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

0.8MiB live, 0.8MiB 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)

sample2.4s (33.2%)

Memory

-58.7MiB live, 2 143.4MiB allocated; 1.4s collecting garbage

Samples

1.2s	5 097×	0	valid
678.0ms	2 566×	1	valid
168.0ms	593×	2	valid

Precisions

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

ival-<=: 798.0ms (48.8% of total)

ival-pow2: 385.0ms (23.5% of total)

adjust: 211.0ms (12.9% of total)

ival-add: 135.0ms (8.3% of total)

ival-sub: 65.0ms (4% of total)

ival-and: 22.0ms (1.3% of total)

exact: 15.0ms (0.9% of total)

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

Bogosity

explain159.0ms (2.2%)

Memory

-32.7MiB live, 126.7MiB allocated; 35ms collecting garbage

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	cancellation	63	0

Confusion

	Predicted +	Predicted -
+	63	0
-	0	193

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	63	0	0
-	0	0	193

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	193
1	63

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

20.0ms	324×	0	valid
17.0ms	134×	1	valid
10.0ms	54×	2	valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-pow2: 15.0ms (50.8% of total)

adjust: 6.0ms (20.3% of total)

ival-add: 4.0ms (13.5% of total)

ival-sub: 3.0ms (10.2% of total)

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

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

exact: 0.0ms (0% of total)

preprocess266.0ms (3.6%)

Memory

45.1MiB live, 276.6MiB allocated; 30ms collecting garbage

Algorithm

1×	egg-herbie

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: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

-46.8MiB live, 0.8MiB allocated; 1ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.7%	(-.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)

simplify222.0ms (3%)

Memory

16.1MiB live, 293.8MiB allocated; 56ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	11	23
1	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)

localize31.0ms (0.4%)

Memory

5.6MiB live, 53.6MiB allocated; 3ms 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	0.04296875	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	13.597584479616092	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

10.0ms	162×	0	valid
9.0ms	67×	1	valid
7.0ms	27×	2	valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-pow2: 7.0ms (43.3% of total)

adjust: 4.0ms (24.8% of total)

ival-add: 2.0ms (12.4% of total)

ival-sub: 2.0ms (12.4% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB allocated; 0ms 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
1.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))

simplify285.0ms (3.9%)

Memory

18.6MiB live, 249.9MiB allocated; 75ms collecting garbage

Algorithm

1×	egg-herbie

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)))

rewrite178.0ms (2.4%)

Memory

2.7MiB live, 190.9MiB allocated; 37ms 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%)

Memory: 0.5MiB live, 103.0MiB allocated; 11ms collecting garbage
Compiler: Compiled 7 675 to 1 120 computations (85.4% saved)

prune8.0ms (0.1%)

Memory

-28.0MiB live, 18.1MiB allocated; 3ms 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
▶	66.8%	(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))
▶	90.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) (+.f64 (/.f64 eps x) #s(literal 2 binary64))))
▶	59.6%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	75.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 154 to 102 computations (33.8% saved)

simplify153.0ms (2.1%)

Memory

24.3MiB live, 209.4MiB allocated; 22ms collecting garbage

Algorithm

1×	egg-herbie

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)

localize98.0ms (1.3%)

Memory

-2.0MiB live, 89.0MiB allocated; 6ms 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	0.01953125	(fma.f64 (+.f64 eps x) eps (*.f64 (neg.f64 x) x))
accuracy	21.235622424702793	(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	6.221848264507097	(.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	25.87411379707176	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0.0	(*.f64 eps eps)
accuracy	15.401189960199389	#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

40.0ms	68×	1	valid
28.0ms	161×	0	valid
14.0ms	27×	2	valid

Compiler

Compiled 128 to 25 computations (80.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-mult: 31.0ms (49.2% of total)

adjust: 10.0ms (15.9% of total)

ival-add: 10.0ms (15.9% of total)

ival-pow2: 7.0ms (11.1% of total)

ival-div: 2.0ms (3.2% of total)

ival-sub: 2.0ms (3.2% of total)

ival-neg: 1.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series16.0ms (0.2%)

