Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.3% → 94.9%

Time: 5.3s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(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: 79.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(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: 94.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(x - t, \frac{z - y}{a - z}, x\right)\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (fma (- x t) (/ (- z y) (- a z)) x))
       (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
  (if (<= t_2 -4e-291)
    t_1
    (if (<= t_2 0.0) (+ t (* (- y a) (/ x z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - t), ((z - y) / (a - z)), x);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-291) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((y - a) * (x / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - t), Float64(Float64(z - y) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -4e-291)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $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, -4e-291], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / 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)))) < -3.9999999999999998e-291 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.3%

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

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

   if -3.9999999999999998e-291 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.3%

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

   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.8%

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

   7. Applied rewrites 41.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 44.8%

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

   9. Applied rewrites 44.8%

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

Alternative 2: 79.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -0.075:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+63}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x - t, \frac{z - y}{a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= a -0.075)
  (fma (/ t (- a z)) (- y z) x)
  (if (<= a 5.8e+63)
    (- t (* (- t x) (/ (- y a) z)))
    (fma (- x t) (/ (- z y) a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.075) {
		tmp = fma((t / (a - z)), (y - z), x);
	} else if (a <= 5.8e+63) {
		tmp = t - ((t - x) * ((y - a) / z));
	} else {
		tmp = fma((x - t), ((z - y) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.075)
		tmp = fma(Float64(t / Float64(a - z)), Float64(y - z), x);
	elseif (a <= 5.8e+63)
		tmp = Float64(t - Float64(Float64(t - x) * Float64(Float64(y - a) / z)));
	else
		tmp = fma(Float64(x - t), Float64(Float64(z - y) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.075], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 5.8e+63], N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.074999999999999997

   1. Initial program 79.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 63.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 63.8%

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

   6. Applied rewrites 63.8%

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

   if -0.074999999999999997 < a < 5.7999999999999999e63

   1. Initial program 79.3%

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

   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 45.6%

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

   4. Applied rewrites 45.6%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lift-/.f64 N/A

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

      7. distribute-neg-frac N/A

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

      8. distribute-frac-neg2 N/A

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

      9. frac-2neg N/A

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

      10. mult-flip N/A

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

      11. lift--.f64 N/A

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

      12. lift-*.f64 N/A

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

      13. lift-*.f64 N/A

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

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

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

      15. associate-*l* N/A

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

      16. lower-*.f64 N/A

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

      17. mult-flip-rev N/A

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

      18. lower-/.f64 N/A

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

      19. lower--.f64 53.1%

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

   6. Applied rewrites 53.1%

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

   if 5.7999999999999999e63 < a

   1. Initial program 79.3%

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

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 53.2%

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

Alternative 3: 76.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{y \cdot \left(x - t\right)}{z - a}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_3 := \mathsf{fma}\left(\frac{t}{a - z}, y - z, x\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-121}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-278}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* y (- x t)) (- z a)))
       (t_2 (+ x (* (- y z) (/ (- t x) (- a z)))))
       (t_3 (fma (/ t (- a z)) (- y z) x)))
  (if (<= t_2 (- INFINITY))
    t_1
    (if (<= t_2 -1e-121)
      t_3
      (if (<= t_2 5e-278)
        (+ t (* (- y a) (/ x z)))
        (if (<= t_2 2e+299) t_3 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (x - t)) / (z - a);
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double t_3 = fma((t / (a - z)), (y - z), x);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-121) {
		tmp = t_3;
	} else if (t_2 <= 5e-278) {
		tmp = t + ((y - a) * (x / z));
	} else if (t_2 <= 2e+299) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(x - t)) / Float64(z - a))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_3 = fma(Float64(t / Float64(a - z)), Float64(y - z), x)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-121)
		tmp = t_3;
	elseif (t_2 <= 5e-278)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(x / z)));
	elseif (t_2 <= 2e+299)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-121], t$95$3, If[LessEqual[t$95$2, 5e-278], N[(t + N[(N[(y - a), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+299], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or 2.0000000000000001e299 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.3%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   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 79.4%

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

      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 79.4%

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

   3. Applied rewrites 79.4%

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

   4. Taylor expanded in y around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 36.7%

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

   6. Applied rewrites 36.7%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999998e-122 or 4.9999999999999998e-278 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2.0000000000000001e299

