Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Percentage Accurate: 85.6% → 99.6%

Time: 8.0s

Alternatives: 12

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ t_2 := \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+295}:\\ \;\;\;\;t\_2 + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ t (- a z)) (- y z) x)) (t_2 (/ (* t (- y z)) (- a z))))
   (if (<= t_2 (- INFINITY)) t_1 (if (<= t_2 1e+295) (+ t_2 x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((t / (a - z)), (y - z), x);
	double t_2 = (t * (y - z)) / (a - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 1e+295) {
		tmp = t_2 + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(t / Float64(a - z)), Float64(y - z), x)
	t_2 = Float64(Float64(t * Float64(y - z)) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 1e+295)
		tmp = Float64(t_2 + 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] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 1e+295], N[(t$95$2 + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0 or 9.9999999999999998e294 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 45.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 9.9999999999999998e294

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \mathbf{elif}\;\frac{t \cdot \left(y - z\right)}{a - z} \leq 10^{+295}:\\ \;\;\;\;\frac{t \cdot \left(y - z\right)}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, t, x\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+59}:\\ \;\;\;\;\frac{t \cdot y}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e-85)
   (fma (/ z (- z a)) t x)
   (if (<= z 3.4e+59) (+ (/ (* t y) (- a z)) x) (fma (- 1.0 (/ y z)) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e-85) {
		tmp = fma((z / (z - a)), t, x);
	} else if (z <= 3.4e+59) {
		tmp = ((t * y) / (a - z)) + x;
	} else {
		tmp = fma((1.0 - (y / z)), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e-85)
		tmp = fma(Float64(z / Float64(z - a)), t, x);
	elseif (z <= 3.4e+59)
		tmp = Float64(Float64(Float64(t * y) / Float64(a - z)) + x);
	else
		tmp = fma(Float64(1.0 - Float64(y / z)), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e-85], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[z, 3.4e+59], N[(N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7999999999999999e-85

   1. Initial program 79.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

         \[\leadsto x + \frac{-1}{\frac{\color{blue}{0 - \left(a - z\right)}}{\left(y - z\right) \cdot t}} \]

      9. lift--.f64 N/A

         \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(a - z\right)}}{\left(y - z\right) \cdot t}} \]

      10. sub-neg N/A

          \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(a + \left(\mathsf{neg}\left(z\right)\right)\right)}}{\left(y - z\right) \cdot t}} \]

      11. +-commutative N/A

          \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + a\right)}}{\left(y - z\right) \cdot t}} \]

      12. associate--r+ N/A

          \[\leadsto x + \frac{-1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - a}}{\left(y - z\right) \cdot t}} \]

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 79.1

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 79.1

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

   4. Applied rewrites 79.1%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 81.4

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

   7. Applied rewrites 81.4%

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

   if -1.7999999999999999e-85 < z < 3.40000000000000006e59

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 86.8

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

   5. Applied rewrites 86.8%

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

   if 3.40000000000000006e59 < z

   1. Initial program 74.5%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

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

      8. div-sub N/A

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

      9. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(0 - \left(\frac{y}{z} - \color{blue}{1}\right), t, x\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \frac{y}{z}\right) + 1}, t, x\right) \]

      11. neg-sub0 N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 98.3

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

   5. Applied rewrites 98.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-85}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, t, x\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+59}:\\ \;\;\;\;\frac{t \cdot y}{a - z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-101}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, t, x\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e-101)
   (fma (/ z (- z a)) t x)
   (if (<= z 5e+49) (fma (/ t a) (- y z) x) (fma (- 1.0 (/ y z)) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e-101) {
		tmp = fma((z / (z - a)), t, x);
	} else if (z <= 5e+49) {
		tmp = fma((t / a), (y - z), x);
	} else {
		tmp = fma((1.0 - (y / z)), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e-101)
		tmp = fma(Float64(z / Float64(z - a)), t, x);
	elseif (z <= 5e+49)
		tmp = fma(Float64(t / a), Float64(y - z), x);
	else
		tmp = fma(Float64(1.0 - Float64(y / z)), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e-101], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[z, 5e+49], N[(N[(t / a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4999999999999996e-101

