Metrics for ENA, Section 1.4, Exercise 4d

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze16.0ms (0.3%)

Memory

-7.2MiB live, 31.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 24 to 18 computations (25% saved)

sample1.5s (23.3%)

Memory

67.6MiB live, 1 746.4MiB allocated

Samples

503.0ms	4 883×	0	valid
379.0ms	2 783×	1	valid
125.0ms	590×	2	valid
10.0ms	156×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 675.0ms

ival-sub: 186.0ms (27.5% of total)

ival-mult: 156.0ms (23.1% of total)

ival-<=: 106.0ms (15.7% of total)

ival-sqrt: 100.0ms (14.8% of total)

adjust: 85.0ms (12.6% of total)

ival-and: 21.0ms (3.1% of total)

exact: 17.0ms (2.5% of total)

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

Bogosity

explain110.0ms (1.7%)

Memory

-45.0MiB live, 157.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
115	-	-	`(-.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	115	1

Confusion

	Predicted +	Predicted -
+	115	0
-	0	141

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	115	0	0
-	0	1	140

Precision?

0.9913793103448276

Recall?

1.0

Freqs

test

number	freq
0	141
1	115

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

34.0ms	186×	1	valid
15.0ms	296×	0	valid
6.0ms	30×	2	valid

Compiler

Compiled 84 to 28 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-sub: 7.0ms (30.8% of total)

ival-sqrt: 6.0ms (26.4% of total)

ival-mult: 5.0ms (22% of total)

adjust: 4.0ms (17.6% of total)

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

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

preprocess397.0ms (6.3%)

Memory

7.1MiB live, 271.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	55	42
2	164	41
3	535	41
4	1383	41
5	1804	41
6	2153	41
7	4196	41
8	4816	41
9	5286	41
10	5812	41
11	6190	41
12	6666	41
13	6952	41
14	7734	41
0	6	8
0	10	8
1	19	8
2	43	8
3	152	8
4	517	8
5	903	8
6	1504	8
7	3467	8
8	4220	8
9	5006	8
10	5358	8
11	5712	8
12	6253	8
13	6510	8
0	8051	8

Stop Event

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

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
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify307.0ms (4.9%)

Memory

-9.0MiB live, 261.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	24
0	10	24
1	19	24
2	43	24
3	152	24
4	517	24
5	903	24
6	1504	24
7	3467	24
8	4220	24
9	5006	24
10	5358	24
11	5712	24
12	6253	24
13	6510	24
0	8051	24

Stop Event

1×	iter limit
1×	node limit
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

localize67.0ms (1.1%)

Memory

-5.6MiB live, 132.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.01953125	(-.f64 (*.f64 x x) eps)
accuracy	0.01953125	(sqrt.f64 (-.f64 (*.f64 x x) eps))
accuracy	25.451215999132007	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Samples

43.0ms	148×	0	valid
16.0ms	93×	1	valid
2.0ms	15×	2	valid

Compiler

Compiled 50 to 14 computations (72% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sub: 4.0ms (35.1% of total)

ival-sqrt: 3.0ms (26.3% of total)

ival-mult: 3.0ms (26.3% of total)

adjust: 2.0ms (17.5% of total)

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

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

series8.0ms (0.1%)

Memory

13.6MiB live, 13.6MiB allocated

Counts

4 → 49

Calls

Call 1

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

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

Calls

6 calls:

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

simplify43.0ms (0.7%)

Memory

-12.7MiB live, 62.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	1067
0	842	1017

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

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

rewrite199.0ms (3.2%)

Memory

-4.6MiB live, 153.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
0	10	22
1	47	22
2	378	22
3	4841	22
0	9913	19

Stop Event

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

Counts

4 → 350

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 (fma.f64 x x (fma.f64 x x eps)) #s(literal 1 binary64)) (pow.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))) #s(literal 2 binary64))) (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x eps)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x eps)) (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (fma.f64 x x (fma.f64 x x eps)) (fma.f64 x x (fma.f64 x x eps))) (-.f64 x (sqrt.f64 (fma.f64 x x eps))))
(*.f64 (/.f64 (fma.f64 x x (fma.f64 x x eps)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal 3/2 binary64)))) (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))))
(*.f64 (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal 3/2 binary64)))) (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) (pow.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))) #s(literal -1 binary64))))
(*.f64 #s(literal -1 binary64) (-.f64 x (sqrt.f64 (fma.f64 x x eps))))
(*.f64 (pow.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x eps) #s(literal 3/2 binary64))))
(*.f64 (pow.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) #s(literal -1 binary64)) (fma.f64 x x (fma.f64 x x eps)))
(*.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 x x eps))))
(*.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) #s(literal 1 binary64))
(*.f64 (fma.f64 x x (fma.f64 x x eps)) (pow.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) #s(literal -1 binary64)))
(*.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))) (/.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps)))))
(.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))) (.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) (pow.f64 (fma.f64 (sqrt.f64 (fma.f64 x x eps)) x (fma.f64 x x (fma.f64 x x eps))) #s(literal -1 binary64))))
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(pow.f64 (/.f64 (pow.f64 (-.f64 x (sqrt.f64 (fma.f64 x x eps))) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
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eval86.0ms (1.4%)

Memory: 2.9MiB live, 82.1MiB allocated
Compiler: Compiled 8 544 to 1 400 computations (83.6% saved)

prune49.0ms (0.8%)

Memory

-11.3MiB live, 28.6MiB allocated

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	388	9	397
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	388	10	398

