Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze21.0ms (0.3%)

Memory

-12.1MiB live, 29.8MiB allocated; 12ms collecting garbage

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 (22.1%)

Memory

21.7MiB live, 2 381.2MiB allocated; 476ms collecting garbage

Samples

493.0ms	2 770×	1	valid
482.0ms	4 838×	0	valid
115.0ms	648×	2	valid
15.0ms	160×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 819.0ms

ival-mult: 200.0ms (24.4% of total)

ival-sub: 174.0ms (21.2% of total)

ival-<=: 145.0ms (17.7% of total)

adjust: 130.0ms (15.9% of total)

ival-sqrt: 126.0ms (15.4% of total)

ival-and: 23.0ms (2.8% of total)

exact: 18.0ms (2.2% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

explain138.0ms (1.8%)

Memory

16.5MiB live, 203.8MiB allocated; 36ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
108	-	-	`(-.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	108	0

Confusion

	Predicted +	Predicted -
+	108	0
-	0	148

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	108	0	0
-	0	0	148

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	148
1	108

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

39.0ms	296×	0	valid
21.0ms	182×	1	valid
6.0ms	34×	2	valid

Compiler

Compiled 60 to 22 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-mult: 25.0ms (55.9% of total)

ival-sub: 7.0ms (15.7% of total)

adjust: 6.0ms (13.4% of total)

ival-sqrt: 6.0ms (13.4% of total)

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

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

preprocess18.0ms (0.2%)

Memory

2.5MiB live, 46.5MiB allocated; 6ms collecting garbage

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: 0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify6.0ms (0.1%)

Memory

-33.9MiB live, 12.3MiB allocated; 3ms collecting garbage

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

localize33.0ms (0.4%)

Memory

-15.7MiB live, 95.8MiB allocated; 14ms collecting garbage

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	0.01171875	(-.f64 (*.f64 x x) eps)
accuracy	24.94809855483297	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

14.0ms	148×	0	valid
10.0ms	91×	1	valid
3.0ms	17×	2	valid

Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-sub: 9.0ms (49.2% of total)

adjust: 3.0ms (16.4% of total)

ival-sqrt: 3.0ms (16.4% of total)

ival-mult: 3.0ms (16.4% of total)

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

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

series9.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated; 0ms collecting garbage

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))

simplify177.0ms (2.4%)

Memory

40.1MiB live, 309.9MiB allocated; 40ms collecting garbage

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)

rewrite187.0ms (2.5%)

Memory

-13.4MiB live, 180.1MiB allocated; 19ms collecting garbage

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

eval37.0ms (0.5%)

Memory: -1.9MiB live, 43.6MiB allocated; 4ms collecting garbage
Compiler: Compiled 6 064 to 978 computations (83.9% saved)

prune26.0ms (0.3%)

Memory

-9.1MiB live, 42.9MiB allocated; 8ms collecting garbage

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	235	10	245
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	235	11	246

Accuracy

99.7%

Counts

246 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.5%	(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)
▶	60.6%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
	60.5%	(-.f64 x (sqrt.f64 (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 4 binary64))))
✓	61.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	43.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x))))
	57.8%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
▶	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	30.3%	#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))
	26.3%	#s(approx (- x (sqrt (- (* x x) eps))) (*.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))
▶	36.8%	#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))
▶	44.9%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))

Compiler

Compiled 368 to 246 computations (33.2% saved)

simplify165.0ms (2.2%)

Memory

38.2MiB live, 124.6MiB allocated; 16ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (*.f64 x x) eps)
cost-diff	0	(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))
cost-diff	9	(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)
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: 2 (0.0ms)

Iter	Nodes	Cost
0	29	192
0	48	192
1	68	184
2	136	183
3	394	183
4	1442	183
5	3575	183
6	4419	183
7	4629	183
8	4712	183
9	5022	183
10	5214	183
11	5922	183
12	6672	183
0	8034	183

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)
(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)
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))
(-.f64 (*.f64 x x) eps)
(*.f64 x x)
x
eps
#s(literal 1/4 binary64)
(neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))

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

localize190.0ms (2.5%)

Memory

-12.4MiB live, 193.3MiB allocated; 47ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.0	(neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
accuracy	0.01171875	(-.f64 (*.f64 x x) eps)
accuracy	0.01953125	(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))
accuracy	25.32036864939694	(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)
accuracy	0.151690976617831	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
accuracy	7.683488119102137	(*.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	10.451081939595197	(fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy	36.61251411856863	#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	0.265625	(*.f64 (/.f64 #s(literal 1/2 binary64) x) eps)
accuracy	35.192287123775074	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 #s(literal 1/2 binary64) x) eps))
accuracy	0.0	(neg.f64 x)
accuracy	24.94809855483297	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy	62.389261519452305	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy	0.0	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	0.01171875	(-.f64 (*.f64 x x) eps)
accuracy	0.3203125	(/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps)))
accuracy	24.94809855483297	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))

Samples

97.0ms	91×	1	valid
62.0ms	148×	0	valid
12.0ms	17×	2	valid

Compiler

Compiled 172 to 26 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 98.0ms

adjust: 50.0ms (51.2% of total)

ival-pow: 14.0ms (14.3% of total)

ival-mult: 11.0ms (11.3% of total)

ival-div: 7.0ms (7.2% of total)

ival-sub: 5.0ms (5.1% of total)

ival-neg: 3.0ms (3.1% of total)

ival-sqrt: 3.0ms (3.1% of total)

ival-add: 3.0ms (3.1% of total)

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

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

exact: 0.0ms (0% of total)

series37.0ms (0.5%)

Memory

-42.8MiB live, 60.2MiB allocated; 18ms collecting garbage

Counts

18 → 124

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 (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)
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 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))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* x (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))))))))
(pow (* -1 eps) 1/4)
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(* -1 (pow (* -1 eps) 1/4))
(- (* 1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(- (* (pow x 2) (- (* 3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))) (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)))) (pow (* -1 eps) 1/4))
(- (* (pow x 2) (- (* (pow x 2) (- (* 7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))) (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)))) (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)))) (pow (* -1 eps) 1/4))
(/ (- (* 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)
(/ (+ (* 1/16 (/ (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))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) x)
(sqrt x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
(* -1 (sqrt x))
(- (* 1/4 (* eps (sqrt (/ 1 (pow x 3))))) (sqrt x))
(- (* -1 (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3)))))))
(- (* -1 (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))) (+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 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 (* -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 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* (sqrt x) (sqrt -1))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(- (* 1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(- (* -1 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))) (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1))))
(- (* -1 (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))) (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 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))))
(+ 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)))
(+ x (* -1 x))
(+ x (+ (* -1 x) (* 1/2 (/ eps x))))
(+ x (+ (* -1 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(+ x (+ (* -1 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(* (pow 1 1/4) (sqrt x))
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt x)))
(* -1 (* (pow 1 1/4) (sqrt x)))
(- (* 1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(- (* eps (- (* 3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))) (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))))) (* (pow 1 1/4) (sqrt x)))
(- (* eps (- (* eps (- (* 7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))) (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))))) (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))))) (* (pow 1 1/4) (sqrt x)))
(* 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)))))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps))))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(* -1 (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))))
(- (* 1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))))
(- (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))) (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps))))
(- (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3))) (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)))))
(* -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)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps)))))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(- (* -1 (/ (- (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(- (* -1 (/ (- (* -1 (/ (- (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	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 (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) (pow (- (* x x) eps) 1/4) (sqrt (- (* x x) eps)) (neg (pow (- (* x x) eps) 1/4)))
5.0ms	eps	@	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 (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) (pow (- (* x x) eps) 1/4) (sqrt (- (* x x) eps)) (neg (pow (- (* x x) eps) 1/4)))
5.0ms	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 (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) (pow (- (* x x) eps) 1/4) (sqrt (- (* x x) eps)) (neg (pow (- (* x x) eps) 1/4)))
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 (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) (pow (- (* x x) eps) 1/4) (sqrt (- (* x x) eps)) (neg (pow (- (* x x) eps) 1/4)))
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 (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) (pow (- (* x x) eps) 1/4) (sqrt (- (* x x) eps)) (neg (pow (- (* x x) eps) 1/4)))

simplify177.0ms (2.4%)