   1. Initial program 80.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

         \[\leadsto x + \frac{-1}{\frac{\color{blue}{0 - \left(a - z\right)}}{\left(y - z\right) \cdot t}} \]

      9. lift--.f64 N/A

         \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(a - z\right)}}{\left(y - z\right) \cdot t}} \]

      10. sub-neg N/A

          \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(a + \left(\mathsf{neg}\left(z\right)\right)\right)}}{\left(y - z\right) \cdot t}} \]

      11. +-commutative N/A

          \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + a\right)}}{\left(y - z\right) \cdot t}} \]

      12. associate--r+ N/A

          \[\leadsto x + \frac{-1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - a}}{\left(y - z\right) \cdot t}} \]

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 80.1

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 80.1

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

   4. Applied rewrites 80.1%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 81.1

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

   7. Applied rewrites 81.1%

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

   if -6.4999999999999996e-101 < z < 5.0000000000000004e49

   1. Initial program 95.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 97.4

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

   4. Applied rewrites 97.4%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 83.5

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

   7. Applied rewrites 83.5%

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

   if 5.0000000000000004e49 < z

   1. Initial program 74.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

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

      8. div-sub N/A

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

      9. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(0 - \left(\frac{y}{z} - \color{blue}{1}\right), t, x\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \frac{y}{z}\right) + 1}, t, x\right) \]

      11. neg-sub0 N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 98.3

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

   5. Applied rewrites 98.3%

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

Alternative 4: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-101}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, t, x\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e-101)
   (fma (/ z (- z a)) t x)
   (if (<= z 9.8e+50) (fma (/ (- y z) a) t x) (fma (- 1.0 (/ y z)) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e-101) {
		tmp = fma((z / (z - a)), t, x);
	} else if (z <= 9.8e+50) {
		tmp = fma(((y - z) / a), t, x);
	} else {
		tmp = fma((1.0 - (y / z)), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e-101)
		tmp = fma(Float64(z / Float64(z - a)), t, x);
	elseif (z <= 9.8e+50)
		tmp = fma(Float64(Float64(y - z) / a), t, x);
	else
		tmp = fma(Float64(1.0 - Float64(y / z)), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e-101], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[z, 9.8e+50], N[(N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] * t + x), $MachinePrecision], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4999999999999996e-101

   1. Initial program 80.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

         \[\leadsto x + \frac{-1}{\frac{\color{blue}{0 - \left(a - z\right)}}{\left(y - z\right) \cdot t}} \]

      9. lift--.f64 N/A

         \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(a - z\right)}}{\left(y - z\right) \cdot t}} \]

      10. sub-neg N/A

          \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(a + \left(\mathsf{neg}\left(z\right)\right)\right)}}{\left(y - z\right) \cdot t}} \]

      11. +-commutative N/A

          \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + a\right)}}{\left(y - z\right) \cdot t}} \]

      12. associate--r+ N/A

          \[\leadsto x + \frac{-1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - a}}{\left(y - z\right) \cdot t}} \]

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 80.1

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 80.1

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

   4. Applied rewrites 80.1%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 81.1

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

   7. Applied rewrites 81.1%

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

   if -6.4999999999999996e-101 < z < 9.8000000000000003e50

   1. Initial program 95.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 82.9

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

   5. Applied rewrites 82.9%

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

   if 9.8000000000000003e50 < z

   1. Initial program 74.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

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

      8. div-sub N/A

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

      9. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(0 - \left(\frac{y}{z} - \color{blue}{1}\right), t, x\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \frac{y}{z}\right) + 1}, t, x\right) \]

      11. neg-sub0 N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 98.3

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

   5. Applied rewrites 98.3%

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

Alternative 5: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-101}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, t, x\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e-101)
   (fma (/ z (- z a)) t x)
   (if (<= z 4.6e+49) (fma y (/ t a) x) (fma (- 1.0 (/ y z)) t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e-101) {
		tmp = fma((z / (z - a)), t, x);
	} else if (z <= 4.6e+49) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = fma((1.0 - (y / z)), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e-101)
		tmp = fma(Float64(z / Float64(z - a)), t, x);
	elseif (z <= 4.6e+49)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = fma(Float64(1.0 - Float64(y / z)), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e-101], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[z, 4.6e+49], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4999999999999996e-101

