Metrics for ENA, Section 1.4, Exercise 4b, n=2

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25.7%	74.3%	0%	0%	0%	0
100%	25.7%	0%	74.3%	0%	0%	0%	1

Compiler

Compiled 25 to 18 computations (28% saved)

sample2.0s (29.5%)

Memory

-39.5MiB live, 1 746.6MiB allocated

Samples

1.1s	2 498×	1	valid
372.0ms	5 236×	0	valid
105.0ms	522×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 938.0ms

ival-sub: 349.0ms (37.2% of total)

ival-pow2: 291.0ms (31% of total)

ival-add: 98.0ms (10.5% of total)

ival-<=: 86.0ms (9.2% of total)

adjust: 70.0ms (7.5% of total)

ival-and: 22.0ms (2.3% of total)

exact: 19.0ms (2% of total)

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

Bogosity

explain137.0ms (2%)

Memory

-69.9MiB live, 88.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
74	2	(3.5234980936585824e-41 3.872562155652639e-283)	-	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	-	`eps`
0	0	-	-	`(pow.f64 x #s(literal 2 binary64))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(pow.f64 (+.f64 x eps) #s(literal 2 binary64))`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	cancellation	76	0

Confusion

	Predicted +	Predicted -
+	74	0
-	2	180

Precision

0.9736842105263158

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	74	0	0
-	2	0	180

Precision?

0.9736842105263158

Recall?

1.0

Freqs

test

number	freq
0	180
1	76

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

19.0ms	318×	0	valid
19.0ms	154×	1	valid
7.0ms	40×	2	valid

Compiler

Compiled 82 to 32 computations (61% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-pow2: 15.0ms (54.8% of total)

adjust: 4.0ms (14.6% of total)

ival-add: 4.0ms (14.6% of total)

ival-sub: 4.0ms (14.6% of total)

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

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

exact: 0.0ms (0% of total)

preprocess454.0ms (6.6%)

Memory

20.9MiB live, 178.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	45	47
2	149	45
3	542	35
4	1660	35
5	3800	35
6	5269	35
7	5989	35
8	6216	35
9	6322	35
10	6343	35
11	6343	35
12	6343	35
13	6343	35
14	6434	35
15	6762	35
16	7560	35
17	7996	35
0	7	9
0	11	9
1	16	9
2	36	9
3	96	9
4	276	7
5	861	7
6	2374	7
7	4277	7
8	5921	7
9	6913	7
10	7338	7
11	7606	7
12	7612	7
13	7612	7
0	8047	6

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.6%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify253.0ms (3.7%)

Memory

7.1MiB live, 117.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x eps)
cost-diff	0	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
cost-diff	6144	(pow.f64 x #s(literal 2 binary64))
cost-diff	6464	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	11	23
1	16	23
2	36	23
3	96	23
4	276	21
5	861	21
6	2374	21
7	4277	21
8	5921	21
9	6913	21
10	7338	21
11	7606	21
12	7612	21
13	7612	21
0	8047	20

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(+.f64 x eps)
x
eps
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(pow.f64 (+.f64 eps x) #s(literal 2 binary64))
(+.f64 x eps)
(+.f64 eps x)
x
eps
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)

localize60.0ms (0.9%)

Memory

-15.4MiB live, 31.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 2 binary64))
accuracy	0	(+.f64 x eps)
accuracy	0.01953125	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	16.251750391303812	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

14.0ms	159×	0	valid
9.0ms	77×	1	valid
3.0ms	20×	2	valid

Compiler

Compiled 48 to 16 computations (66.7% saved)

Precisions

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

ival-pow2: 7.0ms (51.2% of total)

adjust: 2.0ms (14.6% of total)

ival-add: 2.0ms (14.6% of total)

ival-sub: 2.0ms (14.6% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())

Outputs
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow x 2)) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ eps (* 2 x))) (pow x 2)) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* eps (+ eps (* 2 x))) (pow x 2)) (taylor 0 eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))) (taylor inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))) (taylor inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ 1 (/ x eps))) (taylor inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor -inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor -inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps)))) (taylor -inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps)))) (taylor -inf eps) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* eps (- (* -1 (/ x eps)) 1))) (taylor -inf eps) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 2 (* eps x)) (pow eps 2)) (taylor 0 x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ x (* 2 eps))) (pow eps 2)) (taylor 0 x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ x (* 2 eps))) (pow eps 2)) (taylor 0 x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt eps (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (+ eps x) (taylor 0 x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ eps x)))) (taylor inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2))))) (taylor inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2))))) (taylor inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ eps x))) (taylor inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) (patch (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 2 binary64)) (patch (pow.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* 2 (/ eps x)))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x)))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x)))) (taylor -inf x) (#s(alt (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (patch (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 x eps) (patch (+.f64 x eps) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))

simplify121.0ms (1.8%)

