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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB 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)

sample1.2s (21.9%)

Memory

57.6MiB live, 1 692.0MiB allocated

Samples

384.0ms	2 465×	1	valid
373.0ms	5 288×	0	valid
114.0ms	503×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 600.0ms

ival-pow2: 215.0ms (35.8% of total)

ival-add: 98.0ms (16.3% of total)

ival-<=: 93.0ms (15.5% of total)

adjust: 88.0ms (14.7% of total)

ival-sub: 68.0ms (11.3% of total)

ival-and: 20.0ms (3.3% of total)

exact: 16.0ms (2.7% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

explain136.0ms (2.4%)

Memory

6.1MiB live, 83.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
73	-	-	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	-	-	`eps`
0	-	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(pow.f64 (+.f64 x eps) #s(literal 2 binary64))`
0	-	-	`(+.f64 x eps)`
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 -
+	73	0
-	0	183

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	73	0	0
-	0	0	183

Precision?

1.0

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

35.0ms	330×	0	valid
17.0ms	146×	1	valid
6.0ms	36×	2	valid

Compiler

Compiled 82 to 32 computations (61% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-pow2: 30.0ms (72.8% of total)

adjust: 4.0ms (9.7% of total)

ival-add: 4.0ms (9.7% of total)

ival-sub: 3.0ms (7.3% of total)

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

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

exact: 0.0ms (0% of total)

preprocess268.0ms (4.7%)

Memory

-32.6MiB live, 101.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	47	47
2	182	45
3	797	35
4	2770	35
5	5134	35
6	7371	35
0	7	9
0	11	9
1	18	9
2	48	9
3	189	9
4	843	7
5	3805	7
6	5846	7
7	7793	7
0	8048	6

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.9%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify145.0ms (2.5%)

Memory

19.7MiB live, 103.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 x #s(literal 2 binary64))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
cost-diff	3	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	11	23
1	18	23
2	48	23
3	189	23
4	843	21
5	3805	21
6	5846	21
7	7793	21
0	8048	20

Stop Event

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

Calls

Call 1

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

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

localize52.0ms (0.9%)

Memory

-24.2MiB live, 14.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(pow.f64 x #s(literal 2 binary64))
accuracy	0.0	(+.f64 x eps)
accuracy	0.029628759768442016	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	15.398792203090482	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

35.0ms	165×	0	valid
8.0ms	73×	1	valid
3.0ms	18×	2	valid

Compiler

Compiled 48 to 16 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-pow2: 6.0ms (49.8% of total)

adjust: 2.0ms (16.6% of total)

ival-add: 2.0ms (16.6% of total)

ival-sub: 2.0ms (16.6% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated

Counts

4 → 23

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)
(pow.f64 x #s(literal 2 binary64))

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

Calls

6 calls:

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

simplify179.0ms (3.2%)

Memory

27.8MiB live, 101.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	161
1	242	151
2	844	151
3	3601	143
0	8957	124

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 21

Calls

Call 1

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

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

rewrite241.0ms (4.2%)

Memory

-12.1MiB live, 223.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	53	20
2	404	20
3	6082	20
0	8311	20

Stop Event

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

Counts

4 → 445

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)
(pow.f64 x #s(literal 2 binary64))

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

eval100.0ms (1.8%)

Memory: 9.5MiB live, 85.8MiB allocated
Compiler: Compiled 11 846 to 1 368 computations (88.5% saved)

prune16.0ms (0.3%)

Memory

-21.1MiB live, 27.0MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	447	5	452
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	448	5	453

Accuracy

100.0%

Counts

453 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.5%	(fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 (neg.f64 x) x))
▶	66.5%	(fma.f64 (+.f64 eps x) x (-.f64 (.f64 (+.f64 eps x) eps) (.f64 x x)))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	68.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	73.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 138 to 88 computations (36.2% saved)

simplify121.0ms (2.1%)

Memory

30.3MiB live, 141.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (+.f64 eps x) eps)
cost-diff	0	(+.f64 eps x)
cost-diff	1	(-.f64 (.f64 (+.f64 eps x) eps) (.f64 x x))
cost-diff	7	(fma.f64 (+.f64 eps x) x (-.f64 (.f64 (+.f64 eps x) eps) (.f64 x x)))
cost-diff	0	(neg.f64 x)
cost-diff	0	(*.f64 (neg.f64 x) x)
cost-diff	0	(+.f64 eps x)
cost-diff	5	(fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 (neg.f64 x) x))
cost-diff	0	(*.f64 eps x)
cost-diff	0	(.f64 (.f64 eps x) #s(literal 2 binary64))
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
cost-diff	0	(*.f64 eps eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
cost-diff	0	(fma.f64 #s(literal 2 binary64) x eps)
cost-diff	0	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	130
0	39	117
1	87	117
2	231	117
3	929	108
4	3838	108
5	6199	108
0	8161	107