   1. Initial program 80.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

         \[\leadsto x + \frac{-1}{\frac{\color{blue}{0 - \left(a - z\right)}}{\left(y - z\right) \cdot t}} \]

      9. lift--.f64 N/A

         \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(a - z\right)}}{\left(y - z\right) \cdot t}} \]

      10. sub-neg N/A

          \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(a + \left(\mathsf{neg}\left(z\right)\right)\right)}}{\left(y - z\right) \cdot t}} \]

      11. +-commutative N/A

          \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + a\right)}}{\left(y - z\right) \cdot t}} \]

      12. associate--r+ N/A

          \[\leadsto x + \frac{-1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - a}}{\left(y - z\right) \cdot t}} \]

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 80.1

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 80.1

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

   4. Applied rewrites 80.1%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 81.1

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

   7. Applied rewrites 81.1%

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

   if -6.4999999999999996e-101 < z < 4.60000000000000004e49

   1. Initial program 95.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 97.4

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

   4. Applied rewrites 97.4%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 80.2

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

   7. Applied rewrites 80.2%

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

   if 4.60000000000000004e49 < z

   1. Initial program 74.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

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

      8. div-sub N/A

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

      9. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(0 - \left(\frac{y}{z} - \color{blue}{1}\right), t, x\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \frac{y}{z}\right) + 1}, t, x\right) \]

      11. neg-sub0 N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 98.3

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

   5. Applied rewrites 98.3%

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

Alternative 6: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z}{z - a}, t, x\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ z (- z a)) t x)))
   (if (<= z -6.5e-101) t_1 (if (<= z 4.7e-7) (fma y (/ t a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((z / (z - a)), t, x);
	double tmp;
	if (z <= -6.5e-101) {
		tmp = t_1;
	} else if (z <= 4.7e-7) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(z / Float64(z - a)), t, x)
	tmp = 0.0
	if (z <= -6.5e-101)
		tmp = t_1;
	elseif (z <= 4.7e-7)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision]}, If[LessEqual[z, -6.5e-101], t$95$1, If[LessEqual[z, 4.7e-7], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999996e-101 or 4.7e-7 < z

   1. Initial program 80.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. frac-2neg N/A

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

      4. metadata-eval N/A

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

      5. lower-/.f64 N/A

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

      6. distribute-neg-frac N/A

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

      7. lower-/.f64 N/A

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

      8. neg-sub0 N/A

         \[\leadsto x + \frac{-1}{\frac{\color{blue}{0 - \left(a - z\right)}}{\left(y - z\right) \cdot t}} \]

      9. lift--.f64 N/A

         \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(a - z\right)}}{\left(y - z\right) \cdot t}} \]

      10. sub-neg N/A

          \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(a + \left(\mathsf{neg}\left(z\right)\right)\right)}}{\left(y - z\right) \cdot t}} \]

      11. +-commutative N/A

          \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + a\right)}}{\left(y - z\right) \cdot t}} \]

      12. associate--r+ N/A

          \[\leadsto x + \frac{-1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - a}}{\left(y - z\right) \cdot t}} \]

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

      15. lower--.f64 80.1

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

      16. lift-*.f64 N/A

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

      17. *-commutative N/A

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

      18. lower-*.f64 80.1

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

   4. Applied rewrites 80.1%

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

   5. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 83.1

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

   7. Applied rewrites 83.1%

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

   if -6.4999999999999996e-101 < z < 4.7e-7

   1. Initial program 95.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 97.0

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

   4. Applied rewrites 97.0%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 82.7

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

   7. Applied rewrites 82.7%

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

Alternative 7: 76.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+120}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+120) (+ x t) (if (<= z 8.6e+50) (fma y (/ t a) x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+120) {
		tmp = x + t;
	} else if (z <= 8.6e+50) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+120)
		tmp = Float64(x + t);
	elseif (z <= 8.6e+50)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+120], N[(x + t), $MachinePrecision], If[LessEqual[z, 8.6e+50], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.9999999999999998e120 or 8.5999999999999994e50 < z

