Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze29.0ms (0.4%)

Memory

-15.4MiB live, 24.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	12.8%	87.2%	0%	0%	0%	0
0%	0%	12.8%	87.2%	0%	0%	0%	1
0%	0%	12.8%	87.2%	0%	0%	0%	2
50%	6.4%	6.4%	87.2%	0%	0%	0%	3
57.1%	6.4%	4.8%	87.2%	0%	1.6%	0%	4
69.2%	7.2%	3.2%	87.2%	0%	2.4%	0%	5
75%	7.2%	2.4%	87.2%	0%	3.2%	0%	6
82.6%	7.6%	1.6%	87.2%	0%	3.6%	0%	7
86.4%	7.6%	1.2%	87.2%	0%	4%	0%	8
90.7%	7.8%	0.8%	87.2%	0%	4.2%	0%	9
92.6%	7.8%	0.6%	87.2%	0%	4.4%	0%	10
95%	7.9%	0.4%	87.2%	0%	4.5%	0%	11
96.3%	8%	0.3%	87.2%	0%	4.5%	0%	12

Compiler

Compiled 24 to 18 computations (25% saved)

sample1.7s (25%)

Memory

24.2MiB live, 2 098.1MiB allocated

Samples

591.0ms	2 702×	1	valid
441.0ms	4 918×	0	valid
123.0ms	636×	2	valid
11.0ms	161×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 879.0ms

ival-mult: 240.0ms (27.3% of total)

ival-sqrt: 217.0ms (24.7% of total)

ival-<=: 149.0ms (16.9% of total)

ival-sub: 146.0ms (16.6% of total)

adjust: 83.0ms (9.4% of total)

ival-and: 23.0ms (2.6% of total)

exact: 17.0ms (1.9% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain106.0ms (1.6%)

Memory

-50.9MiB live, 203.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
112	-	-	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
0	-	-	`eps`
0	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) eps))`
0	-	-	`(-.f64 (*.f64 x x) eps)`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`	cancellation	112	1

Confusion

	Predicted +	Predicted -
+	112	0
-	0	144

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	112	0	0
-	0	1	143

Precision?

0.9911504424778761

Recall?

1.0

Freqs

test

number	freq
0	144
1	112

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

20.0ms	176×	1	valid
18.0ms	304×	0	valid
5.0ms	32×	2	valid

Compiler

Compiled 60 to 22 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-sub: 9.0ms (34.3% of total)

ival-mult: 7.0ms (26.7% of total)

ival-sqrt: 6.0ms (22.9% of total)

adjust: 4.0ms (15.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

preprocess20.0ms (0.3%)

Memory

-10.8MiB live, 40.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	32	46
2	61	46
3	88	46
4	112	46
0	6	8
0	10	8
1	14	8
2	27	8
3	46	8
4	58	8
0	58	8

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff	0	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	24
0	10	24
1	14	24
2	27	24
3	46	24
4	58	24
0	58	24

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps

localize27.0ms (0.4%)

Memory

20.6MiB live, 65.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.00390625	(-.f64 (*.f64 x x) eps)
accuracy	24.995992693125512	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

10.0ms	152×	0	valid
9.0ms	88×	1	valid
2.0ms	16×	2	valid

Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-sub: 6.0ms (44.3% of total)

ival-sqrt: 3.0ms (22.1% of total)

ival-mult: 3.0ms (22.1% of total)

adjust: 2.0ms (14.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated

Counts

4 → 49

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	inf	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
2.0ms	x	@	inf	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms	x	@	0	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms	eps	@	-inf	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))
1.0ms	eps	@	0	((- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (* x x))

simplify197.0ms (2.9%)

Memory

-14.9MiB live, 166.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	1069
1	807	1054
2	3108	1019
0	8668	960

Stop Event

1×	iter limit
1×	node limit

Counts

49 → 48

Calls

Call 1

Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) x))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/8 binary64))) (.f64 x x) (fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)) x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 x x))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (fma.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* 1/2 (/ eps x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)))) x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(.f64 (neg.f64 x) (-.f64 (.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (neg.f64 x) (-.f64 (/.f64 (.f64 (*.f64 #s(literal 1/8 binary64) eps) eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(.f64 (neg.f64 x) (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (*.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 2 binary64)))))
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 eps x) #s(literal -1 binary64)) x)
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 (neg.f64 x) (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(+ x (* -1/2 (/ eps x)))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 eps x) #s(literal -1/2 binary64)) x) eps x)
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal -1/2 binary64) x)) eps x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(*.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps)) eps)
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps))) eps)
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 x eps)))) eps)
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps)
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64) (fma.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(* eps (- (/ (pow x 2) eps) 1))
(.f64 (-.f64 (.f64 x (/.f64 x eps)) #s(literal 1 binary64)) eps)
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)))) eps)
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (neg.f64 (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (.f64 x x)) #s(literal -1/2 binary64) (neg.f64 x)) eps))) eps)
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 x (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (sqrt.f64 eps) x) x) (.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) eps)) eps)))) eps)
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (neg.f64 eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (neg.f64 eps) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(.f64 (neg.f64 eps) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (*.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)

rewrite196.0ms (2.9%)

Memory

15.8MiB live, 161.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
0	10	22
1	42	22
2	320	22
3	3652	22
0	8870	22

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

4 → 199

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) #s(literal 2 binary64))) (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)) (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (fma.f64 x x (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(.f64 (/.f64 (fma.f64 x x (-.f64 (.f64 x x) eps)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (*.f64 x x) eps))))
(.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps))) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps)))))
(.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (-.f64 (.f64 x x) eps) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal 2 binary64))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (fma.f64 x x (-.f64 (.f64 x x) eps)))) #s(literal 2 binary64))) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) #s(literal 3 binary64)) (pow.f64 (.f64 eps (/.f64 eps (fma.f64 x x eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 eps (/.f64 eps (fma.f64 x x eps))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (.f64 eps (/.f64 eps (fma.f64 x x eps)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))))))
(/.f64 (pow.f64 (hypot.f64 eps (*.f64 x x)) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal 1 binary64)))
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(/.f64 (.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (hypot.f64 eps (.f64 x x))) (hypot.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
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(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (.f64 (fma.f64 x x eps) (*.f64 eps eps))) (pow.f64 (fma.f64 x x eps) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (.f64 (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 eps #s(literal 4 binary64))) (*.f64 (fma.f64 eps eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x eps)))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 eps #s(literal 6 binary64))) (.f64 (+.f64 (pow.f64 (.f64 (fma.f64 x x eps) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 8 binary64))) (fma.f64 x x eps)))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 eps #s(literal 6 binary64))) (*.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 eps #s(literal 9 binary64))) (*.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (fma.f64 eps eps (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x eps))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64))))
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(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 eps eps (pow.f64 x #s(literal 4 binary64)))) (-.f64 (.f64 x x) eps) (.f64 eps (/.f64 eps (fma.f64 x x eps))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (fma.f64 x x eps)) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (fma.f64 x x eps)) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x eps)) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))
(sqrt.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (fma.f64 x x eps) eps (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (*.f64 x x) eps)
(fabs.f64 (-.f64 (*.f64 x x) eps))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (cosh.f64 (.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))
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(+.f64 (cosh.f64 (log.f64 (-.f64 (.f64 x x) eps))) (sinh.f64 (log.f64 (-.f64 (.f64 x x) eps))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x eps)) (*.f64 eps (/.f64 eps (fma.f64 x x eps))))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (+.f64 (/.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))))
(exp.f64 (+.f64 (/.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (log.f64 x) #s(literal 1 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1 binary64) (/.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1 binary64) (*.f64 (log.f64 x) #s(literal 1 binary64))))
(exp.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (/.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (/.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (/.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval32.0ms (0.5%)

Memory: 15.9MiB live, 59.9MiB allocated
Compiler: Compiled 6 064 to 978 computations (83.9% saved)

prune19.0ms (0.3%)

Memory

-23.3MiB live, 22.1MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	236	9	245
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	236	10	246

Accuracy

99.6%

Counts

246 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.1%	(fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) x)
▶	60.5%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	60.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	55.8%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	7.6%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
▶	3.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	33.2%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x))
	23.2%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
▶	38.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
▶	45.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 348 to 230 computations (33.9% saved)

simplify139.0ms (2%)

Memory

16.3MiB live, 169.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x))
cost-diff	2	(fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))
cost-diff	2	(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps)))
cost-diff	0	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
cost-diff	0	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
cost-diff	0	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	268
0	63	268
1	103	268
2	232	266
3	742	264
4	2979	261
5	7011	261
0	8030	254

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
x
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
x
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
eps
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 1/8 binary64)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
eps
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x))
(/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps)))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64)))
(pow.f64 eps #s(literal 3 binary64))
eps
#s(literal 3 binary64)
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
#s(literal 1/16 binary64)
(fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))
(*.f64 (/.f64 eps x) #s(literal 1/8 binary64))
(/.f64 eps x)
#s(literal 1/8 binary64)
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)

Outputs
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
x
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
x
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
eps
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
#s(literal 1/8 binary64)
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
eps
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 eps (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) x)) eps))
(/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x)
(*.f64 (fma.f64 eps (fma.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps)))
(*.f64 eps (fma.f64 eps (fma.f64 (/.f64 eps (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (/.f64 (/.f64 #s(literal 1/8 binary64) x) x)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64)))
(pow.f64 eps #s(literal 3 binary64))
eps
#s(literal 3 binary64)
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 4 binary64)
#s(literal 1/16 binary64)
(fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))
(*.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) x) x) eps #s(literal 1/2 binary64)) eps)
(*.f64 (/.f64 eps x) #s(literal 1/8 binary64))
(/.f64 eps x)
#s(literal 1/8 binary64)
(*.f64 #s(literal 1/2 binary64) eps)
#s(literal 1/2 binary64)

localize136.0ms (2%)

