Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.9s

Alternatives: 13

Speedup: 1.0×

• 34.5% 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: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := z \cdot \left(x - t\right)\\ \mathbf{if}\;y \leq -260000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-146}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-153}:\\ \;\;\;\;\mathsf{fma}\left(z, -t, x\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* z (- x t))))
   (if (<= y -260000000.0)
     t_1
     (if (<= y -1.9e-146)
       t_2
       (if (<= y 2.4e-153) (fma z (- t) x) (if (<= y 1.4e+19) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = z * (x - t);
	double tmp;
	if (y <= -260000000.0) {
		tmp = t_1;
	} else if (y <= -1.9e-146) {
		tmp = t_2;
	} else if (y <= 2.4e-153) {
		tmp = fma(z, -t, x);
	} else if (y <= 1.4e+19) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (y <= -260000000.0)
		tmp = t_1;
	elseif (y <= -1.9e-146)
		tmp = t_2;
	elseif (y <= 2.4e-153)
		tmp = fma(z, Float64(-t), x);
	elseif (y <= 1.4e+19)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -260000000.0], t$95$1, If[LessEqual[y, -1.9e-146], t$95$2, If[LessEqual[y, 2.4e-153], N[(z * (-t) + x), $MachinePrecision], If[LessEqual[y, 1.4e+19], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e8 or 1.4e19 < 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 85.8

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

   5. Simplified 85.8%

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

   if -2.6e8 < y < -1.89999999999999997e-146 or 2.4000000000000002e-153 < y < 1.4e19

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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 71.5

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

   5. Simplified 71.5%

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

   if -1.89999999999999997e-146 < y < 2.4000000000000002e-153

   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

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. unsub-neg N/A

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

      11. remove-double-neg N/A

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

      12. --lowering--.f64 97.1

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

   5. Simplified 97.1%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 79.7

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

   8. Simplified 79.7%

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

Alternative 3: 65.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-258}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* (- y z) t)))
   (if (<= y -7.2e+47)
     t_1
     (if (<= y -4.6e-258)
       t_2
       (if (<= y 1.95e-28) (fma z x x) (if (<= y 1.6e+19) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = (y - z) * t;
	double tmp;
	if (y <= -7.2e+47) {
		tmp = t_1;
	} else if (y <= -4.6e-258) {
		tmp = t_2;
	} else if (y <= 1.95e-28) {
		tmp = fma(z, x, x);
	} else if (y <= 1.6e+19) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (y <= -7.2e+47)
		tmp = t_1;
	elseif (y <= -4.6e-258)
		tmp = t_2;
	elseif (y <= 1.95e-28)
		tmp = fma(z, x, x);
	elseif (y <= 1.6e+19)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -7.2e+47], t$95$1, If[LessEqual[y, -4.6e-258], t$95$2, If[LessEqual[y, 1.95e-28], N[(z * x + x), $MachinePrecision], If[LessEqual[y, 1.6e+19], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.20000000000000015e47 or 1.6e19 < 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 87.3

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

   5. Simplified 87.3%

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

   if -7.20000000000000015e47 < y < -4.59999999999999986e-258 or 1.94999999999999999e-28 < y < 1.6e19

   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 64.2

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

   5. Simplified 64.2%

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

   if -4.59999999999999986e-258 < y < 1.94999999999999999e-28

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. unsub-neg N/A

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

      11. remove-double-neg N/A

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

      12. --lowering--.f64 93.7

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

   5. Simplified 93.7%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 64.4%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-258}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-28}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-62}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -6.5e-21)
     t_1
     (if (<= t -2.5e-267) (* x (- y)) (if (<= t 5.5e-62) (fma z x x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -6.5e-21) {
		tmp = t_1;
	} else if (t <= -2.5e-267) {
		tmp = x * -y;
	} else if (t <= 5.5e-62) {
		tmp = fma(z, x, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -6.5e-21)
		tmp = t_1;
	elseif (t <= -2.5e-267)
		tmp = Float64(x * Float64(-y));
	elseif (t <= 5.5e-62)
		tmp = fma(z, x, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -6.5e-21], t$95$1, If[LessEqual[t, -2.5e-267], N[(x * (-y)), $MachinePrecision], If[LessEqual[t, 5.5e-62], N[(z * x + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.49999999999999987e-21 or 5.50000000000000022e-62 < t