   1. Initial program 79.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 63.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 63.8%

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

   6. Applied rewrites 63.8%

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

   if -9.9999999999999998e-122 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 4.9999999999999998e-278

   1. Initial program 79.3%

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

   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.8%

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

   7. Applied rewrites 41.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 44.8%

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

   9. Applied rewrites 44.8%

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

Alternative 4: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(x - t, \frac{z - y}{a}, x\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-224}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+64}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (fma (- x t) (/ (- z y) a) x)))
  (if (<= a -1.05e+101)
    t_1
    (if (<= a -4.2e-224)
      (* (/ (- y z) (- a z)) t)
      (if (<= a 2e+64) (+ t (* (/ (- y a) z) x)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - t), ((z - y) / a), x);
	double tmp;
	if (a <= -1.05e+101) {
		tmp = t_1;
	} else if (a <= -4.2e-224) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (a <= 2e+64) {
		tmp = t + (((y - a) / z) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - t), Float64(Float64(z - y) / a), x)
	tmp = 0.0
	if (a <= -1.05e+101)
		tmp = t_1;
	elseif (a <= -4.2e-224)
		tmp = Float64(Float64(Float64(y - z) / Float64(a - z)) * t);
	elseif (a <= 2e+64)
		tmp = Float64(t + Float64(Float64(Float64(y - a) / z) * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.05e+101], t$95$1, If[LessEqual[a, -4.2e-224], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 2e+64], N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.05e101 or 2e64 < a

   1. Initial program 79.3%

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

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 53.2%

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

   if -1.05e101 < a < -4.2000000000000001e-224

   1. Initial program 79.3%

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

   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 51.3%

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

   4. Applied rewrites 51.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 51.3%

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 51.3%

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

   6. Applied rewrites 51.3%

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

   if -4.2000000000000001e-224 < a < 2e64

   1. Initial program 79.3%

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

   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.8%

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

   7. Applied rewrites 41.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 45.9%

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

   9. Applied rewrites 45.9%

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

Alternative 5: 65.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -1.22 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-224}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+64}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (- y z) (/ t a)))))
  (if (<= a -1.22e+101)
    t_1
    (if (<= a -4.2e-224)
      (* (/ (- y z) (- a z)) t)
      (if (<= a 2e+64) (+ t (* (/ (- y a) z) x)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -1.22e+101) {
		tmp = t_1;
	} else if (a <= -4.2e-224) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (a <= 2e+64) {
		tmp = t + (((y - a) / z) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y - z) * (t / a))
    if (a <= (-1.22d+101)) then
        tmp = t_1
    else if (a <= (-4.2d-224)) then
        tmp = ((y - z) / (a - z)) * t
    else if (a <= 2d+64) then
        tmp = t + (((y - a) / z) * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -1.22e+101) {
		tmp = t_1;
	} else if (a <= -4.2e-224) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (a <= 2e+64) {
		tmp = t + (((y - a) / z) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / a))
	tmp = 0
	if a <= -1.22e+101:
		tmp = t_1
	elif a <= -4.2e-224:
		tmp = ((y - z) / (a - z)) * t
	elif a <= 2e+64:
		tmp = t + (((y - a) / z) * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / a)))
	tmp = 0.0
	if (a <= -1.22e+101)
		tmp = t_1;
	elseif (a <= -4.2e-224)
		tmp = Float64(Float64(Float64(y - z) / Float64(a - z)) * t);
	elseif (a <= 2e+64)
		tmp = Float64(t + Float64(Float64(Float64(y - a) / z) * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / a));
	tmp = 0.0;
	if (a <= -1.22e+101)
		tmp = t_1;
	elseif (a <= -4.2e-224)
		tmp = ((y - z) / (a - z)) * t;
	elseif (a <= 2e+64)
		tmp = t + (((y - a) / z) * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.22e+101], t$95$1, If[LessEqual[a, -4.2e-224], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 2e+64], N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.22e101 or 2e64 < a

   1. Initial program 79.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 63.8%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 44.2%