Memory

-1.5MiB live, 229.2MiB allocated; 27ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	551	2914
1	1807	2781
2	7268	2752
0	8300	2609

Stop Event

1×	iter limit
1×	node limit

Counts

124 → 123

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))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* x (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))))))))
(pow (* -1 eps) 1/4)
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(* -1 (pow (* -1 eps) 1/4))
(- (* 1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(- (* (pow x 2) (- (* 3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))) (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)))) (pow (* -1 eps) 1/4))
(- (* (pow x 2) (- (* (pow x 2) (- (* 7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))) (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)))) (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)))) (pow (* -1 eps) 1/4))
(/ (- (* 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)
(/ (+ (* 1/16 (/ (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))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) x)
(sqrt x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
(* -1 (sqrt x))
(- (* 1/4 (* eps (sqrt (/ 1 (pow x 3))))) (sqrt x))
(- (* -1 (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3)))))))
(- (* -1 (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))) (+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 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 (* -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 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* (sqrt x) (sqrt -1))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(- (* 1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(- (* -1 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))) (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1))))
(- (* -1 (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))) (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 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))))
(+ 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)))
(+ x (* -1 x))
(+ x (+ (* -1 x) (* 1/2 (/ eps x))))
(+ x (+ (* -1 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(+ x (+ (* -1 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(* (pow 1 1/4) (sqrt x))
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt x)))
(* -1 (* (pow 1 1/4) (sqrt x)))
(- (* 1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(- (* eps (- (* 3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))) (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))))) (* (pow 1 1/4) (sqrt x)))
(- (* eps (- (* eps (- (* 7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))) (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))))) (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))))) (* (pow 1 1/4) (sqrt x)))
(* 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)))))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps))))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(* -1 (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))))
(- (* 1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))))
(- (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))) (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps))))
(- (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3))) (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)))))
(* -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)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps)))))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(- (* -1 (/ (- (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(- (* -1 (/ (- (* -1 (/ (- (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))

Outputs
(* -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 (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 (.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 x x) #s(literal -1 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))) 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 #s(literal -1/8 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 x 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 (.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 #s(literal -1/8 binary64) (/.f64 #s(literal -1 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 (/.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)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) eps)
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* 1/8 (/ eps (pow x 3)))
(*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps)
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64)))
(/ 1/8 (pow x 3))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
(+ 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))) (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (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))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* x (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))))))))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps) (fma.f64 (.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 x x) #s(literal -1 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))) x) x x))
(pow (* -1 eps) 1/4)
(pow.f64 (neg.f64 eps) #s(literal 1/4 binary64))
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(fma.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/4 binary64)) x) x (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(fma.f64 (fma.f64 (.f64 (.f64 x x) #s(literal -3/32 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64)) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (.f64 x x) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 11 binary64))) #s(literal 1/4 binary64)) #s(literal -7/128 binary64)) x) x (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -3/32 binary64))) (.f64 x x) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (.f64 x x) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(* -1 (pow (* -1 eps) 1/4))
(neg.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(- (* 1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(-.f64 (.f64 (.f64 (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) x) x) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(- (* (pow x 2) (- (* 3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))) (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)))) (pow (* -1 eps) 1/4))
(-.f64 (.f64 (fma.f64 (.f64 (.f64 #s(literal 3/32 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64))) x) x (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) (*.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(- (* (pow x 2) (- (* (pow x 2) (- (* 7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))) (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)))) (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)))) (pow (* -1 eps) 1/4))
(-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 7/128 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 11 binary64))) #s(literal 1/4 binary64))) x) x (.f64 #s(literal 3/32 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64)))) (.f64 x x) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) (*.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #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)
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 5 binary64))))
(/ (- (* 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 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) #s(literal 1/2 binary64) (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 (.f64 eps 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)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))))) x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps (/.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) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) x)
(/.f64 (fma.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) #s(literal 1/2 binary64) (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 (.f64 eps eps) x) (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(fma.f64 (*.f64 #s(literal -1/4 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(fma.f64 (.f64 #s(literal -3/32 binary64) (.f64 eps eps)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 (*.f64 #s(literal -1/4 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
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(* eps (- (/ (pow x 2) eps) 1))
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(.f64 (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps))))
(.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 (/.f64 x eps) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps)
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ 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 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))) eps)
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(fma.f64 (.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (.f64 x (/.f64 x eps))) #s(literal -1/4 binary64) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(fma.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)) (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 x x)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (/.f64 (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)))) eps)) eps))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(fma.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -7/128 binary64)) eps)) (.f64 eps eps)) (fma.f64 (.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (.f64 x (/.f64 x eps))) #s(literal -1/4 binary64) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)))))
(* -1 (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))))
(neg.f64 (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))))
(- (* 1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))))
(-.f64 (.f64 (.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (.f64 x (/.f64 x eps))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))))
(- (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))) (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps))))
(-.f64 (.f64 (neg.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)))) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) eps) (/.f64 #s(literal -3/32 binary64) eps))) (fma.f64 (.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (.f64 x (/.f64 x eps))) #s(literal -1/4 binary64) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)))))
(- (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3))) (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)))))
(-.f64 (/.f64 (.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -7/128 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)))) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (fma.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)) (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 x x)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (/.f64 (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)))) eps)) eps)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x 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) (neg.f64 (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) 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) (neg.f64 (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)) 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 (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 (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 (.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)))))
(.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 x 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)
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(*.f64 (neg.f64 eps) (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)))))
(.f64 (neg.f64 eps) (neg.f64 (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) eps))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps)))))
(.f64 (neg.f64 eps) (neg.f64 (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)) eps))))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(fma.f64 (/.f64 (fma.f64 (.f64 (neg.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -3/32 binary64) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))) eps) #s(literal -1 binary64) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (/.f64 (fma.f64 (.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -3/32 binary64) (.f64 (neg.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 7/128 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)))) (neg.f64 eps))) eps) #s(literal -1 binary64) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(- (* -1 (/ (- (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(-.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)))) (neg.f64 eps)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(- (* -1 (/ (- (* -1 (/ (- (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(-.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (/.f64 (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 7/128 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64))) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))) (neg.f64 eps))) (neg.f64 eps)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))

rewrite240.0ms (3.2%)

Memory

23.2MiB live, 410.5MiB allocated; 51ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	164
0	48	155
1	158	155
2	1146	143
0	8813	143

