Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.1% → 92.2%

Time: 7.4s

Alternatives: 17

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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(y - z) * Float64(Float64(t - x) / Float64(a - z))))
end

MATLAB

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

Wolfram

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

Initial Program: 79.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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(y - z) * Float64(Float64(t - x) / Float64(a - z))))
end

MATLAB

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

Wolfram

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

Alternative 1: 92.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{z - a}, t - x, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) (- z a)) (- t x) x))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -1e-227)
     t_1
     (if (<= t_2 0.0)
       (+ t (* -1.0 (/ (- (* y (- t x)) (* a (- t x))) z)))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / (z - a)), (t - x), x);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-227) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / Float64(z - a)), Float64(t - x), x)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-227)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(-1.0 * Float64(Float64(Float64(y * Float64(t - x)) - Float64(a * Float64(t - x))) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-227], t$95$1, If[LessEqual[t$95$2, 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], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.99999999999999945e-228 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. div-flip N/A

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

      6. associate-*r/ N/A

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

      7. mult-flip N/A

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

      8. times-frac N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. frac-2neg N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 83.2

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

   3. Applied rewrites 83.2%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. lift--.f64 N/A

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

      4. sub-negate-rev N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 83.2

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

      10. lift-/.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. metadata-eval N/A

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

      14. mul-1-neg N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 83.3

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

   5. Applied rewrites 83.3%

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

   if -9.99999999999999945e-228 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.1%

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

   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 46.3

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

   4. Applied rewrites 46.3%

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

Alternative 2: 86.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{z - a}, t - x, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{t}{\frac{z - a}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) (- z a)) (- t x) x))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -1e-227) t_1 (if (<= t_2 0.0) (/ t (/ (- z a) (- z y))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / (z - a)), (t - x), x);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-227) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t / ((z - a) / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / Float64(z - a)), Float64(t - x), x)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-227)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t / Float64(Float64(z - a) / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-227], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t / N[(N[(z - a), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.99999999999999945e-228 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. div-flip N/A

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

      6. associate-*r/ N/A

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

      7. mult-flip N/A

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

      8. times-frac N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. frac-2neg N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 83.2

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

   3. Applied rewrites 83.2%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. lift--.f64 N/A

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

      4. sub-negate-rev N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 83.2

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

      10. lift-/.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. metadata-eval N/A

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

      14. mul-1-neg N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 83.3

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

   5. Applied rewrites 83.3%

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

   if -9.99999999999999945e-228 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. sub-div N/A

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

      6. lift--.f64 N/A

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

      7. div-flip N/A

         \[\leadsto t \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}} \]

      8. mult-flip-rev N/A

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

      9. lower-/.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

Alternative 3: 83.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{x - t}{z - a}, y - z, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-256}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- x t) (- z a)) (- y z) x))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 -1e-227)
     t_1
     (if (<= t_2 5e-256) (/ t (/ (- z a) (- z y))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((x - t) / (z - a)), (y - z), x);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -1e-227) {
		tmp = t_1;
	} else if (t_2 <= 5e-256) {
		tmp = t / ((z - a) / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(x - t) / Float64(z - a)), Float64(y - z), x)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -1e-227)
		tmp = t_1;
	elseif (t_2 <= 5e-256)
		tmp = Float64(t / Float64(Float64(z - a) / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-227], t$95$1, If[LessEqual[t$95$2, 5e-256], N[(t / N[(N[(z - a), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.99999999999999945e-228 or 5e-256 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 79.2

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

      6. lift-/.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 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

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 79.2

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

   3. Applied rewrites 79.2%

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

   if -9.99999999999999945e-228 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5e-256

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. sub-div N/A

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

      6. lift--.f64 N/A

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

      7. div-flip N/A

         \[\leadsto t \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}} \]