Memory

-14.9MiB live, 140.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	438
1	214	438
2	570	438
3	1803	438
4	4151	438
5	7221	438
0	8070	390

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

Inputs
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow x 2)
(+ (* 2 (* eps x)) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
x
(+ eps x)
(+ eps x)
(+ eps x)
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
eps
(+ eps x)
(+ eps x)
(+ eps x)
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))

Outputs
(* 2 (* eps x))
(.f64 (.f64 x eps) #s(literal 2 binary64))
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(pow x 2)
(*.f64 x x)
(+ (* 2 (* eps x)) (pow x 2))
(*.f64 (fma.f64 eps #s(literal 2 binary64) x) x)
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(fma.f64 (fma.f64 x #s(literal 2 binary64) eps) eps (*.f64 x x))
(+ (* eps (+ eps (* 2 x))) (pow x 2))
(fma.f64 (fma.f64 x #s(literal 2 binary64) eps) eps (*.f64 x x))
x
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(fma.f64 (fma.f64 x #s(literal 2 binary64) eps) eps (*.f64 x x))
(* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))
(fma.f64 (fma.f64 x #s(literal 2 binary64) eps) eps (*.f64 x x))
eps
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(* eps (+ 1 (/ x eps)))
(+.f64 x eps)
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(fma.f64 (fma.f64 x #s(literal 2 binary64) eps) eps (*.f64 x x))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))
(fma.f64 (fma.f64 x #s(literal 2 binary64) eps) eps (*.f64 x x))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 x eps)
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(fma.f64 (fma.f64 x #s(literal 2 binary64) eps) eps (*.f64 x x))
(+ (* x (+ x (* 2 eps))) (pow eps 2))
(fma.f64 (fma.f64 x #s(literal 2 binary64) eps) eps (*.f64 x x))
eps
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(+ eps x)
(+.f64 x eps)
(* 2 (* eps x))
(.f64 (.f64 x eps) #s(literal 2 binary64))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(*.f64 (fma.f64 eps #s(literal 2 binary64) x) x)
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(fma.f64 (fma.f64 x #s(literal 2 binary64) eps) eps (*.f64 x x))
(* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))
(fma.f64 (fma.f64 x #s(literal 2 binary64) eps) eps (*.f64 x x))
x
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* x (+ 1 (/ eps x)))
(+.f64 x eps)
(* 2 (* eps x))
(.f64 (.f64 x eps) #s(literal 2 binary64))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* 2 (/ eps x))))
(*.f64 (fma.f64 eps #s(literal 2 binary64) x) x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(fma.f64 (fma.f64 x #s(literal 2 binary64) eps) eps (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))
(fma.f64 (fma.f64 x #s(literal 2 binary64) eps) eps (*.f64 x x))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 x eps)

rewrite206.0ms (3%)

Memory

35.9MiB live, 193.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	52	20
2	371	20
3	5109	20
0	8219	20

Stop Event

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

Counts

4 → 371

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(+.f64 x eps)

Outputs
#<batchref>
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eval61.0ms (0.9%)

Memory: -26.5MiB live, 133.1MiB allocated
Compiler: Compiled 9 940 to 1 152 computations (88.4% saved)

prune11.0ms (0.2%)

Memory

-2.4MiB live, 36.7MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	444	5	449
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	445	5	450

Accuracy

100.0%

Counts

450 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.1%	(fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x)))
▶	27.3%	(fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
▶	60.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64)))
▶	72.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 102 to 64 computations (37.3% saved)

simplify389.0ms (5.7%)