Stop Event

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

Calls

Call 1

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

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

localize100.0ms (1.8%)

Memory

4.4MiB live, 129.0MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(*.f64 (+.f64 eps x) eps)
accuracy	0.0078125	(-.f64 (.f64 (+.f64 eps x) eps) (.f64 x x))
accuracy	21.406491945379912	(fma.f64 (+.f64 eps x) x (-.f64 (.f64 (+.f64 eps x) eps) (.f64 x x)))
accuracy	0.0	(+.f64 eps x)
accuracy	0.0	(*.f64 (neg.f64 x) x)
accuracy	0.0	(neg.f64 x)
accuracy	21.429946057453552	(fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 (neg.f64 x) x))
accuracy	0.0	(*.f64 eps x)
accuracy	0.02734375	(.f64 (.f64 eps x) #s(literal 2 binary64))
accuracy	20.170901569734156	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0.0	(*.f64 eps eps)
accuracy	17.086143762560198	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
accuracy	0.0	(fma.f64 #s(literal 2 binary64) x eps)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
accuracy	0.015625	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)

Samples

39.0ms	165×	0	valid
23.0ms	73×	1	valid
8.0ms	18×	2	valid

Compiler

Compiled 249 to 49 computations (80.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-mult: 24.0ms (47.4% of total)

ival-add: 8.0ms (15.8% of total)

ival-pow2: 7.0ms (13.8% of total)

adjust: 5.0ms (9.9% of total)

ival-neg: 4.0ms (7.9% of total)

ival-sub: 3.0ms (5.9% of total)

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

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

exact: 0.0ms (0% of total)

series16.0ms (0.3%)

Memory

-8.0MiB live, 29.2MiB allocated

Counts

16 → 42

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) (+ eps x) (* (neg x) x) (neg x) (+ (* (+ eps x) x) (- (* (+ eps x) eps) (* x x))) (- (* (+ eps x) eps) (* x x)) (* (+ eps x) eps) (* x x))
3.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) (+ eps x) (* (neg x) x) (neg x) (+ (* (+ eps x) x) (- (* (+ eps x) eps) (* x x))) (- (* (+ eps x) eps) (* x x)) (* (+ eps x) eps) (* x x))
2.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) (+ eps x) (* (neg x) x) (neg x) (+ (* (+ eps x) x) (- (* (+ eps x) eps) (* x x))) (- (* (+ eps x) eps) (* x x)) (* (+ eps x) eps) (* x x))
2.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) (+ eps x) (* (neg x) x) (neg x) (+ (* (+ eps x) x) (- (* (+ eps x) eps) (* x x))) (- (* (+ eps x) eps) (* x x)) (* (+ eps x) eps) (* x x))
2.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) (+ eps x) (* (neg x) x) (neg x) (+ (* (+ eps x) x) (- (* (+ eps x) eps) (* x x))) (- (* (+ eps x) eps) (* x x)) (* (+ eps x) eps) (* x x))

simplify179.0ms (3.1%)

Memory

-12.7MiB live, 225.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	250
1	356	224
2	1221	224
3	4720	216
0	8781	197

Stop Event

1×	iter limit
1×	node limit

Counts

42 → 40

Calls

Call 1

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

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

rewrite197.0ms (3.5%)

Memory

-7.1MiB live, 213.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	116
0	39	110
1	180	110
2	1554	107
0	10015	101