   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 78.1

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

   5. Simplified 78.1%

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

   if -6.49999999999999987e-21 < t < -2.5e-267

   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 59.6

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

   5. Simplified 59.6%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 48.7

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

   8. Simplified 48.7%

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

   if -2.5e-267 < t < 5.50000000000000022e-62

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. unsub-neg N/A

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

      11. remove-double-neg N/A

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

      12. --lowering--.f64 61.8

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

   5. Simplified 61.8%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 55.9%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-21}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-267}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-62}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(y, t - x, x\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(z, x - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.4e-12)
   (fma y (- t x) x)
   (if (<= y 2.2e+19) (fma z (- x t) x) (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.4e-12) {
		tmp = fma(y, (t - x), x);
	} else if (y <= 2.2e+19) {
		tmp = fma(z, (x - t), x);
	} else {
		tmp = y * (t - x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.4e-12)
		tmp = fma(y, Float64(t - x), x);
	elseif (y <= 2.2e+19)
		tmp = fma(z, Float64(x - t), x);
	else
		tmp = Float64(y * Float64(t - x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.4e-12], N[(y * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 2.2e+19], N[(z * N[(x - t), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.39999999999999997e-12

   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 84.1

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

   5. Simplified 84.1%

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

   if -7.39999999999999997e-12 < y < 2.2e19

   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

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. unsub-neg N/A

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

      11. remove-double-neg N/A

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

      12. --lowering--.f64 90.6

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

   5. Simplified 90.6%

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

   if 2.2e19 < 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 86.7

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

   5. Simplified 86.7%

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

Alternative 6: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -7800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(y, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -7800000000000.0) t_1 (if (<= z 9.5e+29) (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 <= -7800000000000.0) {
		tmp = t_1;
	} else if (z <= 9.5e+29) {
		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 <= -7800000000000.0)
		tmp = t_1;
	elseif (z <= 9.5e+29)
		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, -7800000000000.0], t$95$1, If[LessEqual[z, 9.5e+29], N[(y * N[(t - x), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.8e12 or 9.5000000000000003e29 < 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 79.6

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

   5. Simplified 79.6%

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

   if -7.8e12 < z < 9.5000000000000003e29

   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 89.3

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

   5. Simplified 89.3%

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

Alternative 7: 69.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -5200000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -5200000000.0) t_1 (if (<= y 8.8e+19) (* z (- x t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -5200000000.0) {
		tmp = t_1;
	} else if (y <= 8.8e+19) {
		tmp = z * (x - 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 = y * (t - x)
    if (y <= (-5200000000.0d0)) then
        tmp = t_1
    else if (y <= 8.8d+19) then
        tmp = z * (x - 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 = y * (t - x);
	double tmp;
	if (y <= -5200000000.0) {
		tmp = t_1;
	} else if (y <= 8.8e+19) {
		tmp = z * (x - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -5200000000.0:
		tmp = t_1
	elif y <= 8.8e+19:
		tmp = z * (x - t)
	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 <= -5200000000.0)
		tmp = t_1;
	elseif (y <= 8.8e+19)
		tmp = Float64(z * Float64(x - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -5200000000.0)
		tmp = t_1;
	elseif (y <= 8.8e+19)
		tmp = z * (x - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5200000000.0], t$95$1, If[LessEqual[y, 8.8e+19], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2e9 or 8.8e19 < 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 85.8

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

   5. Simplified 85.8%

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

   if -5.2e9 < y < 8.8e19

   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 67.0

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

   5. Simplified 67.0%

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

Alternative 8: 54.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;z \leq -165000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{+30}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= z -165000000000.0) t_1 (if (<= z 1e+30) (fma y t x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (z <= -165000000000.0) {
		tmp = t_1;
	} else if (z <= 1e+30) {
		tmp = fma(y, t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (z <= -165000000000.0)
		tmp = t_1;
	elseif (z <= 1e+30)
		tmp = fma(y, t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[z, -165000000000.0], t$95$1, If[LessEqual[z, 1e+30], N[(y * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e11 or 1e30 < 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 59.2

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

   5. Simplified 59.2%

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

   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 47.0

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

   8. Simplified 47.0%

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

   if -1.65e11 < z < 1e30

   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 89.3

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

   5. Simplified 89.3%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 60.2%

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

Alternative 9: 50.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.85e+45) (* x (- y)) (if (<= y 1.6e+47) (fma z x x) (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.85e+45) {
		tmp = x * -y;
	} else if (y <= 1.6e+47) {
		tmp = fma(z, x, x);
	} else {
		tmp = y * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.85e+45)
		tmp = Float64(x * Float64(-y));
	elseif (y <= 1.6e+47)
		tmp = fma(z, x, x);
	else
		tmp = Float64(y * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.85e+45], N[(x * (-y)), $MachinePrecision], If[LessEqual[y, 1.6e+47], N[(z * x + x), $MachinePrecision], N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.85000000000000013e45