Memory

48.5MiB live, 395.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (+.f64 eps x))
cost-diff	0	(*.f64 (sqrt.f64 (+.f64 eps x)) x)
cost-diff	128	(fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x))
cost-diff	2560	(fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)))
cost-diff	0	(*.f64 (neg.f64 x) x)
cost-diff	0	(+.f64 eps x)
cost-diff	128	(fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x))
cost-diff	768	(fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x)))
cost-diff	0	(*.f64 x eps)
cost-diff	0	(.f64 (.f64 x eps) #s(literal 2 binary64))
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64)))
cost-diff	0	(*.f64 eps eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
cost-diff	0	(fma.f64 x #s(literal 2 binary64) eps)
cost-diff	0	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	156
0	40	134
1	71	134
2	112	134
3	230	125
4	568	125
5	1897	125
6	3584	125
7	5150	125
8	5902	125
9	6262	125
10	6406	125
11	6572	125
12	6579	125
13	6579	125
14	6641	125
15	6667	125
16	6667	125
0	8262	123

Stop Event

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

Calls

Call 1

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

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

localize133.0ms (1.9%)

Memory

-10.4MiB live, 160.5MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.00390625	(fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x))
accuracy	0.078125	(*.f64 (sqrt.f64 (+.f64 eps x)) x)
accuracy	12.251236980914296	(fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)))
accuracy	0	(*.f64 (neg.f64 x) x)
accuracy	0	(neg.f64 x)
accuracy	0.00390625	(fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x))
accuracy	12.244098468050865	(fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x)))
accuracy	0	(*.f64 x eps)
accuracy	0.00390625	(.f64 (.f64 x eps) #s(literal 2 binary64))
accuracy	11.387550085561355	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64)))
accuracy	0	(*.f64 eps eps)
accuracy	8.394109172444002	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
accuracy	0	(fma.f64 x #s(literal 2 binary64) eps)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
accuracy	0.0078125	(*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)

Samples

83.0ms	137×	0	invalid
15.0ms	42×	1	valid
12.0ms	67×	0	valid
5.0ms	10×	2	valid

Compiler

Compiled 278 to 45 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-mult: 21.0ms (48% of total)

ival-add: 9.0ms (20.6% of total)

ival-pow2: 6.0ms (13.7% of total)

adjust: 3.0ms (6.9% of total)

ival-sub: 2.0ms (4.6% of total)

ival-sqrt: 2.0ms (4.6% of total)

ival-neg: 1.0ms (2.3% of total)

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

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

exact: 0.0ms (0% of total)

series31.0ms (0.4%)