Stop Event

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

Counts

16 → 1 123

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(/.f64 (fma.f64 (pow.f64 (.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64) (pow.f64 eps #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) (*.f64 eps eps)))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 6 binary64)) (.f64 (pow.f64 (.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64))) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) eps)))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) eps) #s(literal 3 binary64))) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (.f64 (.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) eps) (.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) eps)) (.f64 (.f64 eps eps) (.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) eps)))))
(/.f64 (+.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (neg.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps)) #s(literal 3 binary64))) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (neg.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps))))))
(/.f64 (neg.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) (fma.f64 #s(literal 2 binary64) x eps)) eps)) (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) eps)) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))))
(/.f64 (neg.f64 (.f64 eps (.f64 (fma.f64 #s(literal 2 binary64) x eps) (fma.f64 #s(literal 2 binary64) x eps)))) (neg.f64 (fma.f64 #s(literal 2 binary64) x eps)))
(/.f64 (neg.f64 (.f64 eps (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)))) (neg.f64 (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)))
(/.f64 (neg.f64 (-.f64 (pow.f64 eps #s(literal 6 binary64)) (.f64 (pow.f64 (.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64)))) (neg.f64 (+.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) eps))))))
(/.f64 (.f64 (.f64 (fma.f64 #s(literal 2 binary64) x eps) (fma.f64 #s(literal 2 binary64) x eps)) eps) (fma.f64 #s(literal 2 binary64) x eps))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) eps) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)))
(/.f64 (.f64 eps (.f64 (fma.f64 #s(literal 2 binary64) x eps) (fma.f64 #s(literal 2 binary64) x eps))) (fma.f64 #s(literal 2 binary64) x eps))
(/.f64 (.f64 eps (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64))) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(/.f64 (-.f64 (pow.f64 eps #s(literal 6 binary64)) (.f64 (pow.f64 (.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64))) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) eps)))))
(fma.f64 (neg.f64 (neg.f64 (neg.f64 eps))) (neg.f64 (neg.f64 (neg.f64 eps))) (.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) eps))
(fma.f64 (neg.f64 (neg.f64 (neg.f64 eps))) (neg.f64 (neg.f64 (neg.f64 eps))) (neg.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps)))
(fma.f64 (neg.f64 (neg.f64 (neg.f64 eps))) (neg.f64 (neg.f64 (neg.f64 eps))) (.f64 (.f64 #s(literal 2 binary64) x) eps))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) eps))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (neg.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps)))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (.f64 (.f64 #s(literal 2 binary64) x) eps))
(fma.f64 (.f64 #s(literal 2 binary64) eps) x (.f64 eps eps))
(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
(fma.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 eps)) (.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) eps))
(fma.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 eps)) (neg.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps)))
(fma.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 eps)) (.f64 (.f64 #s(literal 2 binary64) x) eps))
(fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) eps))
(fma.f64 #s(literal 1 binary64) (.f64 eps eps) (neg.f64 (.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps))
(fma.f64 (neg.f64 eps) (neg.f64 eps) (.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) eps))
(fma.f64 (neg.f64 eps) (neg.f64 eps) (neg.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps)))
(fma.f64 (neg.f64 eps) (neg.f64 eps) (.f64 (.f64 #s(literal 2 binary64) x) eps))
(fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 eps eps))
(fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps))
(fma.f64 #s(literal 2 binary64) (.f64 eps x) (.f64 eps eps))
(fma.f64 eps (.f64 #s(literal 2 binary64) x) (.f64 eps eps))
(fma.f64 eps eps (.f64 (neg.f64 (.f64 #s(literal 2 binary64) x)) eps))
(fma.f64 eps eps (neg.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps)))
(fma.f64 eps eps (.f64 (.f64 #s(literal 2 binary64) x) eps))
(fma.f64 x (.f64 #s(literal 2 binary64) eps) (.f64 eps eps))
(fma.f64 x (.f64 eps #s(literal 2 binary64)) (.f64 eps eps))
(-.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)))
(-.f64 (/.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) eps))))) (/.f64 (.f64 (pow.f64 (.f64 eps x) #s(literal 3 binary64)) #s(literal 8 binary64)) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) eps))))))
(-.f64 (.f64 eps eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps))
(+.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) (*.f64 eps eps))
(+.f64 (.f64 eps eps) (.f64 (neg.f64 (*.f64 #s(literal 2 binary64) x)) eps))
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(fma.f64 #s(literal 1 binary64) (.f64 eps eps) (neg.f64 (.f64 eps x)))
(fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 eps x))
(fma.f64 (neg.f64 eps) (neg.f64 eps) (*.f64 (neg.f64 eps) x))
(fma.f64 (neg.f64 eps) (neg.f64 eps) (neg.f64 (*.f64 eps x)))
(fma.f64 (neg.f64 eps) (neg.f64 eps) (*.f64 eps x))
(fma.f64 eps eps (*.f64 (neg.f64 eps) x))
(fma.f64 eps eps (neg.f64 (*.f64 eps x)))
(fma.f64 eps eps (*.f64 eps x))
(fma.f64 eps x (*.f64 eps eps))
(fma.f64 x eps (*.f64 eps eps))
(sqrt.f64 (pow.f64 (*.f64 (-.f64 eps x) eps) #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (-.f64 eps x) eps)) (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (*.f64 (-.f64 eps x) eps)))
(-.f64 (/.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (.f64 eps x))))) (/.f64 (pow.f64 (.f64 eps x) #s(literal 3 binary64)) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (+.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (*.f64 eps x))))))
(-.f64 (.f64 eps eps) (.f64 eps x))
(fabs.f64 (neg.f64 (*.f64 (-.f64 eps x) eps)))
(fabs.f64 (*.f64 (-.f64 eps x) eps))
(+.f64 (.f64 eps x) (.f64 eps eps))
(+.f64 (.f64 eps eps) (.f64 (neg.f64 eps) x))
(+.f64 (.f64 eps eps) (neg.f64 (.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 eps x))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 #s(literal -1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64)))) (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64)))))))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(fabs.f64 (-.f64 (*.f64 x x) #s(literal 0 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (/.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(exp.f64 (/.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval154.0ms (2.7%)

