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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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 (33.4%)

Memory

-88.0MiB live, 2 313.4MiB allocated; 1.6s collecting garbage

Samples

1.0s	2 534×	1	valid
710.0ms	5 180×	0	valid
155.0ms	542×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-pow2: 939.0ms (63.5% of total)

ival-<=: 219.0ms (14.8% of total)

ival-add: 115.0ms (7.8% of total)

adjust: 102.0ms (6.9% of total)

ival-sub: 59.0ms (4% of total)

ival-and: 23.0ms (1.6% of total)

exact: 18.0ms (1.2% of total)

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

Bogosity

explain135.0ms (1.9%)

Memory

-0.9MiB live, 148.0MiB allocated; 16ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
74	1	(1.4707847300571272e-105 3.260832808991291e-219)	1	(-2.211092937794249e-22 -2.901761298669501e-24)	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`(pow.f64 (+.f64 x eps) #s(literal 2 binary64))`
0	0	-	0	-	`(+.f64 x eps)`
0	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	74	2

Confusion

	Predicted +	Predicted -
+	73	2
-	1	180

Precision

0.9864864864864865

Recall

0.9733333333333334

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	73	1	1
-	1	1	179

Precision?

0.9736842105263158

Recall?

0.9866666666666667

Freqs

test

number	freq
0	182
1	74

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

19.0ms	326×	0	valid
18.0ms	144×	1	valid
8.0ms	42×	2	valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

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

ival-pow2: 14.0ms (50.2% of total)

adjust: 6.0ms (21.5% of total)

ival-add: 4.0ms (14.3% of total)

ival-sub: 3.0ms (10.8% of total)

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

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

exact: 0.0ms (0% of total)

preprocess389.0ms (5.6%)

Memory

-26.1MiB live, 161.0MiB allocated; 26ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	30	51
2	97	51
3	472	49
4	1479	37
5	4095	35
0	7	9
0	11	9
1	16	9
2	39	9
3	147	9
4	538	7
5	1669	7
6	5414	7
0	8068	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: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.8%	(-.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)

simplify382.0ms (5.5%)

Memory

13.6MiB live, 146.3MiB allocated; 13ms 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	39	23
3	147	23
4	538	21
5	1669	21
6	5414	21
0	8068	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 (0.4%)

Memory

27.1MiB live, 27.1MiB 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	0.02734375	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	15.453827285213276	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

9.0ms	163×	0	valid
9.0ms	72×	1	valid
4.0ms	21×	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 (51.1% of total)

adjust: 3.0ms (21.9% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series58.0ms (0.8%)

Memory

-43.0MiB live, 15.7MiB allocated; 5ms collecting garbage

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
43.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
11.0ms	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))

simplify158.0ms (2.3%)

Memory

41.9MiB live, 176.4MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	215
1	239	203
2	827	191
3	3630	191
0	8470	176

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

rewrite224.0ms (3.2%)

Memory

-5.7MiB live, 240.5MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	51	20
2	364	20
3	5050	20
0	8368	20

Stop Event

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

Counts

4 → 311

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

eval75.0ms (1.1%)

Memory: -23.0MiB live, 99.2MiB allocated; 36ms collecting garbage
Compiler: Compiled 7 675 to 1 120 computations (85.4% saved)

prune7.0ms (0.1%)

Memory

34.9MiB live, 34.9MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	322	5	327
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	323	5	328

Accuracy

100.0%

Counts

328 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	67.0%	(fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x)))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	90.6%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) (+.f64 (/.f64 eps x) #s(literal 2 binary64))))
▶	66.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	73.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 154 to 102 computations (33.8% saved)

simplify177.0ms (2.5%)

Memory

-41.4MiB live, 204.8MiB allocated; 47ms collecting garbage

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (neg.f64 x) x)
cost-diff	0	(+.f64 eps x)
cost-diff	1	(fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x))
cost-diff	7	(fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x)))
cost-diff	0	(+.f64 (/.f64 eps x) #s(literal 2 binary64))
cost-diff	0	(*.f64 eps x)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) (+.f64 (/.f64 eps x) #s(literal 2 binary64))))
cost-diff	3	(.f64 (.f64 eps x) (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
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	24	148
0	40	134
1	79	134
2	189	134
3	547	130
4	1599	122
5	3790	122
6	6951	122
0	8042	121

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

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

localize132.0ms (1.9%)