Memory

-39.7MiB live, 41.9MiB allocated

Counts

16 → 348

Calls

Call 1

Inputs
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())
#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x eps) #s(literal 2 binary64)) (patch (.f64 (.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x eps) (patch (.f64 x eps) #<representation binary64>) () ())
#s(alt (fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) (patch (fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) #<representation binary64>) () ())
#s(alt (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)) (patch (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)) #<representation binary64>) () ())
#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (+.f64 eps x)) x) (patch (.f64 (sqrt.f64 (+.f64 eps x)) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 eps x)) (patch (sqrt.f64 (+.f64 eps x)) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (+ eps (* 2 x)) (taylor 0 eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (+ eps (* 2 x)) (taylor 0 eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (+ eps (* 2 x)) (taylor 0 eps) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (.f64 (.f64 x eps) #s(literal 2 binary64)) (patch (.f64 (.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (* 2 eps) (/ (pow eps 2) x))) (taylor inf x) (#s(alt (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 3)) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 eps x)) x) (patch (.f64 (sqrt.f64 (+.f64 eps x)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (sqrt (/ 1 x)) (* 1/2 (* eps (sqrt (/ 1 (pow x 3))))))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 eps x)) x) (patch (.f64 (sqrt.f64 (+.f64 eps x)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (pow eps 2) (sqrt (/ 1 (pow x 5))))) (* 1/2 (* eps (sqrt (/ 1 (pow x 3)))))))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 eps x)) x) (patch (.f64 (sqrt.f64 (+.f64 eps x)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (pow eps 2) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (pow eps 3) (sqrt (/ 1 (pow x 7))))) (* 1/2 (* eps (sqrt (/ 1 (pow x 3))))))))) (taylor inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 eps x)) x) (patch (.f64 (sqrt.f64 (+.f64 eps x)) x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 eps x)) (patch (sqrt.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (* eps (sqrt (/ 1 (pow x 3))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 eps x)) (patch (sqrt.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (pow eps 2) (sqrt (/ 1 (pow x 5))))) (* 1/2 (* eps (sqrt (/ 1 (pow x 3)))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 eps x)) (patch (sqrt.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (* (pow eps 2) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (pow eps 3) (sqrt (/ 1 (pow x 7))))) (* 1/2 (* eps (sqrt (/ 1 (pow x 3))))))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 eps x)) (patch (sqrt.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) (patch (.f64 (fma.f64 x #s(literal 2 binary64) eps) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 2))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 2))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 2))) (taylor -inf x) (#s(alt (fma.f64 x #s(literal 2 binary64) eps) (patch (fma.f64 x #s(literal 2 binary64) eps) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x eps) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 (.f64 x eps) #s(literal 2 binary64)) (patch (.f64 (.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 (.f64 x eps) #s(literal 2 binary64)) (patch (.f64 (.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 (.f64 x eps) #s(literal 2 binary64)) (patch (.f64 (.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 (.f64 x eps) #s(literal 2 binary64)) (patch (.f64 (.f64 x eps) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor -inf x) (#s(alt (.f64 x eps) (patch (.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor -inf x) (#s(alt (.f64 x eps) (patch (.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor -inf x) (#s(alt (.f64 x eps) (patch (.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* eps x) (taylor -inf x) (#s(alt (.f64 x eps) (patch (.f64 x eps) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) (patch (fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) (patch (fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) (patch (fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) (patch (fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)) (patch (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ eps x) 1)) (taylor -inf x) (#s(alt (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)) (patch (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) 1)) (taylor -inf x) (#s(alt (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)) (patch (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) 1)) (taylor -inf x) (#s(alt (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)) (patch (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ eps x)) 1))) (taylor -inf x) (#s(alt (+.f64 eps x) (patch (+.f64 eps x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (.f64 (neg.f64 x) x) (patch (.f64 (neg.f64 x) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) (patch (fma.f64 (.f64 (sqrt.f64 (+.f64 eps x)) x) (sqrt.f64 (+.f64 eps x)) (fma.f64 (+.f64 eps x) eps (.f64 (neg.f64 x) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 eps x)) x) (patch (.f64 (sqrt.f64 (+.f64 eps x)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/2 (* eps (sqrt (/ 1 (pow x 3))))))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 eps x)) x) (patch (.f64 (sqrt.f64 (+.f64 eps x)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* eps (sqrt (/ 1 (pow x 3))))) (* 1/8 (* (/ (pow eps 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow x 5)))))))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 eps x)) x) (patch (.f64 (sqrt.f64 (+.f64 eps x)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/2 (* eps (sqrt (/ 1 (pow x 3))))) (+ (* -1/16 (* (/ (pow eps 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow x 7))))) (* 1/8 (* (/ (pow eps 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow x 5))))))))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (+.f64 eps x)) x) (patch (.f64 (sqrt.f64 (+.f64 eps x)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 eps x)) (patch (sqrt.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 eps x)) (patch (sqrt.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (/ (pow eps 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/2 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 eps x)) (patch (sqrt.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (/ (pow eps 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow x 5))))) (+ (* 1/16 (* (/ (pow eps 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow x 7))))) (+ (* 1/2 (* eps (sqrt (/ 1 (pow x 3))))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 eps x)) (patch (sqrt.f64 (+.f64 eps x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

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

simplify202.0ms (2.9%)

Memory

21.2MiB live, 175.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	310	3301
1	980	3180
2	3149	3010
3	7132	2998
0	8131	2833

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 339

Calls

Call 1

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

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

rewrite191.0ms (2.8%)

Memory

12.5MiB live, 242.5MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	127
0	40	121
1	162	111
2	1326	111
0	8553	111

Stop Event

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

Counts

16 → 767

Calls

Call 1

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

Outputs
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eval233.0ms (3.4%)

Memory: 24.9MiB live, 326.2MiB allocated
Compiler: Compiled 49 726 to 2 616 computations (94.7% saved)

prune43.0ms (0.6%)

Memory

-10.5MiB live, 113.6MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1 596	3	1 599
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	1 599	5	1 604

Accuracy

100.0%

Counts

1 604 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
▶	60.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	72.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
▶	34.1%	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Compiler

Compiled 28 to 27 computations (3.6% saved)

simplify470.0ms (6.8%)

