= 4.7e+61)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.66e+44], t$95$1, If[LessEqual[z, -7e-58], t$95$2, If[LessEqual[z, -7.8e-227], N[(y * (-x) + x), $MachinePrecision], If[LessEqual[z, 1.35e-6], N[(y * t + x), $MachinePrecision], If[LessEqual[z, 4.7e+61], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.65999999999999992e44 or 4.6999999999999998e61 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. --lowering--.f64 85.3

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

   5. Simplified 85.3%

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

   if -1.65999999999999992e44 < z < -6.9999999999999998e-58 or 1.34999999999999999e-6 < z < 4.6999999999999998e61

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 70.6

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

   5. Simplified 70.6%

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

   if -6.9999999999999998e-58 < z < -7.7999999999999999e-227

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 90.6

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

   5. Simplified 90.6%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 79.0

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

   8. Simplified 79.0%

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

   if -7.7999999999999999e-227 < z < 1.34999999999999999e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 93.0

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

   5. Simplified 93.0%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{t}, x\right) \]
   7. Step-by-step derivation

   8. Simplified 73.7%

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

Alternative 3: 68.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-56}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{elif}\;y \leq 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -1.0)
     t_1
     (if (<= y -1.6e-56) (fma y t x) (if (<= y 1e+15) (fma x z x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -1.0) {
		tmp = t_1;
	} else if (y <= -1.6e-56) {
		tmp = fma(y, t, x);
	} else if (y <= 1e+15) {
		tmp = fma(x, z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_1;
	elseif (y <= -1.6e-56)
		tmp = fma(y, t, x);
	elseif (y <= 1e+15)
		tmp = fma(x, z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$1, If[LessEqual[y, -1.6e-56], N[(y * t + x), $MachinePrecision], If[LessEqual[y, 1e+15], N[(x * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1e15 < y

   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

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 84.6

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

   5. Simplified 84.6%

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

   if -1 < y < -1.59999999999999993e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 79.1

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

   5. Simplified 79.1%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{t}, x\right) \]
   7. Step-by-step derivation

   8. Simplified 73.8%

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

   if -1.59999999999999993e-56 < y < 1e15

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. distribute-lft-in N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. neg-lowering-neg.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 72.3

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

   7. Simplified 72.3%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + x \cdot z} \]
   9. Step-by-step derivation

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 63.2

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

   10. Simplified 63.2%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, z, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z - y\right)\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 10^{-160}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-33}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- z y))))
   (if (<= x -5.4e+54)
     t_1
     (if (<= x 1e-160) (* (- y z) t) (if (<= x 7e-33) (fma y t x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z - y);
	double tmp;
	if (x <= -5.4e+54) {
		tmp = t_1;
	} else if (x <= 1e-160) {
		tmp = (y - z) * t;
	} else if (x <= 7e-33) {
		tmp = fma(y, t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z - y))
	tmp = 0.0
	if (x <= -5.4e+54)
		tmp = t_1;
	elseif (x <= 1e-160)
		tmp = Float64(Float64(y - z) * t);
	elseif (x <= 7e-33)
		tmp = fma(y, t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.4e+54], t$95$1, If[LessEqual[x, 1e-160], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[x, 7e-33], N[(y * t + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.40000000000000022e54 or 6.9999999999999997e-33 < x

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. distribute-lft-in N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. neg-lowering-neg.f64 98.3

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 92.5

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

   7. Simplified 92.5%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(t - x, y, \color{blue}{x \cdot z}\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 70.7

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

   10. Simplified 70.7%

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

   11. Taylor expanded in t around 0

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

       1. mul-1-neg N/A

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

       2. distribute-rgt-neg-in N/A

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

       3. mul-1-neg N/A

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

       4. distribute-lft-in N/A

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

       5. +-commutative N/A

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

       6. *-lowering-*.f64 N/A

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

       7. mul-1-neg N/A

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

       8. unsub-neg N/A

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

       9. --lowering--.f64 68.1

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

   13. Simplified 68.1%

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

   if -5.40000000000000022e54 < x < 9.9999999999999999e-161

   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

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 74.9

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

   5. Simplified 74.9%

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

   if 9.9999999999999999e-161 < x < 6.9999999999999997e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 80.2