Accuracy

99.7%

Counts

398 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	28.1%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal -1 binary64) #s(literal 1 binary64)) (*.f64 x x)))))
▶	60.0%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (-.f64 (/.f64 (.f64 x x) eps) #s(literal 1 binary64)) eps))))
	54.2%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	7.8%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
▶	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	44.5%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
	31.5%	#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))
▶	41.9%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps))
▶	46.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))

Compiler

Compiled 332 to 228 computations (31.3% saved)

simplify178.0ms (2.8%)

Memory

2.2MiB live, 121.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 eps (pow.f64 x #s(literal 3 binary64)))
cost-diff	0	(fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps))
cost-diff	0	(*.f64 x x)
cost-diff	0	(*.f64 eps eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
cost-diff	320	(fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps))
cost-diff	0	(/.f64 eps x)
cost-diff	0	(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
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	(sqrt.f64 #s(approx (- (* x x) eps) (.f64 (-.f64 (/.f64 (.f64 x x) eps) #s(literal 1 binary64)) eps)))
cost-diff	0	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (-.f64 (/.f64 (.f64 x x) eps) #s(literal 1 binary64)) eps))))
cost-diff	128	(-.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64))
cost-diff	896	(.f64 (-.f64 (/.f64 (.f64 x x) eps) #s(literal 1 binary64)) eps)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	252
0	57	256
1	110	256
2	297	247
3	1545	247
4	5887	231
0	8162	229

Stop Event

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

Calls

Call 1

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

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

localize112.0ms (1.8%)

Memory

18.0MiB live, 56.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x))
accuracy	6.033358729670725	(/.f64 eps (pow.f64 x #s(literal 3 binary64)))
accuracy	6.636162068266119	(*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps)
accuracy	35.19298160951386	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (fma.f64 (/.f64 eps (pow.f64 x #s(literal 3 binary64))) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) eps))
accuracy	0.015625	(fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0.12109375	(/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x)
accuracy	22.21896503423997	(/.f64 (.f64 eps eps) (.f64 x x))
accuracy	35.19298160951386	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (fma.f64 (/.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/8 binary64) (*.f64 #s(literal 1/2 binary64) eps)) x))
accuracy	0	(/.f64 eps x)
accuracy	0	(*.f64 (/.f64 eps x) #s(literal 1/2 binary64))
accuracy	34.27034610285297	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
accuracy	0	(neg.f64 x)
accuracy	25.451215999132007	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
accuracy	62.45952536791358	#s(approx (sqrt (- (* x x) eps)) (neg.f64 x))
accuracy	0.01953125	(sqrt.f64 #s(approx (- (* x x) eps) (.f64 (-.f64 (/.f64 (.f64 x x) eps) #s(literal 1 binary64)) eps)))
accuracy	0.37481270174522724	(.f64 (-.f64 (/.f64 (.f64 x x) eps) #s(literal 1 binary64)) eps)
accuracy	7.906906283913383	(/.f64 (*.f64 x x) eps)
accuracy	25.451215999132007	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (-.f64 (/.f64 (.f64 x x) eps) #s(literal 1 binary64)) eps))))

Samples

32.0ms	93×	1	valid
29.0ms	148×	0	valid
7.0ms	15×	2	valid

Compiler

Compiled 440 to 65 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-mult: 14.0ms (30% of total)

ival-div: 12.0ms (25.7% of total)

adjust: 5.0ms (10.7% of total)

ival-sub: 5.0ms (10.7% of total)

ival-sqrt: 3.0ms (6.4% of total)

ival-pow: 3.0ms (6.4% of total)

ival-add: 3.0ms (6.4% of total)

ival-neg: 1.0ms (2.1% of total)

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

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

exact: 0.0ms (0% of total)

series80.0ms (1.3%)

Memory

-7.2MiB live, 28.6MiB allocated

Counts

21 → 76

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
59.0ms	eps	@	inf	((* (- (/ (* x x) eps) 1) eps) (- (/ (* x x) eps) 1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (* eps eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ eps (pow x 3)) (/ (* x x) eps) (/ (* eps eps) (* x x)) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x))
5.0ms	x	@	0	((* (- (/ (* x x) eps) 1) eps) (- (/ (* x x) eps) 1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (* eps eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ eps (pow x 3)) (/ (* x x) eps) (/ (* eps eps) (* x x)) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x))
5.0ms	eps	@	-inf	((* (- (/ (* x x) eps) 1) eps) (- (/ (* x x) eps) 1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (* eps eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ eps (pow x 3)) (/ (* x x) eps) (/ (* eps eps) (* x x)) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x))
4.0ms	eps	@	0	((* (- (/ (* x x) eps) 1) eps) (- (/ (* x x) eps) 1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (* eps eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ eps (pow x 3)) (/ (* x x) eps) (/ (* eps eps) (* x x)) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x))
3.0ms	x	@	inf	((* (- (/ (* x x) eps) 1) eps) (- (/ (* x x) eps) 1) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (- x (sqrt (- (* x x) eps))) (sqrt (- (* x x) eps)) (neg x) (- x (sqrt (- (* x x) eps))) (* (/ eps x) 1/2) (/ eps x) (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (- x (sqrt (- (* x x) eps))) (* eps eps) (* x x) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ eps (pow x 3)) (/ (* x x) eps) (/ (* eps eps) (* x x)) (/ (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) x))

simplify84.0ms (1.3%)

Memory

-18.0MiB live, 37.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	298	1336
0	971	1274

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

76 → 75

Calls

Call 1

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

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

rewrite270.0ms (4.3%)