Memory

-12.6MiB live, 296.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 eps eps)
cost-diff	0	(*.f64 eps #s(literal 2 binary64))
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
cost-diff	320	(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
cost-diff	0	(*.f64 eps #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
cost-diff	0	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	80
0	26	80
1	48	71
2	84	71
3	212	65
4	544	65
5	1803	65
6	3303	65
7	4669	65
8	5348	65
9	5743	65
10	5934	65
11	6007	65
12	6026	65
13	6029	65
14	6031	65
15	6031	65
16	6031	65
17	7690	65
0	8509	60

Stop Event

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

Calls

Call 1

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

Outputs
#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (.f64 (.f64 x eps) #s(literal 2 binary64)))
(.f64 (.f64 eps #s(literal 2 binary64)) x)
(.f64 (.f64 x eps) #s(literal 2 binary64))
(*.f64 eps #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) eps)
eps
#s(literal 2 binary64)
x
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(*.f64 eps #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) eps)
eps
#s(literal 2 binary64)
x
(*.f64 eps eps)

localize76.0ms (1.1%)

Memory

1.3MiB live, 76.9MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 eps eps)
accuracy	0	(*.f64 eps #s(literal 2 binary64))
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
accuracy	0.00390625	(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
accuracy	0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
accuracy	0	(*.f64 eps #s(literal 2 binary64))
accuracy	25.61641099075781	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
accuracy	42.182882070242165	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Samples

21.0ms	159×	0	valid
20.0ms	77×	1	valid
8.0ms	20×	2	valid

Compiler

Compiled 112 to 32 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 12.0ms (33.1% of total)

ival-add: 8.0ms (22.1% of total)

ival-pow2: 7.0ms (19.3% of total)

adjust: 5.0ms (13.8% of total)

ival-sub: 2.0ms (5.5% of total)

ival-neg: 1.0ms (2.8% of total)

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

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

exact: 0.0ms (0% of total)

series19.0ms (0.3%)

Memory

-23.8MiB live, 14.3MiB allocated

Counts

7 → 144

Calls

Call 1

Inputs
#s(alt #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())
#s(alt (.f64 eps #s(literal 2 binary64)) (patch (.f64 eps #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())
#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) #<representation binary64>) () ())
#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())

Outputs
#s(alt (+ (* -1 (pow x 2)) (pow x 2)) (taylor 0 eps) (#s(alt #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2))) (taylor 0 eps) (#s(alt #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2))) (taylor 0 eps) (#s(alt #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2))) (taylor 0 eps) (#s(alt #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 2 binary64)) (patch (.f64 eps #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 2 binary64)) (patch (.f64 eps #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 2 binary64)) (patch (.f64 eps #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor 0 eps) (#s(alt (.f64 eps #s(literal 2 binary64)) (patch (.f64 eps #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* eps (+ eps (* 2 x))) (taylor 0 eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor 0 eps) (#s(alt (.f64 eps eps) (patch (.f64 eps eps) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))) (taylor inf eps) (#s(alt #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))) (taylor inf eps) (#s(alt #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) (patch #s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf eps) (#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf eps) (#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf eps) (#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor inf eps) (#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 2 binary64)) (patch (.f64 eps #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 2 binary64)) (patch (.f64 eps #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 2 binary64)) (patch (.f64 eps #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 eps) (taylor inf eps) (#s(alt (.f64 eps #s(literal 2 binary64)) (patch (.f64 eps #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (pow eps 2) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* (pow eps 2) (+ 1 (* 2 (/ x eps)))) (taylor inf eps) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (.f64 (.f64 eps #s(literal 2 binary64)) x) (patch (.f64 (.f64 eps #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) (patch (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)) #<representation binary64>) () ())) ())
#s(alt (* 2 (* eps x)) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x))))) (taylor -inf x) (#s(alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) (patch #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	-inf	((+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (* eps 2) x) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps))
3.0ms	eps	@	inf	((+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (* eps 2) x) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps))
1.0ms	eps	@	-inf	((+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (* eps 2) x) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps))
1.0ms	eps	@	0	((+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (* eps 2) x) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps))
1.0ms	x	@	inf	((+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* (* eps 2) x) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps))

simplify175.0ms (2.5%)

Memory

18.2MiB live, 135.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	790
1	142	786
2	423	786
3	1294	786
4	3440	786
5	7579	786
0	8355	715

