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

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

sample1.3s (17.3%)

Memory

57.2MiB live, 2 000.5MiB allocated

Samples

425.0ms	5 273×	0	valid
350.0ms	2 443×	1	valid
99.0ms	540×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 620.0ms

ival-pow2: 249.0ms (40.2% of total)

adjust: 93.0ms (15% of total)

ival-add: 86.0ms (13.9% of total)

ival-<=: 84.0ms (13.5% of total)

ival-sub: 64.0ms (10.3% of total)

ival-and: 22.0ms (3.5% of total)

exact: 18.0ms (2.9% of total)

ival-assert: 4.0ms (0.6% of total)

Bogosity

preprocess735.0ms (10.2%)

Memory

-69.1MiB live, 618.7MiB allocated

Algorithm

1×	egg-herbie

Rules

18 770×	`lower-fma.f64`
18 770×	`lower-fma.f32`
2 836×	`lower-*.f64`
2 836×	`lower-*.f32`
2 498×	`lower-+.f32`

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 eps (+.f64 eps (+.f64 x x)))

explain373.0ms (5.2%)

Memory

5.0MiB live, 234.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
72	1	(-7.413941752726102e-158 -1.557359335859877e-160)	-	`(-.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	73	0

Confusion

	Predicted +	Predicted -
+	72	0
-	1	183

Precision

0.9863013698630136

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	72	0	0
-	1	0	183

Precision?

0.9863013698630136

Recall?

1.0

Freqs

test

number	freq
0	183
1	73

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms	140×	1	valid
21.0ms	48×	2	valid
19.0ms	324×	0	valid

Compiler

Compiled 72 to 32 computations (55.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

adjust: 16.0ms (40.7% of total)

ival-pow2: 14.0ms (35.6% of total)

ival-add: 4.0ms (10.2% of total)

ival-sub: 3.0ms (7.6% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.8%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify635.0ms (8.8%)

Memory

11.2MiB live, 585.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	512	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
✓	cost-diff	5952	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
✓	cost-diff	6144	(pow.f64 x #s(literal 2 binary64))

Rules

18 770×	`lower-fma.f64`
18 770×	`lower-fma.f32`
2 836×	`lower-*.f64`
2 836×	`lower-*.f32`
2 498×	`lower-+.f32`

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

localize52.0ms (0.7%)

Memory

-11.2MiB live, 65.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
✓	accuracy	76.8%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

23.0ms	162×	0	valid
17.0ms	70×	1	valid
4.0ms	24×	2	valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-pow2: 20.0ms (56.9% of total)

ival-sub: 11.0ms (31.3% of total)

adjust: 2.0ms (5.7% of total)

ival-add: 2.0ms (5.7% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Counts

4 → 84

Calls

Call 1

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

Outputs
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* x (+ x (* 2 eps))) (pow eps 2))>
#<alt (+ (* x (+ x (* 2 eps))) (pow eps 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ eps x))))>
#<alt (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ eps x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))>
#<alt (pow x 2)>
#<alt (+ (* 2 (* eps x)) (pow x 2))>
#<alt (+ (* eps (+ eps (* 2 x))) (pow x 2))>
#<alt (+ (* eps (+ eps (* 2 x))) (pow x 2))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>

Calls

21 calls:

Time	Variable		Point	Expression
0.0ms	eps	@	inf	(pow (+ x eps) 2)
0.0ms	x	@	inf	(pow x 2)
0.0ms	x	@	0	(pow (+ x eps) 2)
0.0ms	x	@	0	(pow x 2)
0.0ms	eps	@	0	(- (pow (+ x eps) 2) (pow x 2))

simplify405.0ms (5.6%)

Memory

9.1MiB live, 365.2MiB allocated

Algorithm

1×	egg-herbie

Rules

9 222×	`lower-fma.f64`
9 222×	`lower-fma.f32`
3 242×	`lower-*.f64`
3 242×	`lower-*.f32`
1 646×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	492
1	214	450
2	574	450
3	1825	438
4	4173	438
5	7244	438
0	8097	390