Memory

27.6MiB live, 162.7MiB allocated; 14ms collecting garbage

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 (neg.f64 x) x)
accuracy	0.0	(neg.f64 x)
accuracy	0.01171875	(fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x))
accuracy	21.089651102063872	(fma.f64 (+.f64 eps x) x (fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x)))
accuracy	0.0	(*.f64 eps x)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) (+.f64 (/.f64 eps x) #s(literal 2 binary64))))
accuracy	0.00390625	(+.f64 (/.f64 eps x) #s(literal 2 binary64))
accuracy	6.001944097473396	(.f64 (.f64 eps x) (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
accuracy	0.0	(*.f64 eps x)
accuracy	0.0234375	(.f64 (.f64 eps x) #s(literal 2 binary64))
accuracy	21.591877419791942	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0.0	(*.f64 eps eps)
accuracy	17.29801847893794	#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	0.01171875	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)

Samples

60.0ms	163×	0	valid
45.0ms	72×	1	valid
11.0ms	21×	2	valid

Compiler

Compiled 128 to 25 computations (80.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-mult: 35.0ms (48.9% of total)

ival-add: 14.0ms (19.6% of total)

adjust: 9.0ms (12.6% of total)

ival-pow2: 7.0ms (9.8% of total)

ival-div: 2.0ms (2.8% of total)

ival-sub: 2.0ms (2.8% of total)

ival-neg: 1.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series57.0ms (0.8%)

Memory

-52.8MiB live, 30.0MiB allocated; 72ms collecting garbage

Counts

16 → 43

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

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

Calls

6 calls:

Time	Variable		Point	Expression
43.0ms	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) 2)) (- (pow (+ x eps) 2) (pow x 2)) (+ (/ eps x) 2) (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (+ (* (+ eps x) eps) (* (neg x) x)) (+ eps x) (* (neg x) x) (neg x))
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) 2)) (- (pow (+ x eps) 2) (pow x 2)) (+ (/ eps x) 2) (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (+ (* (+ eps x) eps) (* (neg x) x)) (+ eps x) (* (neg x) x) (neg x))
3.0ms	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) 2)) (- (pow (+ x eps) 2) (pow x 2)) (+ (/ eps x) 2) (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (+ (* (+ eps x) eps) (* (neg x) x)) (+ eps x) (* (neg x) x) (neg 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) 2)) (- (pow (+ x eps) 2) (pow x 2)) (+ (/ eps x) 2) (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (+ (* (+ eps x) eps) (* (neg x) x)) (+ eps x) (* (neg x) x) (neg x))
2.0ms	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) 2)) (- (pow (+ x eps) 2) (pow x 2)) (+ (/ eps x) 2) (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (+ (* (+ eps x) eps) (* (neg x) x)) (+ eps x) (* (neg x) x) (neg x))

simplify183.0ms (2.6%)

Memory

48.6MiB live, 180.0MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	291
1	356	264
2	1189	254
3	4860	250
0	8108	233

Stop Event

1×	iter limit
1×	node limit

Counts

43 → 41

Calls

Call 1

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

rewrite255.0ms (3.7%)

Memory

-31.9MiB live, 253.5MiB allocated; 36ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	130
0	40	130
1	172	125
2	1368	125
0	8329	125

Stop Event

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

Counts

16 → 491

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

eval74.0ms (1.1%)

Memory: 37.4MiB live, 82.6MiB allocated; 5ms collecting garbage
Compiler: Compiled 24 777 to 2 002 computations (91.9% saved)

prune19.0ms (0.3%)

Memory

-14.5MiB live, 31.5MiB allocated; 4ms collecting garbage

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	584	4	588
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	587	6	593

Accuracy

100.0%

Counts

593 → 6

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)) (fma.f64 eps eps (.f64 (.f64 eps x) #s(literal 2 binary64))))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	66.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	73.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
▶	41.4%	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Compiler

Compiled 98 to 66 computations (32.7% saved)

simplify248.0ms (3.6%)

Memory

4.1MiB live, 254.4MiB allocated; 41ms collecting garbage

Localize:

Found 12 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 x)
cost-diff	0	(.f64 (.f64 eps x) #s(literal 2 binary64))
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (.f64 (.f64 eps x) #s(literal 2 binary64))))
cost-diff	2	(fma.f64 eps eps (.f64 (.f64 eps x) #s(literal 2 binary64)))
cost-diff	0	(*.f64 eps #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
cost-diff	0	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	117
0	33	116
1	70	106
2	174	106
3	439	106
4	1233	98
5	3179	98
6	6213	98
0	8245	90

Stop Event

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

Calls

Call 1

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

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

localize78.0ms (1.1%)

Memory

-20.9MiB live, 68.7MiB allocated; 10ms collecting garbage

Localize:

