Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 67.4% → 91.2%

Time: 5.5s

Alternatives: 14

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - y}{z - a}\\ t_2 := \mathsf{fma}\left(t\_1, t - x, x\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 45000:\\ \;\;\;\;\mathsf{fma}\left(x, \mathsf{fma}\left(-1, t\_1, \frac{z}{z - a}\right) - \frac{a}{z - a}, \frac{t \cdot \left(z - y\right)}{z - a}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (- z y) (- z a))) (t_2 (fma t_1 (- t x) x)))
  (if (<= t -1.7e+43)
    t_2
    (if (<= t 45000.0)
      (fma
       x
       (- (fma -1.0 t_1 (/ z (- z a))) (/ a (- z a)))
       (/ (* t (- z y)) (- z a)))
      t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - y) / (z - a);
	double t_2 = fma(t_1, (t - x), x);
	double tmp;
	if (t <= -1.7e+43) {
		tmp = t_2;
	} else if (t <= 45000.0) {
		tmp = fma(x, (fma(-1.0, t_1, (z / (z - a))) - (a / (z - a))), ((t * (z - y)) / (z - a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - y) / Float64(z - a))
	t_2 = fma(t_1, Float64(t - x), x)
	tmp = 0.0
	if (t <= -1.7e+43)
		tmp = t_2;
	elseif (t <= 45000.0)
		tmp = fma(x, Float64(fma(-1.0, t_1, Float64(z / Float64(z - a))) - Float64(a / Float64(z - a))), Float64(Float64(t * Float64(z - y)) / Float64(z - a)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -1.7e+43], t$95$2, If[LessEqual[t, 45000.0], N[(x * N[(N[(-1.0 * t$95$1 + N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.7000000000000001e43 or 45000 < t

   1. Initial program 67.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

   if -1.7000000000000001e43 < t < 45000

   1. Initial program 67.4%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. frac-2neg N/A

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

      4. add-to-fraction N/A

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

      5. lower-/.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lift-*.f64 N/A

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

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

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower-*.f64 N/A

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

      16. lower--.f64 N/A

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

      17. lift--.f64 N/A

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

      18. sub-negate-rev N/A

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

      19. lower--.f64 61.9%

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

   3. Applied rewrites 61.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-fma.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lower--.f64 78.7%

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

   6. Applied rewrites 78.7%

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

Alternative 2: 90.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-271}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\frac{z - a}{z - y}}, t - x, x\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z - a}, t - x, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (/ (* (- y z) (- t x)) (- a z)))))
  (if (<= t_1 -1e-271)
    (fma (/ 1.0 (/ (- z a) (- z y))) (- t x) x)
    (if (<= t_1 0.0)
      (+ t (* -1.0 (/ (- (* y (- t x)) (* a (- t x))) z)))
      (fma (/ (- z y) (- z a)) (- t x) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_1 <= -1e-271) {
		tmp = fma((1.0 / ((z - a) / (z - y))), (t - x), x);
	} else if (t_1 <= 0.0) {
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	} else {
		tmp = fma(((z - y) / (z - a)), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -1e-271)
		tmp = fma(Float64(1.0 / Float64(Float64(z - a) / Float64(z - y))), Float64(t - x), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(-1.0 * Float64(Float64(Float64(y * Float64(t - x)) - Float64(a * Float64(t - x))) / z)));
	else
		tmp = fma(Float64(Float64(z - y) / Float64(z - a)), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-271], N[(N[(1.0 / N[(N[(z - a), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(-1.0 * N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.9999999999999996e-272

   1. Initial program 67.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

      1. lift-/.f64 N/A

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

      2. div-flip N/A

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

      3. lower-unsound-/.f64 N/A

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

      4. lower-unsound-/.f64 83.6%

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

   5. Applied rewrites 83.6%

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

   if -9.9999999999999996e-272 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 0.0

   1. Initial program 67.4%

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

   2. Taylor expanded in z around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 45.6%

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

   4. Applied rewrites 45.6%

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

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

   1. Initial program 67.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

Alternative 3: 84.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq 4.9 \cdot 10^{+241}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{z - a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z 4.9e+241)
  (fma (/ (- z y) (- z a)) (- t x) x)
  (* (/ (- y z) (- a z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 4.9e+241) {
		tmp = fma(((z - y) / (z - a)), (t - x), x);
	} else {
		tmp = ((y - z) / (a - z)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 4.9e+241)
		tmp = fma(Float64(Float64(z - y) / Float64(z - a)), Float64(t - x), x);
	else
		tmp = Float64(Float64(Float64(y - z) / Float64(a - z)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 4.9e+241], N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.8999999999999997e241