Memory

22.7MiB live, 22.7MiB allocated; 0ms 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
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	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))
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	@	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))

simplify210.0ms (2.9%)

Memory

-28.2MiB live, 162.6MiB allocated; 37ms collecting garbage

Algorithm

1×	egg-herbie

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))

rewrite235.0ms (3.2%)

Memory

6.9MiB live, 191.6MiB allocated; 27ms 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)

eval93.0ms (1.3%)

Memory: 7.6MiB live, 107.7MiB allocated; 16ms collecting garbage
Compiler: Compiled 24 777 to 2 002 computations (91.9% saved)

prune15.0ms (0.2%)

Memory

-5.1MiB live, 39.2MiB allocated; 5ms 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 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))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
▶	59.6%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	75.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
▶	37.6%	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Compiler

Compiled 97 to 65 computations (33% saved)

simplify253.0ms (3.4%)

Memory

-1.2MiB live, 230.6MiB allocated; 40ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
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 x)
cost-diff	0	(*.f64 (+.f64 (+.f64 eps x) x) eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
cost-diff	1	(+.f64 (+.f64 eps x) x)
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	27	116
0	37	113
1	75	107
2	166	107
3	429	107
4	1254	99
5	3240	99
6	6273	99
0	8350	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)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
(*.f64 (+.f64 (+.f64 eps x) x) eps)
(+.f64 (+.f64 eps x) x)
(+.f64 eps x)
eps
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)

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

localize139.0ms (1.9%)

Memory

29.7MiB live, 139.8MiB allocated; 20ms collecting garbage

Localize:

Found 12 expressions of interest:

New	Metric	Score
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	0.00390625	(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 eps x)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
accuracy	0.01171875	(*.f64 (+.f64 (+.f64 eps x) x) eps)
accuracy	0.04296875	(+.f64 (+.f64 eps x) x)
accuracy	0.0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
accuracy	0.0	(*.f64 eps #s(literal 2 binary64))
accuracy	25.87411379707176	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
accuracy	39.92782985945553	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Samples

58.0ms	68×	1	valid
53.0ms	161×	0	valid
14.0ms	27×	2	valid

Compiler

Compiled 94 to 25 computations (73.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-mult: 51.0ms (57.1% of total)

ival-pow2: 15.0ms (16.8% of total)

adjust: 10.0ms (11.2% of total)

ival-add: 10.0ms (11.2% of total)

ival-sub: 2.0ms (2.2% of total)

ival-neg: 1.0ms (1.1% of total)

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

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

exact: 0.0ms (0% of total)

series32.0ms (0.4%)

Memory

-33.4MiB live, 12.7MiB allocated; 4ms collecting garbage

Counts

12 → 27

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

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

Calls

6 calls:

Time	Variable		Point	Expression
25.0ms	x	@	-inf	((+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* eps x) 2)) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x))
2.0ms	eps	@	-inf	((+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* eps x) 2)) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x))
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 x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* eps x) 2)) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x))
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 x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* eps x) 2)) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x))
1.0ms	x	@	0	((+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* eps x) 2)) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x))

simplify203.0ms (2.8%)

Memory

11.9MiB live, 155.5MiB allocated; 17ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	186
1	239	176
2	805	172
3	3428	172
0	8175	162

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 25

Calls

Call 1

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

rewrite175.0ms (2.4%)

Memory

10.2MiB live, 158.0MiB allocated; 18ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	107
0	37	104
1	166	98
2	1335	98
0	8247	93