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

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

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

rewrite402.0ms (5.6%)

Memory

-26.5MiB live, 497.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 048×	`lower-fma.f64`
5 048×	`lower-fma.f32`
4 066×	`lower-*.f64`
4 066×	`lower-*.f32`
2 090×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	52	20
2	371	20
3	5107	20
0	8219	20

Stop Event

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

Counts

4 → 371

Calls

Call 1

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

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

eval106.0ms (1.5%)

Memory: 23.8MiB live, 98.1MiB allocated
Compiler: Compiled 14 368 to 1 131 computations (92.1% saved)

prune55.0ms (0.8%)

Memory

-0.3MiB live, 117.8MiB 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
▶	64.5%	(fma.f64 (+.f64 x eps) x (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x))))
▶	76.8%	(*.f64 (+.f64 x (-.f64 eps x)) (+.f64 x (+.f64 x eps)))
▶	68.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
▶	74.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 104 to 54 computations (48.1% saved)

simplify483.0ms (6.7%)

Memory

14.6MiB live, 691.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(neg.f64 (*.f64 x x))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	128	(fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x)))
✓	cost-diff	768	(fma.f64 (+.f64 x eps) x (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x))))
✓	cost-diff	0	(+.f64 x (+.f64 x eps))
✓	cost-diff	0	(-.f64 eps x)
✓	cost-diff	0	(*.f64 (+.f64 x (-.f64 eps x)) (+.f64 x (+.f64 x eps)))
✓	cost-diff	384	(+.f64 x (-.f64 eps x))
✓	cost-diff	0	(.f64 x (.f64 #s(literal 2 binary64) eps))
✓	cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
✓	cost-diff	128	(*.f64 #s(literal 2 binary64) eps)
✓	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 eps (fma.f64 x #s(literal 2 binary64) eps))
✓	cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))

Rules

28 224×	`lower-fma.f32`
28 218×	`lower-fma.f64`
2 858×	`lower-+.f32`
2 852×	`lower-+.f64`
2 770×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	136
0	41	127
1	86	127
2	179	109
3	509	109
4	1587	109
5	4436	109
6	6754	109
0	8066	108

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

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

localize131.0ms (1.8%)

Memory

-6.7MiB live, 206.7MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(neg.f64 (*.f64 x x))
✓	accuracy	100.0%	(fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x)))
✓	accuracy	64.6%	(fma.f64 (+.f64 x eps) x (fma.f64 eps (+.f64 x eps) (neg.f64 (*.f64 x x))))
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(*.f64 (+.f64 x (-.f64 eps x)) (+.f64 x (+.f64 x eps)))
✓	accuracy	100.0%	(+.f64 x (+.f64 x eps))
✓	accuracy	53.5%	(+.f64 x (-.f64 eps x))
✓	accuracy	100.0%	(.f64 x (.f64 #s(literal 2 binary64) eps))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) eps)
✓	accuracy	68.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 x (.f64 #s(literal 2 binary64) eps)))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	74.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	accuracy	100.0%	(fma.f64 x #s(literal 2 binary64) eps)
✓	accuracy	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
✓	accuracy	100.0%	(*.f64 eps (fma.f64 x #s(literal 2 binary64) eps))

Samples

56.0ms	130×	0	valid
34.0ms	100×	1	valid
14.0ms	26×	2	valid

Compiler

Compiled 126 to 25 computations (80.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-add: 41.0ms (49% of total)

ival-mult: 18.0ms (21.5% of total)

ival-pow2: 8.0ms (9.6% of total)

adjust: 7.0ms (8.4% of total)

ival-sub: 7.0ms (8.4% of total)

ival-neg: 2.0ms (2.4% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.2%)