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

   5. Simplified 80.2%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{t}, x\right) \]
   7. Step-by-step derivation

   8. Simplified 65.4%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \mathbf{elif}\;x \leq 10^{-160}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-33}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+161}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e-6)
   (fma x z x)
   (if (<= z 9e+93) (fma y t x) (if (<= z 4.8e+161) (* x z) (* z (- t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e-6) {
		tmp = fma(x, z, x);
	} else if (z <= 9e+93) {
		tmp = fma(y, t, x);
	} else if (z <= 4.8e+161) {
		tmp = x * z;
	} else {
		tmp = z * -t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e-6)
		tmp = fma(x, z, x);
	elseif (z <= 9e+93)
		tmp = fma(y, t, x);
	elseif (z <= 4.8e+161)
		tmp = Float64(x * z);
	else
		tmp = Float64(z * Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e-6], N[(x * z + x), $MachinePrecision], If[LessEqual[z, 9e+93], N[(y * t + x), $MachinePrecision], If[LessEqual[z, 4.8e+161], N[(x * z), $MachinePrecision], N[(z * (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.8e-6

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. distribute-lft-in N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. neg-lowering-neg.f64 96.3

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 77.5

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

   7. Simplified 77.5%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + x \cdot z} \]
   9. Step-by-step derivation

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 56.7

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

   10. Simplified 56.7%

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

   if -3.8e-6 < z < 8.99999999999999981e93

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 88.4

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

   5. Simplified 88.4%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{t}, x\right) \]
   7. Step-by-step derivation

   8. Simplified 62.3%

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

   if 8.99999999999999981e93 < z < 4.7999999999999998e161

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. --lowering--.f64 84.3

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

   5. Simplified 84.3%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 67.6%

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

   if 4.7999999999999998e161 < 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

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 68.8

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

   5. Simplified 68.8%

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

   6. Taylor expanded in y around 0

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. neg-lowering-neg.f64 62.2

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

   8. Simplified 62.2%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+161}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y))))
   (if (<= y -1.15e+232)
     t_1
     (if (<= y -3.5e-56) (fma y t x) (if (<= y 1.8e+23) (fma x z x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -y;
	double tmp;
	if (y <= -1.15e+232) {
		tmp = t_1;
	} else if (y <= -3.5e-56) {
		tmp = fma(y, t, x);
	} else if (y <= 1.8e+23) {
		tmp = fma(x, z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1.15e+232)
		tmp = t_1;
	elseif (y <= -3.5e-56)
		tmp = fma(y, t, x);
	elseif (y <= 1.8e+23)
		tmp = fma(x, z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.15e+232], t$95$1, If[LessEqual[y, -3.5e-56], N[(y * t + x), $MachinePrecision], If[LessEqual[y, 1.8e+23], N[(x * z + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000003e232 or 1.7999999999999999e23 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 85.4

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

   5. Simplified 85.4%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 57.4

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

   8. Simplified 57.4%

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

   9. Taylor expanded in y around inf

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

       1. associate-*r* N/A

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

       2. *-commutative N/A

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

       3. *-lowering-*.f64 N/A

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

       4. mul-1-neg N/A

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

       5. neg-lowering-neg.f64 57.4

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

   11. Simplified 57.4%

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

   if -1.15000000000000003e232 < y < -3.4999999999999998e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 82.5

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

   5. Simplified 82.5%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{t}, x\right) \]
   7. Step-by-step derivation

   8. Simplified 62.1%

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

   if -3.4999999999999998e-56 < y < 1.7999999999999999e23

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. distribute-lft-in N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. neg-lowering-neg.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 72.5