      8. mult-flip-rev N/A

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

      9. lower-/.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

Alternative 4: 71.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+165}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z - y}}\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-158}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-114}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{z - a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e+165)
   (/ t (/ (- z a) (- z y)))
   (if (<= z -5.7e-158)
     (fma (/ (- y z) (- a z)) t x)
     (if (<= z 1.1e-114)
       (+ x (/ (- y z) (/ a (- t x))))
       (if (<= z 2.8e+45)
         (+ x (/ (* y (- t x)) (- a z)))
         (* (/ (- z y) (- z a)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e+165) {
		tmp = t / ((z - a) / (z - y));
	} else if (z <= -5.7e-158) {
		tmp = fma(((y - z) / (a - z)), t, x);
	} else if (z <= 1.1e-114) {
		tmp = x + ((y - z) / (a / (t - x)));
	} else if (z <= 2.8e+45) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else {
		tmp = ((z - y) / (z - a)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e+165)
		tmp = Float64(t / Float64(Float64(z - a) / Float64(z - y)));
	elseif (z <= -5.7e-158)
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), t, x);
	elseif (z <= 1.1e-114)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(a / Float64(t - x))));
	elseif (z <= 2.8e+45)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	else
		tmp = Float64(Float64(Float64(z - y) / Float64(z - a)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e+165], N[(t / N[(N[(z - a), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.7e-158], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[z, 1.1e-114], N[(x + N[(N[(y - z), $MachinePrecision] / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+45], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.2000000000000003e165

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. sub-div N/A

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

      6. lift--.f64 N/A

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

      7. div-flip N/A

         \[\leadsto t \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}} \]

      8. mult-flip-rev N/A

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

      9. lower-/.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

   if -6.2000000000000003e165 < z < -5.69999999999999982e-158

   1. Initial program 79.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. div-flip N/A

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

      6. associate-*r/ N/A

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

      7. mult-flip N/A

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

      8. times-frac N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. frac-2neg N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 83.2

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

   3. Applied rewrites 83.2%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 66.9%

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

   if -5.69999999999999982e-158 < z < 1.10000000000000006e-114

   1. Initial program 79.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 51.9%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. div-flip N/A

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

      4. mult-flip-rev N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 52.0

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

   6. Applied rewrites 52.0%

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

   if 1.10000000000000006e-114 < z < 2.7999999999999999e45

   1. Initial program 79.1%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 54.8

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

   4. Applied rewrites 54.8%

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

   if 2.7999999999999999e45 < z

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   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 51.4

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

      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. frac-2neg N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 51.4

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

   6. Applied rewrites 51.4%

      \[\leadsto \frac{z - y}{z - a} \cdot \color{blue}{t} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 5: 70.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+165}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z - y}}\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-158}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-114}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - x}{a}, y - z, x\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{z - a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e+165)
   (/ t (/ (- z a) (- z y)))
   (if (<= z -5.7e-158)
     (fma (/ (- y z) (- a z)) t x)
     (if (<= z 1.1e-114)
       (fma (/ (- t x) a) (- y z) x)
       (if (<= z 2.8e+45)
         (+ x (/ (* y (- t x)) (- a z)))
         (* (/ (- z y) (- z a)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e+165) {
		tmp = t / ((z - a) / (z - y));
	} else if (z <= -5.7e-158) {
		tmp = fma(((y - z) / (a - z)), t, x);
	} else if (z <= 1.1e-114) {
		tmp = fma(((t - x) / a), (y - z), x);
	} else if (z <= 2.8e+45) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else {
		tmp = ((z - y) / (z - a)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e+165)
		tmp = Float64(t / Float64(Float64(z - a) / Float64(z - y)));
	elseif (z <= -5.7e-158)
		tmp = fma(Float64(Float64(y - z) / Float64(a - z)), t, x);
	elseif (z <= 1.1e-114)
		tmp = fma(Float64(Float64(t - x) / a), Float64(y - z), x);
	elseif (z <= 2.8e+45)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	else
		tmp = Float64(Float64(Float64(z - y) / Float64(z - a)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e+165], N[(t / N[(N[(z - a), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.7e-158], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[z, 1.1e-114], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2.8e+45], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.2000000000000003e165

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. sub-div N/A

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

      6. lift--.f64 N/A

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

      7. div-flip N/A

         \[\leadsto t \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}} \]

      8. mult-flip-rev N/A

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

      9. lower-/.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

   if -6.2000000000000003e165 < z < -5.69999999999999982e-158

   1. Initial program 79.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. div-flip N/A

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

      6. associate-*r/ N/A

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

      7. mult-flip N/A

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

      8. times-frac N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. frac-2neg N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 83.2

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

   3. Applied rewrites 83.2%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 66.9%

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

   if -5.69999999999999982e-158 < z < 1.10000000000000006e-114

   1. Initial program 79.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 51.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 51.9