Memory

38.1MiB live, 147.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	209
0	57	209
1	230	201
2	1892	201
0	8763	197

Stop Event

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

Counts

21 → 826

Calls

Call 1

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

Outputs
(*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)
(*.f64 eps (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)))
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) eps)) (neg.f64 (fma.f64 (/.f64 x eps) x #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (pow.f64 eps #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) eps)) (neg.f64 (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 x eps) x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (*.f64 eps (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (/.f64 x eps) x #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 eps (fma.f64 (pow.f64 eps #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 x eps) x #s(literal 1 binary64)))))
(/.f64 (*.f64 (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) eps) (fma.f64 (/.f64 x eps) x #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 (pow.f64 eps #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) eps) (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 x eps) x #s(literal 1 binary64))))
(/.f64 (*.f64 eps (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (/.f64 x eps) x #s(literal 1 binary64)))
(/.f64 (*.f64 eps (fma.f64 (pow.f64 eps #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 x eps) x #s(literal 1 binary64))))
(fma.f64 (/.f64 (*.f64 x x) eps) eps (neg.f64 eps))
(fma.f64 eps (/.f64 (.f64 x x) eps) (.f64 eps #s(literal -1 binary64)))
(+.f64 (.f64 (/.f64 (.f64 x x) eps) eps) (neg.f64 eps))
(+.f64 (.f64 eps (/.f64 (.f64 x x) eps)) (*.f64 eps #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (/.f64 x eps) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (pow.f64 eps #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 x eps) x #s(literal 1 binary64))) #s(literal -1 binary64)))
(pow.f64 (/.f64 (fma.f64 (/.f64 x eps) x #s(literal 1 binary64)) (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) (fma.f64 (/.f64 x eps) x #s(literal 1 binary64))) (fma.f64 (pow.f64 eps #s(literal -3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 eps #s(literal -2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (/.f64 x eps) x #s(literal 1 binary64)))))
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(/.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps #s(literal 6 binary64)) #s(literal 1/512 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 eps x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (/.f64 eps x)) #s(literal 2 binary64)) (.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) x) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 (/.f64 eps x) #s(literal 4 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 eps eps)))) (neg.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) eps)) x)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (/.f64 eps x) #s(literal 6 binary64)) #s(literal 1/512 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) eps) #s(literal 3 binary64)))) (neg.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 (/.f64 eps x) #s(literal 4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) eps) (-.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)))))) x)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps)))) (neg.f64 (neg.f64 x)))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 (/.f64 eps x) #s(literal 4 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (.f64 #s(literal -1/2 binary64) eps)) x))
(/.f64 (.f64 (fma.f64 (pow.f64 (/.f64 eps x) #s(literal 6 binary64)) #s(literal 1/512 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) eps) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 (/.f64 eps x) #s(literal 4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) eps) (-.f64 (.f64 #s(literal 1/2 binary64) eps) (*.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)))))) x))
(/.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) x (.f64 x (.f64 #s(literal 1/2 binary64) eps))) (.f64 x x))
(/.f64 (-.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 (/.f64 eps x) #s(literal 4 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 eps eps))) (.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) eps)) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps)))))
(/.f64 (fma.f64 (pow.f64 (/.f64 eps x) #s(literal 6 binary64)) #s(literal 1/512 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) eps) #s(literal 3 binary64))) (.f64 (fma.f64 #s(literal 1/64 binary64) (pow.f64 (/.f64 eps x) #s(literal 4 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) eps) (-.f64 (.f64 #s(literal 1/2 binary64) eps) (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)))))) x))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps))) (neg.f64 x))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps)) x)
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps))) x))
(neg.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) eps)) (neg.f64 x)))
(fma.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) (pow.f64 x #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
(fma.f64 (.f64 #s(literal 1/2 binary64) eps) (pow.f64 x #s(literal -1 binary64)) (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) x))
(fma.f64 #s(literal 1/8 binary64) (/.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) x) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
(fma.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (/.f64 #s(literal 1/8 binary64) x) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 eps x) (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) x))
(fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) x))
(fma.f64 eps (/.f64 #s(literal 1/2 binary64) x) (/.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) x))
(-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) x) (.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
(-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) x) (.f64 (neg.f64 (/.f64 eps x)) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) x) (/.f64 (.f64 #s(literal -1/2 binary64) eps) x))
(exp.f64 (.f64 (log.f64 (/.f64 x (fma.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) eps)))) #s(literal -1 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 eps x)) (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) x))
(+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64))) x) (.f64 #s(literal 1/2 binary64) (/.f64 eps x)))

eval240.0ms (3.8%)

Memory: -19.9MiB live, 180.6MiB allocated
Compiler: Compiled 27 073 to 4 115 computations (84.8% saved)

prune81.0ms (1.3%)

Memory

-2.2MiB live, 76.2MiB allocated

Pruning

22 alts after pruning (19 fresh and 3 done)

	Pruned	Kept	Total
New	911	16	927
Fresh	1	3	4
Picked	3	2	5
Done	0	1	1
Total	915	22	937

Accuracy

99.9%

Counts

937 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.9%	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))
	52.4%	(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))
	39.5%	(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))) (.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (pow.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)) #s(literal 3/2 binary64)))) (.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))))
	52.2%	(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x)) (.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x) #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x)))
	59.7%	(/.f64 (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x))
	52.5%	(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))) (/.f64 (pow.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))))
✓	60.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	60.0%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))
	25.3%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 #s(approx (- (/ ( x x) eps) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 x x))) eps))))
▶	54.2%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	7.8%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
▶	45.0%	#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (/.f64 #s(literal 1/8 binary64) x) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
	45.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
	46.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
	31.5%	#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))
	44.7%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
✓	46.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
▶	44.8%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
	41.1%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.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)))) eps))
	46.3%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps))
	27.5%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (/.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)))))