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

   if -1.22e101 < a < -4.2000000000000001e-224

   1. Initial program 79.3%

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

   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 51.3%

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

   4. Applied rewrites 51.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 51.3%

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 51.3%

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

   6. Applied rewrites 51.3%

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

   if -4.2000000000000001e-224 < a < 2e64

   1. Initial program 79.3%

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

   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.8%

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

   7. Applied rewrites 41.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 45.9%

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

   9. Applied rewrites 45.9%

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

Alternative 6: 60.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := t + \frac{y - a}{z} \cdot x\\ t_2 := \frac{y - z}{a - z} \cdot t\\ t_3 := x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-138}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+40}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ t (* (/ (- y a) z) x)))
       (t_2 (* (/ (- y z) (- a z)) t))
       (t_3 (+ x (/ (* y (- t x)) a))))
  (if (<= t -5.6e+51)
    t_2
    (if (<= t -2.65e-236)
      t_1
      (if (<= t 2.35e-138)
        t_3
        (if (<= t 5.2e-20) t_1 (if (<= t 8.5e+40) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) / z) * x);
	double t_2 = ((y - z) / (a - z)) * t;
	double t_3 = x + ((y * (t - x)) / a);
	double tmp;
	if (t <= -5.6e+51) {
		tmp = t_2;
	} else if (t <= -2.65e-236) {
		tmp = t_1;
	} else if (t <= 2.35e-138) {
		tmp = t_3;
	} else if (t <= 5.2e-20) {
		tmp = t_1;
	} else if (t <= 8.5e+40) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t + (((y - a) / z) * x)
    t_2 = ((y - z) / (a - z)) * t
    t_3 = x + ((y * (t - x)) / a)
    if (t <= (-5.6d+51)) then
        tmp = t_2
    else if (t <= (-2.65d-236)) then
        tmp = t_1
    else if (t <= 2.35d-138) then
        tmp = t_3
    else if (t <= 5.2d-20) then
        tmp = t_1
    else if (t <= 8.5d+40) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) / z) * x);
	double t_2 = ((y - z) / (a - z)) * t;
	double t_3 = x + ((y * (t - x)) / a);
	double tmp;
	if (t <= -5.6e+51) {
		tmp = t_2;
	} else if (t <= -2.65e-236) {
		tmp = t_1;
	} else if (t <= 2.35e-138) {
		tmp = t_3;
	} else if (t <= 5.2e-20) {
		tmp = t_1;
	} else if (t <= 8.5e+40) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((y - a) / z) * x)
	t_2 = ((y - z) / (a - z)) * t
	t_3 = x + ((y * (t - x)) / a)
	tmp = 0
	if t <= -5.6e+51:
		tmp = t_2
	elif t <= -2.65e-236:
		tmp = t_1
	elif t <= 2.35e-138:
		tmp = t_3
	elif t <= 5.2e-20:
		tmp = t_1
	elif t <= 8.5e+40:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(y - a) / z) * x))
	t_2 = Float64(Float64(Float64(y - z) / Float64(a - z)) * t)
	t_3 = Float64(x + Float64(Float64(y * Float64(t - x)) / a))
	tmp = 0.0
	if (t <= -5.6e+51)
		tmp = t_2;
	elseif (t <= -2.65e-236)
		tmp = t_1;
	elseif (t <= 2.35e-138)
		tmp = t_3;
	elseif (t <= 5.2e-20)
		tmp = t_1;
	elseif (t <= 8.5e+40)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((y - a) / z) * x);
	t_2 = ((y - z) / (a - z)) * t;
	t_3 = x + ((y * (t - x)) / a);
	tmp = 0.0;
	if (t <= -5.6e+51)
		tmp = t_2;
	elseif (t <= -2.65e-236)
		tmp = t_1;
	elseif (t <= 2.35e-138)
		tmp = t_3;
	elseif (t <= 5.2e-20)
		tmp = t_1;
	elseif (t <= 8.5e+40)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+51], t$95$2, If[LessEqual[t, -2.65e-236], t$95$1, If[LessEqual[t, 2.35e-138], t$95$3, If[LessEqual[t, 5.2e-20], t$95$1, If[LessEqual[t, 8.5e+40], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.6000000000000001e51 or 8.5e40 < t