Memory: -1.7MiB live, 237.3MiB allocated
Compiler: Compiled 40 496 to 3 285 computations (91.9% saved)

prune23.0ms (0.4%)

Memory

3.2MiB live, 81.6MiB allocated

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1 239	3	1 242
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	1 242	5	1 247

Accuracy

100.0%

Counts

1 247 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	68.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	73.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
▶	43.8%	#s(approx (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) #s(literal 0 binary64))

Compiler

Compiled 76 to 52 computations (31.6% saved)

simplify120.0ms (2.1%)

Memory

-17.5MiB live, 103.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	76
0	24	73
1	64	71
2	190	71
3	772	65
4	3265	65
5	5879	65
0	8079	60

Stop Event

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

Calls

Call 1

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

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

localize55.0ms (1%)

Memory

8.7MiB live, 46.6MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 eps eps)
accuracy	0.0	(*.f64 eps #s(literal 2 binary64))
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps)))
accuracy	0.00390625	(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
accuracy	0.0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
accuracy	0.0	(*.f64 eps #s(literal 2 binary64))
accuracy	20.170901569734156	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
accuracy	35.95803924417998	#s(approx (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) #s(literal 0 binary64))

Samples

18.0ms	165×	0	valid
16.0ms	73×	1	valid
6.0ms	18×	2	valid

Compiler

Compiled 138 to 40 computations (71% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 9.0ms (31.8% of total)

ival-pow2: 6.0ms (21.2% of total)

ival-add: 6.0ms (21.2% of total)

adjust: 4.0ms (14.1% of total)

ival-sub: 2.0ms (7.1% of total)

ival-neg: 1.0ms (3.5% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB allocated

Counts

7 → 13

Calls

Call 1

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

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

Calls

6 calls:

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

simplify222.0ms (3.9%)

Memory

19.2MiB live, 177.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	99
1	164	85
2	661	85
3	2993	85
0	8215	77

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 13

Calls

Call 1

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

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

rewrite165.0ms (2.9%)

Memory

-8.0MiB live, 187.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	66
0	24	63
1	139	61
2	1200	61
0	8640	56