Memory

-13.5MiB live, 24.8MiB allocated

Counts

17 → 360

Calls

Call 1

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

Outputs
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* -1 x)>
#<alt (- eps x)>
#<alt (- eps x)>
#<alt (- eps x)>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ x eps))))>
#<alt (* eps (+ 1 (* -1 (/ x eps))))>
#<alt (* eps (+ 1 (* -1 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ x eps) 1)))>
#<alt (* -1 (* eps (- (/ x eps) 1)))>
#<alt (* -1 (* eps (- (/ x eps) 1)))>
#<alt eps>
#<alt (+ eps (* -1 x))>
#<alt (+ eps (* -1 x))>
#<alt (+ eps (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ eps x) 1))>
#<alt (* x (- (/ eps x) 1))>
#<alt (* x (- (/ eps x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1 (/ eps x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ eps x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ eps x)))))>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* -1 (pow x 2))>
#<alt (- (* eps x) (pow x 2))>
#<alt (- (* eps (+ eps x)) (pow x 2))>
#<alt (- (* eps (+ eps x)) (pow x 2))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (pow x 2) (pow eps 2))) (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 x) (/ (pow x 2) eps)) eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 x) (/ (pow x 2) eps)) eps))))>
#<alt (pow eps 2)>
#<alt (+ (* eps x) (pow eps 2))>
#<alt (+ (* x (+ eps (* -1 x))) (pow eps 2))>
#<alt (+ (* x (+ eps (* -1 x))) (pow eps 2))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ eps x) 1))>
#<alt (* (pow x 2) (- (+ (/ eps x) (/ (pow eps 2) (pow x 2))) 1))>
#<alt (* (pow x 2) (- (+ (/ eps x) (/ (pow eps 2) (pow x 2))) 1))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (/ eps x) 1))>
#<alt (* (pow x 2) (- (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) 1))>
#<alt (* (pow x 2) (- (* -1 (/ (+ (* -1 eps) (* -1 (/ (pow eps 2) x))) x)) 1))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

90 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	0	(* eps (+ (* x 2) eps))
1.0ms	eps	@	0	(* x (* 2 eps))
0.0ms	x	@	inf	(* x (* 2 eps))
0.0ms	x	@	-inf	(+ (* (+ x eps) x) (+ (* eps (+ x eps)) (neg (* x x))))
0.0ms	x	@	0	(* x (* 2 eps))

simplify241.0ms (3.3%)

Memory

-4.3MiB live, 387.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8 602×	`lower-fma.f64`
8 602×	`lower-fma.f32`
2 840×	`lower-*.f64`
2 840×	`lower-*.f32`
1 554×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	1920
1	287	1698
2	741	1698
3	2095	1686
4	4812	1686
5	7064	1686
0	8040	1530

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 321

Calls

Call 1

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

Outputs
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* eps (+ eps (* 2 x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(+ (* 2 (* eps x)) (pow eps 2))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* 2 (* eps x))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
eps
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (/ eps x)))
(fma.f64 #s(literal 2 binary64) x eps)
(* x (+ 2 (/ eps x)))
(fma.f64 #s(literal 2 binary64) x eps)
(* x (+ 2 (/ eps x)))
(fma.f64 #s(literal 2 binary64) x eps)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(fma.f64 #s(literal 2 binary64) x eps)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(fma.f64 #s(literal 2 binary64) x eps)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(fma.f64 #s(literal 2 binary64) x eps)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
eps
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 #s(literal 2 binary64) x eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 #s(literal 2 binary64) x eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 #s(literal 2 binary64) x eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 #s(literal 2 binary64) x eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 #s(literal 2 binary64) x eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 #s(literal 2 binary64) x eps)
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rewrite501.0ms (6.9%)

Memory

3.9MiB live, 758.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 574×	`lower-fma.f32`
6 568×	`lower-fma.f64`
4 572×	`lower-*.f32`
4 560×	`lower-*.f64`
4 440×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	122
0	41	114
1	180	114
2	1569	114
0	8785	114

