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

Average Error: 24.2 → 7.1

Time: 28.3s

Precision: binary64

Cost: 8904

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-224}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- y x) (- z t)) (- a t)))))
   (if (<= t_1 -2e-224)
     (+ x (/ (- y x) (/ (- a t) (- z t))))
     (if (<= t_1 0.0)
       (- y (* x (/ (- a z) t)))
       (fma (- y x) (/ (- z t) (- a t)) x)))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -2e-224) {
		tmp = x + ((y - x) / ((a - t) / (z - t)));
	} else if (t_1 <= 0.0) {
		tmp = y - (x * ((a - z) / t));
	} else {
		tmp = fma((y - x), ((z - t) / (a - t)), x);
	}
	return tmp;
}

Julia

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

↓

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

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-224], N[(x + N[(N[(y - x), $MachinePrecision] / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(y - N[(x * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

Target

Original	24.2
Target	8.8
Herbie	7.1

\[\begin{array}{l} \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -2e-224

   1. Initial program 21.4

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

   2. Applied egg-rr 7.7

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

   3. Applied egg-rr 7.6

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

   if -2e-224 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 54.1

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

   2. Simplified 53.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
      Proof
      (fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))) x)): 5 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) x): 87 points increase in error, 13 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in t around inf 6.5

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

   4. Simplified 6.3

      \[\leadsto \color{blue}{y + \frac{a - z}{t} \cdot \left(y - x\right)} \]
      Proof
      (+.f64 y (*.f64 (/.f64 (-.f64 a z) t) (-.f64 y x))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (*.f64 (/.f64 (Rewrite<= unsub-neg_binary64 (+.f64 a (neg.f64 z))) t) (-.f64 y x))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (*.f64 (/.f64 (+.f64 a (Rewrite<= mul-1-neg_binary64 (*.f64 -1 z))) t) (-.f64 y x))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (*.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 z) a)) t) (-.f64 y x))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (*.f64 (/.f64 (+.f64 (*.f64 -1 z) (Rewrite<= *-lft-identity_binary64 (*.f64 1 a))) t) (-.f64 y x))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (*.f64 (/.f64 (+.f64 (*.f64 -1 z) (*.f64 (Rewrite<= metadata-eval (neg.f64 -1)) a)) t) (-.f64 y x))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (*.f64 (/.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (*.f64 -1 z) (*.f64 -1 a))) t) (-.f64 y x))): 0 points increase in error, 0 points decrease in error
      (+.f64 y (Rewrite<= associate-/r/_binary64 (/.f64 (-.f64 (*.f64 -1 z) (*.f64 -1 a)) (/.f64 t (-.f64 y x))))): 19 points increase in error, 22 points decrease in error
      (+.f64 y (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 (*.f64 -1 z) (*.f64 -1 a)) (-.f64 y x)) t))): 48 points increase in error, 23 points decrease in error
      (+.f64 y (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 (-.f64 y x) (-.f64 (*.f64 -1 z) (*.f64 -1 a)))) t)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 (-.f64 y x) (-.f64 (*.f64 -1 z) (*.f64 -1 a))) t) y)): 0 points increase in error, 0 points decrease in error

   5. Taylor expanded in y around 0 6.6

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

   6. Simplified 6.5

      \[\leadsto y + \color{blue}{x \cdot \frac{z - a}{t}} \]
      Proof
      (*.f64 x (/.f64 (-.f64 z a) t)): 0 points increase in error, 0 points decrease in error
      (*.f64 x (/.f64 (Rewrite=> sub-neg_binary64 (+.f64 z (neg.f64 a))) t)): 0 points increase in error, 0 points decrease in error
      (*.f64 x (/.f64 (+.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 z))) (neg.f64 a)) t)): 0 points increase in error, 0 points decrease in error
      (*.f64 x (/.f64 (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 (neg.f64 z) a))) t)): 0 points increase in error, 0 points decrease in error
      (*.f64 x (/.f64 (neg.f64 (Rewrite<= +-commutative_binary64 (+.f64 a (neg.f64 z)))) t)): 0 points increase in error, 0 points decrease in error
      (*.f64 x (/.f64 (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 a z))) t)): 0 points increase in error, 0 points decrease in error
      (*.f64 x (/.f64 (Rewrite=> neg-mul-1_binary64 (*.f64 -1 (-.f64 a z))) t)): 0 points increase in error, 0 points decrease in error
      (*.f64 x (Rewrite=> associate-/l*_binary64 (/.f64 -1 (/.f64 t (-.f64 a z))))): 21 points increase in error, 13 points decrease in error
      (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 x -1) (/.f64 t (-.f64 a z)))): 18 points increase in error, 19 points decrease in error
      (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 -1 x)) (/.f64 t (-.f64 a z))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 x (/.f64 t (-.f64 a z))))): 0 points increase in error, 0 points decrease in error
      (*.f64 -1 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x (-.f64 a z)) t))): 43 points increase in error, 45 points decrease in error

