Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.6% → 90.7%

Time: 11.4s

Alternatives: 14

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z} \cdot \left(y - z\right) + x\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-264}:\\ \;\;\;\;\frac{y - z}{\frac{z - a}{x - t}} + x\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* (/ (- t x) (- a z)) (- y z)) x)))
   (if (<= t_1 -2e-264)
     (+ (/ (- y z) (/ (- z a) (- x t))) x)
     (if (<= t_1 0.0) (fma (/ (- x t) z) (- y a) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (((t - x) / (a - z)) * (y - z)) + x;
	double tmp;
	if (t_1 <= -2e-264) {
		tmp = ((y - z) / ((z - a) / (x - t))) + x;
	} else if (t_1 <= 0.0) {
		tmp = fma(((x - t) / z), (y - a), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(y - z)) + x)
	tmp = 0.0
	if (t_1 <= -2e-264)
		tmp = Float64(Float64(Float64(y - z) / Float64(Float64(z - a) / Float64(x - t))) + x);
	elseif (t_1 <= 0.0)
		tmp = fma(Float64(Float64(x - t) / z), Float64(y - a), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-264], N[(N[(N[(y - z), $MachinePrecision] / N[(N[(z - a), $MachinePrecision] / N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-264

   1. Initial program 92.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

      5. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t - x}}} \]

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

         \[\leadsto x + \frac{y - z}{\frac{\color{blue}{0 - \left(a - z\right)}}{\mathsf{neg}\left(\left(t - x\right)\right)}} \]

      9. lift--.f64 N/A

         \[\leadsto x + \frac{y - z}{\frac{0 - \color{blue}{\left(a - z\right)}}{\mathsf{neg}\left(\left(t - x\right)\right)}} \]

      10. sub-neg N/A

          \[\leadsto x + \frac{y - z}{\frac{0 - \color{blue}{\left(a + \left(\mathsf{neg}\left(z\right)\right)\right)}}{\mathsf{neg}\left(\left(t - x\right)\right)}} \]

      11. +-commutative N/A

          \[\leadsto x + \frac{y - z}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + a\right)}}{\mathsf{neg}\left(\left(t - x\right)\right)}} \]

      12. associate--r+ N/A

          \[\leadsto x + \frac{y - z}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - a}}{\mathsf{neg}\left(\left(t - x\right)\right)}} \]

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 N/A

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

      16. neg-sub0 N/A

          \[\leadsto x + \frac{y - z}{\frac{z - a}{\color{blue}{0 - \left(t - x\right)}}} \]

      17. lift--.f64 N/A

          \[\leadsto x + \frac{y - z}{\frac{z - a}{0 - \color{blue}{\left(t - x\right)}}} \]

      18. sub-neg N/A

          \[\leadsto x + \frac{y - z}{\frac{z - a}{0 - \color{blue}{\left(t + \left(\mathsf{neg}\left(x\right)\right)\right)}}} \]

      19. +-commutative N/A

          \[\leadsto x + \frac{y - z}{\frac{z - a}{0 - \color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + t\right)}}} \]

      20. associate--r+ N/A

          \[\leadsto x + \frac{y - z}{\frac{z - a}{\color{blue}{\left(0 - \left(\mathsf{neg}\left(x\right)\right)\right) - t}}} \]

      21. neg-sub0 N/A

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

      22. remove-double-neg N/A

          \[\leadsto x + \frac{y - z}{\frac{z - a}{\color{blue}{x} - t}} \]

      23. lower--.f64 92.3

          \[\leadsto x + \frac{y - z}{\frac{z - a}{\color{blue}{x - t}}} \]

   4. Applied rewrites 92.3%

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{z - a}{x - t}}} \]

   if -2e-264 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.6%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 2.0