   1. Initial program 67.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

   if 4.8999999999999997e241 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.3%

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

   4. Applied rewrites 51.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 51.3%

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 51.3%

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

   6. Applied rewrites 51.3%

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

Alternative 4: 80.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq 9.4 \cdot 10^{+111}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x - t}{z - a}, y - z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z 9.4e+111)
  (fma (/ (- x t) (- z a)) (- y z) x)
  (* (/ (- y z) (- a z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 9.4e+111) {
		tmp = fma(((x - t) / (z - a)), (y - z), x);
	} else {
		tmp = ((y - z) / (a - z)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 9.4e+111)
		tmp = fma(Float64(Float64(x - t) / Float64(z - a)), Float64(y - z), x);
	else
		tmp = Float64(Float64(Float64(y - z) / Float64(a - z)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 9.4e+111], N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.4000000000000002e111

   1. Initial program 67.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 79.4%

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

   3. Applied rewrites 79.4%

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

   if 9.4000000000000002e111 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.3%

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

   4. Applied rewrites 51.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 51.3%

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 51.3%

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

   6. Applied rewrites 51.3%

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

Alternative 5: 67.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{z - a}, y - z, x\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 235:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (fma (/ x (- z a)) (- y z) x)))
  (if (<= x -5.8e+41)
    t_1
    (if (<= x 235.0) (fma (/ t (- a z)) (- y z) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / (z - a)), (y - z), x);
	double tmp;
	if (x <= -5.8e+41) {
		tmp = t_1;
	} else if (x <= 235.0) {
		tmp = fma((t / (a - z)), (y - z), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / Float64(z - a)), Float64(y - z), x)
	tmp = 0.0
	if (x <= -5.8e+41)
		tmp = t_1;
	elseif (x <= 235.0)
		tmp = fma(Float64(t / Float64(a - z)), Float64(y - z), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[x, -5.8e+41], t$95$1, If[LessEqual[x, 235.0], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.7999999999999998e41 or 235 < x

   1. Initial program 67.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 79.4%

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 41.6%

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

   6. Applied rewrites 41.6%

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

   if -5.7999999999999998e41 < x < 235

   1. Initial program 67.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.7%

      \[\leadsto x + \frac{\left(y - z\right) \cdot \color{blue}{t}}{a - z} \]
   5. 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 63.8%

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

   6. Applied rewrites 63.8%

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

Alternative 6: 64.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x}{z - a}, y - z, x\right)\\ \mathbf{if}\;x \leq -2.05 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 235:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (fma (/ x (- z a)) (- y z) x)))
  (if (<= x -2.05e+27)
    t_1
    (if (<= x 235.0) (* (/ (- y z) (- a z)) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x / (z - a)), (y - z), x);
	double tmp;
	if (x <= -2.05e+27) {
		tmp = t_1;
	} else if (x <= 235.0) {
		tmp = ((y - z) / (a - z)) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x / Float64(z - a)), Float64(y - z), x)
	tmp = 0.0
	if (x <= -2.05e+27)
		tmp = t_1;
	elseif (x <= 235.0)
		tmp = Float64(Float64(Float64(y - z) / Float64(a - z)) * t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[x, -2.05e+27], t$95$1, If[LessEqual[x, 235.0], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0500000000000001e27 or 235 < x

   1. Initial program 67.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 79.4%

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 41.6%

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

   6. Applied rewrites 41.6%

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

   if -2.0500000000000001e27 < x < 235

   1. Initial program 67.4%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.3%

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

   4. Applied rewrites 51.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 51.3%

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 51.3%

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

   6. Applied rewrites 51.3%

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

Alternative 7: 64.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+101}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-41}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -4.1e+101)
  (fma (/ t a) (- y z) x)
  (if (<= a 1.1e-41)
    (* (/ (- y z) (- a z)) t)
    (fma (/ y a) (- t x) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.1e+101) {
		tmp = fma((t / a), (y - z), x);
	} else if (a <= 1.1e-41) {
		tmp = ((y - z) / (a - z)) * t;
	} else {
		tmp = fma((y / a), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.1e+101)
		tmp = fma(Float64(t / a), Float64(y - z), x);
	elseif (a <= 1.1e-41)
		tmp = Float64(Float64(Float64(y - z) / Float64(a - z)) * t);
	else
		tmp = fma(Float64(y / a), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.1e+101], N[(N[(t / a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 1.1e-41], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.1e101