   1. Initial program 79.3%

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

   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 51.3%

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

   4. Applied rewrites 51.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 51.3%

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. lift--.f64 N/A

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

      9. lower-/.f64 51.3%

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

   6. Applied rewrites 51.3%

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

   if -5.6000000000000001e51 < t < -2.6500000000000001e-236 or 2.3500000000000001e-138 < t < 5.1999999999999999e-20

   1. Initial program 79.3%

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

   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.8%

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

   7. Applied rewrites 41.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 45.9%

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

   9. Applied rewrites 45.9%

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

   if -2.6500000000000001e-236 < t < 2.3500000000000001e-138 or 5.1999999999999999e-20 < t < 8.5e40

   1. Initial program 79.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 63.8%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 60.7%

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

   7. Applied rewrites 60.7%

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

   8. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.7%

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

   10. Applied rewrites 43.7%

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

Alternative 7: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := t + \frac{y - a}{z} \cdot x\\ t_2 := \frac{t}{a - z} \cdot \left(y - z\right)\\ t_3 := x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-138}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+40}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ t (* (/ (- y a) z) x)))
       (t_2 (* (/ t (- a z)) (- y z)))
       (t_3 (+ x (/ (* y (- t x)) a))))
  (if (<= t -5.6e+51)
    t_2
    (if (<= t -2.65e-236)
      t_1
      (if (<= t 2.35e-138)
        t_3
        (if (<= t 5.2e-20) t_1 (if (<= t 8.5e+40) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) / z) * x);
	double t_2 = (t / (a - z)) * (y - z);
	double t_3 = x + ((y * (t - x)) / a);
	double tmp;
	if (t <= -5.6e+51) {
		tmp = t_2;
	} else if (t <= -2.65e-236) {
		tmp = t_1;
	} else if (t <= 2.35e-138) {
		tmp = t_3;
	} else if (t <= 5.2e-20) {
		tmp = t_1;
	} else if (t <= 8.5e+40) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t + (((y - a) / z) * x)
    t_2 = (t / (a - z)) * (y - z)
    t_3 = x + ((y * (t - x)) / a)
    if (t <= (-5.6d+51)) then
        tmp = t_2
    else if (t <= (-2.65d-236)) then
        tmp = t_1
    else if (t <= 2.35d-138) then
        tmp = t_3
    else if (t <= 5.2d-20) then
        tmp = t_1
    else if (t <= 8.5d+40) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((y - a) / z) * x);
	double t_2 = (t / (a - z)) * (y - z);
	double t_3 = x + ((y * (t - x)) / a);
	double tmp;
	if (t <= -5.6e+51) {
		tmp = t_2;
	} else if (t <= -2.65e-236) {
		tmp = t_1;
	} else if (t <= 2.35e-138) {
		tmp = t_3;
	} else if (t <= 5.2e-20) {
		tmp = t_1;
	} else if (t <= 8.5e+40) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((y - a) / z) * x)
	t_2 = (t / (a - z)) * (y - z)
	t_3 = x + ((y * (t - x)) / a)
	tmp = 0
	if t <= -5.6e+51:
		tmp = t_2
	elif t <= -2.65e-236:
		tmp = t_1
	elif t <= 2.35e-138:
		tmp = t_3
	elif t <= 5.2e-20:
		tmp = t_1
	elif t <= 8.5e+40:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(y - a) / z) * x))
	t_2 = Float64(Float64(t / Float64(a - z)) * Float64(y - z))
	t_3 = Float64(x + Float64(Float64(y * Float64(t - x)) / a))
	tmp = 0.0
	if (t <= -5.6e+51)
		tmp = t_2;
	elseif (t <= -2.65e-236)
		tmp = t_1;
	elseif (t <= 2.35e-138)
		tmp = t_3;
	elseif (t <= 5.2e-20)
		tmp = t_1;
	elseif (t <= 8.5e+40)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((y - a) / z) * x);
	t_2 = (t / (a - z)) * (y - z);
	t_3 = x + ((y * (t - x)) / a);
	tmp = 0.0;
	if (t <= -5.6e+51)
		tmp = t_2;
	elseif (t <= -2.65e-236)
		tmp = t_1;
	elseif (t <= 2.35e-138)
		tmp = t_3;
	elseif (t <= 5.2e-20)
		tmp = t_1;
	elseif (t <= 8.5e+40)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e+51], t$95$2, If[LessEqual[t, -2.65e-236], t$95$1, If[LessEqual[t, 2.35e-138], t$95$3, If[LessEqual[t, 5.2e-20], t$95$1, If[LessEqual[t, 8.5e+40], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.6000000000000001e51 or 8.5e40 < t

