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

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

1.4MiB live, 1.3MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 25 to 18 computations (28% saved)

sample2.3s (47.5%)

Memory

-110.4MiB live, 1 905.7MiB allocated; 1.4s collecting garbage

Samples

1.4s	5 137×	0	valid
391.0ms	2 543×	1	valid
175.0ms	576×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-pow2: 1.3s (80.7% of total)

ival-add: 119.0ms (7.6% of total)

adjust: 117.0ms (7.5% of total)

ival-sub: 62.0ms (4% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

explain166.0ms (3.4%)

Memory

-10.8MiB live, 241.6MiB allocated; 18ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
70	1	(1.2256559543115053e-118 5.937451827388107e-121)	-	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	-	`eps`
0	0	-	-	`(pow.f64 x #s(literal 2 binary64))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(pow.f64 (+.f64 x eps) #s(literal 2 binary64))`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	cancellation	71	0

Confusion

	Predicted +	Predicted -
+	70	0
-	1	185

Precision

0.9859154929577465

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	70	0	0
-	1	0	185

Precision?

0.9859154929577465

Recall?

1.0

Freqs

test

number	freq
0	185
1	71

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

27.0ms	312×	0	valid
26.0ms	176×	1	valid
5.0ms	24×	2	valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

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

ival-pow2: 19.0ms (54.5% of total)

adjust: 7.0ms (20.1% of total)

ival-add: 5.0ms (14.3% of total)

ival-sub: 4.0ms (11.5% of total)

ival-true: 1.0ms (2.9% of total)

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

exact: 0.0ms (0% of total)

preprocess243.0ms (5%)

Memory

33.1MiB live, 211.0MiB allocated; 42ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	64
1	34	60
2	118	60
3	553	58
4	1771	44
5	5314	44
0	7	9
0	11	9
1	16	9
2	44	9
3	157	9
4	570	7
5	1812	7
0	8588	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; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify134.0ms (2.7%)

Memory

-16.2MiB live, 119.2MiB allocated; 21ms collecting garbage

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	16	23
2	44	23
3	157	23
4	570	21
5	1812	21
0	8588	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)

localize28.0ms (0.6%)

Memory

35.1MiB live, 35.1MiB allocated; 0ms collecting garbage

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	14.753625464374428	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

11.0ms	88×	1	valid
9.0ms	156×	0	valid
2.0ms	12×	2	valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

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

ival-pow2: 7.0ms (51.5% of total)

adjust: 3.0ms (22.1% of total)

ival-add: 2.0ms (14.7% of total)

ival-sub: 2.0ms (14.7% of total)

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

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

exact: 0.0ms (0% of total)

series27.0ms (0.6%)

Memory

-49.6MiB live, 9.5MiB allocated; 34ms collecting garbage

Counts

4 → 27

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
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (pow eps 2)))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* x (+ x (* 2 eps))) (pow eps 2))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ eps x))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* 2 (* eps x)) (pow x 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* eps (+ eps (* 2 x))) (pow x 2))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -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))

simplify230.0ms (4.7%)

Memory

26.4MiB live, 300.9MiB allocated; 63ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	99	415
1	271	401
2	924	377
3	4052	377
0	8199	364

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 27

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (pow eps 2)))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* x (+ x (* 2 eps))) (pow eps 2))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ eps x))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* 2 (* eps x)) (pow x 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* eps (+ eps (* 2 x))) (pow x 2))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

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

rewrite57.0ms (1.2%)

Memory

32.6MiB live, 79.0MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	51	20
0	386	20

Stop Event

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

Counts

4 → 60

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

eval20.0ms (0.4%)

Memory: -29.8MiB live, 19.9MiB allocated; 14ms collecting garbage
Compiler: Compiled 1 390 to 277 computations (80.1% saved)

prune3.0ms (0.1%)

Memory

6.7MiB live, 6.7MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Accuracy

100.0%

Counts

83 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	64.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	74.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Status

Accuracy

Program

▶

100.0%

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

▶

64.0%

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

▶

74.8%

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

Compiler

Compiled 44 to 31 computations (29.5% saved)

simplify124.0ms (2.5%)

Memory

14.5MiB live, 148.0MiB allocated; 17ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
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))
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))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	72
0	21	72
1	38	72
2	106	72
3	318	69
4	938	63
5	3274	63
0	8212	63

Stop Event

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

Calls

Call 1

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

Outputs
#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)
#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

localize99.0ms (2%)