Stop Event

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

Counts

12 → 313

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

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 x eps) #s(literal 2 binary64)))
(.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 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 (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 (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 (fma.f64 x x (pow.f64 (+.f64 x eps) #s(literal 2 binary64))) (fma.f64 x x (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))) (fma.f64 #s(literal 2 binary64) x eps))
(.f64 (/.f64 (+.f64 (+.f64 (pow.f64 (+.f64 x eps) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (+.f64 (+.f64 (pow.f64 (+.f64 x eps) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (*.f64 (+.f64 x eps) x) #s(literal 2 binary64)))) (fma.f64 #s(literal 2 binary64) x eps))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))) (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))))) (.f64 (/.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))))))))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) (.f64 eps (-.f64 eps (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 x (+.f64 x eps))))
(/.f64 (neg.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 eps (*.f64 #s(literal 2 binary64) x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (fma.f64 eps eps (-.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) (.f64 (.f64 x eps) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 x eps) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (-.f64 (+.f64 x eps) x))))
(/.f64 (-.f64 (.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (-.f64 (+.f64 x eps) x)) (.f64 (-.f64 (+.f64 x eps) x) (.f64 x x))) (.f64 (-.f64 (+.f64 x eps) x) (-.f64 (+.f64 x eps) x)))
(/.f64 (fma.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))) (.f64 (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))) (.f64 (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))) (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))) (-.f64 x (+.f64 x eps)))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) (-.f64 eps (*.f64 #s(literal 2 binary64) x)))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) (.f64 (.f64 x eps) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (*.f64 (fma.f64 x x (pow.f64 (+.f64 x eps) #s(literal 2 binary64))) (-.f64 (+.f64 x eps) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (.f64 (+.f64 (+.f64 (pow.f64 (+.f64 x eps) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (-.f64 (+.f64 x eps) x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (*.f64 (+.f64 x eps) x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 x eps) #s(literal 2 binary64)))) (neg.f64 (-.f64 (+.f64 x eps) x)))
(/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (fma.f64 x x (pow.f64 (+.f64 x eps) #s(literal 2 binary64))) (-.f64 (+.f64 x eps) x)))
(/.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (+.f64 (+.f64 (pow.f64 (+.f64 x eps) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (.f64 (+.f64 x eps) x) #s(literal 2 binary64))) (-.f64 (+.f64 x eps) x)))
(/.f64 (+.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (*.f64 (+.f64 x eps) x))))
(/.f64 (+.f64 (pow.f64 (+.f64 x eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x (-.f64 x (+.f64 x eps)) (pow.f64 (+.f64 x eps) #s(literal 2 binary64))))
(/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 x eps) #s(literal 2 binary64))) (-.f64 (+.f64 x eps) x))
(fma.f64 (neg.f64 (sqrt.f64 (+.f64 x eps))) (neg.f64 (sqrt.f64 (+.f64 x eps))) x)
(fma.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)) (+.f64 x eps))
(fma.f64 (fabs.f64 (sqrt.f64 x)) (fabs.f64 (sqrt.f64 x)) (+.f64 x eps))
(fma.f64 (fabs.f64 (sqrt.f64 (+.f64 x eps))) (fabs.f64 (sqrt.f64 (+.f64 x eps))) x)
(fma.f64 (sqrt.f64 (neg.f64 (neg.f64 eps))) (sqrt.f64 (neg.f64 (neg.f64 eps))) (*.f64 #s(literal 2 binary64) x))
(fma.f64 (sqrt.f64 (neg.f64 eps)) (sqrt.f64 (neg.f64 eps)) (*.f64 #s(literal 2 binary64) x))
(fma.f64 (sqrt.f64 eps) (sqrt.f64 eps) (*.f64 #s(literal 2 binary64) x))
(fma.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (+.f64 x eps))
(fma.f64 (pow.f64 (sqrt.f64 (+.f64 x eps)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (+.f64 x eps)) #s(literal 1 binary64)) x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 x eps))
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eval52.0ms (0.7%)

Memory: -15.3MiB live, 30.5MiB allocated; 2ms collecting garbage
Compiler: Compiled 8 049 to 1 097 computations (86.4% saved)

prune6.0ms (0.1%)