Stop Event

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

Counts

7 → 190

Calls

Call 1

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

Outputs
#s(approx (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) #s(literal 0 binary64))
#s(approx (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) (.f64 (.f64 #s(literal 2 binary64) eps) x))
(.f64 (.f64 #s(literal 2 binary64) x) eps)
(.f64 (.f64 x eps) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) eps) x)
(.f64 #s(literal 2 binary64) (.f64 x eps))
(.f64 x (.f64 #s(literal 2 binary64) eps))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) eps)
(*.f64 eps #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 eps eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (.f64 eps eps) (.f64 eps eps))))
(fma.f64 (pow.f64 eps #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64)) eps)
(fma.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps)) eps)
(fma.f64 (sqrt.f64 eps) (sqrt.f64 eps) eps)
(fma.f64 #s(literal 1 binary64) eps eps)
(fma.f64 #s(literal -1 binary64) (neg.f64 eps) eps)
(+.f64 eps eps)
(.f64 (/.f64 (.f64 eps (fma.f64 #s(literal 2 binary64) x eps)) eps) (/.f64 (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))
(.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps (neg.f64 (.f64 (*.f64 #s(literal 2 binary64) eps) x)))))
(.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (.f64 x eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) #s(literal 4 binary64) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) eps) x) eps) eps))))))
(.f64 #s(literal 1 binary64) (.f64 eps (fma.f64 #s(literal 2 binary64) x eps)))
(.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (pow.f64 (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (.f64 x eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) #s(literal 4 binary64) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) (*.f64 (neg.f64 eps) eps))))))
(.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (.f64 x eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) eps) eps)))))
(.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (.f64 x eps) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) #s(literal 4 binary64) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) eps) x) eps) eps))) #s(literal -1 binary64)))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 2 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 2 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))) (.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))) (+.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 2 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
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(+.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) #s(literal 4 binary64) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) eps) eps)))) (/.f64 (pow.f64 eps #s(literal 6 binary64)) (fma.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) #s(literal 4 binary64) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) eps) eps)))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 2 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (neg.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps))))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 2 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (/.f64 (.f64 (.f64 (neg.f64 eps) eps) (.f64 eps eps)) (*.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 2 binary64)) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))) (/.f64 (neg.f64 (pow.f64 eps #s(literal 4 binary64))) (.f64 eps (fma.f64 #s(literal 2 binary64) x (neg.f64 eps)))))
(+.f64 (.f64 eps eps) (neg.f64 (.f64 (neg.f64 (*.f64 #s(literal 2 binary64) eps)) x)))
(+.f64 (.f64 eps eps) (neg.f64 (.f64 (neg.f64 x) (*.f64 #s(literal 2 binary64) eps))))
(+.f64 (.f64 eps eps) (neg.f64 (.f64 (neg.f64 eps) (*.f64 #s(literal 2 binary64) x))))
(+.f64 (.f64 eps eps) (.f64 (*.f64 #s(literal 2 binary64) eps) x))
(+.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) (*.f64 eps eps))
#s(approx (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) (*.f64 eps (fma.f64 #s(literal 2 binary64) x eps)))
(.f64 (sqrt.f64 (.f64 (neg.f64 eps) eps)) (sqrt.f64 (*.f64 (neg.f64 eps) eps)))
(*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 (neg.f64 eps)))
(*.f64 (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))) (sqrt.f64 eps))
(*.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))))
(*.f64 (sqrt.f64 eps) (sqrt.f64 (pow.f64 eps #s(literal 3 binary64))))
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
(.f64 #s(literal 1 binary64) (.f64 eps eps))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 eps) eps))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 eps eps)
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(pow.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 eps) #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 eps #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 eps) eps))
(sqrt.f64 (pow.f64 eps #s(literal 4 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 eps) eps))
(fabs.f64 (*.f64 (neg.f64 eps) eps))
(fabs.f64 (*.f64 eps eps))
(exp.f64 (*.f64 (log.f64 (neg.f64 eps)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))))

eval32.0ms (0.6%)

Memory: -4.1MiB live, 45.5MiB allocated
Compiler: Compiled 6 711 to 638 computations (90.5% saved)

prune25.0ms (0.4%)

Memory

-28.6MiB live, 10.4MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	206	2	208
Fresh	0	0	0
Picked	2	1	3
Done	0	2	2
Total	208	5	213

Accuracy

100.0%

Counts

213 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps eps) x (*.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	68.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	73.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	43.8%	#s(approx (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) #s(literal 0 binary64))

Compiler

Compiled 76 to 50 computations (34.2% saved)

simplify131.0ms (2.3%)

Memory

45.2MiB live, 118.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	59
0	17	59
1	34	59
2	101	57
3	383	53
4	1437	53
5	3520	53
6	5323	53
7	7101	53
0	8007	49

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

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

localize61.0ms (1.1%)

Memory

-12.1MiB live, 68.1MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 eps eps)
accuracy	0.0	(*.f64 eps eps)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps eps) x (*.f64 eps eps)))
accuracy	0.00390625	(fma.f64 (+.f64 eps eps) x (*.f64 eps eps))
accuracy	0.0	(+.f64 eps eps)
accuracy	0.0	(*.f64 (+.f64 eps eps) x)
accuracy	20.170901569734156	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))