   1. Initial program 67.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.7%

      \[\leadsto x + \frac{\left(y - z\right) \cdot \color{blue}{t}}{a - z} \]
   5. 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 63.8%

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

   6. Applied rewrites 63.8%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 44.2%

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

   if -4.1e101 < a < 1.1e-41

   1. Initial program 67.4%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.3%

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

   4. Applied rewrites 51.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 51.3%

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 51.3%

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

   6. Applied rewrites 51.3%

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

   if 1.1e-41 < a

   1. Initial program 67.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 48.7%

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

   6. Applied rewrites 48.7%

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

Alternative 8: 62.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -106:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y - z, x\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-41}:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} - -1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -106.0)
  (fma (/ t a) (- y z) x)
  (if (<= a 1.1e-41)
    (* t (- (/ y (- a z)) -1.0))
    (fma (/ y a) (- t x) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -106.0) {
		tmp = fma((t / a), (y - z), x);
	} else if (a <= 1.1e-41) {
		tmp = t * ((y / (a - z)) - -1.0);
	} else {
		tmp = fma((y / a), (t - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -106.0)
		tmp = fma(Float64(t / a), Float64(y - z), x);
	elseif (a <= 1.1e-41)
		tmp = Float64(t * Float64(Float64(y / Float64(a - z)) - -1.0));
	else
		tmp = fma(Float64(y / a), Float64(t - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -106.0], N[(N[(t / a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 1.1e-41], N[(t * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -106

   1. Initial program 67.4%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 55.7%

      \[\leadsto x + \frac{\left(y - z\right) \cdot \color{blue}{t}}{a - z} \]
   5. 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 63.8%

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

   6. Applied rewrites 63.8%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 44.2%

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

   if -106 < a < 1.1e-41

   1. Initial program 67.4%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.3%

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 41.7%

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

   if 1.1e-41 < a

   1. Initial program 67.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 48.7%

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

   6. Applied rewrites 48.7%

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

Alternative 9: 60.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+124}:\\ \;\;\;\;t \cdot 1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z -1e+124)
  (* t 1.0)
  (if (<= z 9e+86) (fma (/ y a) (- t x) x) (* t 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+124) {
		tmp = t * 1.0;
	} else if (z <= 9e+86) {
		tmp = fma((y / a), (t - x), x);
	} else {
		tmp = t * 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+124)
		tmp = Float64(t * 1.0);
	elseif (z <= 9e+86)
		tmp = fma(Float64(y / a), Float64(t - x), x);
	else
		tmp = Float64(t * 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+124], N[(t * 1.0), $MachinePrecision], If[LessEqual[z, 9e+86], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(t * 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999995e123 or 8.9999999999999999e86 < z

   1. Initial program 67.4%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.3%

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 41.7%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 24.5%

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

   11. Taylor expanded in z around inf

       \[\leadsto t \cdot 1 \]
   12. Step-by-step derivation

   13. Applied rewrites 25.6%

       \[\leadsto t \cdot 1 \]

   if -9.9999999999999995e123 < z < 8.9999999999999999e86

   1. Initial program 67.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 48.7%

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

   6. Applied rewrites 48.7%

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

Alternative 10: 41.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -0.00037:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-138}:\\ \;\;\;\;\frac{t \cdot \left(z - y\right)}{z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -0.00037)
  (+ t x)
  (if (<= a 1.5e-138)
    (/ (* t (- z y)) z)
    (if (<= a 1.8e-107) (/ (* x y) (- z a)) (+ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.00037) {
		tmp = t + x;
	} else if (a <= 1.5e-138) {
		tmp = (t * (z - y)) / z;
	} else if (a <= 1.8e-107) {
		tmp = (x * y) / (z - a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 (a <= (-0.00037d0)) then
        tmp = t + x
    else if (a <= 1.5d-138) then
        tmp = (t * (z - y)) / z
    else if (a <= 1.8d-107) then
        tmp = (x * y) / (z - a)
    else
        tmp = t + 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 (a <= -0.00037) {
		tmp = t + x;
	} else if (a <= 1.5e-138) {
		tmp = (t * (z - y)) / z;
	} else if (a <= 1.8e-107) {
		tmp = (x * y) / (z - a);
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.00037:
		tmp = t + x
	elif a <= 1.5e-138:
		tmp = (t * (z - y)) / z
	elif a <= 1.8e-107:
		tmp = (x * y) / (z - a)
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.00037)
		tmp = Float64(t + x);
	elseif (a <= 1.5e-138)
		tmp = Float64(Float64(t * Float64(z - y)) / z);
	elseif (a <= 1.8e-107)
		tmp = Float64(Float64(x * y) / Float64(z - a));
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.00037)
		tmp = t + x;
	elseif (a <= 1.5e-138)
		tmp = (t * (z - y)) / z;
	elseif (a <= 1.8e-107)
		tmp = (x * y) / (z - a);
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.00037], N[(t + x), $MachinePrecision], If[LessEqual[a, 1.5e-138], N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 1.8e-107], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], N[(t + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.6999999999999999e-4 or 1.7999999999999999e-107 < a