Stop Event

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

Counts

17 → 1 293

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (+.f64 x (+.f64 x eps))))
(+.f64 (.f64 eps eps) (.f64 eps (+.f64 x x)))
(+.f64 (.f64 eps (+.f64 x x)) (.f64 eps eps))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) (-.f64 (.f64 eps (+.f64 x x)) (.f64 eps eps))) (/.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 (.f64 eps (+.f64 x x)) (*.f64 eps eps))))
(fma.f64 x (.f64 eps #s(literal 2 binary64)) (.f64 eps eps))
(fma.f64 eps eps (*.f64 eps (+.f64 x x)))
(fma.f64 eps (+.f64 x x) (*.f64 eps eps))
(fma.f64 #s(literal 2 binary64) (.f64 x eps) (.f64 eps eps))
(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
(fma.f64 (+.f64 x x) eps (*.f64 eps eps))
(fma.f64 (.f64 x eps) #s(literal 2 binary64) (.f64 eps eps))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (*.f64 eps (+.f64 x x)))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) (fma.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 eps (+.f64 x x)) (*.f64 eps eps)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 eps eps))) (-.f64 (.f64 eps (+.f64 x x)) (*.f64 eps eps)))
(/.f64 (.f64 eps (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (fma.f64 eps (-.f64 eps (+.f64 x x)) (.f64 (*.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 eps (.f64 (+.f64 x (+.f64 x eps)) (-.f64 (+.f64 x x) eps))) (-.f64 (+.f64 x x) eps))
(/.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) eps) (fma.f64 eps (-.f64 eps (+.f64 x x)) (.f64 (*.f64 x x) #s(literal 4 binary64))))
(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 (+.f64 x x) eps)) eps) (-.f64 (+.f64 x x) eps))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) (neg.f64 (fma.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 eps (+.f64 x x)) (*.f64 eps eps))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) (.f64 (.f64 eps eps) (.f64 eps eps)))) (neg.f64 (-.f64 (.f64 eps (+.f64 x x)) (*.f64 eps eps))))
(/.f64 (neg.f64 (.f64 eps (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (neg.f64 (fma.f64 eps (-.f64 eps (+.f64 x x)) (.f64 (*.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 eps (.f64 (+.f64 x (+.f64 x eps)) (-.f64 (+.f64 x x) eps)))) (neg.f64 (-.f64 (+.f64 x x) eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) eps)) (neg.f64 (fma.f64 eps (-.f64 eps (+.f64 x x)) (.f64 (*.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 (+.f64 x x) eps)) eps)) (neg.f64 (-.f64 (+.f64 x x) eps)))
(/.f64 (fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps)))) (fma.f64 (.f64 eps eps) (.f64 eps eps) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps)) (.f64 (.f64 eps eps) (*.f64 eps (+.f64 x x))))))
(*.f64 eps (+.f64 x (+.f64 x eps)))
(*.f64 (+.f64 x (+.f64 x eps)) eps)
(+.f64 x (+.f64 x eps))
(+.f64 eps (+.f64 x x))
(+.f64 (+.f64 x eps) x)
(+.f64 (+.f64 x x) eps)
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 (+.f64 x x) eps)) (/.f64 (*.f64 eps eps) (-.f64 (+.f64 x x) eps)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (+.f64 x eps))) (/.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (-.f64 x (+.f64 x eps))))
(-.f64 (/.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 eps (-.f64 x x))) (/.f64 (.f64 x x) (+.f64 eps (-.f64 x x))))
(-.f64 (/.f64 (.f64 eps (+.f64 x eps)) (+.f64 eps (-.f64 x x))) (/.f64 (-.f64 (.f64 x x) (*.f64 x (+.f64 x eps))) (+.f64 eps (-.f64 x x))))
(-.f64 (/.f64 (/.f64 (.f64 (+.f64 x eps) (.f64 x (.f64 x (+.f64 x eps)))) (+.f64 (-.f64 (.f64 x (+.f64 x eps)) (.f64 eps (+.f64 x eps))) (.f64 x x))) (+.f64 eps (-.f64 x x))) (/.f64 (/.f64 (.f64 (-.f64 (.f64 eps (+.f64 x eps)) (.f64 x x)) (-.f64 (.f64 eps (+.f64 x eps)) (.f64 x x))) (+.f64 (-.f64 (.f64 x (+.f64 x eps)) (.f64 eps (+.f64 x eps))) (.f64 x x))) (+.f64 eps (-.f64 x x))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 (+.f64 x eps) (+.f64 x eps)))) (fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 (.f64 x x) (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x x))))) (+.f64 eps (-.f64 x x))) (/.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 (.f64 x x) (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x x))))) (+.f64 eps (-.f64 x x))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (.f64 (+.f64 x eps) (+.f64 x eps))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x x))) (+.f64 eps (-.f64 x x))) (/.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (.f64 x x))) (+.f64 eps (-.f64 x x))))