   1. Initial program 72.6%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 85.3

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

   5. Applied rewrites 85.3%

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

   if -7.9999999999999998e120 < z < 8.5999999999999994e50

   1. Initial program 94.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 96.9

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

   4. Applied rewrites 96.9%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 72.4

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

   7. Applied rewrites 72.4%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+120}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+129}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+129) (+ x t) (if (<= z 2.06e+55) (fma (/ y a) t x) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+129) {
		tmp = x + t;
	} else if (z <= 2.06e+55) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+129)
		tmp = Float64(x + t);
	elseif (z <= 2.06e+55)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+129], N[(x + t), $MachinePrecision], If[LessEqual[z, 2.06e+55], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000024e129 or 2.06e55 < z

   1. Initial program 73.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 86.0

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

   5. Applied rewrites 86.0%

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

   if -5.20000000000000024e129 < z < 2.06e55

   1. Initial program 93.5%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 71.7

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

   5. Applied rewrites 71.7%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+129}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 2.06 \cdot 10^{+55}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 96.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+171}:\\ \;\;\;\;\mathsf{fma}\left(1 - \frac{y}{z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+171)
   (fma (- 1.0 (/ y z)) t x)
   (fma (/ t (- a z)) (- y z) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+171) {
		tmp = fma((1.0 - (y / z)), t, x);
	} else {
		tmp = fma((t / (a - z)), (y - z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+171)
		tmp = fma(Float64(1.0 - Float64(y / z)), t, x);
	else
		tmp = fma(Float64(t / Float64(a - z)), Float64(y - z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+171], N[(N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e171

   1. Initial program 74.3%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. neg-sub0 N/A

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

      8. div-sub N/A

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

      9. *-inverses N/A

         \[\leadsto \mathsf{fma}\left(0 - \left(\frac{y}{z} - \color{blue}{1}\right), t, x\right) \]

      10. associate-+l- N/A

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - \frac{y}{z}\right) + 1}, t, x\right) \]

      11. neg-sub0 N/A

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

      12. mul-1-neg N/A

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

      13. +-commutative N/A

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

      14. mul-1-neg N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 N/A

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

      17. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if -1.0500000000000001e171 < z

   1. Initial program 87.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 96.6

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

   4. Applied rewrites 96.6%

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

Alternative 10: 60.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-148}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.2e-148) (+ x t) (if (<= z 8.2e-138) (* (/ y a) t) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e-148) {
		tmp = x + t;
	} else if (z <= 8.2e-138) {
		tmp = (y / a) * t;
	} else {
		tmp = x + t;
	}
	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) :: tmp
    if (z <= (-3.2d-148)) then
        tmp = x + t
    else if (z <= 8.2d-138) then
        tmp = (y / a) * t
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2e-148) {
		tmp = x + t;
	} else if (z <= 8.2e-138) {
		tmp = (y / a) * t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.2e-148:
		tmp = x + t
	elif z <= 8.2e-138:
		tmp = (y / a) * t
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2e-148)
		tmp = Float64(x + t);
	elseif (z <= 8.2e-138)
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.2e-148)
		tmp = x + t;
	elseif (z <= 8.2e-138)
		tmp = (y / a) * t;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2e-148], N[(x + t), $MachinePrecision], If[LessEqual[z, 8.2e-138], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999993e-148 or 8.19999999999999998e-138 < z

   1. Initial program 82.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-+.f64 66.5

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

   5. Applied rewrites 66.5%

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

   if -3.19999999999999993e-148 < z < 8.19999999999999998e-138

   1. Initial program 94.5%

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

   3. Taylor expanded in t around inf

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

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

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

      2. associate-/l* N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. associate-*r/ N/A

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

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

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower--.f64 60.4

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

   5. Applied rewrites 60.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 50.5%

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

   10. Applied rewrites 55.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-148}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\left(y - z\right) \cdot \frac{-1}{z - a}, t, x\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (fma (* (- y z) (/ -1.0 (- z a))) t x))