Stop Event

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

Counts

18 → 741

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 (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)
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(neg.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))

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

eval312.0ms (4.2%)

Memory: 12.9MiB live, 277.7MiB allocated; 33ms collecting garbage
Compiler: Compiled 37 255 to 3 725 computations (90% saved)

prune45.0ms (0.6%)

Memory

-12.7MiB live, 53.5MiB allocated; 5ms collecting garbage

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	1 088	8	1 096
Fresh	3	2	5
Picked	3	2	5
Done	0	1	1
Total	1 094	13	1 107

Accuracy

99.9%

Counts

1 107 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.6%	(fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)
✓	60.6%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 (-.f64 (.f64 x x) eps))))
	58.1%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
✓	61.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	43.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x))))
	57.8%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	42.6%	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps))
▶	45.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
▶	36.8%	#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))
	42.5%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 eps x) (/.f64 #s(literal 1/8 binary64) x)) x (.f64 x #s(literal 1/2 binary64))) (.f64 x x)) eps))
	43.7%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ 1/8 (pow x 3)) eps) (/ 1/2 x)) eps) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal -1/8 binary64) x) (.f64 #s(literal -1/2 binary64) eps)) (neg.f64 x))))
▶	4.3%	#s(approx (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) #s(literal 0 binary64))

Compiler

Compiled 461 to 293 computations (36.4% saved)

simplify194.0ms (2.6%)

Memory

13.3MiB live, 59.6MiB allocated; 2ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	242
0	65	238
1	101	227
2	209	224
3	536	224
4	1608	224
5	3506	224
6	4248	224
7	4452	224
8	4535	224
9	4841	224
10	5034	224
11	5738	224
12	5852	224
13	5900	224
14	6277	224
15	7672	224
0	8365	224

Stop Event

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

Calls

Call 1

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

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

localize218.0ms (2.9%)

Memory

-2.2MiB live, 87.4MiB allocated; 8ms collecting garbage

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.15234375	(/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x)
accuracy	7.683488119102137	(.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
accuracy	10.451081939595197	(fma.f64 (/.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) x) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy	36.61251411856863	#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))
accuracy	0.07421875	(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.26171875	(/.f64 (/.f64 eps x) x)
accuracy	7.683488119102137	(*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps)
accuracy	36.61251411856863	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps))
accuracy	0.0	(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) eps)
accuracy	35.192287123775074	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
accuracy	61.25558786859486	#s(approx (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) #s(literal 0 binary64))
accuracy	0.01171875	(-.f64 (*.f64 x x) eps)
accuracy	0.01953125	(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64))
accuracy	0.08984375	(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	25.32036864939694	(fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)

Samples

104.0ms	148×	0	valid
48.0ms	91×	1	valid
14.0ms	17×	2	valid

Compiler

Compiled 214 to 36 computations (83.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-div: 24.0ms (28.8% of total)

ival-mult: 16.0ms (19.2% of total)

adjust: 12.0ms (14.4% of total)

ival-pow: 12.0ms (14.4% of total)

ival-add: 6.0ms (7.2% of total)

ival-sub: 5.0ms (6% of total)

ival-sqrt: 5.0ms (6% of total)

ival-neg: 3.0ms (3.6% of total)

exact: 1.0ms (1.2% of total)

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

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

series21.0ms (0.3%)

Memory

10.8MiB live, 10.8MiB allocated; 0ms collecting garbage

Counts

18 → 90

Calls

Call 1

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

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* x (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))))))))
(pow (* -1 eps) 1/4)
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(* -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)))
(* 1/2 (/ eps 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 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ 1/8 (pow x 3))
(/ eps (pow x 2))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) x)
(sqrt x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
(* (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)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
1/2
(+ 1/2 (* 1/8 (/ 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))) (* 1/2 (/ eps (pow x 2)))) 2)))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* (sqrt x) (sqrt -1))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(* -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 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(+ x (* -1 x))
(+ x (+ (* -1 x) (* 1/2 (/ eps x))))
(+ x (+ (* -1 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(+ x (+ (* -1 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(* (pow 1 1/4) (sqrt x))
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* -1 eps) (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))))
(* 1/2 eps)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps))))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(* 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)))))
(* (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)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps)))))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(* -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)))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	-inf	((+ (* (pow (- (* x x) eps) 1/4) (neg (sqrt (sqrt (- (* x x) eps))))) x) (pow (- (* x x) eps) 1/4) (- (* x x) eps) (* x x) (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (/ (/ 1/8 (* x x)) x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (sqrt (sqrt (- (* x x) eps))) (/ (/ eps x) x))
3.0ms	x	@	0	((+ (* (pow (- (* x x) eps) 1/4) (neg (sqrt (sqrt (- (* x x) eps))))) x) (pow (- (* x x) eps) 1/4) (- (* x x) eps) (* x x) (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (/ (/ 1/8 (* x x)) x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (sqrt (sqrt (- (* x x) eps))) (/ (/ eps x) x))
3.0ms	eps	@	inf	((+ (* (pow (- (* x x) eps) 1/4) (neg (sqrt (sqrt (- (* x x) eps))))) x) (pow (- (* x x) eps) 1/4) (- (* x x) eps) (* x x) (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (/ (/ 1/8 (* x x)) x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (sqrt (sqrt (- (* x x) eps))) (/ (/ eps x) x))
3.0ms	x	@	-inf	((+ (* (pow (- (* x x) eps) 1/4) (neg (sqrt (sqrt (- (* x x) eps))))) x) (pow (- (* x x) eps) 1/4) (- (* x x) eps) (* x x) (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (/ (/ 1/8 (* x x)) x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (sqrt (sqrt (- (* x x) eps))) (/ (/ eps x) x))
3.0ms	x	@	inf	((+ (* (pow (- (* x x) eps) 1/4) (neg (sqrt (sqrt (- (* x x) eps))))) x) (pow (- (* x x) eps) 1/4) (- (* x x) eps) (* x x) (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) (- x (sqrt (- (* x x) eps))) (/ (* 1/2 eps) x) (* 1/2 eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (/ (/ 1/8 (* x x)) x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) eps) (+ (* (/ (/ 1/8 (* x x)) x) eps) (/ 1/2 x)) (sqrt (sqrt (- (* x x) eps))) (/ (/ eps x) x))

simplify331.0ms (4.4%)

Memory

10.5MiB live, 193.8MiB allocated; 21ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	427	1801
1	1400	1702
2	5298	1670
0	8385	1578