Compiler

Compiled 1 607 to 676 computations (57.9% saved)

simplify107.0ms (1.7%)

Memory

-2.2MiB live, 118.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 eps x)
cost-diff	0	(pow.f64 (/.f64 eps x) #s(literal 2 binary64))
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (/.f64 #s(literal 1/8 binary64) x) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
cost-diff	704	(fma.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (/.f64 #s(literal 1/8 binary64) x) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
cost-diff	0	(neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))
cost-diff	0	(sqrt.f64 x)
cost-diff	896	(*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)
cost-diff	1600	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))
cost-diff	0	(fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x))
cost-diff	0	(.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.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 (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.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	#s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))
cost-diff	0	(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))
cost-diff	0	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))
cost-diff	896	(*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	353
0	67	349
1	120	344
2	356	342
3	1628	342
4	5257	315
0	8104	315

Stop Event

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

Calls

Call 1

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

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

localize225.0ms (3.6%)

Memory

-11.7MiB live, 272.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
accuracy	0.15234375	(fma.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (/.f64 #s(literal 1/8 binary64) x) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x)))
accuracy	0.32259750976844204	(pow.f64 (/.f64 eps x) #s(literal 2 binary64))
accuracy	35.19298160951386	#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) (/.f64 #s(literal 1/8 binary64) x) (*.f64 #s(literal 1/2 binary64) (/.f64 eps x))))
accuracy	0.01953125	(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))
accuracy	0.12109375	(fma.f64 (/.f64 x eps) x #s(literal -1 binary64))
accuracy	0.37481270174522724	(*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)
accuracy	25.661791740699925	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))
accuracy	0.078125	(/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)
accuracy	6.636162068266119	(.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps)
accuracy	7.64742825126446	(/.f64 eps (*.f64 x x))
accuracy	35.19298160951386	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
accuracy	0	(neg.f64 eps)
accuracy	0.01953125	(sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps)))
accuracy	25.451215999132007	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
accuracy	28.287992535869385	#s(approx (- (* x x) eps) (neg.f64 eps))
accuracy	0.01953125	(sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))
accuracy	0.12109375	(fma.f64 (/.f64 x eps) x #s(literal -1 binary64))
accuracy	0.37481270174522724	(*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)
accuracy	25.451215999132007	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))

Samples

73.0ms	148×	0	valid
55.0ms	92×	1	valid
13.0ms	16×	2	valid

Compiler

Compiled 582 to 82 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 95.0ms

ival-mult: 27.0ms (28.5% of total)

ival-sqrt: 24.0ms (25.4% of total)

ival-div: 14.0ms (14.8% of total)

ival-add: 8.0ms (8.5% of total)

adjust: 7.0ms (7.4% of total)

ival-sub: 4.0ms (4.2% of total)

ival-pow2: 4.0ms (4.2% of total)

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

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

exact: 1.0ms (1.1% of total)

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

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

series25.0ms (0.4%)

Memory

10.1MiB live, 49.0MiB allocated

Counts

23 → 100

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	eps	@	-inf	((* (+ (* (/ x eps) x) -1) eps) (- x (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 (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (+ (* (/ eps (* x x)) 1/8) 1/2) (+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps)))) (sqrt x) (neg (sqrt (- (* x x) eps))) (+ (* (pow (/ eps x) 2) (/ 1/8 x)) (* 1/2 (/ eps x))) (- x (sqrt (- (* x x) eps))) (pow (/ eps x) 2) (/ eps x) (+ (* (/ x eps) x) -1) (/ eps (* x x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (* 1/2 (/ eps x)))
4.0ms	eps	@	inf	((* (+ (* (/ x eps) x) -1) eps) (- x (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 (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (+ (* (/ eps (* x x)) 1/8) 1/2) (+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps)))) (sqrt x) (neg (sqrt (- (* x x) eps))) (+ (* (pow (/ eps x) 2) (/ 1/8 x)) (* 1/2 (/ eps x))) (- x (sqrt (- (* x x) eps))) (pow (/ eps x) 2) (/ eps x) (+ (* (/ x eps) x) -1) (/ eps (* x x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (* 1/2 (/ eps x)))
4.0ms	x	@	-inf	((* (+ (* (/ x eps) x) -1) eps) (- x (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 (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (+ (* (/ eps (* x x)) 1/8) 1/2) (+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps)))) (sqrt x) (neg (sqrt (- (* x x) eps))) (+ (* (pow (/ eps x) 2) (/ 1/8 x)) (* 1/2 (/ eps x))) (- x (sqrt (- (* x x) eps))) (pow (/ eps x) 2) (/ eps x) (+ (* (/ x eps) x) -1) (/ eps (* x x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (* 1/2 (/ eps x)))
3.0ms	x	@	0	((* (+ (* (/ x eps) x) -1) eps) (- x (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 (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (+ (* (/ eps (* x x)) 1/8) 1/2) (+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps)))) (sqrt x) (neg (sqrt (- (* x x) eps))) (+ (* (pow (/ eps x) 2) (/ 1/8 x)) (* 1/2 (/ eps x))) (- x (sqrt (- (* x x) eps))) (pow (/ eps x) 2) (/ eps x) (+ (* (/ x eps) x) -1) (/ eps (* x x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (* 1/2 (/ eps x)))
3.0ms	x	@	inf	((* (+ (* (/ x eps) x) -1) eps) (- x (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 (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (+ (* (/ eps (* x x)) 1/8) 1/2) (+ (* (sqrt x) (sqrt x)) (neg (sqrt (- (* x x) eps)))) (sqrt x) (neg (sqrt (- (* x x) eps))) (+ (* (pow (/ eps x) 2) (/ 1/8 x)) (* 1/2 (/ eps x))) (- x (sqrt (- (* x x) eps))) (pow (/ eps x) 2) (/ eps x) (+ (* (/ x eps) x) -1) (/ eps (* x x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (* 1/2 (/ eps x)))

simplify61.0ms (1%)

