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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 25 to 18 computations (28% saved)

sample1.5s (27.2%)

Memory

24.1MiB live, 2 390.1MiB allocated

Samples

564.0ms	5 132×	0	valid
446.0ms	2 601×	1	valid
133.0ms	523×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 836.0ms

ival-pow2: 306.0ms (36.6% of total)

ival-add: 156.0ms (18.7% of total)

ival-<=: 150.0ms (17.9% of total)

adjust: 111.0ms (13.3% of total)

ival-sub: 66.0ms (7.9% of total)

ival-and: 24.0ms (2.9% of total)

exact: 19.0ms (2.3% of total)

ival-assert: 4.0ms (0.5% of total)

Bogosity

explain131.0ms (2.3%)

Memory

2.9MiB live, 193.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
68	1	(-1.3246331655810722e-107 -2.026606832813049e-217)	-	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	-	`eps`
0	0	-	-	`(pow.f64 x #s(literal 2 binary64))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(pow.f64 (+.f64 x eps) #s(literal 2 binary64))`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	cancellation	69	1

Confusion

	Predicted +	Predicted -
+	68	0
-	1	187

Precision

0.9855072463768116

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	68	0	0
-	1	1	186

Precision?

0.9714285714285714

Recall?

1.0

Freqs

test

number	freq
0	187
1	69

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

49.0ms	156×	1	valid
22.0ms	338×	0	valid
3.0ms	18×	2	valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-pow2: 44.0ms (80% of total)

ival-add: 4.0ms (7.3% of total)

adjust: 3.0ms (5.5% of total)

ival-sub: 3.0ms (5.5% of total)

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

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

exact: 0.0ms (0% of total)

preprocess241.0ms (4.2%)

Memory

39.6MiB live, 313.5MiB allocated

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

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.7%	(-.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)

simplify239.0ms (4.2%)

Memory

-8.6MiB live, 139.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	11	23
1	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)

localize67.0ms (1.2%)

Memory

-12.8MiB live, 31.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.00390625	(pow.f64 x #s(literal 2 binary64))
accuracy	0.03125	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	14.224990739463511	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

9.0ms	169×	0	valid
9.0ms	78×	1	valid
1.0ms	9×	2	valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

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

ival-pow2: 6.0ms (49.4% of total)

adjust: 2.0ms (16.5% of total)

ival-add: 2.0ms (16.5% of total)

ival-sub: 2.0ms (16.5% 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

5.5MiB live, 5.5MiB allocated

Counts

4 → 23

Calls

Call 1

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

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

Calls

6 calls:

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

simplify287.0ms (5.1%)

Memory

-67.8MiB live, 129.9MiB allocated

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)))

rewrite212.0ms (3.7%)

Memory

24.9MiB live, 172.7MiB allocated

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))))

eval71.0ms (1.2%)

Memory: 4.0MiB live, 50.1MiB allocated
Compiler: Compiled 7 675 to 1 120 computations (85.4% saved)

prune36.0ms (0.6%)

Memory

-29.0MiB live, 14.2MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	323	4	327
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	324	4	328

Accuracy

100.0%

Counts

328 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	89.1%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) (+.f64 (/.f64 eps x) #s(literal 2 binary64))))
▶	64.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	73.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 63 to 44 computations (30.2% saved)

simplify189.0ms (3.3%)

Memory

14.3MiB live, 158.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	19	114
0	28	120
1	54	120
2	144	120
3	388	116
4	961	108
5	2364	96
6	7436	96
0	8547	96

Stop Event

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

Calls

Call 1

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

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

localize87.0ms (1.5%)

Memory

-21.1MiB live, 126.1MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 #s(literal 2 binary64) x eps)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
accuracy	0.0234375	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
accuracy	0.0	(+.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 eps x) (+.f64 (/.f64 eps x) #s(literal 2 binary64))))
accuracy	6.954635981515683	(.f64 (.f64 eps x) (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
accuracy	0.0	(*.f64 eps x)
accuracy	0.02734375	(.f64 (.f64 eps x) #s(literal 2 binary64))
accuracy	23.02081118439844	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0.0	(*.f64 eps eps)
accuracy	16.72503128796661	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Samples