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

   5. Applied rewrites 2.0%

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

   7. Applied rewrites 2.0%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z}}} \]

   8. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

      10. distribute-lft-neg-in N/A

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

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

   10. Applied rewrites 99.8%

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

   if 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.9%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Add Preprocessing
3. Recombined 3 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - x}{a - z} \cdot \left(y - z\right) + x \leq -2 \cdot 10^{-264}:\\ \;\;\;\;\frac{y - z}{\frac{z - a}{x - t}} + x\\ \mathbf{elif}\;\frac{t - x}{a - z} \cdot \left(y - z\right) + x \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{a - z} \cdot \left(y - z\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - x}{a - z} \cdot \left(y - z\right) + x\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-264}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* (/ (- t x) (- a z)) (- y z)) x)))
   (if (<= t_1 -2e-264)
     t_1
     (if (<= t_1 0.0) (fma (/ (- x t) z) (- y a) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (((t - x) / (a - z)) * (y - z)) + x;
	double tmp;
	if (t_1 <= -2e-264) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = fma(((x - t) / z), (y - a), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(y - z)) + x)
	tmp = 0.0
	if (t_1 <= -2e-264)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = fma(Float64(Float64(x - t) / z), Float64(y - a), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-264], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-264 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.7%

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

   if -2e-264 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.6%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 2.0

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

   5. Applied rewrites 2.0%

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

   7. Applied rewrites 2.0%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z}}} \]

   8. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

      10. distribute-lft-neg-in N/A

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

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

   10. Applied rewrites 99.8%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t - x}{a - z} \cdot \left(y - z\right) + x \leq -2 \cdot 10^{-264}:\\ \;\;\;\;\frac{t - x}{a - z} \cdot \left(y - z\right) + x\\ \mathbf{elif}\;\frac{t - x}{a - z} \cdot \left(y - z\right) + x \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - x}{a - z} \cdot \left(y - z\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{if}\;a \leq -5.9 \cdot 10^{-119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-305}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) a) x)))
   (if (<= a -5.9e-119)
     t_1
     (if (<= a -1.95e-305)
       (* (- 1.0 (/ y z)) t)
       (if (<= a 3.5e-11) (* (/ y (- a z)) (- t x)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / a), x);
	double tmp;
	if (a <= -5.9e-119) {
		tmp = t_1;
	} else if (a <= -1.95e-305) {
		tmp = (1.0 - (y / z)) * t;
	} else if (a <= 3.5e-11) {
		tmp = (y / (a - z)) * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / a), x)
	tmp = 0.0
	if (a <= -5.9e-119)
		tmp = t_1;
	elseif (a <= -1.95e-305)
		tmp = Float64(Float64(1.0 - Float64(y / z)) * t);
	elseif (a <= 3.5e-11)
		tmp = Float64(Float64(y / Float64(a - z)) * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -5.9e-119], t$95$1, If[LessEqual[a, -1.95e-305], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 3.5e-11], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.9000000000000002e-119 or 3.50000000000000019e-11 < a

   1. Initial program 91.6%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 77.7

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

   5. Applied rewrites 77.7%

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

   if -5.9000000000000002e-119 < a < -1.95000000000000013e-305

   1. Initial program 73.7%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 75.8

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

   5. Applied rewrites 75.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 81.6%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 81.6%

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

   if -1.95000000000000013e-305 < a < 3.50000000000000019e-11

   1. Initial program 71.6%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 60.2

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

   5. Applied rewrites 60.2%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.9 \cdot 10^{-119}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-305}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{if}\;a \leq -6400000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-305}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t x) a) y x)))
   (if (<= a -6400000.0)
     t_1
     (if (<= a -1.95e-305)
       (* (- 1.0 (/ y z)) t)
       (if (<= a 3.5e-11) (* (/ y (- a z)) (- t x)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - x) / a), y, x);
	double tmp;
	if (a <= -6400000.0) {
		tmp = t_1;
	} else if (a <= -1.95e-305) {
		tmp = (1.0 - (y / z)) * t;
	} else if (a <= 3.5e-11) {
		tmp = (y / (a - z)) * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - x) / a), y, x)
	tmp = 0.0
	if (a <= -6400000.0)
		tmp = t_1;
	elseif (a <= -1.95e-305)
		tmp = Float64(Float64(1.0 - Float64(y / z)) * t);
	elseif (a <= 3.5e-11)
		tmp = Float64(Float64(y / Float64(a - z)) * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[a, -6400000.0], t$95$1, If[LessEqual[a, -1.95e-305], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 3.5e-11], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.4e6 or 3.50000000000000019e-11 < a