Memory

26.3MiB live, 102.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	360	1968
0	1154	1886

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

100 → 99

Calls

Call 1

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

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

rewrite204.0ms (3.2%)

Memory

0.3MiB live, 362.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	281
0	67	277
1	276	272
2	2335	272
0	9009	270

Stop Event

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

Counts

23 → 1 000

Calls

Call 1

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

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

eval236.0ms (3.7%)

Memory: -10.6MiB live, 491.7MiB allocated
Compiler: Compiled 40 663 to 4 736 computations (88.4% saved)

prune40.0ms (0.6%)

Memory

31.5MiB live, 110.0MiB allocated

Pruning

24 alts after pruning (17 fresh and 7 done)

	Pruned	Kept	Total
New	1 232	6	1 238
Fresh	3	11	14
Picked	1	4	5
Done	0	3	3
Total	1 236	24	1 260

Accuracy

99.9%

Counts

1 260 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.9%	(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))
▶	59.4%	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))))
✓	59.9%	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))
	39.5%	(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))) (.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (pow.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)) #s(literal 3/2 binary64)))) (.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))))
	52.2%	(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x)) (.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x) #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x)))
	59.7%	(/.f64 (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x))
	52.5%	(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))) (/.f64 (pow.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))))
✓	60.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	60.0%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))
	25.3%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 #s(approx (- (/ ( x x) eps) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 x x))) eps))))
✓	54.2%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	7.8%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	45.0%	#s(approx (- x (sqrt (- (* x x) eps))) (fma.f64 (/.f64 eps x) (.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))))
	24.9%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (+.f64 (sqrt.f64 x) (.f64 (/.f64 x (.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 1/8 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) eps) (sqrt.f64 x)))) (.f64 (/.f64 x (*.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 1/8 binary64))) (sqrt.f64 x))))
	45.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
	46.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
▶	31.5%	#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))
▶	44.7%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
✓	46.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
✓	44.8%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
	41.1%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.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)))) eps))
▶	46.3%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(literal 1/2 binary64)) x)) eps))
	27.5%	#s(approx (- x (sqrt (- (* x x) eps))) #s(approx (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (/.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)))))

Compiler

Compiled 1 647 to 699 computations (57.6% saved)

simplify143.0ms (2.3%)

Memory

-40.9MiB live, 128.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(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))))
cost-diff	0	(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))
cost-diff	0	(*.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)
cost-diff	0	#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))
cost-diff	0	(neg.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))))
cost-diff	0	(sqrt.f64 x)
cost-diff	1600	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))))
cost-diff	3648	(.f64 (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))
cost-diff	0	(*.f64 #s(literal 1/8 binary64) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
cost-diff	1024	(fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))
cost-diff	5760	(.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)
cost-diff	0	(/.f64 #s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(literal 1/2 binary64)) x))
cost-diff	0	(.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(literal 1/2 binary64)) x)) eps)
cost-diff	0	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(literal 1/2 binary64)) x)) eps))
cost-diff	0	(pow.f64 x #s(literal 3/2 binary64))
cost-diff	0	(sqrt.f64 (pow.f64 x #s(literal 3/2 binary64)))
cost-diff	0	(pow.f64 x #s(literal 1/4 binary64))
cost-diff	0	(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	584
0	97	526
1	176	522
2	569	510
3	4010	508
0	8198	496

Stop Event

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

Calls

Call 1

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

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

localize302.0ms (4.8%)

Memory

29.7MiB live, 300.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	5.9720878596579805	(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))
accuracy	8.349726972629286	(/.f64 eps (pow.f64 x #s(literal 5 binary64)))
accuracy	28.87086049881324	(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))))
accuracy	34.15257830028413	#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))
accuracy	0.12109375	(fma.f64 (/.f64 x eps) x #s(literal -1 binary64))
accuracy	0.37481270174522724	(*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)
accuracy	0.5286712890737681	(.f64 (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))
accuracy	25.661791740699925	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))))
accuracy	6.636162068266119	(.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps)
accuracy	7.6526056907960776	(/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 x x))
accuracy	12.659232960932009	(fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 x x)) x (*.f64 x #s(literal 1/2 binary64)))
accuracy	35.19298160951386	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/8 binary64) eps) (.f64 x x)) x (.f64 x #s(literal 1/2 binary64))) (*.f64 x x)) eps))
accuracy	0.078125	(/.f64 #s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(literal 1/2 binary64)) x)
accuracy	6.636162068266119	(.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(literal 1/2 binary64)) x)) eps)
accuracy	35.19298160951386	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(literal 1/2 binary64)) x)) eps))
accuracy	36.00825316618106	#s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(literal 1/2 binary64))
accuracy	0.12109375	(fma.f64 (/.f64 x eps) x #s(literal -1 binary64))
accuracy	0.37481270174522724	(*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)
accuracy	14.053143983766597	(sqrt.f64 (pow.f64 x #s(literal 3/2 binary64)))
accuracy	25.586819109192543	(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))