Stop Event

1×	iter limit
1×	node limit

Counts

90 → 90

Calls

Call 1

Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* x (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))))))))
(pow (* -1 eps) 1/4)
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(* -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)))
(* 1/2 (/ eps 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 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ 1/8 (pow x 3))
(/ eps (pow x 2))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) x)
(sqrt x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
(* (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)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
1/2
(+ 1/2 (* 1/8 (/ 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))) (* 1/2 (/ eps (pow x 2)))) 2)))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* (sqrt x) (sqrt -1))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(* -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 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(+ x (* -1 x))
(+ x (+ (* -1 x) (* 1/2 (/ eps x))))
(+ x (+ (* -1 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(+ x (+ (* -1 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(* (pow 1 1/4) (sqrt x))
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* -1 eps) (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))))
(* 1/2 eps)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps))))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(* 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)))))
(* (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)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps)))))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(* -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)))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 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))) (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (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))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* x (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 x x) #s(literal -1 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))) x #s(literal 1 binary64)) x (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(pow (* -1 eps) 1/4)
(pow.f64 (neg.f64 eps) #s(literal 1/4 binary64))
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(fma.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/4 binary64)) x) x (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -3/32 binary64)) x) x (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (.f64 x x) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 11 binary64))) #s(literal 1/4 binary64)) #s(literal -7/128 binary64)) x) x (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -3/32 binary64))) (.f64 x x) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (.f64 x x) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(* -1 eps)
(neg.f64 eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(- 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 (fma.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 x x) #s(literal -1 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))) x #s(literal 1 binary64)) x (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(* 1/2 (/ eps x))
(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) eps)
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* 1/8 (/ eps (pow x 3)))
(*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps)
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64)))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) (.f64 #s(literal 1/8 binary64) eps)) x) x)
(/ 1/8 (pow x 3))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
(/ eps (pow x 2))
(/.f64 (/.f64 eps x) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps (/.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) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) x)
(/.f64 (fma.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) #s(literal 1/2 binary64) (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(fma.f64 (*.f64 #s(literal -1/4 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(fma.f64 (.f64 (.f64 eps eps) #s(literal -3/32 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 (*.f64 #s(literal -1/4 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
(+.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -7/128 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))) (.f64 (.f64 (*.f64 eps eps) #s(literal -3/32 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))) (sqrt.f64 x))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #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)
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 5 binary64))))
(/ (- (* 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 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) #s(literal 1/2 binary64) (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(* 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))) (* 1/2 (/ eps (pow x 2)))) 2)))
(.f64 (neg.f64 x) (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/8 binary64) (-.f64 (*.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))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(.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) (-.f64 (*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) eps) #s(literal -1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) eps) #s(literal -1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -3/32 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64)))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) eps) #s(literal -1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -7/128 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -3/32 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (neg.f64 x) (fma.f64 (.f64 eps (/.f64 eps (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/8 binary64) (-.f64 (*.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 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(neg.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 eps x) #s(literal -1/2 binary64)) x))
(+ x (* -1 x))
#s(literal 0 binary64)
(+ x (+ (* -1 x) (* 1/2 (/ eps x))))
(fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 0 binary64))
(+ x (+ (* -1 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps #s(literal 0 binary64))
(+ x (+ (* -1 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 #s(literal 0 binary64))
(* (pow 1 1/4) (sqrt x))
(sqrt.f64 x)
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 (*.f64 #s(literal -1/4 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 (fma.f64 (.f64 #s(literal -3/32 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/4 binary64))) eps (sqrt.f64 x))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -7/128 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -3/32 binary64))) eps (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/4 binary64))) eps (sqrt.f64 x))
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #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)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(.f64 (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) eps)
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps))))
(.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 (/.f64 x eps) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))) eps)
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)))))
(.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (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 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 x eps)))) eps)
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(fma.f64 (.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (.f64 x (/.f64 x eps))) #s(literal -1/4 binary64) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(fma.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)) (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 x x)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (/.f64 (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)))) eps)) eps))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(fma.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -7/128 binary64)) eps)) (.f64 eps eps)) (fma.f64 (.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64))) (.f64 x (/.f64 x eps))) #s(literal -1/4 binary64) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 eps #s(literal 1/4 binary64)))))
(* eps (- (/ (pow x 2) eps) 1))
(.f64 (-.f64 (.f64 x (/.f64 x eps)) #s(literal 1 binary64)) eps)
(* eps (- (/ 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)
(* 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)))) (-.f64 (/.f64 x eps) (.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)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (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 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 x eps)))) eps)
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (.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) eps)
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.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)
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 eps))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(*.f64 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)))))
(.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) eps)))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps)))))
(.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)) eps)))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (.f64 (.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)))) eps) #s(literal -1 binary64) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (/.f64 (fma.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -7/128 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) (.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))) (neg.f64 eps))) eps) #s(literal -1 binary64) (pow.f64 (neg.f64 eps) #s(literal 1/4 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 eps (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.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) 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 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)) eps)))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) 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)

rewrite293.0ms (3.9%)

Memory

-40.1MiB live, 267.6MiB allocated; 70ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	199
0	65	199
1	210	178
2	1524	166
0	8475	166

Stop Event

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

Counts

18 → 632

Calls

Call 1

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

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

eval165.0ms (2.2%)

Memory: 10.7MiB live, 343.2MiB allocated; 37ms collecting garbage
Compiler: Compiled 25 207 to 2 881 computations (88.6% saved)

prune40.0ms (0.5%)

Memory

5.9MiB live, 53.1MiB allocated; 3ms collecting garbage

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	655	6	661
Fresh	2	3	5
Picked	3	2	5
Done	1	2	3
Total	661	13	674

Accuracy

99.9%

Counts

674 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.5%	(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)
	58.1%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
✓	61.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	43.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x))))
▶	57.8%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	42.8%	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (/.f64 (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 (/.f64 eps x) x) #s(literal 1/2 binary64)) eps) x))
▶	42.6%	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps))
	42.5%	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) eps) x (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
▶	42.5%	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (/.f64 #s(approx (+ ( (/ (/ eps x) x) 1/8) 1/2) (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps)) x) eps))
✓	45.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
▶	36.8%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (*.f64 (neg.f64 x) x) x)) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
✓	4.3%	#s(approx (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) #s(literal 0 binary64))

Compiler

Compiled 485 to 289 computations (40.4% saved)

simplify209.0ms (2.8%)

Memory

7.9MiB live, 183.4MiB allocated; 81ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps))
cost-diff	0	(/.f64 #s(approx (+ (* (/ (/ eps x) x) 1/8) 1/2) (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps)) x)
cost-diff	0	(.f64 (/.f64 #s(approx (+ ( (/ (/ eps x) x) 1/8) 1/2) (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps)) x) eps)
cost-diff	0	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (/.f64 #s(approx (+ ( (/ (/ eps x) x) 1/8) 1/2) (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps)) x) eps))
cost-diff	0	(.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (*.f64 (neg.f64 x) x) x)) 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) (.f64 (*.f64 (neg.f64 x) x) x)) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
cost-diff	1	(/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (neg.f64 x) x) x))
cost-diff	2	(.f64 (.f64 (neg.f64 x) x) x)
cost-diff	0	(fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
cost-diff	0	(/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
cost-diff	0	(.f64 (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps)
cost-diff	0	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps))
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	(sqrt.f64 (-.f64 (*.f64 x x) eps))
cost-diff	0	(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
cost-diff	9	(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	372
0	78	362
1	118	347
2	238	346
3	734	345
4	2440	345
5	3981	345
6	4607	345
7	4825	345
8	4905	345
9	5216	345
10	5432	345
11	6128	345
12	6825	345
0	8129	345

Stop Event

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

Calls

Call 1

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

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

localize189.0ms (2.5%)