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.4

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

   5. Applied rewrites 75.4%

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

   if -6.4e6 < a < -1.95000000000000013e-305

   1. Initial program 74.8%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 64.9

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 65.4%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 65.4%

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

   if -1.95000000000000013e-305 < a < 3.50000000000000019e-11

   1. Initial program 71.6%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 60.2

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

   5. Applied rewrites 60.2%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6400000:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-305}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{a - z} \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -260000000:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{a} \cdot \left(t - x\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -260000000.0)
   (fma (- y z) (/ (- t x) a) x)
   (if (<= a 2.15e-10)
     (fma (/ (- x t) z) (- y a) t)
     (+ (* (/ (- y z) a) (- t x)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -260000000.0) {
		tmp = fma((y - z), ((t - x) / a), x);
	} else if (a <= 2.15e-10) {
		tmp = fma(((x - t) / z), (y - a), t);
	} else {
		tmp = (((y - z) / a) * (t - x)) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -260000000.0)
		tmp = fma(Float64(y - z), Float64(Float64(t - x) / a), x);
	elseif (a <= 2.15e-10)
		tmp = fma(Float64(Float64(x - t) / z), Float64(y - a), t);
	else
		tmp = Float64(Float64(Float64(Float64(y - z) / a) * Float64(t - x)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -260000000.0], N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 2.15e-10], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.6e8

   1. Initial program 95.5%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 85.1

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

   5. Applied rewrites 85.1%

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

   if -2.6e8 < a < 2.15000000000000007e-10

   1. Initial program 73.1%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 32.5

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

   5. Applied rewrites 32.5%

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

   7. Applied rewrites 33.0%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z}}} \]

   8. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

      10. distribute-lft-neg-in N/A

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

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

   10. Applied rewrites 79.6%

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

   if 2.15000000000000007e-10 < a

   1. Initial program 92.6%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 83.8

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

   5. Applied rewrites 83.8%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -260000000:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{a} \cdot \left(t - x\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a}, x\right)\\ \mathbf{if}\;a \leq -260000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z}, y - a, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) a) x)))
   (if (<= a -260000000.0)
     t_1
     (if (<= a 2.15e-10) (fma (/ (- x t) z) (- y a) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / a), x);
	double tmp;
	if (a <= -260000000.0) {
		tmp = t_1;
	} else if (a <= 2.15e-10) {
		tmp = fma(((x - t) / z), (y - a), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / a), x)
	tmp = 0.0
	if (a <= -260000000.0)
		tmp = t_1;
	elseif (a <= 2.15e-10)
		tmp = fma(Float64(Float64(x - t) / z), Float64(y - a), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -260000000.0], t$95$1, If[LessEqual[a, 2.15e-10], N[(N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision] * N[(y - a), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.6e8 or 2.15000000000000007e-10 < a

   1. Initial program 94.1%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 83.8

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

   5. Applied rewrites 83.8%

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

   if -2.6e8 < a < 2.15000000000000007e-10

   1. Initial program 73.1%

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

   3. Taylor expanded in a around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 32.5

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

   5. Applied rewrites 32.5%

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

   7. Applied rewrites 33.0%

      \[\leadsto x + \frac{t - x}{\color{blue}{\frac{a}{y - z}}} \]