Memory

-13.0MiB live, 222.7MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.234375	(fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))
accuracy	5.257769152434323	(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps)))
accuracy	34.53536227280482	(/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64)))
accuracy	34.88481949276717	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x))
accuracy	0.1328125	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
accuracy	9.017895550233424	(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
accuracy	10.682505493980191	(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy	35.80209620643037	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.24609375	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy	34.76556059981636	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
accuracy	0.0	(neg.f64 x)
accuracy	24.995992693125512	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy	62.39176801243668	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy	0.0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.00390625	(-.f64 (*.f64 x x) eps)
accuracy	0.3125	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
accuracy	24.995992693125512	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))

Samples

68.0ms	152×	0	valid
35.0ms	88×	1	valid
8.0ms	16×	2	valid

Compiler

Compiled 228 to 34 computations (85.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-div: 22.0ms (25% of total)

ival-mult: 19.0ms (21.6% of total)

ival-sub: 12.0ms (13.6% of total)

ival-sqrt: 12.0ms (13.6% of total)

ival-pow: 10.0ms (11.3% of total)

adjust: 7.0ms (7.9% of total)

ival-add: 4.0ms (4.5% of total)

exact: 1.0ms (1.1% of total)

ival-neg: 1.0ms (1.1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series53.0ms (0.8%)

Memory

17.9MiB live, 62.2MiB allocated

Counts

20 → 87

Calls

Call 1

Inputs
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps)))
(fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x))
(/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64)))

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(* -1 x)
(* 1/2 (/ eps x))
(/ 1/2 x)
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/8 (pow x 3))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 4))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 4))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(/ (pow eps 3) (pow x 4))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 2)))) (* 1/16 (/ 1 (pow x 4)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 2))) (+ (/ 1/2 (pow eps 2)) (* 1/16 (/ 1 (pow x 4))))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/8 (/ 1 (* eps (pow x 2))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))) eps)) (* 1/16 (/ 1 (pow x 4))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))

Calls

6 calls:

Time	Variable		Point	Expression
29.0ms	x	@	-inf	((- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) x) (sqrt (- (* x x) eps)) (/ (pow eps 3) (pow x 4)))
6.0ms	eps	@	inf	((- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) x) (sqrt (- (* x x) eps)) (/ (pow eps 3) (pow x 4)))
6.0ms	x	@	0	((- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) x) (sqrt (- (* x x) eps)) (/ (pow eps 3) (pow x 4)))
4.0ms	eps	@	-inf	((- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) x) (sqrt (- (* x x) eps)) (/ (pow eps 3) (pow x 4)))
4.0ms	x	@	inf	((- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ 1/2 x) eps) (/ 1/2 x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) (/ 1/8 (pow x 3)) (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) x) (sqrt (- (* x x) eps)) (/ (pow eps 3) (pow x 4)))

simplify208.0ms (3.1%)

Memory

-26.1MiB live, 160.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	353	1653
1	1133	1620
2	4353	1604
0	8125	1519

Stop Event

1×	iter limit
1×	node limit

Counts

87 → 86

Calls

Call 1

Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(* -1 x)
(* 1/2 (/ eps x))
(/ 1/2 x)
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/8 (pow x 3))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 4))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 4))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(/ (pow eps 3) (pow x 4))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 2)))) (* 1/16 (/ 1 (pow x 4)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 2))) (+ (/ 1/2 (pow eps 2)) (* 1/16 (/ 1 (pow x 4))))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/8 (/ 1 (* eps (pow x 2))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))) eps)) (* 1/16 (/ 1 (pow x 4))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) x))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64) (.f64 (.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -1/8 binary64))) (.f64 x x) x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 (.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal 1/8 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 x (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) #s(literal 1/16 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64))) (.f64 x x) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* -1 x)
(neg.f64 x)
(* 1/2 (/ eps x))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* 1/8 (/ (pow eps 2) (pow x 3)))
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(.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1/2 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))) eps)
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1/2 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x)))) eps)
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) #s(literal -1/16 binary64)) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) #s(literal -1/2 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) x) x))))) eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(*.f64 (fma.f64 x (/.f64 x eps) #s(literal -1 binary64)) eps)
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(*.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps)
(* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/8 (/ 1 (* eps (pow x 2))))))
(.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) eps)) (pow.f64 eps #s(literal 3 binary64)))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))) eps)) (* 1/16 (/ 1 (pow x 4))))))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal -1/8 binary64) (.f64 x x))) (neg.f64 eps)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) (.f64 eps x)) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))

rewrite266.0ms (3.9%)

Memory

-37.8MiB live, 290.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	227
0	63	221
1	214	221
2	1575	211
0	8524	207

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

20 → 805

Calls

Call 1

Inputs
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
(neg.f64 x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
(/.f64 #s(literal 1/2 binary64) x)
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps)))
(fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x))
(/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64)))

Outputs
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)))) (.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (*.f64 x x) eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (.f64 x x) eps)))) (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))))
(-.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(+.f64 (-.f64 x (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (/.f64 (fma.f64 x x eps) (fma.f64 x x eps)) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(.f64 (/.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(.f64 (/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) (/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))))
(.f64 (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))))
(.f64 (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))))
(.f64 (fabs.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)) (pow.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)))) (neg.f64 (/.f64 (fma.f64 x x eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps))))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) eps))) (neg.f64 (-.f64 (.f64 x x) eps)))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (neg.f64 (sqrt.f64 (fma.f64 x x eps))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 x x)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 eps))) (-.f64 (.f64 x x) eps))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 x x)) (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) eps)) (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (-.f64 (.f64 (.f64 x x) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 eps))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(/.f64 (-.f64 (neg.f64 (.f64 x x)) (neg.f64 eps)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (fabs.f64 (sqrt.f64 (fma.f64 x x eps))))
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (fabs.f64 (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)) (pow.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)))) (fabs.f64 (/.f64 (fma.f64 x x eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(/.f64 (fabs.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 3 binary64)))) (fabs.f64 (+.f64 (pow.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps))))))))
(/.f64 (fabs.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) eps)))) (fabs.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))))
(/.f64 (fabs.f64 (-.f64 (.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) eps))) (-.f64 (.f64 x x) eps))
(/.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (fabs.f64 (.f64 (fma.f64 x x eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fabs.f64 (.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(/.f64 (fabs.f64 (neg.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (sqrt.f64 (neg.f64 (fma.f64 x x eps))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)) (pow.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64))) (/.f64 (fma.f64 x x eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (pow.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 eps (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (sqrt.f64 (-.f64 (*.f64 x x) eps)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (neg.f64 (.f64 (fma.f64 x x eps) (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(/.f64 (-.f64 (.f64 (.f64 x x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) eps)) (-.f64 (.f64 x x) eps))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (sqrt.f64 (fma.f64 x x eps)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (.f64 (fma.f64 x x eps) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) eps)) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))))
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(neg.f64 (/.f64 (neg.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))))
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(*.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) x) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (/.f64 (.f64 eps eps) (.f64 x (neg.f64 x))) (/.f64 (neg.f64 eps) (.f64 x (neg.f64 x))))
(.f64 (/.f64 (.f64 eps eps) (.f64 x (neg.f64 x))) (/.f64 eps (.f64 x (neg.f64 x))))
(.f64 (/.f64 (.f64 eps eps) (.f64 (neg.f64 x) x)) (/.f64 (neg.f64 eps) (.f64 (neg.f64 x) x)))
(.f64 (/.f64 (.f64 eps eps) (.f64 (neg.f64 x) x)) (/.f64 eps (.f64 (neg.f64 x) x)))
(.f64 (/.f64 (.f64 eps eps) (neg.f64 (.f64 x x))) (/.f64 (neg.f64 eps) (.f64 x x)))
(.f64 (/.f64 (.f64 eps eps) (neg.f64 (.f64 x x))) (/.f64 eps (neg.f64 (.f64 x x))))
(.f64 (/.f64 (.f64 eps eps) (neg.f64 (.f64 x x))) (/.f64 eps (.f64 x x)))
(.f64 (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 3 binary64))) (/.f64 (neg.f64 eps) x))
(.f64 (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 3 binary64))) (/.f64 eps (neg.f64 x)))
(.f64 (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 3 binary64))) (/.f64 eps x))
(.f64 (/.f64 (.f64 eps eps) (neg.f64 x)) (/.f64 eps (pow.f64 x #s(literal 3 binary64))))
(.f64 (/.f64 (.f64 eps eps) x) (/.f64 eps (pow.f64 x #s(literal 3 binary64))))
(.f64 (/.f64 eps (.f64 x (neg.f64 x))) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 x (neg.f64 x))))
(.f64 (/.f64 eps (.f64 x (neg.f64 x))) (/.f64 (.f64 eps eps) (.f64 x (neg.f64 x))))
(.f64 (/.f64 eps (.f64 (neg.f64 x) x)) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 (neg.f64 x) x)))
(.f64 (/.f64 eps (.f64 (neg.f64 x) x)) (/.f64 (.f64 eps eps) (.f64 (neg.f64 x) x)))
(.f64 (/.f64 eps (neg.f64 (.f64 x x))) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 x x)))
(.f64 (/.f64 eps (neg.f64 (.f64 x x))) (/.f64 (.f64 eps eps) (neg.f64 (.f64 x x))))
(.f64 (/.f64 eps (neg.f64 (.f64 x x))) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)))
(.f64 (neg.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (.f64 x x))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (*.f64 x x))))
(.f64 (fabs.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (.f64 x x))) (fabs.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (*.f64 x x))))
(.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) (/.f64 (neg.f64 (.f64 eps eps)) (neg.f64 x)))
(.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) (/.f64 (neg.f64 (.f64 eps eps)) x))
(.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) (/.f64 (.f64 eps eps) (neg.f64 x)))
(.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) (/.f64 (.f64 eps eps) x))
(.f64 (/.f64 (neg.f64 eps) x) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 3 binary64))))
(.f64 (/.f64 eps (neg.f64 x)) (/.f64 (neg.f64 (.f64 eps eps)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (/.f64 eps (neg.f64 x)) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 3 binary64))))
(.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (/.f64 (neg.f64 eps) (.f64 x x)))
(.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (/.f64 eps (neg.f64 (.f64 x x))))
(.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (/.f64 eps (.f64 x x)))
(.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (.f64 x x)) (/.f64 (neg.f64 (pow.f64 eps #s(literal 3/2 binary64))) (*.f64 x x)))
(.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (.f64 x x)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (neg.f64 (*.f64 x x))))
(.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (.f64 x x)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (*.f64 x x)))
(.f64 (/.f64 eps (.f64 x x)) (/.f64 (neg.f64 (.f64 eps eps)) (.f64 x x)))
(.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 eps eps) (neg.f64 (.f64 x x))))
(.f64 (/.f64 eps (.f64 x x)) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)))
(*.f64 (pow.f64 eps #s(literal 3/2 binary64)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (.f64 eps eps) (/.f64 eps (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 eps x) (/.f64 (neg.f64 (.f64 eps eps)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (/.f64 eps x) (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 3 binary64))))
(.f64 eps (/.f64 (.f64 eps eps) (pow.f64 x #s(literal 4 binary64))))
(pow.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (*.f64 x x)) #s(literal 2 binary64))
(/.f64 (neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 x x))) (neg.f64 (.f64 x x)))
(/.f64 (neg.f64 (pow.f64 (neg.f64 (neg.f64 eps)) #s(literal 3 binary64))) (neg.f64 (neg.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 x x)) (.f64 x x))
(/.f64 (pow.f64 (neg.f64 (neg.f64 eps)) #s(literal 3 binary64)) (neg.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (pow.f64 (neg.f64 (neg.f64 eps)) #s(literal 3 binary64)) (neg.f64 (pow.f64 x #s(literal 4 binary64))))
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (neg.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (neg.f64 (pow.f64 x #s(literal 4 binary64))))
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64)))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (neg.f64 (pow.f64 x #s(literal 4 binary64))))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64)))
(neg.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))))
(exp.f64 (-.f64 (.f64 (log.f64 eps) #s(literal 3 binary64)) (.f64 (log.f64 x) #s(literal 4 binary64))))
(+.f64 (cosh.f64 (-.f64 (.f64 (log.f64 eps) #s(literal 3 binary64)) (.f64 (log.f64 x) #s(literal 4 binary64)))) (sinh.f64 (-.f64 (.f64 (log.f64 eps) #s(literal 3 binary64)) (.f64 (log.f64 x) #s(literal 4 binary64)))))