Memory

10.1MiB live, 243.4MiB allocated; 43ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.13205998016428752	(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
accuracy	7.683488119102137	(.f64 (/.f64 #s(approx (+ ( (/ (/ eps x) x) 1/8) 1/2) (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps)) x) eps)
accuracy	11.766549987171535	(.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps)
accuracy	36.61251411856863	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (/.f64 #s(approx (+ ( (/ (/ eps x) x) 1/8) 1/2) (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps)) x) eps))
accuracy	0.151690976617831	(/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (neg.f64 x) x) x))
accuracy	7.683488119102137	(.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (*.f64 (neg.f64 x) x) x)) eps (/.f64 #s(literal 1/2 binary64) x)) eps)
accuracy	10.451081939595197	(fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (.f64 (neg.f64 x) x) x)) eps (/.f64 #s(literal 1/2 binary64) x))
accuracy	36.61251411856863	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (*.f64 (neg.f64 x) x) x)) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
accuracy	0.07421875	(/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
accuracy	7.683488119102137	(.f64 (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps)
accuracy	11.321422250430597	(/.f64 eps (*.f64 x x))
accuracy	36.61251411856863	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps))
accuracy	0.0	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	0.0	(neg.f64 eps)
accuracy	24.94809855483297	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy	25.976691271442025	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.0	(neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))))
accuracy	0.01171875	(-.f64 (*.f64 x x) eps)
accuracy	0.08984375	(sqrt.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)))
accuracy	25.32036864939694	(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) x)

Samples

50.0ms	91×	1	valid
45.0ms	148×	0	valid
15.0ms	17×	2	valid

Compiler

Compiled 280 to 42 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-mult: 24.0ms (28.3% of total)

ival-div: 20.0ms (23.6% of total)

adjust: 12.0ms (14.2% of total)

ival-add: 11.0ms (13% of total)

ival-sub: 7.0ms (8.3% of total)

ival-sqrt: 5.0ms (5.9% of total)

ival-neg: 4.0ms (4.7% of total)

exact: 1.0ms (1.2% of total)

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

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

series25.0ms (0.3%)

Memory

15.6MiB live, 59.6MiB allocated; 8ms collecting garbage

Counts

25 → 133

Calls

Call 1

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

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* x (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))))))))
(pow (* -1 eps) 1/4)
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(* (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)
(- 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 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 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(* -1 (pow x 3))
(/ 1/8 (pow x 3))
(* -1 (pow (* -1 eps) 1/4))
(- (* 1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(- (* (pow x 2) (- (* 3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))) (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)))) (pow (* -1 eps) 1/4))
(- (* (pow x 2) (- (* (pow x 2) (- (* 7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))) (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)))) (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)))) (pow (* -1 eps) 1/4))
(/ eps (pow x 2))
(/ 1/8 (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))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) x)
(sqrt x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
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)
(* (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)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(* -1 (sqrt x))
(- (* 1/4 (* eps (sqrt (/ 1 (pow x 3))))) (sqrt x))
(- (* -1 (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3)))))))
(- (* -1 (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))) (+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* (sqrt x) (sqrt -1))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(* -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 (- (* 1/8 (/ (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 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (* (sqrt x) (sqrt -1)))
(- (* 1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(- (* -1 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))) (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1))))
(- (* -1 (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))) (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))))
(+ x (* -1 x))
(+ x (+ (* -1 x) (* 1/2 (/ eps x))))
(+ x (+ (* -1 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(+ x (+ (* -1 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(* (pow 1 1/4) (sqrt x))
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt 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 (+ (* 1/8 (/ 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))))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* -1 (* (pow 1 1/4) (sqrt x)))
(- (* 1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(- (* eps (- (* 3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))) (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))))) (* (pow 1 1/4) (sqrt x)))
(- (* eps (- (* eps (- (* 7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))) (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))))) (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))))) (* (pow 1 1/4) (sqrt x)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps))))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(* 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 (- (/ 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)))))
(* (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)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* -1 (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))))
(- (* 1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))))
(- (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))) (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps))))
(- (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3))) (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps)))))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(* -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)))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(- (* -1 (/ (- (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(- (* -1 (/ (- (* -1 (/ (- (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	0	((+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) (sqrt (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* 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)))) (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (/ eps (* x x)) 1/8) 1/2) (* (* (neg x) x) x) (/ -1/8 (* (* (neg x) x) x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ -1/8 (* (* (neg x) x) x)) eps) (/ 1/2 x)) eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (neg (sqrt (sqrt (- (* x x) eps)))) (/ eps (* x x)) (+ (* (/ -1/8 (* (* (neg x) x) x)) eps) (/ 1/2 x)) (* (- (/ 1/8 (* x x)) (/ -1/2 eps)) eps) (/ 1/8 (* x x)))
4.0ms	x	@	0	((+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) (sqrt (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* 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)))) (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (/ eps (* x x)) 1/8) 1/2) (* (* (neg x) x) x) (/ -1/8 (* (* (neg x) x) x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ -1/8 (* (* (neg x) x) x)) eps) (/ 1/2 x)) eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (neg (sqrt (sqrt (- (* x x) eps)))) (/ eps (* x x)) (+ (* (/ -1/8 (* (* (neg x) x) x)) eps) (/ 1/2 x)) (* (- (/ 1/8 (* x x)) (/ -1/2 eps)) eps) (/ 1/8 (* x x)))
3.0ms	eps	@	-inf	((+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) (sqrt (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* 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)))) (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (/ eps (* x x)) 1/8) 1/2) (* (* (neg x) x) x) (/ -1/8 (* (* (neg x) x) x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ -1/8 (* (* (neg x) x) x)) eps) (/ 1/2 x)) eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (neg (sqrt (sqrt (- (* x x) eps)))) (/ eps (* x x)) (+ (* (/ -1/8 (* (* (neg x) x) x)) eps) (/ 1/2 x)) (* (- (/ 1/8 (* x x)) (/ -1/2 eps)) eps) (/ 1/8 (* x x)))
3.0ms	x	@	inf	((+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) (sqrt (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* 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)))) (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (/ eps (* x x)) 1/8) 1/2) (* (* (neg x) x) x) (/ -1/8 (* (* (neg x) x) x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ -1/8 (* (* (neg x) x) x)) eps) (/ 1/2 x)) eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (neg (sqrt (sqrt (- (* x x) eps)))) (/ eps (* x x)) (+ (* (/ -1/8 (* (* (neg x) x) x)) eps) (/ 1/2 x)) (* (- (/ 1/8 (* x x)) (/ -1/2 eps)) eps) (/ 1/8 (* x x)))
3.0ms	eps	@	inf	((+ (* (sqrt (sqrt (- (* x x) eps))) (neg (sqrt (sqrt (- (* x x) eps))))) x) (sqrt (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- (* 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)))) (* (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) eps) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (+ (* (/ eps (* x x)) 1/8) 1/2) (* (* (neg x) x) x) (/ -1/8 (* (* (neg x) x) x)) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ -1/8 (* (* (neg x) x) x)) eps) (/ 1/2 x)) eps) (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (* (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) eps) (/ (+ (* (/ (/ eps x) x) 1/8) 1/2) x) (+ (* (/ (/ eps x) x) 1/8) 1/2) (neg (sqrt (sqrt (- (* x x) eps)))) (/ eps (* x x)) (+ (* (/ -1/8 (* (* (neg x) x) x)) eps) (/ 1/2 x)) (* (- (/ 1/8 (* x x)) (/ -1/2 eps)) eps) (/ 1/8 (* x x)))

simplify185.0ms (2.5%)