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

   6. Applied rewrites 51.9%

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

   if 1.10000000000000006e-114 < z < 2.7999999999999999e45

   1. Initial program 79.1%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 54.8

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

   4. Applied rewrites 54.8%

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

   if 2.7999999999999999e45 < z

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   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 51.4

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

      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. frac-2neg N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 51.4

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

   6. Applied rewrites 51.4%

      \[\leadsto \frac{z - y}{z - a} \cdot \color{blue}{t} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 6: 70.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+165}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z - y}}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-220}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{z - a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y z) (- a z)) t x)))
   (if (<= z -6.2e+165)
     (/ t (/ (- z a) (- z y)))
     (if (<= z -1.1e-158)
       t_1
       (if (<= z 2.5e-220)
         (fma (/ y a) (- t x) x)
         (if (<= z 2.9e+46) t_1 (* (/ (- z y) (- z a)) t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - z) / (a - z)), t, x);
	double tmp;
	if (z <= -6.2e+165) {
		tmp = t / ((z - a) / (z - y));
	} else if (z <= -1.1e-158) {
		tmp = t_1;
	} else if (z <= 2.5e-220) {
		tmp = fma((y / a), (t - x), x);
	} else if (z <= 2.9e+46) {
		tmp = t_1;
	} else {
		tmp = ((z - y) / (z - a)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - z) / Float64(a - z)), t, x)
	tmp = 0.0
	if (z <= -6.2e+165)
		tmp = Float64(t / Float64(Float64(z - a) / Float64(z - y)));
	elseif (z <= -1.1e-158)
		tmp = t_1;
	elseif (z <= 2.5e-220)
		tmp = fma(Float64(y / a), Float64(t - x), x);
	elseif (z <= 2.9e+46)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(z - y) / Float64(z - a)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision]}, If[LessEqual[z, -6.2e+165], N[(t / N[(N[(z - a), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.1e-158], t$95$1, If[LessEqual[z, 2.5e-220], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2.9e+46], t$95$1, N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.2000000000000003e165

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. sub-div N/A

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

      6. lift--.f64 N/A

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

      7. div-flip N/A

         \[\leadsto t \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}} \]

      8. mult-flip-rev N/A

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

      9. lower-/.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

   if -6.2000000000000003e165 < z < -1.1000000000000001e-158 or 2.5000000000000001e-220 < z < 2.9000000000000002e46

   1. Initial program 79.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. div-flip N/A

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

      6. associate-*r/ N/A

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

      7. mult-flip N/A

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

      8. times-frac N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. frac-2neg N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 83.2

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

   3. Applied rewrites 83.2%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 66.9%

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

   if -1.1000000000000001e-158 < z < 2.5000000000000001e-220

   1. Initial program 79.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. div-flip N/A

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

      6. associate-*r/ N/A

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

      7. mult-flip N/A

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

      8. times-frac N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. frac-2neg N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 83.2

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

   3. Applied rewrites 83.2%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. lift--.f64 N/A

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

      4. sub-negate-rev N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 83.2

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

      10. lift-/.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. metadata-eval N/A

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

      14. mul-1-neg N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 48.8

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

   8. Applied rewrites 48.8%

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

   if 2.9000000000000002e46 < z

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   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 51.4

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

      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. frac-2neg N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 51.4

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

   6. Applied rewrites 51.4%

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

Alternative 7: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{t - x}{a}, y - z, x\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z - y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- t x) a) (- y z) x)))
   (if (<= a -3.2e+126)
     t_1
     (if (<= a 5.8e-15) (/ t (/ (- z a) (- z y))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((t - x) / a), (y - z), x);
	double tmp;
	if (a <= -3.2e+126) {
		tmp = t_1;
	} else if (a <= 5.8e-15) {
		tmp = t / ((z - a) / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(t - x) / a), Float64(y - z), x)
	tmp = 0.0
	if (a <= -3.2e+126)
		tmp = t_1;
	elseif (a <= 5.8e-15)
		tmp = Float64(t / Float64(Float64(z - a) / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -3.2e+126], t$95$1, If[LessEqual[a, 5.8e-15], N[(t / N[(N[(z - a), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -3.1999999999999998e126 or 5.80000000000000037e-15 < a

   1. Initial program 79.1%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 51.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 51.9