eval157.0ms (2.3%)

Memory: 39.7MiB live, 221.2MiB allocated
Compiler: Compiled 36 720 to 3 855 computations (89.5% saved)

prune26.0ms (0.4%)

Memory

-4.5MiB live, 85.6MiB allocated

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	884	10	894
Fresh	2	2	4
Picked	4	1	5
Done	0	1	1
Total	890	14	904

Accuracy

99.9%

Counts

904 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	60.1%	(fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) x)
▶	43.2%	(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
▶	60.5%	(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
	55.9%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
✓	60.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	55.8%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	7.6%	(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	23.2%	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
	38.6%	#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) eps) eps)))
	45.2%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (/.f64 eps (.f64 x x))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x))
	45.7%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
▶	44.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
	38.5%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps))

Compiler

Compiled 641 to 360 computations (43.8% saved)

simplify159.0ms (2.3%)

Memory

-19.3MiB live, 90.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff	17	(-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)))
cost-diff	18	(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
cost-diff	0	(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)
cost-diff	0	#s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps))
cost-diff	0	(/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
cost-diff	0	(/.f64 eps x)
cost-diff	0	(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
cost-diff	0	#s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
cost-diff	0	(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
cost-diff	0	(neg.f64 eps)
cost-diff	0	#s(approx (- (* x x) eps) (neg.f64 eps))
cost-diff	0	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
cost-diff	0	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff	8	(-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	419
0	75	384
1	144	357
2	461	342
3	1927	342
0	8019	339

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))
(*.f64 x x)
x
(-.f64 (*.f64 x x) eps)
eps
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
x
#s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
eps
#s(literal -1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
(/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)
#s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)
(fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(/.f64 (/.f64 eps x) x)
(/.f64 eps x)
eps
x
#s(literal 1/8 binary64)
#s(literal 1/2 binary64)
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)))
(.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x x)
x
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
eps
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Outputs
(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))
eps
(*.f64 x x)
x
(-.f64 (*.f64 x x) eps)
eps
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
x
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
eps
(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)))
x
#s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
#s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)
(/.f64 eps x)
eps
#s(literal -1/2 binary64)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
(/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)
#s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)
(fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(/.f64 (/.f64 eps x) x)
(/.f64 eps x)
eps
x
#s(literal 1/8 binary64)
#s(literal 1/2 binary64)
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)
(.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (*.f64 x x))
(*.f64 x x)
x
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
eps
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

localize174.0ms (2.6%)

Memory

26.8MiB live, 253.5MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.19140625	(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))
accuracy	0.29296875	(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy	17.478597251580833	(-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)))
accuracy	18.433088621296157	(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
accuracy	0.1875	(/.f64 (/.f64 eps x) x)
accuracy	6.448421926348702	(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)
accuracy	34.88481949276717	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
accuracy	35.89353213085717	#s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps))
accuracy	0.0	(/.f64 eps x)
accuracy	0.00390625	(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
accuracy	24.995992693125512	(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
accuracy	34.124329019297925	#s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
accuracy	0.0	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	0.0	(neg.f64 eps)
accuracy	24.995992693125512	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy	27.313291282821403	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.00390625	(-.f64 (*.f64 x x) eps)
accuracy	0.015625	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.28515625	(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy	24.65418138161673	(-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))

Samples

70.0ms	88×	1	valid
46.0ms	152×	0	valid
23.0ms	16×	2	valid

Compiler

Compiled 342 to 42 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 92.0ms

adjust: 25.0ms (27% of total)

ival-mult: 18.0ms (19.5% of total)

ival-sub: 14.0ms (15.1% of total)

ival-div: 13.0ms (14.1% of total)

ival-pow: 11.0ms (11.9% of total)

ival-add: 7.0ms (7.6% of total)

ival-sqrt: 3.0ms (3.2% of total)

exact: 1.0ms (1.1% of total)

ival-neg: 1.0ms (1.1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series66.0ms (1%)

Memory

15.9MiB live, 60.3MiB allocated

Counts

23 → 208

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))
(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x x)
(-.f64 (*.f64 x x) eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
#s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
(/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)
#s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)))
(.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(/.f64 (/.f64 eps x) x)
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))