   1. Initial program 79.3%

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

   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 51.3%

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

   4. Applied rewrites 51.3%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      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. sub-div N/A

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

      7. lift--.f64 N/A

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

      8. associate-*l/ N/A

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

      9. mult-flip N/A

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

      10. lower-*.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 39.3%

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

   6. Applied rewrites 39.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip-rev N/A

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

      5. lift-*.f64 N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 45.5%

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

   8. Applied rewrites 45.5%

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

   if -5.6000000000000001e51 < t < -2.6500000000000001e-236 or 2.3500000000000001e-138 < t < 5.1999999999999999e-20

   1. Initial program 79.3%

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

   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.8%

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

   7. Applied rewrites 41.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 45.9%

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

   9. Applied rewrites 45.9%

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

   if -2.6500000000000001e-236 < t < 2.3500000000000001e-138 or 5.1999999999999999e-20 < t < 8.5e40

   1. Initial program 79.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 63.8%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 60.7%

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

   7. Applied rewrites 60.7%

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

   8. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.7%

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

   10. Applied rewrites 43.7%

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

Alternative 8: 59.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+64}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (/ (* y (- t x)) a))))
  (if (<= a -5.6e+45)
    t_1
    (if (<= a 2e+64) (+ t (* (/ (- y a) z) x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (t - x)) / a);
	double tmp;
	if (a <= -5.6e+45) {
		tmp = t_1;
	} else if (a <= 2e+64) {
		tmp = t + (((y - a) / z) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * (t - x)) / a)
    if (a <= (-5.6d+45)) then
        tmp = t_1
    else if (a <= 2d+64) then
        tmp = t + (((y - a) / z) * x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (t - x)) / a);
	double tmp;
	if (a <= -5.6e+45) {
		tmp = t_1;
	} else if (a <= 2e+64) {
		tmp = t + (((y - a) / z) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * (t - x)) / a)
	tmp = 0
	if a <= -5.6e+45:
		tmp = t_1
	elif a <= 2e+64:
		tmp = t + (((y - a) / z) * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * Float64(t - x)) / a))
	tmp = 0.0
	if (a <= -5.6e+45)
		tmp = t_1;
	elseif (a <= 2e+64)
		tmp = Float64(t + Float64(Float64(Float64(y - a) / z) * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * (t - x)) / a);
	tmp = 0.0;
	if (a <= -5.6e+45)
		tmp = t_1;
	elseif (a <= 2e+64)
		tmp = t + (((y - a) / z) * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e+45], t$95$1, If[LessEqual[a, 2e+64], N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5999999999999999e45 or 2e64 < a

   1. Initial program 79.3%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 63.8%

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

   5. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 60.7%

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

   7. Applied rewrites 60.7%

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

   8. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 43.7%

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

   10. Applied rewrites 43.7%

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

   if -5.5999999999999999e45 < a < 2e64

   1. Initial program 79.3%

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

   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.8%

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

   7. Applied rewrites 41.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 45.9%

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

   9. Applied rewrites 45.9%

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

Alternative 9: 58.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(x - t, \frac{z}{a}, x\right)\\ \mathbf{if}\;a \leq -1.26 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+64}:\\ \;\;\;\;t + \frac{y - a}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (fma (- x t) (/ z a) x)))
  (if (<= a -1.26e+69)
    t_1
    (if (<= a 2e+64) (+ t (* (/ (- y a) z) x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - t), (z / a), x);
	double tmp;
	if (a <= -1.26e+69) {
		tmp = t_1;
	} else if (a <= 2e+64) {
		tmp = t + (((y - a) / z) * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - t), Float64(z / a), x)
	tmp = 0.0
	if (a <= -1.26e+69)
		tmp = t_1;
	elseif (a <= 2e+64)
		tmp = Float64(t + Float64(Float64(Float64(y - a) / z) * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * N[(z / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -1.26e+69], t$95$1, If[LessEqual[a, 2e+64], N[(t + N[(N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2600000000000001e69 or 2e64 < a