26.0ms	169×	0	valid
16.0ms	78×	1	valid
3.0ms	9×	2	valid

Compiler

Compiled 91 to 18 computations (80.2% saved)

Precisions

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

ival-mult: 13.0ms (42.9% of total)

ival-pow2: 7.0ms (23.1% of total)

ival-add: 4.0ms (13.2% of total)

adjust: 3.0ms (9.9% of total)

ival-div: 2.0ms (6.6% of total)

ival-sub: 2.0ms (6.6% of total)

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

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

exact: 0.0ms (0% of total)

series12.0ms (0.2%)

Memory

23.5MiB live, 23.5MiB allocated

Counts

11 → 20

Calls

Call 1

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

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

Calls

6 calls:

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

simplify90.0ms (1.6%)

Memory

-3.8MiB live, 88.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	115
1	148	105
2	426	99
3	1339	99
4	4408	99
0	8216	90

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 19

Calls

Call 1

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

rewrite248.0ms (4.4%)

Memory

-0.2MiB live, 318.1MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	98
0	28	98
1	115	98
2	782	94
0	9348	94

Stop Event

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

Counts

11 → 449

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 eps eps)
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(pow.f64 (neg.f64 eps) #s(literal 2 binary64))
(pow.f64 (*.f64 eps eps) #s(literal 1 binary64))
(pow.f64 eps #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 eps) eps))
(sqrt.f64 (pow.f64 eps #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 eps) eps))
(fabs.f64 (*.f64 eps eps))
(exp.f64 (*.f64 (log.f64 (neg.f64 eps)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 eps) #s(literal 2 binary64))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 #s(literal -2 binary64) (.f64 eps x)))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 (*.f64 eps #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 #s(literal -2 binary64) eps) x)
(.f64 (.f64 (neg.f64 eps) #s(literal 2 binary64)) x)
(.f64 (.f64 #s(literal 2 binary64) eps) x)
(.f64 (.f64 eps #s(literal 2 binary64)) x)
(.f64 (.f64 (neg.f64 x) eps) #s(literal 2 binary64))
(.f64 #s(literal -2 binary64) (.f64 eps x))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 #s(literal 2 binary64) eps)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 eps #s(literal 2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) x) eps)
(.f64 (neg.f64 eps) (.f64 #s(literal -2 binary64) x))
(.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)))
(/.f64 (*.f64 eps #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (*.f64 (neg.f64 eps) #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (-.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (pow.f64 (.f64 eps x) #s(literal 2 binary64))) (-.f64 (.f64 eps x) (.f64 eps x)))
(/.f64 (+.f64 (pow.f64 (.f64 eps x) #s(literal 3 binary64)) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (pow.f64 (*.f64 eps x) #s(literal 2 binary64)))))
(/.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) (fma.f64 x x #s(literal 0 binary64)))
(neg.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)))
(fma.f64 (.f64 (neg.f64 eps) (sqrt.f64 x)) (sqrt.f64 x) (.f64 (neg.f64 x) eps))
(fma.f64 (.f64 eps (sqrt.f64 x)) (sqrt.f64 x) (.f64 eps x))
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) eps) (.f64 eps x))
(fma.f64 (neg.f64 x) eps (*.f64 (neg.f64 x) eps))
(fma.f64 (neg.f64 eps) x (*.f64 (neg.f64 x) eps))
(fma.f64 eps (neg.f64 x) (*.f64 (neg.f64 x) eps))
(fma.f64 eps x (*.f64 eps x))
(fma.f64 x (neg.f64 eps) (*.f64 (neg.f64 x) eps))
(fma.f64 x eps (*.f64 eps x))
(-.f64 (.f64 eps x) (.f64 (neg.f64 x) eps))
(+.f64 (.f64 (neg.f64 x) eps) (.f64 (neg.f64 x) eps))
(+.f64 (.f64 eps x) (.f64 eps x))
(.f64 (.f64 eps (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) eps))
(*.f64 eps x)
(*.f64 x eps)