Memory

17.0MiB live, 17.0MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	244	2	246
Fresh	0	0	0
Picked	2	2	4
Done	0	2	2
Total	246	6	252

Accuracy

100.0%

Counts

252 → 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 x eps) eps (*.f64 x eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
▶	59.6%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	75.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	37.6%	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Compiler

Compiled 97 to 63 computations (35.1% saved)

simplify290.0ms (3.9%)

Memory

17.5MiB live, 203.3MiB allocated; 29ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x eps)
cost-diff	0	(+.f64 x eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 x eps) eps (*.f64 x eps)))
cost-diff	2	(fma.f64 (+.f64 x eps) eps (*.f64 x 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	14	59
0	20	57
1	35	57
2	81	57
3	239	57
4	693	53
5	2072	53
6	6514	53
0	8092	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 x eps) eps (*.f64 x eps)))
(fma.f64 (+.f64 x eps) eps (*.f64 x eps))
(+.f64 x eps)
x
eps
(*.f64 x 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 x eps) eps (*.f64 x eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(fma.f64 (+.f64 x eps) eps (*.f64 x eps))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
(+.f64 x eps)
(+.f64 eps x)
x
eps
(*.f64 x eps)
(*.f64 eps x)

localize51.0ms (0.7%)

Memory

9.4MiB live, 92.8MiB allocated; 13ms collecting garbage

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(*.f64 x eps)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 x eps) eps (*.f64 x eps)))
accuracy	0.01171875	(fma.f64 (+.f64 x eps) eps (*.f64 x eps))
accuracy	0.0	(+.f64 eps eps)
accuracy	0.0	(*.f64 (+.f64 eps eps) x)
accuracy	25.87411379707176	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))

Samples

18.0ms	162×	0	valid
17.0ms	67×	1	valid
7.0ms	27×	2	valid

Compiler

Compiled 47 to 13 computations (72.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-mult: 10.0ms (31.4% of total)

ival-pow2: 10.0ms (31.4% of total)

adjust: 5.0ms (15.7% of total)

ival-add: 5.0ms (15.7% of total)

ival-sub: 2.0ms (6.3% of total)

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

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

series171.0ms (2.3%)

Memory

-58.9MiB live, 106.1MiB allocated; 109ms collecting garbage

Counts

7 → 16

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

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

Calls

6 calls:

Time	Variable		Point	Expression
103.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ eps eps) x) (+ eps eps) (+ (* (+ x eps) eps) (* x eps)) (- (pow (+ x eps) 2) (pow x 2)) (+ x eps) (* x eps))
65.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ eps eps) x) (+ eps eps) (+ (* (+ x eps) eps) (* x eps)) (- (pow (+ x eps) 2) (pow x 2)) (+ x eps) (* x eps))
1.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ eps eps) x) (+ eps eps) (+ (* (+ x eps) eps) (* x eps)) (- (pow (+ x eps) 2) (pow x 2)) (+ x eps) (* x eps))
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ eps eps) x) (+ eps eps) (+ (* (+ x eps) eps) (* x eps)) (- (pow (+ x eps) 2) (pow x 2)) (+ x eps) (* x eps))
1.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (+ eps eps) x) (+ eps eps) (+ (* (+ x eps) eps) (* x eps)) (- (pow (+ x eps) 2) (pow x 2)) (+ x eps) (* x eps))

simplify100.0ms (1.4%)

Memory

38.5MiB live, 136.5MiB allocated; 18ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	76
1	135	66
2	366	66
3	1202	66
4	3569	66
5	6118	66
0	8122	61

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 14

Calls

Call 1

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

rewrite36.0ms (0.5%)

Memory

-6.8MiB live, 38.0MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
0	20	53
1	87	53
0	639	53

Stop Event

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

Counts

7 → 62

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

eval33.0ms (0.4%)