Samples

143.0ms	92×	1	valid
71.0ms	148×	0	valid
25.0ms	16×	2	valid

Compiler

Compiled 968 to 119 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 206.0ms

ival-div: 82.0ms (39.7% of total)

ival-pow: 44.0ms (21.3% of total)

ival-mult: 35.0ms (17% of total)

ival-sqrt: 14.0ms (6.8% of total)

ival-add: 12.0ms (5.8% of total)

adjust: 11.0ms (5.3% of total)

ival-sub: 4.0ms (1.9% of total)

ival-neg: 3.0ms (1.5% of total)

exact: 1.0ms (0.5% of total)

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

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

series145.0ms (2.3%)

Memory

-4.4MiB live, 152.4MiB allocated

Counts

25 → 140

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
52.0ms	x	@	0	((+ (* (pow x 1/4) (sqrt (pow x 3/2))) (neg (sqrt (- (* x x) eps)))) (pow x 1/4) (sqrt (pow x 3/2)) (pow x 3/2) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (* (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) eps) (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (- x (sqrt (- (* x x) eps))) (* 1/8 eps) (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) (+ (* (sqrt x) (sqrt x)) (neg (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))))) (sqrt x) (neg (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps))))) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (* (+ (* (/ x eps) x) -1) eps) (+ (* (/ x eps) x) -1) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ (* 1/8 eps) (* x x)) (/ eps (pow x 5)))
44.0ms	x	@	inf	((+ (* (pow x 1/4) (sqrt (pow x 3/2))) (neg (sqrt (- (* x x) eps)))) (pow x 1/4) (sqrt (pow x 3/2)) (pow x 3/2) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (* (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) eps) (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (- x (sqrt (- (* x x) eps))) (* 1/8 eps) (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) (+ (* (sqrt x) (sqrt x)) (neg (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))))) (sqrt x) (neg (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps))))) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (* (+ (* (/ x eps) x) -1) eps) (+ (* (/ x eps) x) -1) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ (* 1/8 eps) (* x x)) (/ eps (pow x 5)))
24.0ms	x	@	-inf	((+ (* (pow x 1/4) (sqrt (pow x 3/2))) (neg (sqrt (- (* x x) eps)))) (pow x 1/4) (sqrt (pow x 3/2)) (pow x 3/2) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (* (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) eps) (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (- x (sqrt (- (* x x) eps))) (* 1/8 eps) (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) (+ (* (sqrt x) (sqrt x)) (neg (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))))) (sqrt x) (neg (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps))))) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (* (+ (* (/ x eps) x) -1) eps) (+ (* (/ x eps) x) -1) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ (* 1/8 eps) (* x x)) (/ eps (pow x 5)))
13.0ms	eps	@	0	((+ (* (pow x 1/4) (sqrt (pow x 3/2))) (neg (sqrt (- (* x x) eps)))) (pow x 1/4) (sqrt (pow x 3/2)) (pow x 3/2) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (* (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) eps) (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (- x (sqrt (- (* x x) eps))) (* 1/8 eps) (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) (+ (* (sqrt x) (sqrt x)) (neg (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))))) (sqrt x) (neg (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps))))) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (* (+ (* (/ x eps) x) -1) eps) (+ (* (/ x eps) x) -1) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ (* 1/8 eps) (* x x)) (/ eps (pow x 5)))
5.0ms	eps	@	-inf	((+ (* (pow x 1/4) (sqrt (pow x 3/2))) (neg (sqrt (- (* x x) eps)))) (pow x 1/4) (sqrt (pow x 3/2)) (pow x 3/2) (- x (sqrt (- (* x x) eps))) (* (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) eps) (+ (* (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/ (+ (* (/ eps (* x x)) 1/8) 1/2) x) (* (/ (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (* x x)) eps) (+ (* (/ (* 1/8 eps) (* x x)) x) (* x 1/2)) (- x (sqrt (- (* x x) eps))) (* 1/8 eps) (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))) (+ (* (sqrt x) (sqrt x)) (neg (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps)))))) (sqrt x) (neg (* (sqrt (sqrt (- (* x x) eps))) (sqrt (sqrt (- (* x x) eps))))) (- x (sqrt (- (* x x) eps))) (* (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) eps) (+ (* (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) eps) (/ 1/2 x)) (+ (* (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (* (+ (* (/ x eps) x) -1) eps) (+ (* (/ x eps) x) -1) (+ (* (/ eps (* x x)) 1/8) 1/2) (/ (* 1/8 eps) (* x x)) (/ eps (pow x 5)))

simplify106.0ms (1.7%)

Memory

21.2MiB live, 57.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	474	2597
0	1548	2483