Outputs
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(pow x 2)
(* -1 eps)
(- (pow x 2) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 4))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 4))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(+ (* x (- (* x (- (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* x (- (/ 1 (* eps (pow (sqrt -1) 4))) (* 2 (* (sqrt (/ 1 eps)) (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (sqrt -1))))))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* (sqrt (pow eps 3)) (sqrt -1))
(- (* eps x) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(- (* x (- (* 1/2 (* (sqrt eps) (/ x (sqrt -1)))) (* -1 eps))) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(- (* x (- (* x (- (* -1/8 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))))) (* -1 eps))) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(* (sqrt eps) (* (pow x 2) (sqrt -1)))
(* (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))
(* (pow x 2) (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))))
(* (pow x 2) (+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(/ eps (pow x 2))
(* eps (pow (sqrt -1) 2))
(+ (* 2 (* (sqrt eps) (* x (sqrt -1)))) (* eps (pow (sqrt -1) 2)))
(+ (* eps (pow (sqrt -1) 2)) (* x (+ (* 2 x) (* 2 (* (sqrt eps) (sqrt -1))))))
(+ (* eps (pow (sqrt -1) 2)) (* x (+ (* 2 (* (sqrt eps) (sqrt -1))) (* x (+ 2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1))))))))
(* -1 (* (sqrt (pow eps 3)) (sqrt -1)))
(+ (* -1 (* eps x)) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(+ (* -1 (* (sqrt (pow eps 3)) (sqrt -1))) (* x (+ (* -1 eps) (* x (+ (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))))
(+ (* -1 (* (sqrt (pow eps 3)) (sqrt -1))) (* x (+ (* -1 eps) (* x (+ x (+ (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt eps) (sqrt -1))))))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(/ (- (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) (* -1/4 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))) (+ (* -1/2 (/ (* eps (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (* 1/8 (/ (* eps (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4)))))) x)
(/ (- (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (+ (* -1/64 (/ (pow eps 4) (pow x 6))) (* 1/2 eps)))) (+ (* -1/2 (/ (* eps (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/2 (/ (* eps (- (* -1/32 (pow eps 3)) (+ (* -1/2 (* eps (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2))))) (* 1/8 (* eps (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2)))))))) (pow x 6))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/8 (/ (* eps (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4))) (+ (* 1/8 (/ (* eps (+ (* -1/4 (pow eps 3)) (* 1/8 (pow eps 3)))) (pow x 6))) (* 1/4 (/ (* (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2))) (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2)))) (pow x 6))))))))) x)
(* 2 (* eps x))
(* x (- (* -1/2 (/ (pow eps 2) (pow x 2))) (* -2 eps)))
(* x (- (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -2 eps) (* 1/2 (/ (pow eps 2) (pow x 2))))))
(* x (- (* -1/16 (/ (pow eps 4) (pow x 6))) (+ (* -2 eps) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))
(* 2 (pow x 3))
(* (pow x 3) (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* (pow x 3) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* (pow x 3) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* 4 (pow x 2))
(* (pow x 2) (+ 4 (* -2 (/ eps (pow x 2)))))
(* (pow x 2) (+ 4 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(* (pow x 2) (+ 4 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/4 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 6))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))))
(* (pow x 3) (+ 2 (+ (* -2 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))
(* (pow x 3) (+ 2 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 4))))))))
(* (pow x 3) (+ 2 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* -1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 6))) (* 1/2 (/ (pow eps 2) (pow x 4))))))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (* x (- (* -1/2 (/ eps (pow x 2))) (+ 2 (* -1 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* -1/2 (/ eps (pow x 2))) (* -1/4 (/ (pow eps 2) (pow x 4)))) (+ 2 (+ (* -8 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 4)))) (+ (* -1 (/ eps (pow x 2))) (* 1/2 (/ (* eps (- (* -1/2 eps) (* -1 eps))) (pow x 4)))))))))
(* -1 (* x (- (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6)))) (+ (* -1/2 (/ eps (pow x 2))) (* -1/4 (/ (pow eps 2) (pow x 4))))) (+ 2 (+ (* -8 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 4)))) (+ (* -8 (/ (+ (* 1/64 (pow eps 5)) (* 1/2 (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))))) (* (pow eps 2) (pow x 6)))) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/2 (/ (* eps (- (* -1/2 eps) (* -1 eps))) (pow x 4))) (+ (* 1/2 (/ (* eps (- (* -1/4 (pow eps 2)) (+ (* -8 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (* 1/2 (* eps (- (* -1/2 eps) (* -1 eps))))))) (pow x 6))) (* 4 (/ (* (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (- (* -1/2 eps) (* -1 eps))) (* (pow eps 2) (pow x 6)))))))))))))
(* 1/2 (/ (pow eps 2) x))
(* -1 (/ (- (* -1/8 (/ (pow eps 3) (pow x 2))) (* 1/2 (pow eps 2))) x))
(* -1 (/ (- (* -1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/2 (pow eps 2)))) x))
(* -1 (/ (- (* -1/2 (/ (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))) (pow x 6))) (+ (* 1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/2 (pow eps 2))))) x))
(* 1/2 (* eps x))
(* -1 (* x (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))))))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (pow eps 2))) (pow x 2))
(/ (+ (* 1/64 (/ (pow eps 4) (pow x 4))) (+ (* 1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (pow eps 2))))) (pow x 2))
(/ (+ (* 1/64 (/ (pow eps 4) (pow x 4))) (+ (* 1/64 (/ (pow eps 5) (pow x 6))) (+ (* 1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (+ (* 1/4 (pow eps 2)) (* 1/2 (/ (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))) (pow x 6)))))))) (pow x 2))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/16 (/ (pow eps 4) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ (* -1 eps) (pow x 2))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))))
(* eps (- (* -1/2 (/ eps x)) (* -2 x)))
(* eps (- (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (* -2 x)))
(* eps (- (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (* -2 x)))
(+ (* -1/2 (* eps x)) (* 2 (pow x 3)))
(+ (* 2 (pow x 3)) (* eps (+ (* -1/2 x) (* -1/8 (/ eps x)))))
(+ (* 2 (pow x 3)) (* eps (+ (* -1/2 x) (* eps (- (* -1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -2 eps) (* 4 (pow x 2)))
(+ (* 4 (pow x 2)) (* eps (- (* -1/4 (/ eps (pow x 2))) 2)))
(+ (* 4 (pow x 2)) (* eps (- (* eps (- (* -1/8 (/ eps (pow x 4))) (* 1/4 (/ 1 (pow x 2))))) 2)))
(+ (* 2 (pow x 3)) (* eps (+ (* -2 x) (* -1/2 x))))
(+ (* 2 (pow x 3)) (* eps (+ (* -2 x) (+ (* -1/2 x) (* 3/8 (/ eps x))))))
(+ (* 2 (pow x 3)) (* eps (+ (* -2 x) (+ (* -1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x))))))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 2)))) (* 1/16 (/ 1 (pow x 4)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 2))) (+ (/ 1/2 (pow eps 2)) (* 1/16 (/ 1 (pow x 4))))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2))) (* 2 (/ x (pow (sqrt -1) 2))))
(- (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (/ x (pow (sqrt -1) 2))))))
(- (+ (* -1 (/ (+ (* 2 (* (sqrt eps) (/ (* x (- (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt eps) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))))) (sqrt -1)))) (+ (* 2 (/ (* eps (* (pow x 2) (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2))) (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2))))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (/ x (pow (sqrt -1) 2))))))
(* (pow eps 2) (- (/ x eps) (* -1 (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (pow eps 2) (- (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(* (pow eps 2) (- (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1))))))))
(* eps (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 6) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps)))))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (/ (pow (sqrt -1) 2) eps)))
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (+ (* 2 (/ (pow x 2) (pow eps 2))) (/ (pow (sqrt -1) 2) eps))))
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 3) (sqrt -1))) (/ (pow (sqrt -1) 2) eps)))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))) (/ (pow x 3) (pow eps 2)))))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))) (/ (pow x 3) (pow eps 2))))))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))
(* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/8 (/ 1 (* eps (pow x 2))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))) eps)) (* 1/16 (/ 1 (pow x 4))))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* eps x) (* 2 (* eps x))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x))))))))) eps)) (* eps x)) (* 2 (* eps x))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (* (pow x 2) (- (* eps x) (* 2 (* eps x))))) (+ (* -1 (* eps (pow x 3))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x)))))))))))))))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x))))))))) eps)) (* eps x)) (* 2 (* eps x))) eps)))
(* (pow eps 2) (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (- (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* -1 (* (sqrt eps) (* (pow x 2) (sqrt -1))))
(* -1 (* eps (+ (* -1 (/ (pow x 3) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(* -1 (* eps (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(* -1 (* eps (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 6) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) eps)) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (pow eps 2) (- (* -2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (/ 1 eps)))
(* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ (pow x 2) eps)) (* 2 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) eps)) (/ 1 eps)))
(* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps)) (* 2 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) eps)) (/ 1 eps)))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (+ (* -1 (/ (+ x (+ (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (+ (* -1 (/ (+ x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (pow x 3))) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))

Calls

6 calls:

Time	Variable		Point	Expression
27.0ms	x	@	inf	((- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) x) (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (* (+ (* (/ (/ eps x) x) 1/8) 1/2) eps) (/ (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (/ (/ eps x) x) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps)))
12.0ms	eps	@	inf	((- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) x) (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (* (+ (* (/ (/ eps x) x) 1/8) 1/2) eps) (/ (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (/ (/ eps x) x) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps)))
9.0ms	eps	@	-inf	((- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) x) (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (* (+ (* (/ (/ eps x) x) 1/8) 1/2) eps) (/ (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (/ (/ eps x) x) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps)))
6.0ms	x	@	-inf	((- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) x) (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (* (+ (* (/ (/ eps x) x) 1/8) 1/2) eps) (/ (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (/ (/ eps x) x) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps)))
5.0ms	x	@	0	((- (* x x) (- (* x x) eps)) (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* x x) (- (* x x) eps) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* x x) eps) (neg eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (+ (* (/ eps x) -1/2) x) (/ eps x) (- x (sqrt (- (* x x) eps))) (/ (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) x) (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (* (+ (* (/ (/ eps x) x) 1/8) 1/2) eps) (/ (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x))) (- (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps))) (* (* x x) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (/ (/ eps x) x) (* (+ (sqrt (- (* x x) eps)) x) (+ (sqrt (- (* x x) eps)) x)) (* (+ (sqrt (- (* x x) eps)) x) (- (* x x) eps)))

simplify333.0ms (4.9%)

Memory

-34.7MiB live, 266.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1046	5824
1	3689	5419
0	8883	5131