(-.f64 (/.f64 (fma.f64 (+.f64 x eps) (+.f64 x eps) #s(literal 0 binary64)) (+.f64 eps (-.f64 x x))) (/.f64 (*.f64 x x) (+.f64 eps (-.f64 x x))))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps (+.f64 x x))) (/.f64 (.f64 (*.f64 x x) #s(literal 4 binary64)) (-.f64 eps (+.f64 x x))))
(fma.f64 x #s(literal 2 binary64) eps)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) x)
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x)
(fma.f64 (/.f64 (+.f64 x eps) (*.f64 (+.f64 x eps) (-.f64 eps x))) (/.f64 (-.f64 eps x) (/.f64 #s(literal 1 binary64) (+.f64 x eps))) x)
(fma.f64 (sqrt.f64 (+.f64 x eps)) (sqrt.f64 (+.f64 x eps)) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 x eps))
(fma.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (+.f64 x eps))
(fma.f64 (pow.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 eps (-.f64 eps x)))) #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 (sqrt.f64 (+.f64 x eps)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (+.f64 x eps)) #s(literal 1 binary64)) x)
(fma.f64 (/.f64 (+.f64 x eps) (.f64 (fma.f64 x (+.f64 x eps) (.f64 eps eps)) (-.f64 eps x))) (/.f64 (-.f64 eps x) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x eps) (*.f64 eps eps)))) x)
(fma.f64 (/.f64 (+.f64 x eps) (/.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))))) (/.f64 (-.f64 eps x) (fma.f64 x x (*.f64 eps (-.f64 eps x)))) x)
(fma.f64 (/.f64 (+.f64 x eps) (/.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (.f64 (+.f64 x eps) (-.f64 x eps)))) (/.f64 (-.f64 eps x) (-.f64 x eps)) x)
(/.f64 (*.f64 (+.f64 eps (-.f64 x x)) (+.f64 x (+.f64 x eps))) (+.f64 eps (-.f64 x x)))
(/.f64 (fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps) (.f64 x (.f64 x x))) (fma.f64 (+.f64 eps (-.f64 x x)) (+.f64 x eps) (.f64 x x)))
(/.f64 (fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps) (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (*.f64 x (+.f64 x eps)))))
(/.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (fma.f64 eps (-.f64 eps (+.f64 x x)) (.f64 (.f64 x x) #s(literal 4 binary64))))
(/.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (fma.f64 eps eps (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (*.f64 eps (+.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 eps (-.f64 eps (+.f64 x x)) (.f64 (.f64 x x) #s(literal 4 binary64))) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (+.f64 x x) eps) (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 (+.f64 x x) eps)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (+.f64 eps (-.f64 x x)) (+.f64 x eps) (.f64 x x)) (fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps) (.f64 x (.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 x (+.f64 x eps)) (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))))))
(/.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))) (-.f64 x (+.f64 x eps)))
(/.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 (+.f64 x x) eps)) (-.f64 (+.f64 x x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps (-.f64 eps (+.f64 x x)) (.f64 (.f64 x x) #s(literal 4 binary64))) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 x x) eps) (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 (+.f64 x x) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 eps (-.f64 x x)) (+.f64 x eps) (.f64 x x)) (fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps) (.f64 x (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (+.f64 x eps)) (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps)))))