   1. Initial program 79.3%

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

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 47.0%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 31.3%

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

   if -1.2600000000000001e69 < a < 2e64

   1. Initial program 79.3%

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

   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.8%

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

   7. Applied rewrites 41.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 45.9%

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

   9. Applied rewrites 45.9%

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

Alternative 10: 53.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(x - t, \frac{z}{a}, x\right)\\ \mathbf{if}\;a \leq -5000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+64}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (fma (- x t) (/ z a) x)))
  (if (<= a -5000.0) t_1 (if (<= a 4.8e+64) (+ t (/ (* x y) z)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((x - t), (z / a), x);
	double tmp;
	if (a <= -5000.0) {
		tmp = t_1;
	} else if (a <= 4.8e+64) {
		tmp = t + ((x * y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(x - t), Float64(z / a), x)
	tmp = 0.0
	if (a <= -5000.0)
		tmp = t_1;
	elseif (a <= 4.8e+64)
		tmp = Float64(t + Float64(Float64(x * y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * N[(z / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -5000.0], t$95$1, If[LessEqual[a, 4.8e+64], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -5e3 or 4.8e64 < a

   1. Initial program 79.3%

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

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

      6. frac-2neg N/A

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

      7. associate-*l/ N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lower--.f64 83.7%

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

   3. Applied rewrites 83.7%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 47.0%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 31.3%

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

   if -5e3 < a < 4.8e64

   1. Initial program 79.3%

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

   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.8%

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

   7. Applied rewrites 41.8%

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

   8. Taylor expanded in y around inf

      \[\leadsto t + \frac{x \cdot y}{z} \]
   9. Step-by-step derivation

      1. lower-*.f64 38.4%

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

   10. Applied rewrites 38.4%

       \[\leadsto t + \frac{x \cdot y}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 39.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot y}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= y -1.8e+51) (* t (/ y (- a z))) (+ t (/ (* x y) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.8e+51) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.8d+51)) then
        tmp = t * (y / (a - z))
    else
        tmp = t + ((x * y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.8e+51) {
		tmp = t * (y / (a - z));
	} else {
		tmp = t + ((x * y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.8e+51:
		tmp = t * (y / (a - z))
	else:
		tmp = t + ((x * y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.8e+51)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	else
		tmp = Float64(t + Float64(Float64(x * y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.8e+51)
		tmp = t * (y / (a - z));
	else
		tmp = t + ((x * y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.8e+51], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8000000000000001e51

   1. Initial program 79.3%

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

   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 51.3%

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 25.6%

      \[\leadsto t \cdot 1 \]

   8. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 23.8%

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

   10. Applied rewrites 23.8%

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

   if -1.8000000000000001e51 < y

   1. Initial program 79.3%

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

   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 45.6%

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

   4. Applied rewrites 45.6%

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

   5. Taylor expanded in x around -inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 41.8%

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

   7. Applied rewrites 41.8%

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

   8. Taylor expanded in y around inf

      \[\leadsto t + \frac{x \cdot y}{z} \]
   9. Step-by-step derivation

      1. lower-*.f64 38.4%

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

   10. Applied rewrites 38.4%

       \[\leadsto t + \frac{x \cdot y}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 35.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+170}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* t (/ y (- a z)))))
  (if (<= y -1.4e-34) t_1 (if (<= y 9e+170) t t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -1.4e-34) {
		tmp = t_1;
	} else if (y <= 9e+170) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (a - z))
    if (y <= (-1.4d-34)) then
        tmp = t_1
    else if (y <= 9d+170) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (y <= -1.4e-34) {
		tmp = t_1;
	} else if (y <= 9e+170) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if y <= -1.4e-34:
		tmp = t_1
	elif y <= 9e+170:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -1.4e-34)
		tmp = t_1;
	elseif (y <= 9e+170)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (y <= -1.4e-34)
		tmp = t_1;
	elseif (y <= 9e+170)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e-34], t$95$1, If[LessEqual[y, 9e+170], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e-34 or 9.0000000000000004e170 < y