Stop Event

1×	iter limit
1×	node limit

Counts

208 → 206

Calls

Call 1

Inputs
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(pow x 2)
(* -1 eps)
(- (pow x 2) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ eps x)
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 4))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 4))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 2))
(+ (* x (- (* x (- (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* x (- (/ 1 (* eps (pow (sqrt -1) 4))) (* 2 (* (sqrt (/ 1 eps)) (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (sqrt -1))))))) (+ (* -2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* (sqrt (pow eps 3)) (sqrt -1))
(- (* eps x) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(- (* x (- (* 1/2 (* (sqrt eps) (/ x (sqrt -1)))) (* -1 eps))) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(- (* x (- (* x (- (* -1/8 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))))) (* -1 eps))) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(* (sqrt eps) (* (pow x 2) (sqrt -1)))
(* (pow x 2) (+ x (* (sqrt eps) (sqrt -1))))
(* (pow x 2) (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1))))
(* (pow x 2) (+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1))))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(/ eps (pow x 2))
(* eps (pow (sqrt -1) 2))
(+ (* 2 (* (sqrt eps) (* x (sqrt -1)))) (* eps (pow (sqrt -1) 2)))
(+ (* eps (pow (sqrt -1) 2)) (* x (+ (* 2 x) (* 2 (* (sqrt eps) (sqrt -1))))))
(+ (* eps (pow (sqrt -1) 2)) (* x (+ (* 2 (* (sqrt eps) (sqrt -1))) (* x (+ 2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1))))))))
(* -1 (* (sqrt (pow eps 3)) (sqrt -1)))
(+ (* -1 (* eps x)) (* -1 (* (sqrt (pow eps 3)) (sqrt -1))))
(+ (* -1 (* (sqrt (pow eps 3)) (sqrt -1))) (* x (+ (* -1 eps) (* x (+ (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt eps) (sqrt -1)))))))
(+ (* -1 (* (sqrt (pow eps 3)) (sqrt -1))) (* x (+ (* -1 eps) (* x (+ x (+ (* -1/2 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt eps) (sqrt -1))))))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(/ (- (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) (* -1/4 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))) (+ (* -1/2 (/ (* eps (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (* 1/8 (/ (* eps (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4)))))) x)
(/ (- (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/32 (/ (pow eps 3) (pow x 4))) (+ (* -1/64 (/ (pow eps 4) (pow x 6))) (* 1/2 eps)))) (+ (* -1/2 (/ (* eps (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2)))) (pow x 4))) (+ (* -1/2 (/ (* eps (- (* -1/32 (pow eps 3)) (+ (* -1/2 (* eps (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2))))) (* 1/8 (* eps (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2)))))))) (pow x 6))) (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/8 (/ (* eps (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2)))) (pow x 4))) (+ (* 1/8 (/ (* eps (+ (* -1/4 (pow eps 3)) (* 1/8 (pow eps 3)))) (pow x 6))) (* 1/4 (/ (* (+ (* -1/2 (pow eps 2)) (* 1/4 (pow eps 2))) (- (* -1/8 (pow eps 2)) (* -1/4 (pow eps 2)))) (pow x 6))))))))) x)
(* 2 (* eps x))
(* x (- (* -1/2 (/ (pow eps 2) (pow x 2))) (* -2 eps)))
(* x (- (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -2 eps) (* 1/2 (/ (pow eps 2) (pow x 2))))))
(* x (- (* -1/16 (/ (pow eps 4) (pow x 6))) (+ (* -2 eps) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))
(* 2 (pow x 3))
(* (pow x 3) (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* (pow x 3) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* (pow x 3) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* 4 (pow x 2))
(* (pow x 2) (+ 4 (* -2 (/ eps (pow x 2)))))
(* (pow x 2) (+ 4 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))
(* (pow x 2) (+ 4 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 4))) (+ (* -1/4 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 6))) (* 1/4 (/ (pow eps 2) (pow x 4)))))))))
(* (pow x 3) (+ 2 (+ (* -2 (/ eps (pow x 2))) (* -1/2 (/ eps (pow x 2))))))
(* (pow x 3) (+ 2 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 4))))))))
(* (pow x 3) (+ 2 (+ (* -2 (/ eps (pow x 2))) (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (+ (* -1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 6))) (* 1/2 (/ (pow eps 2) (pow x 4))))))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (* x (- (* -1/2 (/ eps (pow x 2))) (+ 2 (* -1 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* -1/2 (/ eps (pow x 2))) (* -1/4 (/ (pow eps 2) (pow x 4)))) (+ 2 (+ (* -8 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 4)))) (+ (* -1 (/ eps (pow x 2))) (* 1/2 (/ (* eps (- (* -1/2 eps) (* -1 eps))) (pow x 4)))))))))
(* -1 (* x (- (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* eps (pow x 6)))) (+ (* -1/2 (/ eps (pow x 2))) (* -1/4 (/ (pow eps 2) (pow x 4))))) (+ 2 (+ (* -8 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (* (pow eps 2) (pow x 4)))) (+ (* -8 (/ (+ (* 1/64 (pow eps 5)) (* 1/2 (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))))) (* (pow eps 2) (pow x 6)))) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/2 (/ (* eps (- (* -1/2 eps) (* -1 eps))) (pow x 4))) (+ (* 1/2 (/ (* eps (- (* -1/4 (pow eps 2)) (+ (* -8 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (* 1/2 (* eps (- (* -1/2 eps) (* -1 eps))))))) (pow x 6))) (* 4 (/ (* (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (- (* -1/2 eps) (* -1 eps))) (* (pow eps 2) (pow x 6)))))))))))))
(* 1/2 (/ (pow eps 2) x))
(* -1 (/ (- (* -1/8 (/ (pow eps 3) (pow x 2))) (* 1/2 (pow eps 2))) x))
(* -1 (/ (- (* -1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/2 (pow eps 2)))) x))
(* -1 (/ (- (* -1/2 (/ (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))) (pow x 6))) (+ (* 1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/2 (pow eps 2))))) x))
(* 1/2 (* eps x))
(* -1 (* x (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))))))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(/ (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (pow eps 2))) (pow x 2))
(/ (+ (* 1/64 (/ (pow eps 4) (pow x 4))) (+ (* 1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (* 1/4 (pow eps 2))))) (pow x 2))
(/ (+ (* 1/64 (/ (pow eps 4) (pow x 4))) (+ (* 1/64 (/ (pow eps 5) (pow x 6))) (+ (* 1/16 (/ (pow eps 4) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 2))) (+ (* 1/4 (pow eps 2)) (* 1/2 (/ (* eps (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4)))) (pow x 6)))))))) (pow x 2))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))))
(* -1 (* x (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (+ (* -1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/16 (/ (pow eps 4) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (* 1/2 (/ (pow eps 2) (pow x 2)))))))))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ (* -1 eps) (pow x 2))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))))
(* eps (- (* -1/2 (/ eps x)) (* -2 x)))
(* eps (- (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))) (* -2 x)))
(* eps (- (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))) (* -2 x)))
(+ (* -1/2 (* eps x)) (* 2 (pow x 3)))
(+ (* 2 (pow x 3)) (* eps (+ (* -1/2 x) (* -1/8 (/ eps x)))))
(+ (* 2 (pow x 3)) (* eps (+ (* -1/2 x) (* eps (- (* -1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -2 eps) (* 4 (pow x 2)))
(+ (* 4 (pow x 2)) (* eps (- (* -1/4 (/ eps (pow x 2))) 2)))
(+ (* 4 (pow x 2)) (* eps (- (* eps (- (* -1/8 (/ eps (pow x 4))) (* 1/4 (/ 1 (pow x 2))))) 2)))
(+ (* 2 (pow x 3)) (* eps (+ (* -2 x) (* -1/2 x))))
(+ (* 2 (pow x 3)) (* eps (+ (* -2 x) (+ (* -1/2 x) (* 3/8 (/ eps x))))))
(+ (* 2 (pow x 3)) (* eps (+ (* -2 x) (+ (* -1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x))))))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 2)))) (* 1/16 (/ 1 (pow x 4)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 2))) (+ (/ 1/2 (pow eps 2)) (* 1/16 (/ 1 (pow x 4))))))
(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2))) (* 2 (/ x (pow (sqrt -1) 2))))
(- (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2)))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (/ x (pow (sqrt -1) 2))))))
(- (+ (* -1 (/ (+ (* 2 (* (sqrt eps) (/ (* x (- (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt eps) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))))) (sqrt -1)))) (+ (* 2 (/ (* eps (* (pow x 2) (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2))) (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2))))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (/ x (pow (sqrt -1) 2))))))
(* (pow eps 2) (- (/ x eps) (* -1 (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (pow eps 2) (- (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(* (pow eps 2) (- (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1))))))))
(* eps (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 6) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps)))))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (/ (pow (sqrt -1) 2) eps)))
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (+ (* 2 (/ (pow x 2) (pow eps 2))) (/ (pow (sqrt -1) 2) eps))))
(* (pow eps 2) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (+ (* 2 (/ (pow x 2) (pow eps 2))) (+ (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 3) (sqrt -1))) (/ (pow (sqrt -1) 2) eps)))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))) (/ (pow x 3) (pow eps 2)))))))
(* (pow eps 2) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1))) (/ (pow x 3) (pow eps 2))))))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))
(* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/8 (/ 1 (* eps (pow x 2))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))) eps)) (* 1/16 (/ 1 (pow x 4))))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* eps x) (* 2 (* eps x))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x))))))))) eps)) (* eps x)) (* 2 (* eps x))) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1 (/ (- (+ (* -2 (* (pow x 2) (- (* eps x) (* 2 (* eps x))))) (+ (* -1 (* eps (pow x 3))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x)))))))))))))))) (+ (* -2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 2 (* (sqrt eps) (* x (* (sqrt -1) (- (* eps x) (* 2 (* eps x))))))))) eps)) (* eps x)) (* 2 (* eps x))) eps)))
(* (pow eps 2) (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (- (* -1 (/ (- (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (- (* -1 (/ (- (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps)) x) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* -1 (* (sqrt eps) (* (pow x 2) (sqrt -1))))
(* -1 (* eps (+ (* -1 (/ (pow x 3) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(* -1 (* eps (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(* -1 (* eps (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 6) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) eps)) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (pow eps 2) (- (* -2 (* (sqrt (/ 1 (pow eps 3))) (* x (sqrt -1)))) (/ 1 eps)))
(* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ (pow x 2) eps)) (* 2 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) eps)) (/ 1 eps)))
(* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps)) (* 2 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) eps)) (/ 1 eps)))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (+ (* -1 (/ (+ x (+ (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (pow eps 2) (+ (* -1 (/ (+ x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (pow x 3))) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))