(.f64 (.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 eps (+.f64 (/.f64 eps x) #s(literal 2 binary64))) x)
(.f64 (.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps) x)
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 eps (+.f64 (/.f64 eps x) #s(literal 2 binary64)))))
(.f64 (.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x) eps)
(.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 (.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 (.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x))
(.f64 x (-.f64 (.f64 (/.f64 eps x) eps) (*.f64 #s(literal 2 binary64) eps)))
(.f64 x (fma.f64 (/.f64 eps x) eps (.f64 eps #s(literal 2 binary64))))
(.f64 x (fma.f64 eps #s(literal 2 binary64) (.f64 (/.f64 eps x) eps)))
(.f64 x (-.f64 (.f64 eps (/.f64 eps x)) (*.f64 #s(literal 2 binary64) eps)))
(.f64 x (fma.f64 eps (/.f64 eps x) (.f64 #s(literal 2 binary64) eps)))
(.f64 x (fma.f64 #s(literal 2 binary64) eps (.f64 eps (/.f64 eps x))))
(.f64 x (-.f64 (.f64 eps (/.f64 eps x)) (*.f64 eps #s(literal 2 binary64))))
(.f64 x (-.f64 (.f64 (/.f64 eps x) eps) (*.f64 eps #s(literal 2 binary64))))
(.f64 x (.f64 eps (+.f64 (/.f64 eps x) #s(literal 2 binary64))))
(.f64 x (.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) eps))
(/.f64 (.f64 (.f64 eps x) (-.f64 #s(literal 4 binary64) (pow.f64 (/.f64 eps x) #s(literal 2 binary64)))) (-.f64 #s(literal 2 binary64) (/.f64 eps x)))
(/.f64 (.f64 (.f64 eps x) (neg.f64 (-.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)))) (neg.f64 (-.f64 (/.f64 eps x) #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 eps x) (neg.f64 (+.f64 #s(literal 8 binary64) (pow.f64 (/.f64 eps x) #s(literal 3 binary64))))) (neg.f64 (-.f64 (+.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (/.f64 eps x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) eps) (pow.f64 (.f64 (.f64 (/.f64 eps x) eps) x) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) (.f64 (*.f64 (/.f64 eps x) eps) x)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 eps x) eps) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (/.f64 eps x) eps) x) #s(literal 2 binary64)) (fma.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64) (.f64 (.f64 (/.f64 eps x) eps) (.f64 x (.f64 #s(literal -2 binary64) (.f64 eps x)))))))
(/.f64 (fma.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2 binary64) (pow.f64 (.f64 (.f64 (/.f64 eps x) eps) x) #s(literal 3 binary64))) (fma.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64) (-.f64 (pow.f64 (.f64 (.f64 (/.f64 eps x) eps) x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) (.f64 (*.f64 (/.f64 eps x) eps) x)))))
(/.f64 (neg.f64 (.f64 (.f64 (-.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) eps) x)) (neg.f64 (-.f64 (/.f64 eps x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 (.f64 (+.f64 #s(literal 8 binary64) (pow.f64 (/.f64 eps x) #s(literal 3 binary64))) eps) x)) (neg.f64 (-.f64 (+.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (/.f64 eps x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 eps x) (-.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)))) (neg.f64 (-.f64 (/.f64 eps x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 (.f64 eps x) (+.f64 #s(literal 8 binary64) (pow.f64 (/.f64 eps x) #s(literal 3 binary64))))) (neg.f64 (-.f64 (+.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (/.f64 eps x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 eps x) eps) x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) eps))) (neg.f64 (.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x) eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (/.f64 eps x) eps) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (/.f64 eps x) eps) x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) (-.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) (.f64 (*.f64 (/.f64 eps x) eps) x))))))