C

double code(double x, double y, double z, double t, double a) {
	return fma(((y - z) * (-1.0 / (z - a))), t, x);
}

Julia

function code(x, y, z, t, a)
	return fma(Float64(Float64(y - z) * Float64(-1.0 / Float64(z - a))), t, x)
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(y - z), $MachinePrecision] * N[(-1.0 / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision]

Derivation

1. Initial program 86.0%

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

   1. lift-/.f64 N/A

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

   2. clear-num N/A

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

   3. frac-2neg N/A

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

   4. metadata-eval N/A

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

   5. lower-/.f64 N/A

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

   6. distribute-neg-frac N/A

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

   7. lower-/.f64 N/A

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

   8. neg-sub0 N/A

      \[\leadsto x + \frac{-1}{\frac{\color{blue}{0 - \left(a - z\right)}}{\left(y - z\right) \cdot t}} \]

   9. lift--.f64 N/A

      \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(a - z\right)}}{\left(y - z\right) \cdot t}} \]

   10. sub-neg N/A

       \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(a + \left(\mathsf{neg}\left(z\right)\right)\right)}}{\left(y - z\right) \cdot t}} \]

   11. +-commutative N/A

       \[\leadsto x + \frac{-1}{\frac{0 - \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) + a\right)}}{\left(y - z\right) \cdot t}} \]

   12. associate--r+ N/A

       \[\leadsto x + \frac{-1}{\frac{\color{blue}{\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - a}}{\left(y - z\right) \cdot t}} \]

   13. neg-sub0 N/A

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

   14. remove-double-neg N/A

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

   15. lower--.f64 86.0

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

   16. lift-*.f64 N/A

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

   17. *-commutative N/A

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

   18. lower-*.f64 86.0

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

4. Applied rewrites 86.0%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. associate-/r/ N/A

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

   6. lift-*.f64 N/A

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

   7. *-commutative N/A

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

   8. associate-*r* N/A

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

   9. lower-fma.f64 N/A

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

   10. lower-*.f64 N/A

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

   11. lower-/.f64 98.1

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

6. Applied rewrites 98.1%

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

7. Final simplification 98.1%

   \[\leadsto \mathsf{fma}\left(\left(y - z\right) \cdot \frac{-1}{z - a}, t, x\right) \]
8. Add Preprocessing

Alternative 12: 60.5% accurate, 6.5× speedup

Math

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

FPCore

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

C

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

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 + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

3. Taylor expanded in z around inf

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

   1. lower-+.f64 55.9

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

5. Applied rewrites 55.9%

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

6. Final simplification 55.9%

   \[\leadsto x + t \]
7. Add Preprocessing

Developer Target 1: 99.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{a - z} \cdot t\\ \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y z) (- a z)) t))))
   (if (< t -1.0682974490174067e-39)
     t_1
     (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} 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 = x + (((y - z) / (a - z)) * t)
    if (t < (-1.0682974490174067d-39)) then
        tmp = t_1
    else if (t < 3.9110949887586375d-141) then
        tmp = x + (((y - z) * t) / (a - z))
    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 = x + (((y - z) / (a - z)) * t);
	double tmp;
	if (t < -1.0682974490174067e-39) {
		tmp = t_1;
	} else if (t < 3.9110949887586375e-141) {
		tmp = x + (((y - z) * t) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - z) / (a - z)) * t)
	tmp = 0
	if t < -1.0682974490174067e-39:
		tmp = t_1
	elif t < 3.9110949887586375e-141:
		tmp = x + (((y - z) * t) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) / Float64(a - z)) * t))
	tmp = 0.0
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = Float64(x + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - z) / (a - z)) * t);
	tmp = 0.0;
	if (t < -1.0682974490174067e-39)
		tmp = t_1;
	elseif (t < 3.9110949887586375e-141)
		tmp = x + (((y - z) * t) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.0682974490174067e-39], t$95$1, If[Less[t, 3.9110949887586375e-141], N[(x + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024249 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -10682974490174067/10000000000000000000000000000000000000000000000000000000) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 312887599100691/80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t)))))

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