   8. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-sub N/A

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

      7. associate-/l* N/A

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

      8. associate-/l* N/A

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

      9. distribute-rgt-out-- N/A

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

      10. distribute-lft-neg-in N/A

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

      11. mul-1-neg N/A

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

      12. lower-fma.f64 N/A

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

   10. Applied rewrites 79.6%

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

Alternative 7: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{if}\;t \leq -2.6 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ t (- a z)) (- y z))))
   (if (<= t -2.6e-42) t_1 (if (<= t 1.2e+31) (fma (/ (- t x) a) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (a - z)) * (y - z);
	double tmp;
	if (t <= -2.6e-42) {
		tmp = t_1;
	} else if (t <= 1.2e+31) {
		tmp = fma(((t - x) / a), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / Float64(a - z)) * Float64(y - z))
	tmp = 0.0
	if (t <= -2.6e-42)
		tmp = t_1;
	elseif (t <= 1.2e+31)
		tmp = fma(Float64(Float64(t - x) / a), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.6e-42], t$95$1, If[LessEqual[t, 1.2e+31], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6e-42 or 1.19999999999999991e31 < t

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 75.7

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

   5. Applied rewrites 75.7%

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

   if -2.6e-42 < t < 1.19999999999999991e31

   1. Initial program 75.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 59.2

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

   5. Applied rewrites 59.2%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-42}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - x}{a}, y, x\right)\\ \mathbf{if}\;a \leq -6400000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-75}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t x) a) y x)))
   (if (<= a -6400000.0) t_1 (if (<= a 7.8e-75) (* (- 1.0 (/ y z)) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - x) / a), y, x);
	double tmp;
	if (a <= -6400000.0) {
		tmp = t_1;
	} else if (a <= 7.8e-75) {
		tmp = (1.0 - (y / z)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - x) / a), y, x)
	tmp = 0.0
	if (a <= -6400000.0)
		tmp = t_1;
	elseif (a <= 7.8e-75)
		tmp = Float64(Float64(1.0 - Float64(y / z)) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[a, -6400000.0], t$95$1, If[LessEqual[a, 7.8e-75], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.4e6 or 7.8000000000000003e-75 < a

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 72.3

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

   5. Applied rewrites 72.3%

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

   if -6.4e6 < a < 7.8000000000000003e-75

   1. Initial program 73.3%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 66.4

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 60.4%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 60.4%

       \[\leadsto \left(1 - \frac{y}{z}\right) \cdot \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 60.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{if}\;a \leq -6400000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-75}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y a) (- t x) x)))
   (if (<= a -6400000.0) t_1 (if (<= a 7.8e-75) (* (- 1.0 (/ y z)) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / a), (t - x), x);
	double tmp;
	if (a <= -6400000.0) {
		tmp = t_1;
	} else if (a <= 7.8e-75) {
		tmp = (1.0 - (y / z)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / a), Float64(t - x), x)
	tmp = 0.0
	if (a <= -6400000.0)
		tmp = t_1;
	elseif (a <= 7.8e-75)
		tmp = Float64(Float64(1.0 - Float64(y / z)) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -6400000.0], t$95$1, If[LessEqual[a, 7.8e-75], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.4e6 or 7.8000000000000003e-75 < a

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 72.3

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

   5. Applied rewrites 72.3%

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

   7. Applied rewrites 72.3%

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

   if -6.4e6 < a < 7.8000000000000003e-75

   1. Initial program 73.3%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 66.4

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

   5. Applied rewrites 66.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 60.4%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 60.4%

       \[\leadsto \left(1 - \frac{y}{z}\right) \cdot \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 55.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{if}\;a \leq -1.12 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.7 \cdot 10^{-34}:\\ \;\;\;\;\left(1 - \frac{y}{z}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t a) y x)))
   (if (<= a -1.12e+32) t_1 (if (<= a 5.7e-34) (* (- 1.0 (/ y z)) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / a), y, x);
	double tmp;
	if (a <= -1.12e+32) {
		tmp = t_1;
	} else if (a <= 5.7e-34) {
		tmp = (1.0 - (y / z)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / a), y, x)
	tmp = 0.0
	if (a <= -1.12e+32)
		tmp = t_1;
	elseif (a <= 5.7e-34)
		tmp = Float64(Float64(1.0 - Float64(y / z)) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[a, -1.12e+32], t$95$1, If[LessEqual[a, 5.7e-34], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.12000000000000007e32 or 5.69999999999999974e-34 < a