Outputs
eps
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (-.f64 (.f64 (neg.f64 x) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1/2 binary64))) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (-.f64 (.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps)) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))) x (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) #s(literal -1/2 binary64))) x) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(pow x 2)
(*.f64 x x)
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- x (* (sqrt eps) (sqrt -1)))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) #s(literal -1/2 binary64) #s(literal 1 binary64)) x (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal -1 binary64))) (.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) x #s(literal 1 binary64)) x (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 x #s(literal -1 binary64))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (/.f64 (.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64))) (.f64 x x) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) (.f64 x x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps)))
(* -1/2 (/ eps x))
(*.f64 #s(literal -1/2 binary64) (/.f64 eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/.f64 (fma.f64 #s(literal -1/2 binary64) eps (*.f64 x x)) x)
(/ eps x)
(/.f64 eps x)
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 5 binary64)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/8 binary64)) (.f64 x x) (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
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(* 1/16 (/ (pow eps 3) (pow x 4)))
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(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))))
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(* eps (- (* -1/2 (/ eps x)) (* -2 x)))
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(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
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(* eps (- (/ (pow x 2) eps) 1))
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(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
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(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
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(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(*.f64 (-.f64 (/.f64 x eps) (/.f64 #s(literal 1/2 binary64) x)) eps)
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
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(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
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(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 2)))) (* 1/16 (/ 1 (pow x 4)))))
(.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) eps))) (pow.f64 eps #s(literal 3 binary64)))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 2))) (+ (/ 1/2 (pow eps 2)) (* 1/16 (/ 1 (pow x 4))))))
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(* (pow eps 2) (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) eps) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (*.f64 eps eps))
(- (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2))) (* 2 (/ x (pow (sqrt -1) 2))))
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(- (+ (* -1 (/ (+ (* 2 (* (sqrt eps) (/ (* x (- (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt eps) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))))) (sqrt -1)))) (+ (* 2 (/ (* eps (* (pow x 2) (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2))) (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* (sqrt eps) (/ 1 (sqrt -1))) (/ x (pow (sqrt -1) 2))))) (+ (* 2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 2 (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (/ (* eps x) (pow (sqrt -1) 2)) (* 2 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (* 2 (/ x (pow (sqrt -1) 2))))))
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(* (pow eps 2) (- (/ x eps) (* -1 (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* (pow eps 2) (- (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
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(* (pow eps 2) (- (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1 (/ x eps)) (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1))))))))
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(* eps (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps)))
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(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 6) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 4) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))) (/ (pow x 3) eps)))))
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(.f64 (-.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps eps))
(* (pow eps 2) (- (* -1 (/ (+ (* -2 (/ (pow x 2) eps)) (* 2 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) eps)) (/ 1 eps)))
(.f64 (-.f64 (/.f64 (.f64 #s(literal -2 binary64) (-.f64 (/.f64 (.f64 x x) eps) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (neg.f64 eps)) (/.f64 #s(literal 1 binary64) eps)) (.f64 eps eps))
(* (pow eps 2) (- (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 eps)) (* (pow x 3) (sqrt -1)))) (* 2 (pow x 2))) eps)) (* 2 (* (sqrt (/ 1 eps)) (* x (sqrt -1))))) eps)) (/ 1 eps)))
(.f64 (-.f64 (/.f64 (fma.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) x) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) #s(literal 2 binary64))) (neg.f64 eps))) (neg.f64 eps)) (/.f64 #s(literal 1 binary64) eps)) (*.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1)))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) x) (neg.f64 eps))) (.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (+ x (+ (* -1 (/ (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (pow x 3)) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) x) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64))) (neg.f64 eps))) (neg.f64 eps))) (*.f64 eps eps))
(* (pow eps 2) (+ (* -1 (/ (+ x (+ (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (pow x 3))) eps)) (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (+.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) x) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 eps))) (neg.f64 eps))) (*.f64 eps eps))

rewrite258.0ms (3.8%)

Memory

14.7MiB live, 157.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	367
0	75	333
1	297	292
2	2476	274
0	8447	268

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

23 → 601

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))
(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(*.f64 x x)
(-.f64 (*.f64 x x) eps)
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
#s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x))
(fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)
(/.f64 eps x)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
(/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)
#s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps))
(*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)))
(.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(/.f64 (/.f64 eps x) x)
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps))

Outputs
(.f64 (+.f64 (neg.f64 x) (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (neg.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 eps #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 eps eps) (.f64 #s(literal 0 binary64) eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 2 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (.f64 x x) eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x (-.f64 (*.f64 x x) eps)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 2 binary64))) (fma.f64 x x (-.f64 (.f64 x x) eps)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3 binary64))) (fma.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x (-.f64 (*.f64 x x) eps)) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 x))) (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (neg.f64 x) (neg.f64 x) (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 x x (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x (-.f64 (.f64 x x) eps))) (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 2 binary64)) (fma.f64 x x (-.f64 (*.f64 x x) eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x (-.f64 (.f64 x x) eps)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3 binary64)) (fma.f64 (-.f64 (.f64 x x) eps) (fma.f64 x x (-.f64 (*.f64 x x) eps)) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))
(+.f64 #s(literal 0 binary64) eps)
(+.f64 eps #s(literal 0 binary64))
(+.f64 (.f64 x x) (.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (.f64 x x) eps))))
(.f64 (/.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(.f64 (/.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (*.f64 x x) eps)))
(.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))
(.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)))
(/.f64 (fma.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) eps)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64)))
(/.f64 (fma.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64)) (.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 (.f64 x x) eps)))) (.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))))
(/.f64 (fma.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 (.f64 x x) eps)))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 3 binary64)))
(/.f64 (fma.f64 (neg.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64)) (.f64 (neg.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64))) (.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 (.f64 x x) eps)))) (.f64 (neg.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64))))
(/.f64 (fma.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64)) (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64)) (.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 (.f64 x x) eps)))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 4 binary64)))
(/.f64 (-.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (-.f64 (neg.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x))) (.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 (.f64 x x) eps))) (neg.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64))))
(/.f64 (-.f64 (neg.f64 (.f64 x x)) (neg.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 #s(literal 0 binary64) eps)) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64))) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64))) #s(literal 2 binary64))) (fma.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (/.f64 (.f64 x x) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64))) (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64)) (pow.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64))) (fma.f64 x (/.f64 x (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64))) (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))))))
(/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 3 binary64))) (pow.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x (-.f64 (*.f64 x x) eps)))))
(/.f64 (neg.f64 (/.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 #s(literal 0 binary64) eps)) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x))) (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(/.f64 (neg.f64 (neg.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 #s(literal 0 binary64) eps)))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 2 binary64)))
(/.f64 (neg.f64 (+.f64 #s(literal 0 binary64) (neg.f64 eps))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))))
(/.f64 (-.f64 (.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (.f64 x x)) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64))) (.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) #s(literal 2 binary64)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps)))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) #s(literal 4 binary64)))
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(/.f64 (.f64 (-.f64 (.f64 x x) eps) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (*.f64 x x) eps)))
(/.f64 (.f64 (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (fma.f64 x x eps)))
(/.f64 (.f64 (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps)) (fma.f64 x x eps)))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (*.f64 x x) eps)) (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (.f64 (fma.f64 x x eps) (-.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps eps)) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (.f64 (fma.f64 x x eps) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x))) (.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (*.f64 x x) eps))))
(fma.f64 (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64))) (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64))) (.f64 x (-.f64 (.f64 x x) eps)))
(fma.f64 (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64))) (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64))) (.f64 (-.f64 (.f64 x x) eps) x))
(fma.f64 (fabs.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64))) (fabs.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64))) (.f64 x (-.f64 (.f64 x x) eps)))
(fma.f64 (fabs.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64))) (fabs.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64))) (.f64 (-.f64 (.f64 x x) eps) x))
(fma.f64 (pow.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 3 binary64)) (.f64 x (-.f64 (.f64 x x) eps)))
(fma.f64 (pow.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 3 binary64)) (.f64 (-.f64 (.f64 x x) eps) x))
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 3/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 3/2 binary64)) (.f64 x (-.f64 (.f64 x x) eps)))
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 3/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 3/2 binary64)) (.f64 (-.f64 (.f64 x x) eps) x))
(fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64)) (.f64 x (-.f64 (.f64 x x) eps)))
(fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64)) (.f64 (-.f64 (.f64 x x) eps) x))
(fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps) (.f64 x (-.f64 (.f64 x x) eps)))
(fma.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (-.f64 (.f64 x x) eps) (.f64 (-.f64 (.f64 x x) eps) x))
(fma.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)) (.f64 x (-.f64 (.f64 x x) eps)))
(fma.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)) (.f64 (-.f64 (.f64 x x) eps) x))
(fma.f64 (-.f64 (.f64 x x) eps) x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))
(fma.f64 x (-.f64 (.f64 x x) eps) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))
(sqrt.f64 (pow.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64)))
(fabs.f64 (.f64 (neg.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (-.f64 (*.f64 x x) eps)))
(fabs.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (*.f64 x x) eps)))
(+.f64 (.f64 x (-.f64 (.f64 x x) eps)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))
(+.f64 (.f64 (-.f64 (.f64 x x) eps) x) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))
(+.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (.f64 x (-.f64 (*.f64 x x) eps)))
(+.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (.f64 (-.f64 (*.f64 x x) eps) x))

eval403.0ms (5.9%)

Memory: 1.9MiB live, 322.3MiB allocated
Compiler: Compiled 76 192 to 4 939 computations (93.5% saved)

prune52.0ms (0.8%)

Memory

-3.8MiB live, 58.8MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	1 432	2	1 434
Fresh	6	1	7
Picked	3	2	5
Done	0	2	2
Total	1 441	7	1 448

Accuracy

100.0%

Counts

1 448 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
▶	55.9%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
✓	60.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	55.8%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.6%	(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	45.7%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))

Compiler

Compiled 104 to 65 computations (37.5% saved)

simplify252.0ms (3.7%)