   1. Initial program 79.3%

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

   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 51.3%

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 25.6%

      \[\leadsto t \cdot 1 \]

   8. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 23.8%

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

   10. Applied rewrites 23.8%

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

   if -1.4e-34 < y < 9.0000000000000004e170

   1. Initial program 79.3%

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

   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 51.3%

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 25.6%

      \[\leadsto t \cdot 1 \]

   8. Taylor expanded in z around inf

      \[\leadsto t \]
   9. Step-by-step derivation

   10. Applied rewrites 25.6%

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

Alternative 13: 34.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+76}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z -9.2e+76) t (if (<= z 2.05e-7) (* t (/ y a)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+76) {
		tmp = t;
	} else if (z <= 2.05e-7) {
		tmp = t * (y / 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 <= (-9.2d+76)) then
        tmp = t
    else if (z <= 2.05d-7) then
        tmp = t * (y / 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 <= -9.2e+76) {
		tmp = t;
	} else if (z <= 2.05e-7) {
		tmp = t * (y / a);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+76:
		tmp = t
	elif z <= 2.05e-7:
		tmp = t * (y / a)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+76)
		tmp = t;
	elseif (z <= 2.05e-7)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.2e+76)
		tmp = t;
	elseif (z <= 2.05e-7)
		tmp = t * (y / a);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+76], t, If[LessEqual[z, 2.05e-7], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2e76 or 2.05e-7 < z

   1. Initial program 79.3%

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

   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 51.3%

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 25.6%

      \[\leadsto t \cdot 1 \]

   8. Taylor expanded in z around inf

      \[\leadsto t \]
   9. Step-by-step derivation

   10. Applied rewrites 25.6%

       \[\leadsto t \]

   if -9.2e76 < z < 2.05e-7

   1. Initial program 79.3%

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

   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 51.3%

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 25.6%

      \[\leadsto t \cdot 1 \]

   8. Taylor expanded in z around 0

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

      1. lower-/.f64 18.9%

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

   10. Applied rewrites 18.9%

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

Alternative 14: 34.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-19}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-79}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z -5.5e-19) t (if (<= z 8e-79) (/ (* t y) a) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-19) {
		tmp = t;
	} else if (z <= 8e-79) {
		tmp = (t * y) / 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 <= (-5.5d-19)) then
        tmp = t
    else if (z <= 8d-79) then
        tmp = (t * y) / 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 <= -5.5e-19) {
		tmp = t;
	} else if (z <= 8e-79) {
		tmp = (t * y) / a;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e-19:
		tmp = t
	elif z <= 8e-79:
		tmp = (t * y) / a
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e-19)
		tmp = t;
	elseif (z <= 8e-79)
		tmp = Float64(Float64(t * y) / a);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e-19)
		tmp = t;
	elseif (z <= 8e-79)
		tmp = (t * y) / a;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e-19], t, If[LessEqual[z, 8e-79], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999996e-19 or 8e-79 < z

   1. Initial program 79.3%

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

   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 51.3%

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 25.6%

      \[\leadsto t \cdot 1 \]

   8. Taylor expanded in z around inf

      \[\leadsto t \]
   9. Step-by-step derivation

   10. Applied rewrites 25.6%

       \[\leadsto t \]

   if -5.4999999999999996e-19 < z < 8e-79

   1. Initial program 79.3%

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

   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 51.3%

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

   4. Applied rewrites 51.3%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 25.6%

      \[\leadsto t \cdot 1 \]

   8. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 16.5%

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

   10. Applied rewrites 16.5%

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

Alternative 15: 25.6% accurate, 18.2× speedup

Math

\[t \]

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 79.3%

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

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 51.3%

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

4. Applied rewrites 51.3%

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

5. Taylor expanded in z around inf

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

7. Applied rewrites 25.6%

   \[\leadsto t \cdot 1 \]

8. Taylor expanded in z around inf

   \[\leadsto t \]
9. Step-by-step derivation

10. Applied rewrites 25.6%

    \[\leadsto t \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025212 
(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)))))