Memory

-14.1MiB live, 173.8MiB allocated; 20ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
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	0.00390625	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
accuracy	0.0	(*.f64 eps x)
accuracy	0.02734375	(.f64 (.f64 eps x) #s(literal 2 binary64))
accuracy	22.991792412081494	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0.0	(*.f64 eps eps)
accuracy	16.110001370322124	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Samples

20.0ms	156×	0	valid
19.0ms	88×	1	valid
3.0ms	12×	2	valid

Compiler

Compiled 59 to 15 computations (74.6% saved)

Precisions

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

ival-pow2: 10.0ms (36.3% of total)

ival-mult: 7.0ms (25.4% of total)

adjust: 4.0ms (14.5% of total)

ival-add: 3.0ms (10.9% of total)

ival-sub: 2.0ms (7.3% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.2%)

Memory

15.1MiB live, 15.1MiB allocated; 0ms collecting garbage

Counts

8 → 24

Calls

Call 1

Inputs
#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)
#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)

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (* eps x) 2) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps))
2.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps))
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps))
1.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps))
1.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps))

simplify154.0ms (3.1%)

Memory

5.8MiB live, 158.2MiB allocated; 51ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	322
1	170	322
2	508	322
3	1811	294
4	7985	294
0	8051	258

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (* eps x) 2) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))

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

rewrite44.0ms (0.9%)

Memory

1.6MiB live, 46.0MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
0	21	65
1	83	65
0	592	65

Stop Event

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

Counts

8 → 76

Calls

Call 1

Inputs
#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)
#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)

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

eval16.0ms (0.3%)

Memory: -32.8MiB live, 24.0MiB allocated; 7ms collecting garbage
Compiler: Compiled 1 610 to 242 computations (85% saved)

prune4.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	82	4	86

Accuracy

100.0%

Counts

86 → 4

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))
▶	64.1%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	74.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 62 to 43 computations (30.6% saved)

simplify116.0ms (2.4%)

Memory

38.9MiB live, 170.3MiB allocated; 22ms collecting garbage

Localize:

Found 7 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))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	61
0	17	61
1	33	59
2	105	59
3	342	59
4	927	55
5	3443	55
0	8633	51

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 #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 (- (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 #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 (- (pow (+ x eps) 2) (pow x 2)) (*.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)

localize83.0ms (1.7%)

Memory

-35.8MiB live, 63.9MiB allocated; 15ms collecting garbage

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
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	0.0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
accuracy	0.0	(*.f64 eps #s(literal 2 binary64))
accuracy	22.991792412081494	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))

Samples

38.0ms	156×	0	valid
34.0ms	88×	1	valid
3.0ms	12×	2	valid

Compiler

Compiled 49 to 13 computations (73.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-mult: 29.0ms (63.1% of total)

ival-pow2: 7.0ms (15.2% of total)

adjust: 4.0ms (8.7% of total)

ival-add: 4.0ms (8.7% of total)

ival-sub: 2.0ms (4.3% 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

11.8MiB live, 11.8MiB allocated; 0ms collecting garbage

Counts

6 → 17

Calls

Call 1

Inputs
#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 (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (* eps 2) x) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* eps 2) #s(hole binary64 (* 2 eps)))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (* (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 2) x) (* eps 2) (+ (* (* eps 2) x) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps))
1.0ms	eps	@	-inf	((- (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	((- (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	((- (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	((- (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))

simplify160.0ms (3.3%)

Memory

7.5MiB live, 197.1MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	259
1	132	259
2	421	259
3	1632	231
4	7079	231
0	8290	207

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 17

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (* eps 2) x) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* eps 2) #s(hole binary64 (* 2 eps)))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* (* eps 2) x) (* eps eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))

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

rewrite46.0ms (0.9%)

Memory

-13.1MiB live, 33.0MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	52
0	17	52
1	80	50
0	641	48

Stop Event

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

Counts

6 → 69

Calls

Call 1

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

eval8.0ms (0.2%)

Memory: 11.7MiB live, 11.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 786 to 247 computations (86.2% saved)

prune4.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	0	0
Picked	2	0	2
Done	0	2	2
Total	84	4	88

Accuracy

100.0%

Counts

88 → 4

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))
▶	64.1%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	74.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 62 to 41 computations (33.9% saved)

simplify169.0ms (3.5%)

Memory

-4.8MiB live, 104.7MiB allocated; 72ms collecting garbage

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	31	59
2	92	57
3	295	57
4	879	53
5	3035	53
0	8190	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)

localize51.0ms (1%)