Memory

17.8MiB live, 238.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff	0	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
cost-diff	0	(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
cost-diff	2	(+.f64 eps #s(literal 0 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))
cost-diff	0	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
cost-diff	0	(/.f64 eps x)
cost-diff	0	(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
cost-diff	0	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	136
0	39	132
1	60	124
2	152	124
3	269	124
4	466	124
5	782	124
6	1392	124
7	4671	124
0	8374	124

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
#s(literal 1/2 binary64)
(/.f64 eps x)
eps
x
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
x
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 eps #s(literal 0 binary64))
eps
#s(literal 0 binary64)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x

Outputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 eps x)
eps
x
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
x
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
eps
(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 eps)
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 eps #s(literal 0 binary64))
eps
eps
#s(literal 0 binary64)
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x

localize82.0ms (1.2%)

Memory

3.6MiB live, 152.2MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.00390625	(-.f64 (*.f64 x x) eps)
accuracy	0.015625	(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
accuracy	0.28515625	(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
accuracy	0.00390625	(-.f64 (*.f64 x x) eps)
accuracy	0.3125	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))
accuracy	24.995992693125512	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
accuracy	27.313291282821403	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.0	(/.f64 eps x)
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
accuracy	34.76556059981636	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))

Samples

23.0ms	88×	1	valid
20.0ms	152×	0	valid
6.0ms	16×	2	valid

Compiler

Compiled 120 to 19 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-div: 11.0ms (34.6% of total)

ival-sub: 5.0ms (15.7% of total)

adjust: 4.0ms (12.6% of total)

ival-mult: 4.0ms (12.6% of total)

ival-sqrt: 3.0ms (9.4% of total)

ival-add: 3.0ms (9.4% of total)

ival-neg: 1.0ms (3.1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series31.0ms (0.5%)

Memory

-22.3MiB live, 25.8MiB allocated

Counts

12 → 83

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 eps x)
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
(+.f64 eps #s(literal 0 binary64))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
#s(approx (- (* x x) eps) (neg.f64 eps))

Outputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/2 (/ eps x))
(/ eps x)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
eps
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))

Calls

6 calls:

Time	Variable		Point	Expression
24.0ms	x	@	inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* 1/2 (/ eps x)) (/ eps x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps))
1.0ms	eps	@	-inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* 1/2 (/ eps x)) (/ eps x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps))
1.0ms	x	@	-inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* 1/2 (/ eps x)) (/ eps x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps))
1.0ms	eps	@	inf	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* 1/2 (/ eps x)) (/ eps x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps))
1.0ms	x	@	0	((/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (* 1/2 (/ eps x)) (/ eps x) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (- (* x x) eps) (* x x) (+ eps 0) (/ (+ eps 0) (+ (sqrt (- (* x x) eps)) x)) (+ (sqrt (- (* x x) eps)) x) (sqrt (- (* x x) eps)) (- (* x x) eps))

simplify177.0ms (2.6%)

Memory

9.0MiB live, 226.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	430	2004
1	1444	1912
2	6007	1893
0	8586	1786

Stop Event

1×	iter limit
1×	node limit

Counts

83 → 81

Calls

Call 1

Inputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/2 (/ eps x))
(/ eps x)
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(* -1 eps)
(- (pow x 2) eps)
(pow x 2)
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+ (* -1 eps) (pow x 2))
eps
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))

Outputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (-.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(fma.f64 (-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)) eps))) x (.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) x) #s(literal -1 binary64)) x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(/ eps x)
(/.f64 eps x)
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps))
(- x (* (sqrt eps) (sqrt -1)))
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(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps)
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (fma.f64 (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(* eps (- (/ (pow x 2) eps) 1))
(.f64 (-.f64 (.f64 x (/.f64 x eps)) #s(literal 1 binary64)) eps)
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)) eps)
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps))) eps)
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)))) eps)
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) x)
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) (.f64 (neg.f64 eps) x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps) (/.f64 (fma.f64 (neg.f64 eps) x (/.f64 (fma.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) eps) (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 #s(literal -1 binary64))) (.f64 x x))) (.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (.f64 x x)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (neg.f64 eps))) eps)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) x) (neg.f64 eps))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (neg.f64 eps) (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (-.f64 x (/.f64 (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/8 binary64)))) eps)) (neg.f64 eps))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (neg.f64 eps) (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (neg.f64 eps) (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(.f64 (neg.f64 eps) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (pow.f64 x #s(literal 6 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/16 binary64)) (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)) (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(fma.f64 (*.f64 x (/.f64 x eps)) eps (neg.f64 eps))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (neg.f64 eps) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)) x) (neg.f64 eps))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (neg.f64 eps) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 x (/.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/8 binary64)))) eps)) (neg.f64 eps))))

rewrite289.0ms (4.3%)

Memory

3.8MiB live, 246.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	109
0	39	105
1	129	97
2	1082	93
0	8582	93

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

12 → 577

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 eps x)
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
(+.f64 eps #s(literal 0 binary64))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
#s(approx (- (* x x) eps) (neg.f64 eps))

Outputs
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) eps)) (neg.f64 (neg.f64 x)))
(/.f64 (*.f64 #s(literal -1/2 binary64) eps) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(neg.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) eps) x))
(neg.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) eps) (neg.f64 x)))
(neg.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (neg.f64 eps) x)))
(neg.f64 (*.f64 (/.f64 (neg.f64 eps) x) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) x))
(fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) (/.f64 #s(literal 0 binary64) x))
(+.f64 (/.f64 #s(literal 0 binary64) x) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
(+.f64 (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)) (/.f64 #s(literal 0 binary64) x))
(*.f64 (/.f64 (fabs.f64 eps) eps) (/.f64 (fabs.f64 eps) x))
(*.f64 (/.f64 (neg.f64 eps) eps) (/.f64 (neg.f64 eps) x))
(*.f64 (/.f64 eps eps) (/.f64 eps x))
(.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (.f64 eps eps)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) x))
(.f64 (/.f64 (.f64 eps eps) (*.f64 eps eps)) (/.f64 eps x))
(.f64 (/.f64 eps (.f64 eps eps)) (/.f64 (*.f64 eps eps) x))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 0 binary64) x)) (.f64 (/.f64 eps x) (/.f64 eps x))) (-.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 eps x)))
(/.f64 (-.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 0 binary64) x))) (/.f64 eps x))
(/.f64 (+.f64 (pow.f64 (/.f64 #s(literal 0 binary64) x) #s(literal 3 binary64)) (pow.f64 (/.f64 eps x) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 0 binary64) x) (-.f64 (.f64 (/.f64 eps x) (/.f64 eps x)) (.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 eps x)))))
(/.f64 (+.f64 (pow.f64 (/.f64 eps x) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 0 binary64) x) #s(literal 3 binary64))) (fma.f64 (/.f64 eps x) (/.f64 eps x) (-.f64 (.f64 (/.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 0 binary64) x)) (.f64 (/.f64 eps x) (/.f64 #s(literal 0 binary64) x)))))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 x)) (.f64 x eps)) (.f64 x x))
(/.f64 (fma.f64 #s(literal 0 binary64) (.f64 eps x) (.f64 x (.f64 eps eps))) (.f64 x (*.f64 eps x)))
(/.f64 (fma.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) x) (.f64 x (pow.f64 eps #s(literal 3 binary64)))) (.f64 x (.f64 (.f64 eps eps) x)))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 x) (.f64 x (neg.f64 eps))) (.f64 (neg.f64 x) x))
(/.f64 (fma.f64 #s(literal 0 binary64) x (.f64 x eps)) (.f64 x x))
(/.f64 (fma.f64 eps x (.f64 (neg.f64 (neg.f64 x)) #s(literal 0 binary64))) (.f64 x x))
(/.f64 (fma.f64 (.f64 eps eps) x (.f64 (.f64 eps x) #s(literal 0 binary64))) (.f64 (*.f64 eps x) x))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) x (.f64 (.f64 (.f64 eps eps) x) #s(literal 0 binary64))) (.f64 (.f64 (.f64 eps eps) x) x))
(/.f64 (fma.f64 (neg.f64 eps) x (.f64 (neg.f64 x) #s(literal 0 binary64))) (.f64 (neg.f64 x) x))
(/.f64 (fma.f64 eps x (.f64 x #s(literal 0 binary64))) (.f64 x x))
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (neg.f64 (.f64 (.f64 eps eps) x)))
(/.f64 (.f64 (neg.f64 eps) eps) (neg.f64 (.f64 eps x)))
(/.f64 (.f64 eps eps) (.f64 eps x))
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 (.f64 eps eps) x))
(/.f64 (neg.f64 eps) (neg.f64 (neg.f64 (neg.f64 x))))
(/.f64 (neg.f64 eps) (neg.f64 x))
(/.f64 eps (neg.f64 (neg.f64 x)))
(/.f64 eps x)
(neg.f64 (/.f64 (neg.f64 eps) x))
(fma.f64 (/.f64 (fabs.f64 eps) eps) (/.f64 (fabs.f64 eps) x) (/.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) x)))
(fma.f64 (/.f64 (fabs.f64 eps) eps) (/.f64 (fabs.f64 eps) x) (/.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) x))
(fma.f64 (/.f64 (fabs.f64 eps) eps) (/.f64 (fabs.f64 eps) x) (/.f64 #s(literal 0 binary64) (*.f64 eps x)))
(fma.f64 (/.f64 (fabs.f64 eps) eps) (/.f64 (fabs.f64 eps) x) (/.f64 #s(literal 0 binary64) x))
(fma.f64 (/.f64 (neg.f64 eps) eps) (/.f64 (neg.f64 eps) x) (/.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) x)))
(fma.f64 (/.f64 (neg.f64 eps) eps) (/.f64 (neg.f64 eps) x) (/.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) x))
(fma.f64 (/.f64 (neg.f64 eps) eps) (/.f64 (neg.f64 eps) x) (/.f64 #s(literal 0 binary64) (*.f64 eps x)))
(fma.f64 (/.f64 (neg.f64 eps) eps) (/.f64 (neg.f64 eps) x) (/.f64 #s(literal 0 binary64) x))
(fma.f64 (/.f64 eps eps) (/.f64 eps x) (/.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) x)))
(fma.f64 (/.f64 eps eps) (/.f64 eps x) (/.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) x))
(fma.f64 (/.f64 eps eps) (/.f64 eps x) (/.f64 #s(literal 0 binary64) (*.f64 eps x)))
(fma.f64 (/.f64 eps eps) (/.f64 eps x) (/.f64 #s(literal 0 binary64) x))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (.f64 eps eps)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) x) (/.f64 #s(literal 0 binary64) (.f64 (*.f64 eps eps) x)))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (.f64 eps eps)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) x) (/.f64 (/.f64 #s(literal 0 binary64) (.f64 eps eps)) x))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (.f64 eps eps)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) x) (/.f64 #s(literal 0 binary64) (.f64 eps x)))
(fma.f64 (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) (*.f64 eps eps)) (/.f64 (pow.f64 eps #s(literal 3/2 binary64)) x) (/.f64 #s(literal 0 binary64) x))
(fma.f64 (/.f64 (.f64 eps eps) (.f64 eps eps)) (/.f64 eps x) (/.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) x)))
(fma.f64 (/.f64 (.f64 eps eps) (.f64 eps eps)) (/.f64 eps x) (/.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) x))
(fma.f64 (/.f64 (.f64 eps eps) (.f64 eps eps)) (/.f64 eps x) (/.f64 #s(literal 0 binary64) (*.f64 eps x)))
(fma.f64 (/.f64 (.f64 eps eps) (.f64 eps eps)) (/.f64 eps x) (/.f64 #s(literal 0 binary64) x))
(fma.f64 (/.f64 eps (.f64 eps eps)) (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 0 binary64) (.f64 (.f64 eps eps) x)))
(fma.f64 (/.f64 eps (.f64 eps eps)) (/.f64 (.f64 eps eps) x) (/.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) x))
(fma.f64 (/.f64 eps (.f64 eps eps)) (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 0 binary64) (*.f64 eps x)))
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(.f64 (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))))
(.f64 (fabs.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sqrt.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))))
(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1 binary64))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (neg.f64 (sqrt.f64 (fma.f64 x x eps))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps)))) (fabs.f64 (sqrt.f64 (fma.f64 x x eps))))
(/.f64 (fabs.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (fabs.f64 (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (hypot.f64 (*.f64 x x) eps) (sqrt.f64 (neg.f64 (fma.f64 x x eps))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 eps eps))) (sqrt.f64 (fma.f64 x x eps)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 eps (fma.f64 x x eps) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(fabs.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fabs.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(exp.f64 (log.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (sinh.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(.f64 (fabs.f64 (neg.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))) (fabs.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))))
(.f64 (fabs.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) (fabs.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
(.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))) (neg.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))))
(.f64 (neg.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
(.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(pow.f64 (.f64 #s(approx (- ( x x) eps) (neg.f64 eps)) #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 1/2 binary64))
(pow.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) #s(literal 1 binary64))
(pow.f64 (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 2 binary64))
#s(approx (- (* x x) eps) (neg.f64 eps))
(neg.f64 (neg.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(sqrt.f64 (.f64 #s(approx (- ( x x) eps) (neg.f64 eps)) #s(approx (- (* x x) eps) (neg.f64 eps))))
(exp.f64 (fma.f64 (log.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 1/2 binary64) (.f64 (log.f64 #s(approx (- ( x x) eps) (neg.f64 eps))) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 #s(approx (- (* x x) eps) (neg.f64 eps))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))