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
(+ (* -1 (pow x 2)) (pow x 2))
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))

Outputs
(+ (* -1 (pow x 2)) (pow x 2))
#s(literal 0 binary64)
(+ (* -1 (pow x 2)) (+ (* 2 (* eps x)) (pow x 2)))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* -1 (pow x 2)) (+ (* eps (+ eps (* 2 x))) (pow x 2)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* eps (+ eps (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2))))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (+ (* -1 (pow x 2)) (pow x 2)) eps))) eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* 2 (* eps x))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)

rewrite234.0ms (3.4%)

Memory

13.1MiB live, 198.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	70
0	26	70
1	128	61
2	1119	61
0	8234	59

Stop Event

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

Counts

7 → 70

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval45.0ms (0.7%)

Memory: -22.5MiB live, 62.7MiB allocated
Compiler: Compiled 2 650 to 276 computations (89.6% saved)

prune11.0ms (0.2%)

Memory

33.2MiB live, 33.2MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	228	5	233

Accuracy

100.0%

Counts

233 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
✓	60.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	72.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	34.1%	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Compiler

Compiled 105 to 57 computations (45.7% saved)

regimes13.0ms (0.2%)

Memory

-8.5MiB live, 27.3MiB allocated

Counts

9 → 1

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))

Calls

3 calls:

6.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
3.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes9.0ms (0.1%)

Memory

-18.1MiB live, 20.1MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))

Calls

3 calls:

4.0ms	x
2.0ms	eps
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes7.0ms (0.1%)

Memory

19.9MiB live, 19.9MiB allocated

Counts

4 → 2

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Calls

3 calls:

2.0ms	eps
2.0ms	x
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
93.4%	3	`x`
85.0%	3	`eps`
97.6%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes5.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Calls

3 calls:

2.0ms	x
2.0ms	eps
1.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
72.5%	1	`eps`
72.5%	1	`x`
72.5%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes13.0ms (0.2%)

Memory

-47.4MiB live, 8.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Outputs
#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Calls

3 calls:

3.0ms	x
1.0ms	eps
1.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
34.1%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
34.1%	1	`x`
34.1%	1	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	3.8e-322

Compiler

Compiled 12 to 12 computations (0% saved)

simplify23.0ms (0.3%)

Memory

34.6MiB live, 34.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	105
1	38	105
2	42	105
3	44	105
4	45	105

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 #s(literal 2 binary64) eps) x (.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 x #s(literal 2 binary64) eps) eps))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps))) #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

soundness1.1s (15.7%)

Memory

5.8MiB live, 594.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	127
0	40	121
1	162	111
2	1326	111
0	8553	111
0	7	20
0	11	20
1	52	20
2	371	20
3	5109	20
0	8219	20
0	310	3301
1	980	3180
2	3149	3010
3	7132	2998
0	8131	2833
0	69	438
1	214	438
2	570	438
3	1803	438
4	4151	438
5	7221	438
0	8070	390

Stop Event

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

Compiler

Compiled 78 to 58 computations (25.6% saved)

preprocess137.0ms (2%)

Memory: -25.1MiB live, 62.1MiB allocated
Compiler: Compiled 106 to 56 computations (47.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample2.0s (29.5%)

explain137.0ms (2%)

preprocess454.0ms (6.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify253.0ms (3.7%)

localize60.0ms (0.9%)

series6.0ms (0.1%)

simplify121.0ms (1.8%)

rewrite206.0ms (3%)

eval61.0ms (0.9%)

prune11.0ms (0.2%)

simplify389.0ms (5.7%)

localize133.0ms (1.9%)

series31.0ms (0.4%)

simplify202.0ms (2.9%)

rewrite191.0ms (2.8%)

eval233.0ms (3.4%)

prune43.0ms (0.6%)

simplify470.0ms (6.8%)

localize76.0ms (1.1%)

series19.0ms (0.3%)

simplify175.0ms (2.5%)

rewrite234.0ms (3.4%)

eval45.0ms (0.7%)

prune11.0ms (0.2%)

regimes13.0ms (0.2%)

regimes9.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes13.0ms (0.2%)

bsearch0.0ms (0%)

simplify23.0ms (0.3%)

soundness1.1s (15.7%)

preprocess137.0ms (2%)

end0.0ms (0%)

Profiling