Memory: -27.3MiB live, 19.4MiB allocated; 3ms collecting garbage
Compiler: Compiled 1 586 to 246 computations (84.5% saved)

prune4.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	68	6	74

Accuracy

100.0%

Counts

74 → 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 x eps) eps (*.f64 x eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
✓	59.6%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	75.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
✓	37.6%	#s(approx (+ (* (+ eps x) x) (+ (* (+ eps x) eps) (* (neg x) x))) #s(literal 0 binary64))

Compiler

Compiled 284 to 115 computations (59.5% saved)

regimes11.0ms (0.1%)

Memory

16.4MiB live, 16.4MiB 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 (+.f64 (+.f64 eps x) x) eps))
#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 x eps) eps (*.f64 x 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)) (.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
4.0ms	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)

regimes7.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated; 0ms collecting garbage

Counts

6 → 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 (+.f64 (+.f64 eps x) x) eps))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
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)

regimes23.0ms (0.3%)

Memory

-32.9MiB live, 14.4MiB allocated; 2ms 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:

18.0ms	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
97.2%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
92.0%	3	`x`
86.9%	3	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0.1%)

Memory

8.4MiB live, 8.4MiB 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	x
1.0ms	eps
1.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
75.9%	1	`eps`
75.9%	1	`x`
75.9%	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

7.8MiB live, 7.8MiB 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
37.6%	1	`x`
37.6%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
37.6%	1	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	8.6e-322

Compiler

Compiled 12 to 12 computations (0% saved)

simplify70.0ms (0.9%)

Memory

-2.4MiB live, 49.3MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	34	103
1	54	97
2	109	97
3	361	97
4	1128	85
5	2871	85
6	5587	85
7	7470	85

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

derivations1.1s (14.6%)

Memory

7.4MiB live, 533.2MiB allocated; 46ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	107
0	37	104
1	166	98
2	1335	98
0	8247	93
0	24	130
0	40	130
1	172	125
2	1368	125
0	8329	125
0	7	20
0	11	20
1	51	20
2	364	20
3	5050	20
0	8368	20
0	69	215
1	239	203
2	827	191
3	3630	191
0	8470	176
0	107	291
1	356	264
2	1189	254
3	4860	250
0	8108	233

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 97 to 28 computations (71.1% saved)

preprocess123.0ms (1.7%)

Memory: -31.0MiB live, 65.5MiB allocated; 13ms collecting garbage
Compiler: Compiled 212 to 70 computations (67% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample2.4s (33.2%)

explain159.0ms (2.2%)

preprocess266.0ms (3.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify222.0ms (3%)

localize31.0ms (0.4%)

series5.0ms (0.1%)

simplify285.0ms (3.9%)

rewrite178.0ms (2.4%)

eval75.0ms (1%)

prune8.0ms (0.1%)

simplify153.0ms (2.1%)

localize98.0ms (1.3%)

series16.0ms (0.2%)

simplify210.0ms (2.9%)

rewrite235.0ms (3.2%)

eval93.0ms (1.3%)

prune15.0ms (0.2%)

simplify253.0ms (3.4%)

localize139.0ms (1.9%)

series32.0ms (0.4%)

simplify203.0ms (2.8%)

rewrite175.0ms (2.4%)

eval52.0ms (0.7%)

prune6.0ms (0.1%)

simplify290.0ms (3.9%)

localize51.0ms (0.7%)

series171.0ms (2.3%)

simplify100.0ms (1.4%)

rewrite36.0ms (0.5%)

eval33.0ms (0.4%)

prune4.0ms (0.1%)

regimes11.0ms (0.1%)

regimes7.0ms (0.1%)

regimes23.0ms (0.3%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

bsearch0.0ms (0%)

simplify70.0ms (0.9%)

derivations1.1s (14.6%)

preprocess123.0ms (1.7%)

end0.0ms (0%)

Profiling