eval141.0ms (2.1%)

Memory: 13.4MiB live, 152.3MiB allocated
Compiler: Compiled 24 346 to 2 583 computations (89.4% saved)

prune40.0ms (0.6%)

Memory

1.1MiB live, 46.9MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	739	2	741
Fresh	0	0	0
Picked	2	1	3
Done	0	4	4
Total	741	7	748

Accuracy

100.0%

Counts

748 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.6%	(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
	55.4%	(-.f64 x (/.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
✓	60.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	55.8%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	7.6%	(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.7%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
✓	45.7%	#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))

Compiler

Compiled 632 to 189 computations (70.1% saved)

regimes65.0ms (1%)

Memory

-23.0MiB live, 30.9MiB allocated

Counts

24 → 1

Calls

Call 1

Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (/.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
(/.f64 (+.f64 eps #s(literal 0 binary64)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (pow eps 3) (pow x 4)) 1/16) (+ (* (* (/ eps x) 1/8) (/ eps x)) (* 1/2 eps))) (*.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (-.f64 (.f64 x x) eps))) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) x) (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) eps (.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) eps) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (/.f64 eps (.f64 x x))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x))
(fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) x)
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 eps x) #s(literal 1/8 binary64)) (/.f64 eps x) (.f64 #s(literal 1/2 binary64) eps))) x))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (*.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))

Outputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))

Calls

3 calls:

51.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
7.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
99.6%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
99.6%	1	`x`
99.6%	1	`eps`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes10.0ms (0.1%)

Memory

15.9MiB live, 15.9MiB allocated

Counts

9 → 2

Calls

Call 1

Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (/.f64 #s(approx (- (* x x) eps) (neg.f64 eps)) (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))))

Outputs
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))

Calls

3 calls:

3.0ms	eps
3.0ms	x
3.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
97.9%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
90.2%	2	`x`
85.5%	2	`eps`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes3.0ms (0%)

Memory

5.0MiB live, 5.1MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
#s(approx (/ (- (* x x) (- (* x x) eps)) (+ (sqrt (- (* x x) eps)) x)) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
(-.f64 x #s(approx (/ (- (* x x) eps) (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))

Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))

Calls

1 calls:

2.0ms

(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
96.3%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0%)

Memory

3.5MiB live, 3.4MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))

#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Calls

1 calls:

2.0ms

(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
96.2%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes4.0ms (0.1%)

Memory

8.6MiB live, 8.6MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))

Outputs
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Calls

3 calls:

1.0ms	eps
1.0ms	x
1.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
57.4%	2	`eps`
55.8%	1	`x`
57.4%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes3.0ms (0%)

Memory

7.5MiB live, 7.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Outputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Calls

3 calls:

1.0ms	eps
1.0ms	x
1.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
3.7%	1	`x`
3.7%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
3.7%	1	`eps`

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.7495992088051317e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.7495992088051317e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.7495992088051317e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch71.0ms (1%)

Memory

-14.9MiB live, 30.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
69.0ms	-3.061097391451543e-308	2.7091369220330327e-306

Samples

55.0ms	61×	2	valid
5.0ms	46×	1	valid
2.0ms	47×	0	invalid
1.0ms	21×	0	valid

Compiler

Compiled 187 to 155 computations (17.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-sub: 49.0ms (86.1% of total)

adjust: 3.0ms (5.3% of total)

ival-sqrt: 3.0ms (5.3% of total)

ival-mult: 2.0ms (3.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

simplify17.0ms (0.2%)

Memory

-24.3MiB live, 20.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	152
1	52	152
2	76	152
3	98	152
4	110	152

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(if (<=.f64 eps #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Outputs
(/.f64 eps (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/30191699398572330817932436647906151127335369763331523427009650401964993299137190816689013801421270140331747000246110759198164677039398341060491474011461568349195162615808 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(if (<=.f64 eps #s(literal -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))) (-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

soundness804.0ms (11.8%)

Memory

26.2MiB live, 777.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
0	10	22
1	42	22
2	320	22
3	3652	22
0	8870	22
0	257	1069
1	807	1054
2	3108	1019
0	8668	960
0	24	109
0	39	105
1	129	97
2	1082	93
0	8582	93
0	37	227
0	63	221
1	214	221
2	1575	211
0	8524	207
0	48	367
0	75	333
1	297	292
2	2476	274
0	8447	268

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 306 to 128 computations (58.2% saved)

preprocess40.0ms (0.6%)

Memory: 39.5MiB live, 85.6MiB allocated
Compiler: Compiled 340 to 94 computations (72.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze29.0ms (0.4%)

sample1.7s (25%)

explain106.0ms (1.6%)

preprocess20.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize27.0ms (0.4%)

series8.0ms (0.1%)

simplify197.0ms (2.9%)

rewrite196.0ms (2.9%)

eval32.0ms (0.5%)

prune19.0ms (0.3%)

simplify139.0ms (2%)

localize136.0ms (2%)

series53.0ms (0.8%)

simplify208.0ms (3.1%)

rewrite266.0ms (3.9%)

eval157.0ms (2.3%)

prune26.0ms (0.4%)

simplify159.0ms (2.3%)

localize174.0ms (2.6%)

series66.0ms (1%)

simplify333.0ms (4.9%)

rewrite258.0ms (3.8%)

eval403.0ms (5.9%)

prune52.0ms (0.8%)

simplify252.0ms (3.7%)

localize82.0ms (1.2%)

series31.0ms (0.5%)

simplify177.0ms (2.6%)

rewrite289.0ms (4.3%)

eval141.0ms (2.1%)

prune40.0ms (0.6%)

regimes65.0ms (1%)

regimes10.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch71.0ms (1%)

simplify17.0ms (0.2%)

soundness804.0ms (11.8%)

preprocess40.0ms (0.6%)

end0.0ms (0%)

Profiling