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

140 → 139

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)))
(pow (* 1 x) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(sqrt (pow x 3))
(* 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 x))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) x)
(* (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)))))))))
(sqrt x)
(- (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (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) (- (* (pow x 2) (- (* -1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))) (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(* 1/16 (/ (pow eps 2) (pow x 5)))
(/ (+ (* 1/16 (pow eps 2)) (* 1/8 (* eps (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 2)) (* (pow x 2) (+ (* 1/8 eps) (* 1/2 (pow x 2))))) (pow x 5))
(* 1/16 (/ eps (pow x 5)))
(/ (+ (* 1/16 eps) (* 1/8 (pow x 2))) (pow x 5))
(* -1 eps)
(+ (* -1 eps) (pow x 2))
-1
(- (/ (pow x 2) eps) 1)
(* 1/8 (/ eps (pow x 2)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 2))
(/ eps (pow x 5))
(* 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)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(* 1/2 x)
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* x (- (* 1/2 (/ eps (pow x 2))) 1))
(* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ 1/2 (+ (* 1/16 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ eps (pow x 2))))) x)
(/ 1/8 (pow x 3))
(/ (+ 1/8 (* 1/16 (/ eps (pow x 2)))) (pow x 3))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(/ (pow x 2) eps)
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
1/2
(+ 1/2 (* 1/8 (/ eps (pow x 2))))
(* -1 (* x (- (* (pow -1 1/4) (sqrt (sqrt -1))) 1)))
(* -1 (* x (- (+ (* 1/2 (/ eps (pow x 2))) (* (pow -1 1/4) (sqrt (sqrt -1)))) 1)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (* (pow -1 1/4) (sqrt (sqrt -1)))) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (* (pow -1 1/4) (sqrt (sqrt -1)))) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(* (pow (* -1 (pow x 3)) 1/4) (sqrt (sqrt -1)))
(* (sqrt (pow x 3)) (pow (sqrt -1) 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 (/ (+ (* -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 (/ eps (pow x 2))) 1/2)))
(* -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 (- (pow (sqrt -1) 2) 1)))
(* -1 (* x (- (+ (* 1/2 (/ eps (pow x 2))) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (+ (* 1/8 (/ (pow eps 2) (pow x 4))) (pow (sqrt -1) 2)) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (+ (* 1/16 (/ (pow eps 3) (pow x 6))) (pow (sqrt -1) 2)) (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 1 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 1 (+ (* -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))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (- (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4)))) 1/2) x))
(* -1 (/ (- (* -1/16 (/ eps (pow x 2))) 1/8) (pow x 3)))
(* 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)))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(* 1/8 eps)
(+ 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)))))
(- (* 1/2 (/ 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)))) x)
(+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))
(+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))
(/ (+ (* -1 eps) (pow x 2)) eps)
(* 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 (/ x eps)) (* 1/8 (/ 1 x))))
(* 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 (- (* -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 (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* -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))))))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* (pow eps 2) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 2) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* eps (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 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)))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* -1 (* eps (- (* -1/2 (/ x eps)) (* 1/8 (/ 1 x)))))
(* -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 (- (* -1/2 (* (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 (- (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* -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 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))
(* eps (+ (* 1/16 (/ 1 (pow x 5))) (* 1/8 (/ 1 (* eps (pow x 3))))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* eps (+ (* 1/8 (/ 1 (pow x 2))) (* 1/2 (/ 1 eps))))

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

rewrite413.0ms (6.6%)

Memory

-14.1MiB live, 191.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	416
0	97	361
1	380	346
2	3152	336
0	8611	325

Stop Event

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

Counts

25 → 552

Calls

Call 1

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

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

eval173.0ms (2.8%)

Memory: 21.7MiB live, 209.8MiB allocated
Compiler: Compiled 27 291 to 3 055 computations (88.8% saved)

prune36.0ms (0.6%)

Memory

-19.1MiB live, 102.1MiB allocated

Pruning

25 alts after pruning (17 fresh and 8 done)

	Pruned	Kept	Total
New	730	8	738
Fresh	3	9	12
Picked	4	1	5
Done	0	7	7
Total	737	25	762

Accuracy

99.9%

Counts

762 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	59.4%	(fma.f64 (pow.f64 (.f64 x x) #s(literal 1/4 binary64)) (sqrt.f64 x) (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))))
	59.9%	(fma.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))
	59.4%	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (sqrt.f64 (sqrt.f64 #s(approx (- ( x x) eps) #s(approx (* (+ (* (/ x eps) x) -1) eps) (fma.f64 x x (neg.f64 eps)))))))))
✓	59.9%	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))))
	39.5%	(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))) (.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (pow.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)) #s(literal 3/2 binary64)))) (.f64 (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))))
	52.2%	(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x)) (.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x) #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)))) (.f64 (+.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x)))
	59.7%	(/.f64 (-.f64 (.f64 x x) #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) (+.f64 (sqrt.f64 #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x))
	52.5%	(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- (* x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))) (/.f64 (pow.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps)) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 #s(approx (- ( x x) eps) (.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))) x #s(approx (- ( x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))))
✓	60.2%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	60.0%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (*.f64 (fma.f64 (/.f64 x eps) x #s(literal -1 binary64)) eps))))
	25.3%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (.f64 #s(approx (- (/ ( x x) eps) 1) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 x x))) eps))))
✓	54.2%	(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
	7.8%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) x)))
✓	3.5%	(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
	34.5%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (/.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (.f64 #s(literal 1/8 binary64) eps) x)) eps) x) x))
	34.3%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (.f64 #s(literal 1/8 binary64) eps) x)) eps) (*.f64 x x)))
	45.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x))
	34.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (*.f64 #s(literal 1/8 binary64) eps) x)) eps))))
	46.0%	#s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
	32.7%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (fma.f64 #s(approx (+ ( (/ eps (pow x 5)) 1/16) (/ 1/8 (pow x 3))) (/.f64 (fma.f64 #s(literal 1/16 binary64) eps (.f64 (.f64 x x) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 5 binary64)))) eps (/.f64 #s(literal 1/2 binary64) x)) eps))
	45.0%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (/.f64 (.f64 #s(literal 1/8 binary64) eps) x)) x) (/.f64 eps x)))
✓	46.5%	#s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64)))
✓	44.8%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 (fma.f64 (/.f64 eps (*.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) x)) eps))
	41.1%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.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)))) eps))
✓	46.3%	#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #s(literal 1/2 binary64)) x)) eps))