(/.f64 (.f64 (.f64 (-.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) eps) x) (-.f64 (/.f64 eps x) #s(literal 2 binary64)))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 8 binary64) (pow.f64 (/.f64 eps x) #s(literal 3 binary64))) eps) x) (-.f64 (+.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (/.f64 eps x) #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 eps x) (-.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64))) (-.f64 (/.f64 eps x) #s(literal 2 binary64)))
(/.f64 (.f64 (.f64 eps x) (+.f64 #s(literal 8 binary64) (pow.f64 (/.f64 eps x) #s(literal 3 binary64)))) (+.f64 #s(literal 4 binary64) (*.f64 (/.f64 eps x) (-.f64 (/.f64 eps x) #s(literal 2 binary64)))))
(/.f64 (.f64 (.f64 eps x) (+.f64 #s(literal 8 binary64) (pow.f64 (/.f64 eps x) #s(literal 3 binary64)))) (-.f64 (+.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 4 binary64)) (*.f64 (/.f64 eps x) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 eps x) eps) x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) eps)) (.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 2 binary64)) x) eps))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (/.f64 eps x) eps) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (/.f64 eps x) eps) x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) (-.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) (.f64 (*.f64 (/.f64 eps x) eps) x)))))
(fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x) (.f64 (.f64 x (/.f64 eps x)) eps))
(fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x) (.f64 eps (.f64 (/.f64 eps x) x)))
(fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x) (.f64 (.f64 (/.f64 eps x) eps) x))
(fma.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x) (.f64 (.f64 x (/.f64 eps x)) eps))
(fma.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x) (.f64 eps (.f64 (/.f64 eps x) x)))
(fma.f64 (.f64 (.f64 eps #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x) (.f64 (.f64 (/.f64 eps x) eps) x))
(fma.f64 (.f64 (.f64 (/.f64 eps x) eps) (sqrt.f64 x)) (sqrt.f64 x) (.f64 (neg.f64 (.f64 (neg.f64 x) eps)) #s(literal 2 binary64)))
(fma.f64 (.f64 (.f64 (/.f64 eps x) eps) (sqrt.f64 x)) (sqrt.f64 x) (.f64 (neg.f64 (.f64 #s(literal 2 binary64) eps)) x))
(fma.f64 (.f64 (.f64 (/.f64 eps x) eps) (sqrt.f64 x)) (sqrt.f64 x) (.f64 (neg.f64 x) (.f64 #s(literal 2 binary64) eps)))
(fma.f64 (.f64 (.f64 (/.f64 eps x) eps) (sqrt.f64 x)) (sqrt.f64 x) (.f64 (neg.f64 x) (.f64 eps #s(literal 2 binary64))))
(fma.f64 (.f64 (.f64 (/.f64 eps x) eps) (sqrt.f64 x)) (sqrt.f64 x) (.f64 #s(literal -2 binary64) (.f64 eps x)))
(fma.f64 (.f64 eps (sqrt.f64 x)) (sqrt.f64 x) (fma.f64 eps x (.f64 (*.f64 (/.f64 eps x) eps) x)))
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(+.f64 (.f64 eps (+.f64 eps x)) (.f64 eps x))
(+.f64 (.f64 #s(literal -2 binary64) (.f64 eps x)) (*.f64 eps eps))
(+.f64 (.f64 eps x) (.f64 (+.f64 eps x) eps))
(+.f64 (.f64 eps x) (.f64 eps (+.f64 eps x)))
(+.f64 (.f64 eps eps) (.f64 (neg.f64 (*.f64 #s(literal 2 binary64) eps)) x))
(+.f64 (.f64 eps eps) (.f64 (neg.f64 x) (*.f64 #s(literal 2 binary64) eps)))
(+.f64 (.f64 eps eps) (.f64 (neg.f64 x) (*.f64 eps #s(literal 2 binary64))))
(+.f64 (.f64 eps eps) (.f64 #s(literal -2 binary64) (*.f64 eps x)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x eps)) (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x eps))) (.f64 (/.f64 (.f64 (neg.f64 eps) eps) (fma.f64 #s(literal -2 binary64) x eps)) (/.f64 (.f64 (neg.f64 eps) eps) (fma.f64 #s(literal -2 binary64) x eps)))) (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))) (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)))) (.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))))) (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)))