Memory

-15.9MiB live, 170.1MiB allocated; 31ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	561	2994
1	1838	2847
2	7335	2818
0	8355	2673

Stop Event

1×	iter limit
1×	node limit

Counts

133 → 132

Calls

Call 1

Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* x (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))))))))
(pow (* -1 eps) 1/4)
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(* (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)
(- 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 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 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(* -1 (pow x 3))
(/ 1/8 (pow x 3))
(* -1 (pow (* -1 eps) 1/4))
(- (* 1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(- (* (pow x 2) (- (* 3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))) (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)))) (pow (* -1 eps) 1/4))
(- (* (pow x 2) (- (* (pow x 2) (- (* 7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))) (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)))) (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)))) (pow (* -1 eps) 1/4))
(/ eps (pow x 2))
(/ 1/8 (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))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) x)
(sqrt x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
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)
(* (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)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(* -1 (sqrt x))
(- (* 1/4 (* eps (sqrt (/ 1 (pow x 3))))) (sqrt x))
(- (* -1 (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3)))))))
(- (* -1 (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))) (+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2)))) 2)))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
(* (sqrt x) (sqrt -1))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))))
(+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (+ (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))) (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3)))))))))
(* -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 (- (* 1/8 (/ (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 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (* (sqrt x) (sqrt -1)))
(- (* 1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
(- (* -1 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))) (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1))))
(- (* -1 (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))) (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))))
(+ x (* -1 x))
(+ x (+ (* -1 x) (* 1/2 (/ eps x))))
(+ x (+ (* -1 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
(+ x (+ (* -1 x) (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))))
(* (pow 1 1/4) (sqrt x))
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* -3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))))) (* (pow 1 1/4) (sqrt x)))
(+ (* eps (+ (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))) (* eps (+ (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))) (* -7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))))))) (* (pow 1 1/4) (sqrt 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 (+ (* 1/8 (/ 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))))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* -1 (* (pow 1 1/4) (sqrt x)))
(- (* 1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(- (* eps (- (* 3/32 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 7)))))) (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))))) (* (pow 1 1/4) (sqrt x)))
(- (* eps (- (* eps (- (* 7/128 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 11)))))) (* -3/32 (* (pow 1 1/4) (sqrt (/ 1 (pow x 7))))))) (* -1/4 (* (pow 1 1/4) (sqrt (/ 1 (pow x 3))))))) (* (pow 1 1/4) (sqrt x)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (/ x eps)))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps))))
(* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))))
(+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (+ (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3)))))
(* 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 (- (/ 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)))))
(* (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)))))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(* -1 (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))))
(- (* 1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))))
(- (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))) (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps))))
(- (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3))) (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps)))))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(* -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)))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(- (* -1 (/ (- (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(- (* -1 (/ (- (* -1 (/ (- (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 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))) (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (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))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* x (+ 1 (* x (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 x x) #s(literal -1 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))) x #s(literal 1 binary64)) x (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(pow (* -1 eps) 1/4)
(pow.f64 (neg.f64 eps) #s(literal 1/4 binary64))
(+ (* -1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/4 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* -3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))))) (pow (* -1 eps) 1/4))
(fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -3/32 binary64)) x) x (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (.f64 x x) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* (pow x 2) (+ (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)) (* (pow x 2) (+ (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)) (* -7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))))))) (pow (* -1 eps) 1/4))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 11 binary64))) #s(literal 1/4 binary64)) #s(literal -7/128 binary64)) x) x (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64)) #s(literal -3/32 binary64))) (.f64 x x) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal -1/4 binary64))) (.f64 x x) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(* (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 #s(literal -1/8 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 x 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 (.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 #s(literal -1/8 binary64) (/.f64 #s(literal -1 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 (/.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)
(- 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 (fma.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 x x) #s(literal -1 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))) x #s(literal 1 binary64)) x (.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 eps)))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps) eps)
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* 1/8 (/ eps (pow x 3)))
(*.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) eps)
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 #s(literal 1/8 binary64) eps)) (pow.f64 x #s(literal 3 binary64)))
(* 1/8 (/ eps (pow x 2)))
(*.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 #s(literal 1/8 binary64) eps)) x) x)
(* -1 (pow x 3))
(pow.f64 (neg.f64 x) #s(literal 3 binary64))
(/ 1/8 (pow x 3))
(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))
(* -1 (pow (* -1 eps) 1/4))
(neg.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(- (* 1/4 (* (pow (/ -1 (pow eps 3)) 1/4) (pow x 2))) (pow (* -1 eps) 1/4))
(-.f64 (.f64 (.f64 (*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) x) x) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(- (* (pow x 2) (- (* 3/32 (* (pow (/ -1 (pow eps 7)) 1/4) (pow x 2))) (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)))) (pow (* -1 eps) 1/4))
(-.f64 (.f64 (fma.f64 (.f64 (.f64 #s(literal 3/32 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64))) x) x (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) (*.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(- (* (pow x 2) (- (* (pow x 2) (- (* 7/128 (* (pow (/ -1 (pow eps 11)) 1/4) (pow x 2))) (* -3/32 (pow (/ -1 (pow eps 7)) 1/4)))) (* -1/4 (pow (/ -1 (pow eps 3)) 1/4)))) (pow (* -1 eps) 1/4))
(-.f64 (.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 7/128 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 11 binary64))) #s(literal 1/4 binary64))) x) x (.f64 #s(literal 3/32 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 7 binary64))) #s(literal 1/4 binary64)))) (.f64 x x) (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64))) (*.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(/ eps (pow x 2))
(/.f64 (/.f64 eps x) x)
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps (/.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) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (+ (* 1/2 eps) (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6)))))) x)
(/.f64 (fma.f64 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) #s(literal 1/2 binary64) (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))))
(fma.f64 (*.f64 #s(literal -1/4 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))
(fma.f64 (.f64 (.f64 eps eps) #s(literal -3/32 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 (*.f64 #s(literal -1/4 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x)))
(+ (sqrt x) (+ (* -1/4 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt (/ 1 (pow x 7))) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))) (* (sqrt (/ 1 (pow x 11))) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))))
(+.f64 (sqrt.f64 x) (fma.f64 (.f64 #s(literal -1/4 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -7/128 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 11 binary64)))) (.f64 (.f64 (*.f64 eps eps) #s(literal -3/32 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))
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)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 eps x) (fma.f64 (.f64 eps eps) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 6 binary64))))) x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(*.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #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)
(fma.f64 (/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 5 binary64))))
(/ (- (* 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 (fma.f64 (pow.f64 eps #s(literal 4 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64))) eps) #s(literal 1/2 binary64) (fma.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x) (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 x #s(literal 4 binary64))))) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/.f64 (fma.f64 (/.f64 (/.f64 eps x) x) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
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(* 2 x)
(*.f64 #s(literal 2 binary64) x)
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(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* 1/2 (/ eps (pow x 2))))) 2)))
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(* (sqrt x) (sqrt -1))
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(* -1 x)
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(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
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(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
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(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
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(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 #s(literal -1 binary64)))
(- (* 1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1)))
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(- (* -1 (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2)))))) (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (* (sqrt x) (sqrt -1))))
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(- (* -1 (* (sqrt (/ 1 (pow x 11))) (* (sqrt -1) (+ (* -1/12 (pow eps 3)) (+ (* -1/384 (pow eps 3)) (* 1/32 (pow eps 3))))))) (+ (* -1/4 (* (* eps (sqrt -1)) (sqrt (/ 1 (pow x 3))))) (+ (* (sqrt x) (sqrt -1)) (* (sqrt (/ 1 (pow x 7))) (* (sqrt -1) (+ (* -1/8 (pow eps 2)) (* 1/32 (pow eps 2))))))))
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(+ x (* -1 x))
#s(literal 0 binary64)
(+ x (+ (* -1 x) (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) #s(literal 0 binary64))
(+ x (+ (* -1 x) (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))))
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(* (pow 1 1/4) (sqrt x))
(sqrt.f64 x)
(+ (* -1/4 (* (pow 1 1/4) (* eps (sqrt (/ 1 (pow x 3)))))) (* (pow 1 1/4) (sqrt x)))
(fma.f64 (*.f64 #s(literal -1/4 binary64) eps) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 x))
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(+ x (* -1/2 (/ eps x)))
(fma.f64 #s(literal -1/2 binary64) (/.f64 eps x) x)
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
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(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
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(* 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))))
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(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
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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)))))
(.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 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 #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 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)
(* eps (- (/ 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)
(* 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)))) (-.f64 (/.f64 x eps) (.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)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (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 x (/.f64 x (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 x eps)))) eps)
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(.f64 (.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) eps)
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(*.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)
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))))
(.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps)
(* -1 (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))))
(neg.f64 (*.f64 (pow.f64 eps #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))))
(- (* 1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))))
(-.f64 (.f64 (.f64 (.f64 (pow.f64 eps #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))) (.f64 x (/.f64 x eps))) #s(literal 1/4 binary64)) (*.f64 (pow.f64 eps #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))))
(- (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2))) (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps))))
(-.f64 (.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)))) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) eps) (/.f64 #s(literal -3/32 binary64) eps))) (fma.f64 (.f64 (.f64 (pow.f64 eps #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))) (.f64 x (/.f64 x eps))) #s(literal -1/4 binary64) (*.f64 (pow.f64 eps #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)))))
(- (* -1 (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/12 (pow x 6)) (+ (* -1/384 (pow x 6)) (* 1/32 (pow x 6))))) (pow eps 3))) (+ (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/4 (/ (* (pow x 2) (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps))))))) eps)) (/ (* (exp (* 1/4 (+ (log -1) (* -1 (log (/ 1 eps)))))) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (pow eps 2)))))
(-.f64 (/.f64 (.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -7/128 binary64)) (.f64 (pow.f64 eps #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)))) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (fma.f64 (pow.f64 eps #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 x x)) (.f64 (pow.f64 eps #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)) (*.f64 (pow.f64 eps #s(literal 1/4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)))) eps)) eps)))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ x eps)))))
(*.f64 (neg.f64 eps) (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x eps))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)))))
(.f64 (neg.f64 eps) (neg.f64 (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) eps))))
(* -1 (* eps (+ (* -1 (* (sqrt (/ 1 eps)) (sqrt -1))) (* -1 (/ (+ x (* -1 (/ (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1))))) eps))) eps)))))
(.f64 (neg.f64 eps) (neg.f64 (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)) eps))))
(+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (.f64 (.f64 (neg.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -3/32 binary64))) eps) #s(literal -1 binary64) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6)))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (/.f64 (fma.f64 (.f64 (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -3/32 binary64) (.f64 (neg.f64 (*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 7/128 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)))) (neg.f64 eps))) eps) #s(literal -1 binary64) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(* -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 (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 (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 (.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)))))
(.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (.f64 x (/.f64 x eps))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(*.f64 (neg.f64 eps) (neg.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)) (/.f64 x 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) (neg.f64 (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) 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) (neg.f64 (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)) eps))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))
(.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps)
(- (* -1 (/ (- (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4)))) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(-.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64)))) (neg.f64 eps)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(- (* -1 (/ (- (* -1 (/ (- (* (pow (/ -1 (pow eps 3)) 1/4) (+ (* -1/32 (pow x 6)) (+ (* 1/384 (pow x 6)) (* 1/12 (pow x 6))))) (* (pow (* -1 eps) 1/4) (+ (* -1/8 (pow x 4)) (* 1/32 (pow x 4))))) eps)) (* 1/4 (* (pow (* -1 eps) 1/4) (pow x 2)))) eps)) (pow (* -1 eps) 1/4))
(-.f64 (/.f64 (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 x x)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)) (/.f64 (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 7/128 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 eps #s(literal 3 binary64))) #s(literal 1/4 binary64))) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -3/32 binary64)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))) (neg.f64 eps))) (neg.f64 eps)) (pow.f64 (neg.f64 eps) #s(literal 1/4 binary64)))
(* 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)