Found 12 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	0.01171875	(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
accuracy	0.0	(*.f64 eps x)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (.f64 (.f64 eps x) #s(literal 2 binary64))))
accuracy	0.01171875	(fma.f64 eps eps (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0.0234375	(.f64 (.f64 eps x) #s(literal 2 binary64))
accuracy	0.0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
accuracy	0.0	(*.f64 eps #s(literal 2 binary64))
accuracy	21.591877419791942	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
accuracy	37.49485087754014	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Samples

28.0ms	163×	0	valid
24.0ms	72×	1	valid
10.0ms	21×	2	valid

Compiler

Compiled 95 to 24 computations (74.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 20.0ms (41.5% of total)

ival-add: 10.0ms (20.7% of total)

adjust: 9.0ms (18.7% of total)

ival-pow2: 7.0ms (14.5% of total)

ival-sub: 2.0ms (4.1% of total)

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

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.1%)

Memory

12.0MiB live, 12.0MiB allocated; 0ms collecting garbage

Counts

11 → 14

Calls

Call 1

Inputs
#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
(.f64 (.f64 eps #s(literal 2 binary64)) x)
(*.f64 eps #s(literal 2 binary64))
(fma.f64 eps eps (.f64 (.f64 eps x) #s(literal 2 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (.f64 (.f64 eps x) #s(literal 2 binary64))))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(*.f64 eps x)
(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))
(* 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) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* eps eps) (* (* eps x) 2)) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (+ (* (* eps 2) x) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps))
1.0ms	eps	@	inf	((+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* eps eps) (* (* eps x) 2)) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (+ (* (* eps 2) x) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps))
1.0ms	x	@	-inf	((+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* eps eps) (* (* eps x) 2)) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (+ (* (* eps 2) x) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps))
1.0ms	x	@	inf	((+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* eps eps) (* (* eps x) 2)) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (+ (* (* eps 2) x) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps))
1.0ms	eps	@	0	((+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* eps eps) (* (* eps x) 2)) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (+ (* (* eps 2) x) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps))

simplify165.0ms (2.4%)

Memory

-8.7MiB live, 130.9MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	102
1	164	88
2	655	88
3	3067	88
0	8345	80

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 14

Calls

Call 1

Inputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* 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))
(* eps x)
(*.f64 x eps)
(* 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)

rewrite189.0ms (2.7%)

Memory

26.5MiB live, 172.2MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	104
0	33	103
1	159	93
2	1419	93
0	8183	89