(/.f64 (neg.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps (+.f64 x x)) (.f64 (.f64 x x) #s(literal 4 binary64)))))
(/.f64 (neg.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (neg.f64 (fma.f64 eps eps (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (*.f64 eps (+.f64 x x))))))
(/.f64 (neg.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 (+.f64 x x) eps))) (neg.f64 (-.f64 (+.f64 x x) eps)))
(/.f64 (neg.f64 (fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps) (.f64 x (.f64 x x)))) (neg.f64 (fma.f64 (+.f64 eps (-.f64 x x)) (+.f64 x eps) (.f64 x x))))
(/.f64 (neg.f64 (fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps) (.f64 x (.f64 x x)))) (neg.f64 (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (*.f64 x (+.f64 x eps))))))
(/.f64 (neg.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps)))) (neg.f64 (-.f64 x (+.f64 x eps))))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal 4 binary64))) (-.f64 eps (+.f64 x x)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (-.f64 (+.f64 x x) eps)) (.f64 (-.f64 (+.f64 x x) eps) (.f64 eps eps))) (.f64 (-.f64 (+.f64 x x) eps) (-.f64 (+.f64 x x) eps)))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x (+.f64 x eps))) (.f64 (-.f64 x (+.f64 x eps)) (.f64 (+.f64 x eps) (+.f64 x eps)))) (*.f64 (-.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))))
(/.f64 (neg.f64 (*.f64 (+.f64 eps (-.f64 x x)) (+.f64 x (+.f64 x eps)))) (neg.f64 (+.f64 eps (-.f64 x x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (neg.f64 (neg.f64 (fma.f64 eps (-.f64 eps (+.f64 x x)) (.f64 (.f64 x x) #s(literal 4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 (+.f64 x x) eps)))) (neg.f64 (neg.f64 (-.f64 (+.f64 x x) eps))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps) (.f64 x (.f64 x x))))) (neg.f64 (neg.f64 (fma.f64 (+.f64 eps (-.f64 x x)) (+.f64 x eps) (.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))))) (neg.f64 (neg.f64 (-.f64 x (+.f64 x eps)))))
(/.f64 (neg.f64 (-.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal 4 binary64)))) (neg.f64 (-.f64 eps (+.f64 x x))))
(pow.f64 (/.f64 (fma.f64 eps (-.f64 eps (+.f64 x x)) (.f64 (.f64 x x) #s(literal 4 binary64))) (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (+.f64 x x) eps) (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 (+.f64 x x) eps))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (+.f64 eps (-.f64 x x)) (+.f64 x eps) (.f64 x x)) (fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps) (.f64 x (.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x (+.f64 x eps)) (*.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps)))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (+.f64 x eps) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 eps (-.f64 x x)) (+.f64 x eps) (*.f64 x x))))
(.f64 (fma.f64 eps (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps (+.f64 x x)) (.f64 (*.f64 x x) #s(literal 4 binary64)))))
(.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 x (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (-.f64 x (+.f64 x eps))))
(.f64 (.f64 (+.f64 x (+.f64 x eps)) (-.f64 (+.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 x x) eps)))
(.f64 (/.f64 (+.f64 eps (-.f64 x x)) (fma.f64 x (.f64 x x) (.f64 (-.f64 eps x) (.f64 (-.f64 eps x) (-.f64 eps x))))) (/.f64 (+.f64 x (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 eps x) (-.f64 (-.f64 eps x) x) (*.f64 x x)))))
(.f64 (/.f64 (+.f64 eps (-.f64 x x)) (.f64 (+.f64 eps (-.f64 x x)) (+.f64 (-.f64 x eps) x))) (/.f64 (+.f64 x (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 x eps) x))))
(.f64 (/.f64 (+.f64 x (+.f64 x eps)) (fma.f64 x (.f64 x x) (.f64 (-.f64 eps x) (.f64 (-.f64 eps x) (-.f64 eps x))))) (/.f64 (+.f64 eps (-.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 eps x) (-.f64 (-.f64 eps x) x) (*.f64 x x)))))
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eval276.0ms (3.8%)