Compiler

Compiled 2 257 to 646 computations (71.4% saved)

regimes41.0ms (0.6%)

Memory

21.3MiB live, 96.8MiB allocated

Counts

40 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

14.0ms	x
13.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
12.0ms	eps

Results

Accuracy	Segments	Branch
86.9%	2	`x`
82.6%	2	`eps`
98.1%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes7.0ms (0.1%)

Memory

-25.4MiB live, 13.0MiB allocated

Counts

11 → 2

Calls

Call 1

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

Calls

1 calls:

6.0ms

(-.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)

regimes4.0ms (0.1%)

Memory

11.4MiB live, 11.4MiB allocated

Counts

10 → 2

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

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

Results

Accuracy	Segments	Branch
97.7%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory

9.0MiB live, 9.0MiB allocated

Counts

6 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

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

Results

Accuracy	Segments	Branch
94.4%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes2.0ms (0%)

Memory

7.7MiB live, 7.7MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps))
#s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(approx (+ (* (/ eps (* x x)) 1/8) 1/2) #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 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.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
94.3%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes15.0ms (0.2%)

Memory

-33.6MiB live, 12.2MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

12.0ms	x
2.0ms	eps
2.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

Accuracy	Segments	Branch
54.2%	1	`eps`
54.2%	1	`x`
54.2%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes4.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
3.5%	1	`x`
3.5%	1	`eps`
3.5%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 10 to 10 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.567518593011957e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.567518593011957e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.567518593011957e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.567518593011957e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-3.567518593011957e-154	0.0

Compiler

Compiled 11 to 11 computations (0% saved)

simplify59.0ms (0.9%)

Memory

-7.9MiB live, 107.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	245
1	71	245
2	88	245
3	121	245
4	184	245
5	268	245
6	386	245
7	495	245
8	613	245
9	733	245
10	804	245
11	842	245
12	844	245

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.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 -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

Outputs
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (/.f64 #s(approx (+ (* (/ (* eps eps) (* x x)) 1/8) (* 1/2 eps)) (.f64 (fma.f64 (/.f64 eps (.f64 x x)) #s(literal 1/8 binary64) #s(literal 1/2 binary64)) eps)) x)))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.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 -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (*.f64 (/.f64 eps x) #s(literal 1/2 binary64))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -3019169939857233/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 #s(approx (- ( x x) eps) (neg.f64 eps)))) #s(approx (- x (sqrt (- (* x x) eps))) (.f64 #s(approx (+ ( (/ eps (pow x 3)) 1/8) (/ 1/2 x)) (/.f64 #s(literal 1/2 binary64) x)) eps)))
(-.f64 x (sqrt.f64 #s(approx (- (* x x) eps) (neg.f64 eps))))
(-.f64 x #s(approx (sqrt (- (* x x) eps)) (neg.f64 x)))

soundness99.0ms (1.6%)

Memory

4.7MiB live, 121.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	1067
0	842	1017
0	298	1336
0	971	1274

Stop Event

1×	fuel
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Compiler

Compiled 312 to 121 computations (61.2% saved)

preprocess53.0ms (0.8%)

Memory: 23.0MiB live, 104.5MiB allocated
Compiler: Compiled 526 to 138 computations (73.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	54	245
1	71	245
2	88	245
3	121	245
4	184	245
5	268	245
6	386	245
7	495	245
8	613	245
9	733	245
10	804	245
11	842	245
12	844	245

Iter	Nodes	Cost
0	54	245
1	71	245
2	88	245
3	121	245
4	184	245
5	268	245
6	386	245
7	495	245
8	613	245
9	733	245
10	804	245
11	842	245
12	844	245

start0.0ms (0%)

analyze16.0ms (0.3%)

sample1.5s (23.3%)

explain110.0ms (1.7%)

preprocess397.0ms (6.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify307.0ms (4.9%)

localize67.0ms (1.1%)

series8.0ms (0.1%)

simplify43.0ms (0.7%)

rewrite199.0ms (3.2%)

eval86.0ms (1.4%)

prune49.0ms (0.8%)

simplify178.0ms (2.8%)

localize112.0ms (1.8%)

series80.0ms (1.3%)

simplify84.0ms (1.3%)

rewrite270.0ms (4.3%)

eval240.0ms (3.8%)

prune81.0ms (1.3%)

simplify107.0ms (1.7%)

localize225.0ms (3.6%)

series25.0ms (0.4%)

simplify61.0ms (1%)

rewrite204.0ms (3.2%)

eval236.0ms (3.7%)

prune40.0ms (0.6%)

simplify143.0ms (2.3%)

localize302.0ms (4.8%)

series145.0ms (2.3%)

simplify106.0ms (1.7%)

rewrite413.0ms (6.6%)

eval173.0ms (2.8%)

prune36.0ms (0.6%)

regimes41.0ms (0.6%)

regimes7.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes15.0ms (0.2%)

regimes4.0ms (0.1%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify59.0ms (0.9%)

soundness99.0ms (1.6%)

preprocess53.0ms (0.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	54	245
1	71	245
2	88	245
3	121	245
4	184	245
5	268	245
6	386	245
7	495	245
8	613	245
9	733	245
10	804	245
11	842	245
12	844	245