   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 88.3

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

   5. Simplified 88.3%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 54.8

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

   8. Simplified 54.8%

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

   if -2.85000000000000013e45 < y < 1.6e47

   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

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

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

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

      4. mul-1-neg N/A

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

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

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

      6. mul-1-neg N/A

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

      7. sub-neg N/A

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

      8. +-commutative N/A

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

      9. distribute-neg-in N/A

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

      10. unsub-neg N/A

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

      11. remove-double-neg N/A

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

      12. --lowering--.f64 85.9

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

   5. Simplified 85.9%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 48.3%

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

   if 1.6e47 < y

   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 88.5

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

   5. Simplified 88.5%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 54.1%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+57}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.9e+57) (* x z) (if (<= z 1.1e+135) (fma y t x) (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.9e+57) {
		tmp = x * z;
	} else if (z <= 1.1e+135) {
		tmp = fma(y, t, x);
	} else {
		tmp = x * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.9e+57)
		tmp = Float64(x * z);
	elseif (z <= 1.1e+135)
		tmp = fma(y, t, x);
	else
		tmp = Float64(x * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.9e+57], N[(x * z), $MachinePrecision], If[LessEqual[z, 1.1e+135], N[(y * t + x), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e57 or 1.1e135 < 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%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 46.7%

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

   if -1.8999999999999999e57 < z < 1.1e135

   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 79.4

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

   5. Simplified 79.4%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 53.1%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+57}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+135}:\\ \;\;\;\;\mathsf{fma}\left(y, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+59}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+134}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.95e+59) (* x z) (if (<= z 8.5e+134) (* y t) (* x z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.95e+59) {
		tmp = x * z;
	} else if (z <= 8.5e+134) {
		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 <= (-1.95d+59)) then
        tmp = x * z
    else if (z <= 8.5d+134) 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 <= -1.95e+59) {
		tmp = x * z;
	} else if (z <= 8.5e+134) {
		tmp = y * t;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.95e+59:
		tmp = x * z
	elif z <= 8.5e+134:
		tmp = y * t
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.95e+59)
		tmp = Float64(x * z);
	elseif (z <= 8.5e+134)
		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 <= -1.95e+59)
		tmp = x * z;
	elseif (z <= 8.5e+134)
		tmp = y * t;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.95e+59], N[(x * z), $MachinePrecision], If[LessEqual[z, 8.5e+134], N[(y * t), $MachinePrecision], N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95000000000000011e59 or 8.50000000000000024e134 < 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%

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

   6. Taylor expanded in x around inf

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

   8. Simplified 46.7%

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

   if -1.95000000000000011e59 < z < 8.50000000000000024e134

   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 61.3

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

   5. Simplified 61.3%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 35.1%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+59}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+134}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-42}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-6}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e-42) (* y t) (if (<= y 2.45e-6) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-42) {
		tmp = y * t;
	} else if (y <= 2.45e-6) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.8d-42)) then
        tmp = y * t
    else if (y <= 2.45d-6) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-42) {
		tmp = y * t;
	} else if (y <= 2.45e-6) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e-42:
		tmp = y * t
	elif y <= 2.45e-6:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e-42)
		tmp = Float64(y * t);
	elseif (y <= 2.45e-6)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.8e-42)
		tmp = y * t;
	elseif (y <= 2.45e-6)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e-42], N[(y * t), $MachinePrecision], If[LessEqual[y, 2.45e-6], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000006e-42 or 2.44999999999999984e-6 < 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 79.7

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

   5. Simplified 79.7%

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

   6. Taylor expanded in t around inf

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

   8. Simplified 44.2%

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

   if -5.8000000000000006e-42 < y < 2.44999999999999984e-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 34.0

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

   5. Simplified 34.0%

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

   6. Taylor expanded in y around 0

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

   8. Simplified 27.1%

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

Alternative 13: 17.8% 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 60.1

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

5. Simplified 60.1%

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

6. Taylor expanded in y around 0

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

8. Simplified 13.8%

   \[\leadsto \color{blue}{x} \]
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 2024198 
(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))))