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 19.6%

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

   4. Applied rewrites 19.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

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

   9. Applied rewrites 2.8%

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

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 35.2%

       \[\leadsto t + x \]

   if -3.6999999999999999e-4 < a < 1.5e-138

   1. Initial program 67.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*l* N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. mult-flip-rev N/A

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

      11. frac-2neg N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 N/A

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

      16. lift--.f64 N/A

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

      17. sub-negate-rev N/A

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

      18. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

   4. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.4%

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

   6. Applied rewrites 39.4%

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

   7. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 27.0%

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

   9. Applied rewrites 27.0%

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

   if 1.5e-138 < a < 1.7999999999999999e-107

   1. Initial program 67.4%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 40.8%

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

   4. Applied rewrites 40.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. associate-*l/ N/A

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

      8. mult-flip N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. frac-2neg N/A

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

      13. metadata-eval N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. lower-/.f64 36.7%

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

   6. Applied rewrites 36.7%

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

   7. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 20.6%

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

   9. Applied rewrites 20.6%

      \[\leadsto \frac{x \cdot y}{\color{blue}{z - a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 40.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+31}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+171}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= y -9.6e+31)
  (/ (* t y) (- a z))
  (if (<= y 1.42e+171) (+ t x) (/ (* x y) (- z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9.6e+31) {
		tmp = (t * y) / (a - z);
	} else if (y <= 1.42e+171) {
		tmp = t + x;
	} else {
		tmp = (x * y) / (z - a);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 (y <= (-9.6d+31)) then
        tmp = (t * y) / (a - z)
    else if (y <= 1.42d+171) then
        tmp = t + x
    else
        tmp = (x * y) / (z - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9.6e+31) {
		tmp = (t * y) / (a - z);
	} else if (y <= 1.42e+171) {
		tmp = t + x;
	} else {
		tmp = (x * y) / (z - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9.6e+31:
		tmp = (t * y) / (a - z)
	elif y <= 1.42e+171:
		tmp = t + x
	else:
		tmp = (x * y) / (z - a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9.6e+31)
		tmp = Float64(Float64(t * y) / Float64(a - z));
	elseif (y <= 1.42e+171)
		tmp = Float64(t + x);
	else
		tmp = Float64(Float64(x * y) / Float64(z - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9.6e+31)
		tmp = (t * y) / (a - z);
	elseif (y <= 1.42e+171)
		tmp = t + x;
	else
		tmp = (x * y) / (z - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9.6e+31], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.42e+171], N[(t + x), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5999999999999993e31

   1. Initial program 67.4%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.3%

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 20.8%

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

   7. Applied rewrites 20.8%

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

   if -9.5999999999999993e31 < y < 1.4199999999999999e171

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 19.6%

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

   4. Applied rewrites 19.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

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

   9. Applied rewrites 2.8%

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

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 35.2%

       \[\leadsto t + x \]

   if 1.4199999999999999e171 < y

   1. Initial program 67.4%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 40.8%

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

   4. Applied rewrites 40.8%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. associate-*l/ N/A

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

      8. mult-flip N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 N/A

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

      11. lift--.f64 N/A

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

      12. frac-2neg N/A

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

      13. metadata-eval N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lift--.f64 N/A