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

   1. Initial program 21.0

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

   2. Simplified 6.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)} \]
      Proof
      (fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t))) x)): 5 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) x): 87 points increase in error, 13 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))): 0 points increase in error, 0 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 7.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{-224}:\\ \;\;\;\;x + \frac{y - x}{\frac{a - t}{z - t}}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - x, \frac{z - t}{a - t}, x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	7.1
Cost	2632

\[\begin{array}{l} t_1 := x + \frac{y - x}{\frac{a - t}{z - t}}\\ t_2 := x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	28.7
Cost	1368

\[\begin{array}{l} t_1 := x - z \cdot \frac{x}{a}\\ t_2 := \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{if}\;y \leq -0.0395243672788389:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.525701762701239 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.098295133570548 \cdot 10^{-118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.0193345566533125 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2440516113226724 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.362635666923476 \cdot 10^{+79}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	28.7
Cost	1368

\[\begin{array}{l} t_1 := x - z \cdot \frac{x}{a}\\ t_2 := \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{if}\;y \leq -0.0395243672788389:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.525701762701239 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.098295133570548 \cdot 10^{-118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.0193345566533125 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2440516113226724 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq 3.362635666923476 \cdot 10^{+79}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	15.6
Cost	1100

\[\begin{array}{l} \mathbf{if}\;t \leq -1963.4044917957049:\\ \;\;\;\;y + \frac{y - x}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 201.64235178438435:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 1.611851665267204 \cdot 10^{+124}:\\ \;\;\;\;x + \frac{x - y}{\frac{a - t}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]

Alternative 5
Error	15.6
Cost	1100

\[\begin{array}{l} \mathbf{if}\;t \leq -1963.4044917957049:\\ \;\;\;\;y + \left(y - x\right) \cdot \frac{a - z}{t}\\ \mathbf{elif}\;t \leq 201.64235178438435:\\ \;\;\;\;x + \frac{z}{\frac{a - t}{y - x}}\\ \mathbf{elif}\;t \leq 1.611851665267204 \cdot 10^{+124}:\\ \;\;\;\;x + \frac{x - y}{\frac{a - t}{t}}\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \frac{z - a}{t}\\ \end{array} \]

Alternative 6
Error	34.7
Cost	976

\[\begin{array}{l} t_1 := x - z \cdot \frac{x}{a}\\ \mathbf{if}\;a \leq -2.6176168668280983 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4109254594059845 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -2.5843016839884563 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.538622384782759 \cdot 10^{-32}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	31.8
Cost	976

\[\begin{array}{l} t_1 := x - z \cdot \frac{x}{a}\\ \mathbf{if}\;a \leq -2.6176168668280983 \cdot 10^{+213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.4109254594059845 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;a \leq -2.5843016839884563 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6541608736872038 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	18.6
Cost	972

\[\begin{array}{l} t_1 := y - x \cdot \frac{a - z}{t}\\ \mathbf{if}\;t \leq -1963.4044917957049:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.614886412289549 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.611851665267204 \cdot 10^{+124}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	17.5
Cost	972

\[\begin{array}{l} \mathbf{if}\;t \leq -1963.4044917957049:\\ \;\;\;\;y + \frac{y - x}{\frac{t}{a - z}}\\ \mathbf{elif}\;t \leq 2.614886412289549 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.611851665267204 \cdot 10^{+124}:\\ \;\;\;\;\frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot \frac{a - z}{t}\\ \end{array} \]

Alternative 10
Error	19.8
Cost	968

\[\begin{array}{l} \mathbf{if}\;a \leq -2.5843016839884563 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{x - y}{\frac{a - t}{t}}\\ \mathbf{elif}\;a \leq 8.098915601890683 \cdot 10^{+145}:\\ \;\;\;\;y + \frac{y - x}{\frac{t}{a - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \end{array} \]

Alternative 11
Error	21.0
Cost	840

\[\begin{array}{l} t_1 := \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{if}\;t \leq -1572990.2481996443:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.614886412289549 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y - x}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	27.9
Cost	776

\[\begin{array}{l} t_1 := y \cdot \frac{-t}{a - t}\\ \mathbf{if}\;t \leq -4.940652433337238 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 19266624313572516:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	36.1
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -1963.4044917957049:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-289}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-234}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 9.814298483613382 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 14
Error	36.0
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -1963.4044917957049:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-289}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 9.814298483613382 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 15
Error	36.1
Cost	716

\[\begin{array}{l} \mathbf{if}\;t \leq -1963.4044917957049:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-289}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-234}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 9.814298483613382 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 16
Error	28.3
Cost	712

\[\begin{array}{l} t_1 := y \cdot \left(1 - \frac{z}{t}\right)\\ \mathbf{if}\;t \leq -1.086956201023489 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8296769391725386 \cdot 10^{-12}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	35.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -1963.4044917957049:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 9.814298483613382 \cdot 10^{+39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 18
Error	45.2
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022316 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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