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

   7. Simplified 72.5%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + x \cdot z} \]
   9. Step-by-step derivation

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 62.7

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

   10. Simplified 62.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, z, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+232}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -55:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+93}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -55.0)
   (* x z)
   (if (<= z -1.55e-198) x (if (<= z 9e+93) (* y t) (* x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -55.0) {
		tmp = x * z;
	} else if (z <= -1.55e-198) {
		tmp = x;
	} else if (z <= 9e+93) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	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 <= (-55.0d0)) then
        tmp = x * z
    else if (z <= (-1.55d-198)) then
        tmp = x
    else if (z <= 9d+93) then
        tmp = y * t
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -55.0) {
		tmp = x * z;
	} else if (z <= -1.55e-198) {
		tmp = x;
	} else if (z <= 9e+93) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -55.0:
		tmp = x * z
	elif z <= -1.55e-198:
		tmp = x
	elif z <= 9e+93:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -55.0)
		tmp = Float64(x * z);
	elseif (z <= -1.55e-198)
		tmp = x;
	elseif (z <= 9e+93)
		tmp = Float64(y * t);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -55.0)
		tmp = x * z;
	elseif (z <= -1.55e-198)
		tmp = x;
	elseif (z <= 9e+93)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -55.0], N[(x * z), $MachinePrecision], If[LessEqual[z, -1.55e-198], x, If[LessEqual[z, 9e+93], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -55 or 8.99999999999999981e93 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. --lowering--.f64 83.7

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

   5. Simplified 83.7%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 50.5%

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

   if -55 < z < -1.5499999999999999e-198

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 86.2

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

   5. Simplified 86.2%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 37.4%

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

   if -1.5499999999999999e-198 < z < 8.99999999999999981e93

   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

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 50.2

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

   5. Simplified 50.2%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 41.6

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

   8. Simplified 41.6%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -55:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+93}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(y, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -2.6e+44) t_1 (if (<= z 7.6e+61) (fma y (- t x) x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -2.6e+44) {
		tmp = t_1;
	} else if (z <= 7.6e+61) {
		tmp = fma(y, (t - x), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -2.6e+44)
		tmp = t_1;
	elseif (z <= 7.6e+61)
		tmp = fma(y, Float64(t - x), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+44], t$95$1, If[LessEqual[z, 7.6e+61], N[(y * N[(t - x), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5999999999999999e44 or 7.5999999999999999e61 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. --lowering--.f64 85.3

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

   5. Simplified 85.3%

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

   if -2.5999999999999999e44 < z < 7.5999999999999999e61

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 88.7

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

   5. Simplified 88.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, t - x, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, z - y, x\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-183}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (- z y) x)))
   (if (<= x -3.4e+52) t_1 (if (<= x 5.6e-183) (* (- y z) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(x, (z - y), x);
	double tmp;
	if (x <= -3.4e+52) {
		tmp = t_1;
	} else if (x <= 5.6e-183) {
		tmp = (y - z) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(x, Float64(z - y), x)
	tmp = 0.0
	if (x <= -3.4e+52)
		tmp = t_1;
	elseif (x <= 5.6e-183)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z - y), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[x, -3.4e+52], t$95$1, If[LessEqual[x, 5.6e-183], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4e52 or 5.5999999999999997e-183 < 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

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

      1. +-commutative N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. --lowering--.f64 80.2

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

   5. Simplified 80.2%

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

   if -3.4e52 < x < 5.5999999999999997e-183

   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

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 78.9

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

   5. Simplified 78.9%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(x, z - y, x\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-183}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z - y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;x \leq 4.15 \cdot 10^{-35}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2e+55) (fma x z x) (if (<= x 4.15e-35) (* (- y z) t) (fma x z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2e+55) {
		tmp = fma(x, z, x);
	} else if (x <= 4.15e-35) {
		tmp = (y - z) * t;
	} else {
		tmp = fma(x, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2e+55)
		tmp = fma(x, z, x);
	elseif (x <= 4.15e-35)
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = fma(x, z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2e+55], N[(x * z + x), $MachinePrecision], If[LessEqual[x, 4.15e-35], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.00000000000000002e55 or 4.1499999999999998e-35 < x

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. distribute-lft-in N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. neg-lowering-neg.f64 98.3