Stop Event

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

Counts

11 → 280

Calls

Call 1

Inputs
#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
(.f64 (.f64 eps #s(literal 2 binary64)) x)
(*.f64 eps #s(literal 2 binary64))
(fma.f64 eps eps (.f64 (.f64 eps x) #s(literal 2 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (.f64 (.f64 eps x) #s(literal 2 binary64))))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(*.f64 eps x)
(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(literal 0 binary64))
#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 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 (-.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) (pow.f64 (.f64 x eps) #s(literal 2 binary64))) (-.f64 (.f64 x eps) (.f64 x eps)))
(/.f64 (+.f64 (pow.f64 (.f64 x eps) #s(literal 3 binary64)) (pow.f64 (.f64 x eps) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) (pow.f64 (*.f64 x eps) #s(literal 2 binary64)))))
(fma.f64 x eps (*.f64 x eps))
(fma.f64 eps x (*.f64 x eps))
(+.f64 (.f64 x eps) (.f64 x eps))
(*.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 (neg.f64 eps))) (sqrt.f64 (neg.f64 (neg.f64 eps))) eps)
(fma.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps)) eps)
(fma.f64 (sqrt.f64 eps) (sqrt.f64 eps) eps)
(+.f64 eps eps)
(.f64 (/.f64 (.f64 eps (fma.f64 #s(literal 2 binary64) x eps)) eps) (/.f64 (.f64 eps (-.f64 eps (.f64 #s(literal 2 binary64) x))) (-.f64 eps (*.f64 #s(literal 2 binary64) x))))
(.f64 (/.f64 (.f64 eps (fma.f64 #s(literal 2 binary64) x eps)) eps) (/.f64 (.f64 eps (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(*.f64 eps (fma.f64 #s(literal 2 binary64) x eps))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (-.f64 (.f64 #s(literal 2 binary64) x) eps))) (.f64 (/.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (-.f64 (.f64 #s(literal 2 binary64) x) eps)))) (.f64 (/.f64 (pow.f64 eps #s(literal 4 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))))) (fma.f64 (/.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (-.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 (.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 #s(literal 2 binary64) x)))) (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (/.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (-.f64 eps (.f64 #s(literal 2 binary64) x)))) (.f64 (/.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (-.f64 eps (.f64 #s(literal 2 binary64) x)))))) (+.f64 (/.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 eps (-.f64 eps (.f64 #s(literal 2 binary64) x)))) (.f64 (/.f64 (pow.f64 (.f64 x eps) #s(literal 2 binary64)) eps) (/.f64 #s(literal 4 binary64) (-.f64 eps (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (neg.f64 (.f64 #s(literal 2 binary64) eps)) x) (.f64 (neg.f64 (.f64 #s(literal 2 binary64) eps)) x))) (fma.f64 eps eps (.f64 (neg.f64 (*.f64 #s(literal 2 binary64) eps)) x)))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (neg.f64 x) (.f64 #s(literal 2 binary64) eps)) (.f64 (neg.f64 x) (.f64 #s(literal 2 binary64) eps)))) (fma.f64 eps eps (.f64 (neg.f64 x) (*.f64 #s(literal 2 binary64) eps))))
(/.f64 (-.f64 (.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 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal 2 binary64) x))))) (/.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 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal 2 binary64) x)))))) (.f64 (/.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 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal 2 binary64) x))))) (/.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 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal 2 binary64) x))))))) (-.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 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal 2 binary64) x))))) (/.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 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal 2 binary64) x)))))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 eps #s(literal 6 binary64)) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) (.f64 eps (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (pow.f64 eps #s(literal 4 binary64)))) (/.f64 (pow.f64 eps #s(literal 6 binary64)) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) (.f64 eps (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (pow.f64 eps #s(literal 4 binary64))))) (.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 3 binary64)) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) (.f64 eps (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (pow.f64 eps #s(literal 4 binary64)))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 3 binary64)) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) (.f64 eps (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (pow.f64 eps #s(literal 4 binary64)))))) (-.f64 (/.f64 (pow.f64 eps #s(literal 6 binary64)) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) (.f64 eps (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (pow.f64 eps #s(literal 4 binary64)))) (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 3 binary64)) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) (.f64 eps (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (pow.f64 eps #s(literal 4 binary64))))))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (neg.f64 (.f64 (neg.f64 eps) x)) #s(literal 2 binary64)) (.f64 (neg.f64 (.f64 (neg.f64 eps) x)) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (neg.f64 (.f64 (neg.f64 eps) x)) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 2 binary64)) (.f64 (.f64 (neg.f64 (neg.f64 eps)) eps) (.f64 (neg.f64 (neg.f64 eps)) eps))) (-.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) (.f64 (neg.f64 (neg.f64 eps)) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) eps) x) #s(literal 2 binary64)) (.f64 (.f64 (neg.f64 (neg.f64 eps)) (neg.f64 eps)) (.f64 (neg.f64 (neg.f64 eps)) (neg.f64 eps)))) (.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 x eps)) (.f64 #s(literal -2 binary64) (.f64 x eps)))) (.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x))))
(/.f64 (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 (neg.f64 eps) (.f64 #s(literal 2 binary64) x)) (.f64 (neg.f64 eps) (.f64 #s(literal 2 binary64) x)))) (.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x))))
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(+.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 (neg.f64 eps))) (neg.f64 (neg.f64 (neg.f64 eps))))
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
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(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 (0.5%)

Memory: -15.4MiB live, 28.0MiB allocated; 7ms collecting garbage
Compiler: Compiled 6 244 to 661 computations (89.4% saved)

prune5.0ms (0.1%)

Memory

14.5MiB live, 14.5MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	0	0	0
Picked	2	2	4
Done	0	2	2
Total	174	6	180

Accuracy

100.0%

Counts

180 → 6

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)) (fma.f64 eps eps (.f64 (.f64 eps x) #s(literal 2 binary64))))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	66.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	73.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	41.4%	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Compiler

Compiled 98 to 64 computations (34.7% saved)

simplify240.0ms (3.4%)

Memory

9.8MiB live, 240.3MiB allocated; 49ms 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	87	57
3	272	57
4	708	53
5	1804	53
6	5838	53
0	8255	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)

localize140.0ms (2%)

Memory

-39.2MiB live, 119.7MiB allocated; 42ms collecting garbage

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	0.01171875	(fma.f64 (+.f64 eps eps) x (*.f64 eps eps))
accuracy	0.0	(+.f64 eps eps)
accuracy	0.0	(*.f64 (+.f64 eps eps) x)
accuracy	21.591877419791942	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))