Memory: 25.8MiB live, 407.1MiB allocated
Compiler: Compiled 84 639 to 2 848 computations (96.6% saved)

prune141.0ms (1.9%)

Memory

5.8MiB live, 220.9MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1 725	3	1 728
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	1 728	5	1 733

Accuracy

100.0%

Counts

1 733 → 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 x x) eps (*.f64 eps eps)))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x (+.f64 x eps)) eps))
▶	68.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
✓	74.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 44 to 22 computations (50% saved)

simplify365.0ms (5%)

Memory

1.1MiB live, 462.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 x x) eps (*.f64 eps eps)))
✓	cost-diff	192	(fma.f64 (+.f64 x x) eps (*.f64 eps eps))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(+.f64 x (+.f64 x eps))
✓	cost-diff	0	(*.f64 (+.f64 x (+.f64 x eps)) eps)
✓	cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x (+.f64 x eps)) eps))
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(*.f64 (+.f64 x x) eps)
✓	cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))

Rules

18 196×	`lower-fma.f32`
18 194×	`lower-fma.f64`
2 596×	`lower-*.f32`
2 590×	`lower-*.f64`
2 534×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	93
0	24	95
1	36	95
2	69	95
3	133	95
4	270	85
5	837	85
6	2341	85
7	4322	85
8	5987	85
9	6993	85
10	7423	85
11	7692	85
12	7698	85
13	7698	85
0	8014	77

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

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

localize56.0ms (0.8%)

Memory

12.3MiB live, 90.3MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 (+.f64 x x) eps (*.f64 eps eps))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 x x) eps (*.f64 eps eps)))
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x (+.f64 x eps)) eps))
✓	accuracy	100.0%	(*.f64 (+.f64 x (+.f64 x eps)) eps)
✓	accuracy	100.0%	(+.f64 x (+.f64 x eps))
✓	accuracy	100.0%	(+.f64 x x)
✓	accuracy	100.0%	(*.f64 (+.f64 x x) eps)
✓	accuracy	68.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))

Samples

17.0ms	70×	1	valid
16.0ms	162×	0	valid
7.0ms	24×	2	valid

Compiler

Compiled 73 to 14 computations (80.8% saved)

Precisions

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

ival-pow2: 8.0ms (29.4% of total)

ival-mult: 7.0ms (25.8% of total)

ival-add: 6.0ms (22.1% of total)

adjust: 4.0ms (14.7% of total)

ival-sub: 2.0ms (7.4% of total)

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

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

series3.0ms (0%)

Memory

6.2MiB live, 6.2MiB allocated

Counts

10 → 216

Calls

Call 1

Inputs
#<alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))>
#<alt (*.f64 (+.f64 x x) eps)>
#<alt (+.f64 x x)>
#<alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x (+.f64 x eps)) eps))>
#<alt (*.f64 (+.f64 x (+.f64 x eps)) eps)>
#<alt (+.f64 x (+.f64 x eps))>
#<alt (+.f64 x eps)>
#<alt (fma.f64 (+.f64 x x) eps (*.f64 eps eps))>
#<alt #s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 x x) eps (*.f64 eps eps)))>
#<alt (*.f64 eps eps)>

Outputs
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>

Calls

54 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ x x)
0.0ms	x	@	0	(+ (* (+ x x) eps) (* eps eps))
0.0ms	x	@	0	(+ x x)
0.0ms	x	@	-inf	(+ (* (+ x x) eps) (* eps eps))
0.0ms	x	@	inf	(* (+ x x) eps)

simplify203.0ms (2.8%)