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

   6. Applied rewrites 51.9%

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

   if -3.1999999999999998e126 < a < 5.80000000000000037e-15

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. sub-div N/A

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

      6. lift--.f64 N/A

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

      7. div-flip N/A

         \[\leadsto t \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}} \]

      8. mult-flip-rev N/A

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

      9. lower-/.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

Alternative 8: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-149}:\\ \;\;\;\;\frac{t}{\frac{z - a}{z - y}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+44}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{z - a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e-149)
   (/ t (/ (- z a) (- z y)))
   (if (<= z 9.5e+44) (fma (/ y a) (- t x) x) (* (/ (- z y) (- z a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e-149) {
		tmp = t / ((z - a) / (z - y));
	} else if (z <= 9.5e+44) {
		tmp = fma((y / a), (t - x), x);
	} else {
		tmp = ((z - y) / (z - a)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e-149)
		tmp = Float64(t / Float64(Float64(z - a) / Float64(z - y)));
	elseif (z <= 9.5e+44)
		tmp = fma(Float64(y / a), Float64(t - x), x);
	else
		tmp = Float64(Float64(Float64(z - y) / Float64(z - a)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e-149], N[(t / N[(N[(z - a), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+44], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9500000000000001e-149

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   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. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. sub-div N/A

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

      6. lift--.f64 N/A

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

      7. div-flip N/A

         \[\leadsto t \cdot \frac{1}{\color{blue}{\frac{a - z}{y - z}}} \]

      8. mult-flip-rev N/A

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

      9. lower-/.f64 N/A

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

      10. frac-2neg N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 51.3

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

   6. Applied rewrites 51.3%

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

   if -1.9500000000000001e-149 < z < 9.5000000000000004e44

   1. Initial program 79.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. div-flip N/A

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

      6. associate-*r/ N/A

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

      7. mult-flip N/A

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

      8. times-frac N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. frac-2neg N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 83.2

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

   3. Applied rewrites 83.2%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. lift--.f64 N/A

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

      4. sub-negate-rev N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 83.2

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

      10. lift-/.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. metadata-eval N/A

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

      14. mul-1-neg N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 48.8

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

   8. Applied rewrites 48.8%

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

   if 9.5000000000000004e44 < z

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   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 51.4

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

      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. frac-2neg N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 51.4

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

   6. Applied rewrites 51.4%

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

Alternative 9: 64.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - y}{z - a} \cdot t\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+44}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- z y) (- z a)) t)))
   (if (<= z -1.95e-149) t_1 (if (<= z 9.5e+44) (fma (/ y a) (- t x) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - y) / (z - a)) * t;
	double tmp;
	if (z <= -1.95e-149) {
		tmp = t_1;
	} else if (z <= 9.5e+44) {
		tmp = fma((y / a), (t - x), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - y) / Float64(z - a)) * t)
	tmp = 0.0
	if (z <= -1.95e-149)
		tmp = t_1;
	elseif (z <= 9.5e+44)
		tmp = fma(Float64(y / a), Float64(t - x), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -1.95e-149], t$95$1, If[LessEqual[z, 9.5e+44], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9500000000000001e-149 or 9.5000000000000004e44 < z

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

      \[\leadsto \color{blue}{t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)} \]
   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 51.4

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

      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. frac-2neg N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lift--.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 51.4

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

   6. Applied rewrites 51.4%

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

   if -1.9500000000000001e-149 < z < 9.5000000000000004e44

   1. Initial program 79.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. div-flip N/A

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

      6. associate-*r/ N/A

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

      7. mult-flip N/A

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

      8. times-frac N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. frac-2neg N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 83.2

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

   3. Applied rewrites 83.2%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. lift--.f64 N/A

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

      4. sub-negate-rev N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 83.2

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

      10. lift-/.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. metadata-eval N/A

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

      14. mul-1-neg N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 48.8

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

   8. Applied rewrites 48.8%

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

Alternative 10: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} - -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y a) (- t x) x)))
   (if (<= a -1.15e+74)
     t_1
     (if (<= a 5.8e-15) (* t (- (/ y (- a z)) -1.0)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / a), (t - x), x);
	double tmp;
	if (a <= -1.15e+74) {
		tmp = t_1;
	} else if (a <= 5.8e-15) {
		tmp = t * ((y / (a - z)) - -1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / a), Float64(t - x), x)
	tmp = 0.0
	if (a <= -1.15e+74)
		tmp = t_1;
	elseif (a <= 5.8e-15)
		tmp = Float64(t * Float64(Float64(y / Float64(a - z)) - -1.0));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.15e+74], t$95$1, If[LessEqual[a, 5.8e-15], N[(t * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1499999999999999e74 or 5.80000000000000037e-15 < a