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

      17. lower-/.f64 36.7%

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

   6. Applied rewrites 36.7%

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

   7. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 20.6%

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

   9. Applied rewrites 20.6%

      \[\leadsto \frac{x \cdot y}{\color{blue}{z - a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 40.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \frac{t \cdot y}{a - z}\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+170}:\\ \;\;\;\;t + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* t y) (- a z))))
  (if (<= y -9.6e+31) t_1 (if (<= y 2.4e+170) (+ t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / (a - z);
	double tmp;
	if (y <= -9.6e+31) {
		tmp = t_1;
	} else if (y <= 2.4e+170) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * y) / (a - z)
    if (y <= (-9.6d+31)) then
        tmp = t_1
    else if (y <= 2.4d+170) then
        tmp = t + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / (a - z);
	double tmp;
	if (y <= -9.6e+31) {
		tmp = t_1;
	} else if (y <= 2.4e+170) {
		tmp = t + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * y) / (a - z)
	tmp = 0
	if y <= -9.6e+31:
		tmp = t_1
	elif y <= 2.4e+170:
		tmp = t + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * y) / Float64(a - z))
	tmp = 0.0
	if (y <= -9.6e+31)
		tmp = t_1;
	elseif (y <= 2.4e+170)
		tmp = Float64(t + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * y) / (a - z);
	tmp = 0.0;
	if (y <= -9.6e+31)
		tmp = t_1;
	elseif (y <= 2.4e+170)
		tmp = t + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.6e+31], t$95$1, If[LessEqual[y, 2.4e+170], N[(t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5999999999999993e31 or 2.4e170 < y

   1. Initial program 67.4%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.3%

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 20.8%

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

   7. Applied rewrites 20.8%

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

   if -9.5999999999999993e31 < y < 2.4e170

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 19.6%

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

   4. Applied rewrites 19.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

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

   9. Applied rewrites 2.8%

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

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 35.2%

       \[\leadsto t + x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 38.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -0.00039:\\ \;\;\;\;t + x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-133}:\\ \;\;\;\;t \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t + x\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -0.00039) (+ t x) (if (<= a 3.3e-133) (* t 1.0) (+ t x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.00039) {
		tmp = t + x;
	} else if (a <= 3.3e-133) {
		tmp = t * 1.0;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 (a <= (-0.00039d0)) then
        tmp = t + x
    else if (a <= 3.3d-133) then
        tmp = t * 1.0d0
    else
        tmp = t + 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 (a <= -0.00039) {
		tmp = t + x;
	} else if (a <= 3.3e-133) {
		tmp = t * 1.0;
	} else {
		tmp = t + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.00039:
		tmp = t + x
	elif a <= 3.3e-133:
		tmp = t * 1.0
	else:
		tmp = t + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.00039)
		tmp = Float64(t + x);
	elseif (a <= 3.3e-133)
		tmp = Float64(t * 1.0);
	else
		tmp = Float64(t + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.00039)
		tmp = t + x;
	elseif (a <= 3.3e-133)
		tmp = t * 1.0;
	else
		tmp = t + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.00039], N[(t + x), $MachinePrecision], If[LessEqual[a, 3.3e-133], N[(t * 1.0), $MachinePrecision], N[(t + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.8999999999999999e-4 or 3.3000000000000001e-133 < a

   1. Initial program 67.4%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 19.6%

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

   4. Applied rewrites 19.6%

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

   5. Taylor expanded in x around inf

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

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

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

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + -1 \cdot x} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      3. lower-+.f64 2.8%

         \[\leadsto \color{blue}{-1 \cdot x + x} \]

      4. lift-*.f64 N/A

         \[\leadsto -1 \cdot x + x \]

      5. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

      6. lower-neg.f64 2.8%

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

   9. Applied rewrites 2.8%

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

   10. Taylor expanded in x around 0

       \[\leadsto t + x \]
   11. Step-by-step derivation

   12. Applied rewrites 35.2%

       \[\leadsto t + x \]

   if -3.8999999999999999e-4 < a < 3.3000000000000001e-133

   1. Initial program 67.4%

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

   2. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.3%

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 41.7%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 24.5%

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

   11. Taylor expanded in z around inf

       \[\leadsto t \cdot 1 \]
   12. Step-by-step derivation

   13. Applied rewrites 25.6%

       \[\leadsto t \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 35.2% accurate, 5.1× speedup

Math

\[t + x \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.4%

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

2. Taylor expanded in z around inf

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

   1. lower--.f64 19.6%

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

4. Applied rewrites 19.6%

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

5. Taylor expanded in x around inf

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

   1. lower-*.f64 2.8%

      \[\leadsto x + -1 \cdot x \]

7. Applied rewrites 2.8%

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

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + -1 \cdot x} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{-1 \cdot x + x} \]

   3. lower-+.f64 2.8%

      \[\leadsto \color{blue}{-1 \cdot x + x} \]

   4. lift-*.f64 N/A

      \[\leadsto -1 \cdot x + x \]

   5. mul-1-neg N/A

      \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

   6. lower-neg.f64 2.8%

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

9. Applied rewrites 2.8%

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

10. Taylor expanded in x around 0

    \[\leadsto t + x \]
11. Step-by-step derivation

12. Applied rewrites 35.2%

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

Reproduce

herbie shell --seed 2025212 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64
  (+ x (/ (* (- y z) (- t x)) (- a z))))