Memory

-6.8MiB live, 201.8MiB allocated

Algorithm

1×	egg-herbie

Rules

4 622×	`lower-fma.f64`
4 622×	`lower-fma.f32`
3 318×	`lower-*.f64`
3 318×	`lower-*.f32`
1 398×	`associate-/r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	1284
1	159	1104
2	378	1104
3	1058	1104
4	2682	1104
5	4380	1104
6	6837	1104
0	8135	996

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 207

Calls

Call 1

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

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

rewrite68.0ms (0.9%)

Memory

-25.4MiB live, 90.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

576×	`lower-fma.f32`
574×	`lower-fma.f64`
380×	`lower-*.f32`
374×	`lower-*.f64`
266×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	84
0	24	82
1	99	82
0	744	77

Stop Event

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

Counts

10 → 142

Calls

Call 1

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

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

eval34.0ms (0.5%)

Memory: 13.9MiB live, 56.0MiB allocated
Compiler: Compiled 4 351 to 292 computations (93.3% saved)

prune19.0ms (0.3%)

Memory

-5.8MiB live, 32.7MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	373	0	373
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	373	5	378

Accuracy

100.0%

Counts

378 → 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 x x) eps (*.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x (+.f64 x eps)) eps))
✓	68.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps (fma.f64 x #s(literal 2 binary64) eps)))
✓	74.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 120 to 46 computations (61.7% saved)

regimes10.0ms (0.1%)

Memory

15.4MiB live, 15.4MiB allocated

Counts

9 → 1

Calls

Call 1

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

Calls

3 calls:

3.0ms	x
3.0ms	eps
3.0ms	(-.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 17 to 11 computations (35.3% saved)

regimes8.0ms (0.1%)

Memory

-27.8MiB live, 10.8MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	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 17 to 11 computations (35.3% saved)

regimes6.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
#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
94.0%	3	`x`
87.4%	3	`eps`
97.6%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 17 to 11 computations (35.3% saved)

regimes4.0ms (0.1%)

Memory

7.2MiB live, 7.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#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:

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

Results

Accuracy	Segments	Branch
74.2%	1	`eps`
74.2%	1	`x`
74.2%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 17 to 11 computations (35.3% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	5.3675e-320

Compiler

Compiled 14 to 12 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	87
1	29	87
2	33	87
3	35	87
4	36	87

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness604.0ms (8.4%)

Memory

-1.3MiB live, 231.9MiB allocated

Rules

9 222×	`lower-fma.f64`
9 222×	`lower-fma.f32`
6 574×	`lower-fma.f32`
6 568×	`lower-fma.f64`
4 572×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	492
1	214	450
2	574	450
3	1825	438
4	4173	438
5	7244	438
0	8097	390
0	24	122
0	41	114
1	180	114
2	1569	114
0	8785	114

Stop Event

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

Compiler

Compiled 82 to 41 computations (50% saved)

preprocess35.0ms (0.5%)

Memory: -11.7MiB live, 61.3MiB allocated
Compiler: Compiled 110 to 46 computations (58.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample1.3s (17.3%)

preprocess735.0ms (10.2%)

explain373.0ms (5.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify635.0ms (8.8%)

localize52.0ms (0.7%)

series4.0ms (0.1%)

simplify405.0ms (5.6%)

rewrite402.0ms (5.6%)

eval106.0ms (1.5%)

prune55.0ms (0.8%)

simplify483.0ms (6.7%)

localize131.0ms (1.8%)

series15.0ms (0.2%)

simplify241.0ms (3.3%)

rewrite501.0ms (6.9%)

eval276.0ms (3.8%)

prune141.0ms (1.9%)

simplify365.0ms (5%)

localize56.0ms (0.8%)

series3.0ms (0%)

simplify203.0ms (2.8%)

rewrite68.0ms (0.9%)

eval34.0ms (0.5%)

prune19.0ms (0.3%)

regimes10.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

soundness604.0ms (8.4%)

preprocess35.0ms (0.5%)

end0.0ms (0%)

Profiling