   1. Initial program 79.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. div-flip N/A

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

      6. associate-*r/ N/A

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

      7. mult-flip N/A

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

      8. times-frac N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. frac-2neg N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 83.2

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

   3. Applied rewrites 83.2%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. lift--.f64 N/A

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

      4. sub-negate-rev N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 83.2

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

      10. lift-/.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. metadata-eval N/A

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

      14. mul-1-neg N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 48.8

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

   8. Applied rewrites 48.8%

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

   if -1.1499999999999999e74 < a < 5.80000000000000037e-15

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

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

   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 41.5%

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

Alternative 11: 60.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+75}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+75) t (if (<= z 2.3e+33) (fma (/ y a) (- t x) x) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+75) {
		tmp = t;
	} else if (z <= 2.3e+33) {
		tmp = fma((y / a), (t - x), x);
	} else {
		tmp = t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+75)
		tmp = t;
	elseif (z <= 2.3e+33)
		tmp = fma(Float64(y / a), Float64(t - x), x);
	else
		tmp = t;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+75], t, If[LessEqual[z, 2.3e+33], N[(N[(y / a), $MachinePrecision] * N[(t - x), $MachinePrecision] + x), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -9.1999999999999994e75 or 2.30000000000000011e33 < z

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 16.4

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

   7. Applied rewrites 16.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 17.9

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

   9. Applied rewrites 17.9%

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

   10. Taylor expanded in z around inf

       \[\leadsto \color{blue}{t} \]
   11. Step-by-step derivation

   12. Applied rewrites 25.1%

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

   if -9.1999999999999994e75 < z < 2.30000000000000011e33

   1. Initial program 79.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. div-flip N/A

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

      6. associate-*r/ N/A

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

      7. mult-flip N/A

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

      8. times-frac N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. frac-2neg N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 83.2

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

   3. Applied rewrites 83.2%

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

      1. lift-/.f64 N/A

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

      2. frac-2neg N/A

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

      3. lift--.f64 N/A

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

      4. sub-negate-rev N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lower--.f64 83.2

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

      10. lift-/.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. associate-/r/ N/A

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

      13. metadata-eval N/A

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

      14. mul-1-neg N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lift--.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 48.8

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

   8. Applied rewrites 48.8%

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

Alternative 12: 36.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z - a} \cdot x\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -75000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-293}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y (- z a)) x)))
   (if (<= z -3.2e+55)
     t
     (if (<= z -75000000000000.0)
       t_1
       (if (<= z -6.5e-293) (/ (* t y) (- a z)) (if (<= z 2.25e+33) t_1 t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * x;
	double tmp;
	if (z <= -3.2e+55) {
		tmp = t;
	} else if (z <= -75000000000000.0) {
		tmp = t_1;
	} else if (z <= -6.5e-293) {
		tmp = (t * y) / (a - z);
	} else if (z <= 2.25e+33) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	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 = (y / (z - a)) * x
    if (z <= (-3.2d+55)) then
        tmp = t
    else if (z <= (-75000000000000.0d0)) then
        tmp = t_1
    else if (z <= (-6.5d-293)) then
        tmp = (t * y) / (a - z)
    else if (z <= 2.25d+33) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (z - a)) * x;
	double tmp;
	if (z <= -3.2e+55) {
		tmp = t;
	} else if (z <= -75000000000000.0) {
		tmp = t_1;
	} else if (z <= -6.5e-293) {
		tmp = (t * y) / (a - z);
	} else if (z <= 2.25e+33) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (z - a)) * x
	tmp = 0
	if z <= -3.2e+55:
		tmp = t
	elif z <= -75000000000000.0:
		tmp = t_1
	elif z <= -6.5e-293:
		tmp = (t * y) / (a - z)
	elif z <= 2.25e+33:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(z - a)) * x)
	tmp = 0.0
	if (z <= -3.2e+55)
		tmp = t;
	elseif (z <= -75000000000000.0)
		tmp = t_1;
	elseif (z <= -6.5e-293)
		tmp = Float64(Float64(t * y) / Float64(a - z));
	elseif (z <= 2.25e+33)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (z - a)) * x;
	tmp = 0.0;
	if (z <= -3.2e+55)
		tmp = t;
	elseif (z <= -75000000000000.0)
		tmp = t_1;
	elseif (z <= -6.5e-293)
		tmp = (t * y) / (a - z);
	elseif (z <= 2.25e+33)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -3.2e+55], t, If[LessEqual[z, -75000000000000.0], t$95$1, If[LessEqual[z, -6.5e-293], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.25e+33], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2000000000000003e55 or 2.25e33 < z