Memory

-30.1MiB live, 60.1MiB allocated; 23ms collecting garbage

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (+.f64 eps eps) x (*.f64 eps eps))
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	0.0	(+.f64 eps eps)
accuracy	0.0	(*.f64 (+.f64 eps eps) x)
accuracy	22.991792412081494	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))

Samples

22.0ms	88×	1	valid
18.0ms	156×	0	valid
3.0ms	12×	2	valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-pow2: 7.0ms (33% of total)

ival-add: 5.0ms (23.6% of total)

adjust: 4.0ms (18.9% of total)

ival-mult: 4.0ms (18.9% of total)

ival-sub: 2.0ms (9.4% of total)

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

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

series6.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated; 0ms collecting garbage

Counts

6 → 17

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)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (+ eps eps) x) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (+ eps eps) #s(hole binary64 (* 2 eps)))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (* (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))

simplify197.0ms (4%)

Memory

23.9MiB live, 170.4MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	275
1	130	259
2	420	259
3	1628	231
4	7099	231
0	8314	207

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 17

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (+ eps eps) x) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (+ eps eps) #s(hole binary64 (* 2 eps)))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* (+ eps eps) x) (* eps eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))

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

rewrite63.0ms (1.3%)

Memory

-23.0MiB live, 65.0MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	52
0	17	52
1	84	42
0	744	42

Stop Event

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

Counts

6 → 79

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

eval9.0ms (0.2%)

Memory: 19.4MiB live, 19.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 771 to 262 computations (85.2% saved)

prune5.0ms (0.1%)

Memory

10.7MiB live, 10.7MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	0	0
Picked	0	2	2
Done	0	2	2
Total	87	5	92

Accuracy

100.0%

Counts

92 → 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))
✓	64.1%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
	5.4%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x #s(literal 2 binary64)))
✓	74.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 207 to 83 computations (59.9% saved)

regimes15.0ms (0.3%)

Memory

-42.0MiB live, 15.7MiB allocated; 9ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

9.0ms	eps
3.0ms	x
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes7.0ms (0.1%)

Memory

18.9MiB live, 18.9MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes6.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated; 0ms collecting garbage

Counts

5 → 2

Calls

Call 1

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

Results

Accuracy	Segments	Branch
97.5%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
92.2%	3	`x`
85.4%	3	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes6.0ms (0.1%)

Memory

-34.2MiB live, 11.4MiB allocated; 3ms collecting garbage

Accuracy

Total -44.5b remaining (-276.1%)

Threshold costs -44.5b (-276.1%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
74.8%	1	`eps`
74.8%	1	`x`
74.8%	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)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	4.849497e-317

Compiler

Compiled 12 to 12 computations (0% saved)

simplify62.0ms (1.3%)

Memory

34.6MiB live, 34.6MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	87
1	31	87
2	62	87
3	181	87
4	606	77
5	2081	77
6	7836	77

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))

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))

derivations167.0ms (3.4%)

Memory

-44.7MiB live, 101.1MiB allocated; 14ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 87 to 25 computations (71.3% saved)

preprocess22.0ms (0.4%)

Memory: 19.5MiB live, 19.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 192 to 64 computations (66.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample2.3s (47.5%)

explain166.0ms (3.4%)

preprocess243.0ms (5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify134.0ms (2.7%)

localize28.0ms (0.6%)

series27.0ms (0.6%)

simplify230.0ms (4.7%)

rewrite57.0ms (1.2%)

eval20.0ms (0.4%)

prune3.0ms (0.1%)

simplify124.0ms (2.5%)

localize99.0ms (2%)

series10.0ms (0.2%)

simplify154.0ms (3.1%)

rewrite44.0ms (0.9%)

eval16.0ms (0.3%)

prune4.0ms (0.1%)

simplify116.0ms (2.4%)

localize83.0ms (1.7%)

series6.0ms (0.1%)

simplify160.0ms (3.3%)

rewrite46.0ms (0.9%)

eval8.0ms (0.2%)

prune4.0ms (0.1%)

simplify169.0ms (3.5%)

localize51.0ms (1%)

series6.0ms (0.1%)

simplify197.0ms (4%)

rewrite63.0ms (1.3%)

eval9.0ms (0.2%)

prune5.0ms (0.1%)

regimes15.0ms (0.3%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch0.0ms (0%)

simplify62.0ms (1.3%)

derivations167.0ms (3.4%)

preprocess22.0ms (0.4%)

end0.0ms (0%)

Profiling