rewrite235.0ms (3.1%)

Memory

27.0MiB live, 274.2MiB allocated; 56ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	47	326
0	78	318
1	253	305
2	1715	286
0	8400	286

Stop Event

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

Counts

25 → 709

Calls

Call 1

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

Outputs
(/.f64 (neg.f64 (neg.f64 (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x)))) (neg.f64 (neg.f64 (-.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps))) x))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 (*.f64 x x) eps)))))
(/.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))))))
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(-.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (pow.f64 x #s(literal 3 binary64)))))
(+.f64 (/.f64 (.f64 #s(literal -1/512 binary64) (pow.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64))) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 6 binary64)) (.f64 eps eps) (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (.f64 eps (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 4 binary64)))))) (/.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 6 binary64)) (.f64 eps eps) (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)) (*.f64 eps (pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 4 binary64)))))))
(+.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 eps (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) x))
(+.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (pow.f64 x #s(literal 3 binary64)))))
(.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps)
(.f64 eps (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)))
(/.f64 (neg.f64 (.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64))) eps)) (neg.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))))
(/.f64 (neg.f64 (.f64 (-.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 3 binary64))) eps)) (neg.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (+.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) eps (.f64 (.f64 (neg.f64 x) x) #s(literal -1/2 binary64))) eps)) (neg.f64 (.f64 eps (*.f64 x x))))
(/.f64 (neg.f64 (.f64 eps (-.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64))))) (neg.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))))
(/.f64 (neg.f64 (.f64 eps (-.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (+.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (.f64 eps (fma.f64 #s(literal 1/8 binary64) eps (.f64 (.f64 (neg.f64 x) x) #s(literal -1/2 binary64))))) (neg.f64 (.f64 eps (*.f64 x x))))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64))) eps) (+.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
(/.f64 (.f64 (-.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 3 binary64))) eps) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (+.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) eps (.f64 (.f64 (neg.f64 x) x) #s(literal -1/2 binary64))) eps) (.f64 eps (*.f64 x x)))
(/.f64 (.f64 eps (-.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)))) (+.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))
(/.f64 (.f64 eps (-.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (/.f64 #s(literal -1/2 binary64) eps) #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) eps) (+.f64 (/.f64 #s(literal -1/2 binary64) eps) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 eps (fma.f64 #s(literal 1/8 binary64) eps (.f64 (.f64 (neg.f64 x) x) #s(literal -1/2 binary64)))) (.f64 eps (*.f64 x x)))
(/.f64 (neg.f64 (/.f64 #s(literal -1/8 binary64) x)) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1/8 binary64) x))) (neg.f64 (neg.f64 x)))
(/.f64 (fabs.f64 (neg.f64 (/.f64 #s(literal 1/8 binary64) x))) x)
(/.f64 (fabs.f64 (/.f64 #s(literal -1/8 binary64) x)) x)
(/.f64 (fabs.f64 (/.f64 #s(literal 1/8 binary64) x)) x)
(/.f64 (/.f64 #s(literal -1/8 binary64) x) (neg.f64 x))
(/.f64 (neg.f64 (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1/8 binary64) x) x)
(/.f64 #s(literal -1/8 binary64) (*.f64 (neg.f64 x) x))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(neg.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(sqrt.f64 (/.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))))
(fabs.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(fabs.f64 (neg.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))
(fabs.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))

eval258.0ms (3.4%)

