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

Percentage Accurate: 77.3% → 92.3%

Time: 10.6s

Alternatives: 9

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 1 + \frac{z - t}{t - a}, x\right)\\ t_2 := \left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (+ 1.0 (/ (- z t) (- t a))) x))
        (t_2 (+ (+ x y) (/ (* y (- z t)) (- t a)))))
   (if (<= t_2 -5e-193) t_1 (if (<= t_2 0.0) (fma (/ y t) (- z a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (1.0 + ((z - t) / (t - a))), x);
	double t_2 = (x + y) + ((y * (z - t)) / (t - a));
	double tmp;
	if (t_2 <= -5e-193) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = fma((y / t), (z - a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(1.0 + Float64(Float64(z - t) / Float64(t - a))), x)
	t_2 = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)))
	tmp = 0.0
	if (t_2 <= -5e-193)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = fma(Float64(y / t), Float64(z - a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 + N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-193], t$95$1, If[LessEqual[t$95$2, 0.0], N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.0000000000000005e-193 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 85.4%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. unsub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 94.1

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

   5. Applied rewrites 94.1%

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

   if -5.0000000000000005e-193 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 8.2%

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

   3. Taylor expanded in t around inf

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

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

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -5 \cdot 10^{-193}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 + \frac{z - t}{t - a}, x\right)\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 0:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 + \frac{z - t}{t - a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{z}{t - a}, x\right)\\ t_2 := \left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a}\\ t_3 := \left(x + y\right) + \frac{y \cdot z}{t - a}\\ \mathbf{if}\;t\_2 \leq -1.5 \cdot 10^{+305}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-193}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 10^{-211}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+197}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ z (- t a)) x))
        (t_2 (+ (+ x y) (/ (* y (- z t)) (- t a))))
        (t_3 (+ (+ x y) (/ (* y z) (- t a)))))
   (if (<= t_2 -1.5e+305)
     t_1
     (if (<= t_2 -5e-193)
       t_3
       (if (<= t_2 1e-211)
         (fma (/ y t) (- z a) x)
         (if (<= t_2 4e+197) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (z / (t - a)), x);
	double t_2 = (x + y) + ((y * (z - t)) / (t - a));
	double t_3 = (x + y) + ((y * z) / (t - a));
	double tmp;
	if (t_2 <= -1.5e+305) {
		tmp = t_1;
	} else if (t_2 <= -5e-193) {
		tmp = t_3;
	} else if (t_2 <= 1e-211) {
		tmp = fma((y / t), (z - a), x);
	} else if (t_2 <= 4e+197) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(z / Float64(t - a)), x)
	t_2 = Float64(Float64(x + y) + Float64(Float64(y * Float64(z - t)) / Float64(t - a)))
	t_3 = Float64(Float64(x + y) + Float64(Float64(y * z) / Float64(t - a)))
	tmp = 0.0
	if (t_2 <= -1.5e+305)
		tmp = t_1;
	elseif (t_2 <= -5e-193)
		tmp = t_3;
	elseif (t_2 <= 1e-211)
		tmp = fma(Float64(y / t), Float64(z - a), x);
	elseif (t_2 <= 4e+197)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + y), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1.5e+305], t$95$1, If[LessEqual[t$95$2, -5e-193], t$95$3, If[LessEqual[t$95$2, 1e-211], N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 4e+197], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.49999999999999991e305 or 3.9999999999999998e197 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 57.6%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. unsub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 91.3

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

   5. Applied rewrites 91.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 87.8%

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

   if -1.49999999999999991e305 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.0000000000000005e-193 or 1.00000000000000009e-211 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 3.9999999999999998e197

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 96.6

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

   5. Applied rewrites 96.6%

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

   if -5.0000000000000005e-193 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.00000000000000009e-211

   1. Initial program 17.2%

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

   3. Taylor expanded in t around inf

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

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

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -1.5 \cdot 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t - a}, x\right)\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq -5 \cdot 10^{-193}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot z}{t - a}\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 10^{-211}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{elif}\;\left(x + y\right) + \frac{y \cdot \left(z - t\right)}{t - a} \leq 4 \cdot 10^{+197}:\\ \;\;\;\;\left(x + y\right) + \frac{y \cdot z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t - a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \mathbf{if}\;a \leq -900000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (- 1.0 (/ z a)) x)))
   (if (<= a -900000.0) t_1 (if (<= a 5.3e-31) (fma y (/ z (- t a)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (1.0 - (z / a)), x);
	double tmp;
	if (a <= -900000.0) {
		tmp = t_1;
	} else if (a <= 5.3e-31) {
		tmp = fma(y, (z / (t - a)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(1.0 - Float64(z / a)), x)
	tmp = 0.0
	if (a <= -900000.0)
		tmp = t_1;
	elseif (a <= 5.3e-31)
		tmp = fma(y, Float64(z / Float64(t - a)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -900000.0], t$95$1, If[LessEqual[a, 5.3e-31], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -9e5 or 5.3000000000000001e-31 < a

   1. Initial program 80.5%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 87.8

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

   5. Applied rewrites 87.8%

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

   if -9e5 < a < 5.3000000000000001e-31

   1. Initial program 75.4%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. unsub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 86.3

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

   5. Applied rewrites 86.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 90.4%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -900000:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-31}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{t}, z - a, x\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-62}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y t) (- z a) x)))
   (if (<= t -2.3e-64) t_1 (if (<= t 1.8e-62) (fma y (- 1.0 (/ z a)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / t), (z - a), x);
	double tmp;
	if (t <= -2.3e-64) {
		tmp = t_1;
	} else if (t <= 1.8e-62) {
		tmp = fma(y, (1.0 - (z / a)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / t), Float64(z - a), x)
	tmp = 0.0
	if (t <= -2.3e-64)
		tmp = t_1;
	elseif (t <= 1.8e-62)
		tmp = fma(y, Float64(1.0 - Float64(z / a)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * N[(z - a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -2.3e-64], t$95$1, If[LessEqual[t, 1.8e-62], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3000000000000001e-64 or 1.8e-62 < t