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 16.4

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

   7. Applied rewrites 16.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 17.9

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

   9. Applied rewrites 17.9%

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

   10. Taylor expanded in z around inf

       \[\leadsto \color{blue}{t} \]
   11. Step-by-step derivation

   12. Applied rewrites 25.1%

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

   if -3.2000000000000003e55 < z < -7.5e13 or -6.50000000000000033e-293 < z < 2.25e33

   1. Initial program 79.1%

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

      1. lift-+.f64 N/A

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

      2. sum-to-mult N/A

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

      3. lower-*.f64 N/A

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

      4. +-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

      8. lower-fma.f64 N/A

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

      9. lift-/.f64 N/A

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

      10. frac-2neg N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 N/A

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

      15. lift--.f64 N/A

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

      16. sub-negate-rev N/A

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

      17. lower--.f64 N/A

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

      18. lower-/.f64 62.9

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

   3. Applied rewrites 62.9%

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

   4. Taylor expanded in y around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 31.6

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

   6. Applied rewrites 31.6%

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

   7. Taylor expanded in x around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 24.5

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

   9. Applied rewrites 24.5%

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

   if -7.5e13 < z < -6.50000000000000033e-293

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

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

   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 21.1

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

   7. Applied rewrites 21.1%

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

Alternative 13: 36.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+36}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+36) t (if (<= z 4.2e+26) (/ (* t y) (- a z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+36) {
		tmp = t;
	} else if (z <= 4.2e+26) {
		tmp = (t * y) / (a - z);
	} else {
		tmp = t;
	}
	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 (z <= (-7.2d+36)) then
        tmp = t
    else if (z <= 4.2d+26) then
        tmp = (t * y) / (a - z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+36) {
		tmp = t;
	} else if (z <= 4.2e+26) {
		tmp = (t * y) / (a - z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+36:
		tmp = t
	elif z <= 4.2e+26:
		tmp = (t * y) / (a - z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+36)
		tmp = t;
	elseif (z <= 4.2e+26)
		tmp = Float64(Float64(t * y) / Float64(a - z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e+36)
		tmp = t;
	elseif (z <= 4.2e+26)
		tmp = (t * y) / (a - z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+36], t, If[LessEqual[z, 4.2e+26], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -7.1999999999999995e36 or 4.2000000000000002e26 < z

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 16.4

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

   7. Applied rewrites 16.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 17.9

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

   9. Applied rewrites 17.9%

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

   10. Taylor expanded in z around inf

       \[\leadsto \color{blue}{t} \]
   11. Step-by-step derivation

   12. Applied rewrites 25.1%

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

   if -7.1999999999999995e36 < z < 4.2000000000000002e26

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

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

   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 21.1

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

   7. Applied rewrites 21.1%

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

Alternative 14: 35.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+39) t (if (<= z 8.5e-12) (/ y (/ a t)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+39) {
		tmp = t;
	} else if (z <= 8.5e-12) {
		tmp = y / (a / t);
	} else {
		tmp = t;
	}
	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 (z <= (-1.15d+39)) then
        tmp = t
    else if (z <= 8.5d-12) then
        tmp = y / (a / t)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+39) {
		tmp = t;
	} else if (z <= 8.5e-12) {
		tmp = y / (a / t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+39:
		tmp = t
	elif z <= 8.5e-12:
		tmp = y / (a / t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+39)
		tmp = t;
	elseif (z <= 8.5e-12)
		tmp = Float64(y / Float64(a / t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+39)
		tmp = t;
	elseif (z <= 8.5e-12)
		tmp = y / (a / t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+39], t, If[LessEqual[z, 8.5e-12], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000006e39 or 8.4999999999999997e-12 < z