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 92.6

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

   7. Simplified 92.6%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + x \cdot z} \]
   9. Step-by-step derivation

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 56.6

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

   10. Simplified 56.6%

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

   if -2.00000000000000002e55 < x < 4.1499999999999998e-35

   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

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 69.8

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

   5. Simplified 69.8%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;x \leq 4.15 \cdot 10^{-35}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e-8) (fma x z x) (if (<= z 1.36e+94) (fma y t x) (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e-8) {
		tmp = fma(x, z, x);
	} else if (z <= 1.36e+94) {
		tmp = fma(y, t, x);
	} else {
		tmp = x * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e-8)
		tmp = fma(x, z, x);
	elseif (z <= 1.36e+94)
		tmp = fma(y, t, x);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e-8], N[(x * z + x), $MachinePrecision], If[LessEqual[z, 1.36e+94], N[(y * t + x), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e-8

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. distribute-lft-in N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. neg-lowering-neg.f64 96.3

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 77.5

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

   7. Simplified 77.5%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + x \cdot z} \]
   9. Step-by-step derivation

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 56.7

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

   10. Simplified 56.7%

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

   if -1e-8 < z < 1.36e94

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 88.4

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

   5. Simplified 88.4%

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

   6. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{t}, x\right) \]
   7. Step-by-step derivation

   8. Simplified 62.3%

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

   if 1.36e94 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-rgt-neg-in N/A

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

      3. mul-1-neg N/A

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

      4. *-lowering-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. sub-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. remove-double-neg N/A

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

      11. --lowering--.f64 87.2

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

   5. Simplified 87.2%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 43.3%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-7}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(x, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e-7) (* y t) (if (<= y 5.2e+53) (fma x z x) (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-7) {
		tmp = y * t;
	} else if (y <= 5.2e+53) {
		tmp = fma(x, z, x);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e-7)
		tmp = Float64(y * t);
	elseif (y <= 5.2e+53)
		tmp = fma(x, z, x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e-7], N[(y * t), $MachinePrecision], If[LessEqual[y, 5.2e+53], N[(x * z + x), $MachinePrecision], N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e-7 or 5.19999999999999996e53 < 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

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 54.1

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

   5. Simplified 54.1%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 46.4

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

   8. Simplified 46.4%

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

   if -1.6e-7 < y < 5.19999999999999996e53

   1. Initial program 100.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. sub-neg N/A

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

      4. distribute-lft-in N/A

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

      5. associate-+l+ N/A

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

      6. *-commutative N/A

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

      7. accelerator-lowering-fma.f64 N/A

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

      8. --lowering--.f64 N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. --lowering--.f64 N/A

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

      12. neg-lowering-neg.f64 100.0

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 73.7

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

   7. Simplified 73.7%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + x \cdot z} \]
   9. Step-by-step derivation

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 58.6

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

   10. Simplified 58.6%

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, z, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 38.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-8}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7e-8) (* y t) (if (<= y 1.2e-27) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e-8) {
		tmp = y * t;
	} else if (y <= 1.2e-27) {
		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 <= (-7d-8)) then
        tmp = y * t
    else if (y <= 1.2d-27) 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 <= -7e-8) {
		tmp = y * t;
	} else if (y <= 1.2e-27) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7e-8:
		tmp = y * t
	elif y <= 1.2e-27:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7e-8)
		tmp = Float64(y * t);
	elseif (y <= 1.2e-27)
		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 <= -7e-8)
		tmp = y * t;
	elseif (y <= 1.2e-27)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7e-8], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.2e-27], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.00000000000000048e-8 or 1.20000000000000001e-27 < 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

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

      1. *-lowering-*.f64 N/A

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

      2. --lowering--.f64 51.5

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

   5. Simplified 51.5%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 42.8

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

   8. Simplified 42.8%

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

   if -7.00000000000000048e-8 < y < 1.20000000000000001e-27

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 44.2

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

   5. Simplified 44.2%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 35.7%

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

Alternative 14: 18.5% accurate, 15.0× 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 z around 0

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

   1. +-commutative N/A

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

   2. accelerator-lowering-fma.f64 N/A

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

   3. --lowering--.f64 64.2

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

5. Simplified 64.2%

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

6. Taylor expanded in y around 0

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

8. Simplified 18.5%

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

Developer Target 1: 96.0% 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 2024205 
(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))))