Memory: 10.8MiB live, 288.7MiB allocated; 24ms collecting garbage
Compiler: Compiled 29 605 to 3 402 computations (88.5% saved)

prune27.0ms (0.4%)

Memory

-17.9MiB live, 80.8MiB allocated; 10ms collecting garbage

Pruning

12 alts after pruning (5 fresh and 7 done)

	Pruned	Kept	Total
New	861	2	863
Fresh	1	3	4
Picked	2	3	5
Done	0	4	4
Total	864	12	876

Accuracy

99.9%

Counts

876 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	57.6%	(fma.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x x) eps))) (neg.f64 (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps))))) x)
	58.1%	(-.f64 x (/.f64 (-.f64 (.f64 x x) eps) (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))))
✓	61.0%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	43.9%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 eps x) x)) x) x))))
✓	57.8%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	42.7%	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x)))
	42.5%	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (/.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) eps) x (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
✓	42.5%	#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (/.f64 #s(approx (+ ( (/ (/ eps x) x) 1/8) 1/2) (.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) eps)) eps)) x) eps))
✓	45.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (*.f64 #s(literal 1/2 binary64) eps) x))
✓	36.8%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (.f64 (*.f64 (neg.f64 x) x) x)) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
✓	4.3%	#s(approx (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) #s(literal 0 binary64))

Compiler

Compiled 831 to 306 computations (63.2% saved)

regimes24.0ms (0.3%)

Memory

13.6MiB live, 59.4MiB allocated; 3ms collecting garbage

Counts

27 → 2

Calls

Call 1

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

Outputs

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

#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (*.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x)))

Calls

3 calls:

9.0ms	eps
7.0ms	x
7.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
99.2%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
86.8%	2	`x`
80.6%	2	`eps`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.1%)

Memory

-39.2MiB live, 7.2MiB allocated; 2ms collecting garbage

Counts

8 → 2

Calls

Call 1

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

Outputs

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

#s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (*.f64 (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps))

Calls

1 calls:

4.0ms

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

Results

Accuracy	Segments	Branch
99.1%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory

6.6MiB live, 6.6MiB allocated; 0ms collecting garbage

Counts

7 → 2

Calls

Call 1

Inputs
#s(approx (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) #s(literal 0 binary64))
(-.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))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 x (/.f64 (-.f64 (.f64 x x) 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

1 calls:

2.0ms

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

Results

Accuracy	Segments	Branch
99.0%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0%)

Memory

6.5MiB live, 6.5MiB allocated; 0ms collecting garbage

Counts

5 → 2

Calls

Call 1

Inputs
#s(approx (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) #s(literal 0 binary64))
(-.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))

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
97.9%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated; 0ms collecting garbage

Counts

4 → 2

Calls

Call 1

Inputs
#s(approx (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) #s(literal 0 binary64))
(-.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
97.8%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes5.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) #s(literal 0 binary64))

(-.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))))

Calls

3 calls:

2.0ms	eps
2.0ms	x
1.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
57.8%	1	`eps`
57.8%	1	`x`
57.8%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated; 0ms collecting garbage

Accuracy

Total -0.8b remaining (-1.3%)

Threshold costs -0.8b (-1.3%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) #s(literal 0 binary64))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Outputs
#s(approx (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) #s(literal 0 binary64))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
4.3%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
4.3%	1	`eps`
4.3%	1	`x`

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.423904047212526e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.423904047212526e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.423904047212526e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.423904047212526e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch3.0ms (0%)

Memory

-45.2MiB live, 0.8MiB allocated; 3ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.423904047212526e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

simplify53.0ms (0.7%)

Memory

17.5MiB live, 65.0MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	228
1	67	221
2	105	221
3	166	221
4	233	221
5	302	221
6	385	221
7	1023	221
8	5572	221

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 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 -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 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 -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 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)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) #s(literal 0 binary64))

Outputs
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (fma.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x x)) #s(literal 1/2 binary64)) (/.f64 eps x))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (/ (- (* x x) eps) (sqrt (- (* x x) eps)))) (.f64 (/.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x) eps)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 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 -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 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 -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 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)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (+ (* (pow (- (* x x) eps) 1/4) (neg (pow (- (* x x) eps) 1/4))) x) #s(literal 0 binary64))

derivations1.5s (19.8%)

Memory

-119.8MiB live, 855.5MiB allocated; 1.2s collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	164
0	48	155
1	158	155
2	1146	143
0	8813	143
0	39	199
0	65	199
1	210	178
2	1524	166
0	8475	166
0	257	1069
1	807	1054
2	3108	1019
0	8668	960
0	551	2914
1	1807	2781
2	7268	2752
0	8300	2609
0	47	326
0	78	318
1	253	305
2	1715	286
0	8400	286
0	6	22
0	10	22
1	42	22
2	320	22
3	3652	22
0	8870	22

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

Compiler

Compiled 228 to 47 computations (79.4% saved)

preprocess45.0ms (0.6%)

Memory: 33.8MiB live, 78.4MiB allocated; 5ms collecting garbage
Compiler: Compiled 492 to 120 computations (75.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze21.0ms (0.3%)

sample1.7s (22.1%)

explain138.0ms (1.8%)

preprocess18.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize33.0ms (0.4%)

series9.0ms (0.1%)

simplify177.0ms (2.4%)

rewrite187.0ms (2.5%)

eval37.0ms (0.5%)

prune26.0ms (0.3%)

simplify165.0ms (2.2%)

localize190.0ms (2.5%)

series37.0ms (0.5%)

simplify177.0ms (2.4%)

rewrite240.0ms (3.2%)

eval312.0ms (4.2%)

prune45.0ms (0.6%)

simplify194.0ms (2.6%)

localize218.0ms (2.9%)

series21.0ms (0.3%)

simplify331.0ms (4.4%)

rewrite293.0ms (3.9%)

eval165.0ms (2.2%)

prune40.0ms (0.5%)

simplify209.0ms (2.8%)

localize189.0ms (2.5%)

series25.0ms (0.3%)

simplify185.0ms (2.5%)

rewrite235.0ms (3.1%)

eval258.0ms (3.4%)

prune27.0ms (0.4%)

regimes24.0ms (0.3%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch3.0ms (0%)

simplify53.0ms (0.7%)

derivations1.5s (19.8%)

preprocess45.0ms (0.6%)

end0.0ms (0%)

Profiling