   1. Initial program 91.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 72.2

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

   5. Applied rewrites 72.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 65.3%

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

   if -1.12000000000000007e32 < a < 5.69999999999999974e-34

   1. Initial program 75.0%

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

   3. Taylor expanded in a around 0

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower--.f64 65.4

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

   5. Applied rewrites 65.4%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 59.2%

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

   9. Taylor expanded in t around inf

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

   11. Applied rewrites 59.2%

       \[\leadsto \left(1 - \frac{y}{z}\right) \cdot \color{blue}{t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 47.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) + x\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+141}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (- t x) x)))
   (if (<= z -1.22e+175) t_1 (if (<= z 3.8e+141) (fma (/ t a) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) + x;
	double tmp;
	if (z <= -1.22e+175) {
		tmp = t_1;
	} else if (z <= 3.8e+141) {
		tmp = fma((t / a), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) + x)
	tmp = 0.0
	if (z <= -1.22e+175)
		tmp = t_1;
	elseif (z <= 3.8e+141)
		tmp = fma(Float64(t / a), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.22e+175], t$95$1, If[LessEqual[z, 3.8e+141], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22e175 or 3.79999999999999976e141 < z

   1. Initial program 63.8%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 51.7

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

   5. Applied rewrites 51.7%

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

   if -1.22e175 < z < 3.79999999999999976e141

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 65.9

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

   5. Applied rewrites 65.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 55.2%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+175}:\\ \;\;\;\;\left(t - x\right) + x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+141}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 28.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) + x\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (- t x) x)))
   (if (<= z -1.22e+160) t_1 (if (<= z 2.9e+56) (* (/ y a) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) + x;
	double tmp;
	if (z <= -1.22e+160) {
		tmp = t_1;
	} else if (z <= 2.9e+56) {
		tmp = (y / a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) + x
    if (z <= (-1.22d+160)) then
        tmp = t_1
    else if (z <= 2.9d+56) then
        tmp = (y / a) * 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 a) {
	double t_1 = (t - x) + x;
	double tmp;
	if (z <= -1.22e+160) {
		tmp = t_1;
	} else if (z <= 2.9e+56) {
		tmp = (y / a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) + x
	tmp = 0
	if z <= -1.22e+160:
		tmp = t_1
	elif z <= 2.9e+56:
		tmp = (y / a) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) + x)
	tmp = 0.0
	if (z <= -1.22e+160)
		tmp = t_1;
	elseif (z <= 2.9e+56)
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) + x;
	tmp = 0.0;
	if (z <= -1.22e+160)
		tmp = t_1;
	elseif (z <= 2.9e+56)
		tmp = (y / a) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.22e+160], t$95$1, If[LessEqual[z, 2.9e+56], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22e160 or 2.90000000000000007e56 < z

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 42.0

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

   5. Applied rewrites 42.0%

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

   if -1.22e160 < z < 2.90000000000000007e56

   1. Initial program 90.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 40.3

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

   5. Applied rewrites 40.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 21.3%

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

   10. Applied rewrites 28.5%

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

4. Final simplification 32.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+160}:\\ \;\;\;\;\left(t - x\right) + x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 18.7% accurate, 4.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 18.6

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

5. Applied rewrites 18.6%

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

6. Final simplification 18.6%

   \[\leadsto \left(t - x\right) + x \]
7. Add Preprocessing

Alternative 14: 2.8% accurate, 4.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[((-x) + x), $MachinePrecision]

Derivation

1. Initial program 83.8%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 18.6

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

5. Applied rewrites 18.6%

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

6. Taylor expanded in t around 0

   \[\leadsto x + -1 \cdot \color{blue}{x} \]
7. Step-by-step derivation

8. Applied rewrites 2.6%

   \[\leadsto x + \left(-x\right) \]

9. Final simplification 2.6%

   \[\leadsto \left(-x\right) + x \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024235 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))