Samples

28.0ms	73×	1	valid
17.0ms	165×	0	valid
7.0ms	18×	2	valid

Compiler

Compiled 106 to 25 computations (76.4% saved)

Precisions

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

ival-add: 8.0ms (34.8% of total)

ival-pow2: 6.0ms (26.1% of total)

ival-mult: 4.0ms (17.4% of total)

adjust: 3.0ms (13% of total)

ival-sub: 2.0ms (8.7% of total)

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

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

series5.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB allocated

Counts

6 → 8

Calls

Call 1

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

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

Calls

6 calls:

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

simplify112.0ms (2%)

Memory

9.8MiB live, 83.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	56
1	89	46
2	283	46
3	940	46
4	2729	46
5	5835	46
6	7804	46
0	8029	41

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 8

Calls

Call 1

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

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

rewrite90.0ms (1.6%)

Memory

-25.6MiB live, 98.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	52
0	17	52
1	87	52
0	756	52

Stop Event

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

Counts

6 → 74

Calls

Call 1

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

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

eval9.0ms (0.2%)

Memory: 18.0MiB live, 18.0MiB allocated
Compiler: Compiled 2 069 to 277 computations (86.6% saved)

prune6.0ms (0.1%)

Memory

-28.2MiB live, 11.3MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	91	5	96

Accuracy

100.0%

Counts

96 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps eps) x (*.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	68.5%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	73.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	43.8%	#s(approx (+ (* (+ eps x) (+ eps x)) (* (neg x) x)) #s(literal 0 binary64))

Compiler

Compiled 234 to 95 computations (59.4% saved)

regimes11.0ms (0.2%)

Memory

22.9MiB live, 22.9MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	x
4.0ms	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 11 to 11 computations (0% saved)

regimes15.0ms (0.3%)

Memory

-23.4MiB live, 19.6MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	x
3.0ms	eps
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes7.0ms (0.1%)

Memory

9.3MiB live, 9.3MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
93.8%	3	`x`
88.7%	3	`eps`
97.2%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
73.3%	1	`eps`
73.3%	1	`x`
73.3%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
43.8%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
43.8%	1	`x`
43.8%	1	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	5e-324

Compiler

Compiled 12 to 12 computations (0% saved)

simplify54.0ms (1%)

Memory

-19.9MiB live, 18.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	98
1	60	98
2	149	98
3	596	86
4	2998	86
5	5687	86

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness1.3s (23%)

Memory

3.8MiB live, 561.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	116
0	39	110
1	180	110
2	1554	107
0	10015	101
0	20	66
0	24	63
1	139	61
2	1200	61
0	8640	56
0	69	161
1	242	151
2	844	151
3	3601	143
0	8957	124
0	7	20
0	11	20
1	53	20
2	404	20
3	6082	20
0	8311	20
0	105	250
1	356	224
2	1221	224
3	4720	216
0	8781	197

Stop Event

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

Compiler

Compiled 194 to 100 computations (48.5% saved)

preprocess70.0ms (1.2%)

Memory: -1.2MiB live, 45.5MiB allocated
Compiler: Compiled 214 to 66 computations (69.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.2s (21.9%)

explain136.0ms (2.4%)

preprocess268.0ms (4.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify145.0ms (2.5%)

localize52.0ms (0.9%)

series5.0ms (0.1%)

simplify179.0ms (3.2%)

rewrite241.0ms (4.2%)

eval100.0ms (1.8%)

prune16.0ms (0.3%)

simplify121.0ms (2.1%)

localize100.0ms (1.8%)

series16.0ms (0.3%)

simplify179.0ms (3.1%)

rewrite197.0ms (3.5%)

eval154.0ms (2.7%)

prune23.0ms (0.4%)

simplify120.0ms (2.1%)

localize55.0ms (1%)

series6.0ms (0.1%)

simplify222.0ms (3.9%)

rewrite165.0ms (2.9%)

eval32.0ms (0.6%)

prune25.0ms (0.4%)

simplify131.0ms (2.3%)

localize61.0ms (1.1%)

series5.0ms (0.1%)

simplify112.0ms (2%)

rewrite90.0ms (1.6%)

eval9.0ms (0.2%)

prune6.0ms (0.1%)

regimes11.0ms (0.2%)

regimes15.0ms (0.3%)

regimes7.0ms (0.1%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

simplify54.0ms (1%)

soundness1.3s (23%)

preprocess70.0ms (1.2%)

end0.0ms (0%)

Profiling