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 16.4

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

   7. Applied rewrites 16.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 17.9

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

   9. Applied rewrites 17.9%

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

   10. Taylor expanded in z around inf

       \[\leadsto \color{blue}{t} \]
   11. Step-by-step derivation

   12. Applied rewrites 25.1%

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

   if -1.15000000000000006e39 < z < 8.4999999999999997e-12

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 16.4

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

   7. Applied rewrites 16.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 17.9

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

   9. Applied rewrites 17.9%

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

       1. lift-*.f64 N/A

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

       2. lift-/.f64 N/A

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

       3. div-flip N/A

          \[\leadsto y \cdot \frac{1}{\frac{a}{\color{blue}{t}}} \]

       4. mult-flip-rev N/A

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

       5. lower-/.f64 N/A

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

       6. lower-/.f64 17.9

          \[\leadsto \frac{y}{\frac{a}{t}} \]

   11. Applied rewrites 17.9%

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

Alternative 15: 34.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+39) t (if (<= z 8.5e-12) (* (/ y a) t) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+39) {
		tmp = t;
	} else if (z <= 8.5e-12) {
		tmp = (y / a) * t;
	} else {
		tmp = t;
	}
	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 (z <= (-1.15d+39)) then
        tmp = t
    else if (z <= 8.5d-12) then
        tmp = (y / a) * t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+39) {
		tmp = t;
	} else if (z <= 8.5e-12) {
		tmp = (y / a) * t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+39:
		tmp = t
	elif z <= 8.5e-12:
		tmp = (y / a) * t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+39)
		tmp = t;
	elseif (z <= 8.5e-12)
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+39)
		tmp = t;
	elseif (z <= 8.5e-12)
		tmp = (y / a) * t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+39], t, If[LessEqual[z, 8.5e-12], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000006e39 or 8.4999999999999997e-12 < z

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 16.4

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

   7. Applied rewrites 16.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 17.9

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

   9. Applied rewrites 17.9%

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

   10. Taylor expanded in z around inf

       \[\leadsto \color{blue}{t} \]
   11. Step-by-step derivation

   12. Applied rewrites 25.1%

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

   if -1.15000000000000006e39 < z < 8.4999999999999997e-12

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 16.4

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

   7. Applied rewrites 16.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 18.9

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

   9. Applied rewrites 18.9%

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

Alternative 16: 34.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+39}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+39) t (if (<= z 8.5e-12) (* y (/ t a)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+39) {
		tmp = t;
	} else if (z <= 8.5e-12) {
		tmp = y * (t / a);
	} else {
		tmp = t;
	}
	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 (z <= (-1.2d+39)) then
        tmp = t
    else if (z <= 8.5d-12) then
        tmp = y * (t / a)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+39) {
		tmp = t;
	} else if (z <= 8.5e-12) {
		tmp = y * (t / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+39:
		tmp = t
	elif z <= 8.5e-12:
		tmp = y * (t / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+39)
		tmp = t;
	elseif (z <= 8.5e-12)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+39)
		tmp = t;
	elseif (z <= 8.5e-12)
		tmp = y * (t / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+39], t, If[LessEqual[z, 8.5e-12], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e39 or 8.4999999999999997e-12 < z

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 16.4

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

   7. Applied rewrites 16.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 17.9

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

   9. Applied rewrites 17.9%

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

   10. Taylor expanded in z around inf

       \[\leadsto \color{blue}{t} \]
   11. Step-by-step derivation

   12. Applied rewrites 25.1%

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

   if -1.2e39 < z < 8.4999999999999997e-12

   1. Initial program 79.1%

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

   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 51.4

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

   4. Applied rewrites 51.4%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 16.4

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

   7. Applied rewrites 16.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 17.9

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

   9. Applied rewrites 17.9%

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

Alternative 17: 25.1% accurate, 17.9× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.1%

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

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 51.4

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

4. Applied rewrites 51.4%

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

5. Taylor expanded in z around 0

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 16.4

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

7. Applied rewrites 16.4%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-/l* N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 17.9

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

9. Applied rewrites 17.9%

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

10. Taylor expanded in z around inf

    \[\leadsto \color{blue}{t} \]
11. Step-by-step derivation

12. Applied rewrites 25.1%

    \[\leadsto \color{blue}{t} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2025142 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))