   1. Initial program 69.3%

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

   3. Taylor expanded in t around inf

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative N/A

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

      5. +-commutative N/A

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

      6. associate-+r+ N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. associate-/l* N/A

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

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

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

      13. lower-fma.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 85.2

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

   5. Applied rewrites 85.2%

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

   if -2.3000000000000001e-64 < t < 1.8e-62

   1. Initial program 91.5%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 89.7

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

   5. Applied rewrites 89.7%

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

Alternative 5: 78.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{-64}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-79}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma y (/ z t) x)))
   (if (<= t -2.2e-64) t_1 (if (<= t 3.5e-79) (fma y (- 1.0 (/ z a)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, (z / t), x);
	double tmp;
	if (t <= -2.2e-64) {
		tmp = t_1;
	} else if (t <= 3.5e-79) {
		tmp = fma(y, (1.0 - (z / a)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(z / t), x)
	tmp = 0.0
	if (t <= -2.2e-64)
		tmp = t_1;
	elseif (t <= 3.5e-79)
		tmp = fma(y, Float64(1.0 - Float64(z / a)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -2.2e-64], t$95$1, If[LessEqual[t, 3.5e-79], N[(y * N[(1.0 - N[(z / a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2e-64 or 3.5000000000000003e-79 < t

   1. Initial program 69.5%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. unsub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 87.6

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

   5. Applied rewrites 87.6%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 82.9%

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

   if -2.2e-64 < t < 3.5000000000000003e-79

   1. Initial program 91.4%

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

   3. Taylor expanded in t around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 89.6

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

   5. Applied rewrites 89.6%

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

Alternative 6: 77.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-49}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+70) (+ x y) (if (<= a 1.45e-49) (fma y (/ z t) x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+70) {
		tmp = x + y;
	} else if (a <= 1.45e-49) {
		tmp = fma(y, (z / t), x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e+70)
		tmp = Float64(x + y);
	elseif (a <= 1.45e-49)
		tmp = fma(y, Float64(z / t), x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+70], N[(x + y), $MachinePrecision], If[LessEqual[a, 1.45e-49], N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.19999999999999993e70 or 1.45e-49 < a

   1. Initial program 81.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 83.1

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

   5. Applied rewrites 83.1%

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

   if -1.19999999999999993e70 < a < 1.45e-49

   1. Initial program 74.8%

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

   3. Taylor expanded in x around 0

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. *-rgt-identity N/A

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

      4. associate-/l* N/A

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

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

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

      6. unsub-neg N/A

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

      7. mul-1-neg N/A

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

      8. lower-fma.f64 N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 76.4%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+70}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-49}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+239}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.4e+239) x (if (<= t 1.25e+117) (+ x y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.4e+239) {
		tmp = x;
	} else if (t <= 1.25e+117) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	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 (t <= (-6.4d+239)) then
        tmp = x
    else if (t <= 1.25d+117) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.4e+239) {
		tmp = x;
	} else if (t <= 1.25e+117) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.4e+239:
		tmp = x
	elif t <= 1.25e+117:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.4e+239)
		tmp = x;
	elseif (t <= 1.25e+117)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.4e+239)
		tmp = x;
	elseif (t <= 1.25e+117)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.4e+239], x, If[LessEqual[t, 1.25e+117], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -6.4000000000000003e239 or 1.24999999999999996e117 < t

   1. Initial program 44.2%

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

   3. Taylor expanded in a around 0

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

      1. cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 52.5

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

   5. Applied rewrites 52.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 75.3%

      \[\leadsto x + \color{blue}{0} \]
   9. Step-by-step derivation

   10. Applied rewrites 75.3%

       \[\leadsto x \]

   if -6.4000000000000003e239 < t < 1.24999999999999996e117

   1. Initial program 85.8%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 70.2

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

   5. Applied rewrites 70.2%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+239}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{+117}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.9% accurate, 29.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return 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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.2%

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

3. Taylor expanded in a around 0

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

   1. cancel-sign-sub-inv N/A

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

   2. metadata-eval N/A

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

   3. *-lft-identity N/A

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

   4. +-commutative N/A

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

   5. associate-/l* N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-/.f64 N/A

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

   8. lower--.f64 N/A

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

   9. +-commutative N/A

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

   10. lower-+.f64 49.9

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

5. Applied rewrites 49.9%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 57.7%

   \[\leadsto x + \color{blue}{0} \]
9. Step-by-step derivation

10. Applied rewrites 57.7%

    \[\leadsto x \]
11. Add Preprocessing

Alternative 9: 2.7% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 78.2%

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

3. Taylor expanded in z around 0

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

   1. cancel-sign-sub-inv N/A

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

   2. metadata-eval N/A

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

   3. *-lft-identity N/A

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

   4. +-commutative N/A

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

   5. *-commutative N/A

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

   6. associate-/l* N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lower--.f64 N/A

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

   10. +-commutative N/A

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

   11. lower-+.f64 67.4

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

5. Applied rewrites 67.4%

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

6. Taylor expanded in y around inf

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

8. Applied rewrites 19.6%

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

9. Taylor expanded in t around inf

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

11. Applied rewrites 2.7%

    \[\leadsto 0 \]
12. Add Preprocessing

Developer Target 1: 88.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (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) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (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 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024233 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

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