Samples

17.0ms	163×	0	valid
13.0ms	72×	1	valid
5.0ms	21×	2	valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 7.0ms (28.3% of total)

ival-pow2: 7.0ms (28.3% of total)

ival-add: 5.0ms (20.2% of total)

adjust: 4.0ms (16.2% of total)

ival-sub: 2.0ms (8.1% of total)

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

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

series5.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated; 0ms collecting garbage

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))

simplify89.0ms (1.3%)

Memory

40.2MiB live, 127.9MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	56
1	89	46
2	281	46
3	942	46
4	2846	46
5	5640	46
0	8021	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)

rewrite54.0ms (0.8%)

Memory

-19.5MiB live, 43.8MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	52
0	17	52
1	84	52
0	691	52

Stop Event

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

Counts

6 → 66

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 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 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 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 (-.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 (fabs.f64 (fabs.f64 eps)) (fabs.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 (fabs.f64 (fabs.f64 eps)) (fabs.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))
(fabs.f64 (*.f64 eps eps))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))

eval17.0ms (0.2%)

Memory: -30.0MiB live, 16.5MiB allocated; 2ms collecting garbage
Compiler: Compiled 1 744 to 242 computations (86.1% saved)

prune5.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	79	6	85

Accuracy

100.0%

Counts

85 → 6

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)) (fma.f64 eps eps (.f64 (.f64 eps x) #s(literal 2 binary64))))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	66.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	73.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	41.4%	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Compiler

Compiled 286 to 114 computations (60.1% saved)

regimes11.0ms (0.2%)

Memory

23.1MiB live, 23.1MiB allocated; 0ms collecting garbage

Counts

12 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	eps
3.0ms	x
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	`(-.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)

regimes9.0ms (0.1%)

Memory

-32.1MiB live, 13.1MiB allocated; 4ms collecting garbage

Counts

5 → 2

Calls

Call 1

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

5.0ms	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
97.0%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
92.5%	3	`x`
88.6%	3	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
73.0%	1	`eps`
73.0%	1	`x`
73.0%	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)

regimes3.0ms (0%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
41.4%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
41.4%	1	`x`
41.4%	1	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	1.4e-322

Compiler

Compiled 12 to 12 computations (0% saved)

simplify59.0ms (0.9%)

Memory

0.4MiB live, 45.4MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	86
1	50	80
2	105	80
3	357	80
4	1123	70
5	2880	70
6	5561	70
7	7457	70

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations869.0ms (12.5%)

Memory

3.2MiB live, 292.3MiB allocated; 26ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	51	20
2	364	20
3	5050	20
0	8368	20
0	26	104
0	33	103
1	159	93
2	1419	93
0	8183	89
0	24	130
0	40	130
1	172	125
2	1368	125
0	8329	125
0	107	291
1	356	264
2	1189	254
3	4860	250
0	8108	233
0	69	215
1	239	203
2	827	191
3	3630	191
0	8470	176

Stop Event

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

Compiler

Compiled 80 to 24 computations (70% saved)

preprocess48.0ms (0.7%)

Memory: -25.6MiB live, 20.3MiB allocated; 6ms collecting garbage
Compiler: Compiled 178 to 62 computations (65.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample2.3s (33.4%)

explain135.0ms (1.9%)

preprocess389.0ms (5.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify382.0ms (5.5%)

localize28.0ms (0.4%)

series58.0ms (0.8%)

simplify158.0ms (2.3%)

rewrite224.0ms (3.2%)

eval75.0ms (1.1%)

prune7.0ms (0.1%)

simplify177.0ms (2.5%)

localize132.0ms (1.9%)

series57.0ms (0.8%)

simplify183.0ms (2.6%)

rewrite255.0ms (3.7%)

eval74.0ms (1.1%)

prune19.0ms (0.3%)

simplify248.0ms (3.6%)

localize78.0ms (1.1%)

series7.0ms (0.1%)

simplify165.0ms (2.4%)

rewrite189.0ms (2.7%)

eval32.0ms (0.5%)

prune5.0ms (0.1%)

simplify240.0ms (3.4%)

localize140.0ms (2%)

series5.0ms (0.1%)

simplify89.0ms (1.3%)

rewrite54.0ms (0.8%)

eval17.0ms (0.2%)

prune5.0ms (0.1%)

regimes11.0ms (0.2%)

regimes9.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

bsearch0.0ms (0%)

simplify59.0ms (0.9%)

derivations869.0ms (12.5%)

preprocess48.0ms (0.7%)

end0.0ms (0%)

Profiling