(/.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (-.f64 x (+.f64 eps x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (neg.f64 eps) eps) (fma.f64 #s(literal -2 binary64) x eps)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x eps)) (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x eps)) (fma.f64 (/.f64 (.f64 (neg.f64 eps) eps) (fma.f64 #s(literal -2 binary64) x eps)) (/.f64 (.f64 (neg.f64 eps) eps) (fma.f64 #s(literal -2 binary64) x eps)) (.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x eps)) (/.f64 (*.f64 (neg.f64 eps) eps) (fma.f64 #s(literal -2 binary64) x eps))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))) (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))) (-.f64 (.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)))) (.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)))))))
(/.f64 (+.f64 (pow.f64 (+.f64 eps x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (-.f64 (.f64 x x) (.f64 (+.f64 eps x) x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (+.f64 eps x) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) (*.f64 x (+.f64 eps x)))))
(/.f64 (neg.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 eps eps))) (neg.f64 (fma.f64 #s(literal -2 binary64) x eps)))
(/.f64 (neg.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)))))
(/.f64 (neg.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))) (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)))
(/.f64 (-.f64 (fma.f64 #s(literal -2 binary64) x (.f64 #s(literal -2 binary64) (.f64 eps x))) (.f64 (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)) (.f64 eps eps))) (*.f64 (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)) (fma.f64 #s(literal -2 binary64) x (neg.f64 eps))))
(/.f64 (fma.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)) (.f64 (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)) (pow.f64 eps #s(literal 3 binary64)))) (.f64 (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)) (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))))
(/.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 eps eps)) (fma.f64 #s(literal -2 binary64) x eps))
(/.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (neg.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))))
(/.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 (neg.f64 eps) eps)) (neg.f64 (fma.f64 #s(literal -2 binary64) x eps)))
(/.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 (neg.f64 eps) eps)) (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)))
(/.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -2 binary64) x (fma.f64 eps eps (.f64 (.f64 #s(literal -2 binary64) x) (neg.f64 eps)))))
(/.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))) (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)))
(/.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) (fma.f64 #s(literal -2 binary64) x eps)) (+.f64 eps #s(literal 0 binary64)))
(neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 eps eps)) (fma.f64 #s(literal -2 binary64) x (neg.f64 eps))))
(neg.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))) (neg.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)))))
(neg.f64 (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)))
(fma.f64 (*.f64 #s(literal -2 binary64) (sqrt.f64 x)) (sqrt.f64 x) eps)
(fma.f64 (*.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) eps)
(fma.f64 (.f64 #s(literal 8 binary64) (.f64 x x)) x eps)
(fma.f64 (*.f64 #s(literal 4 binary64) (neg.f64 x)) (neg.f64 x) eps)
(fma.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (sqrt.f64 x) eps)
(fma.f64 (.f64 (.f64 #s(literal -2 binary64) x) (sqrt.f64 x)) (sqrt.f64 x) eps)
(fma.f64 (.f64 #s(literal 8 binary64) x) (.f64 x x) eps)
(fma.f64 (pow.f64 eps #s(literal 1/2 binary64)) (pow.f64 eps #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3/4 binary64)) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3/4 binary64)) eps)
(fma.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) eps)
(fma.f64 (neg.f64 (sqrt.f64 (+.f64 eps x))) (neg.f64 (sqrt.f64 (+.f64 eps x))) x)
(fma.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)) (+.f64 eps x))
(fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) (neg.f64 (-.f64 x eps)))
(fma.f64 (fabs.f64 (sqrt.f64 x)) (fabs.f64 (sqrt.f64 x)) (+.f64 eps x))
(fma.f64 (fabs.f64 (sqrt.f64 (+.f64 eps x))) (fabs.f64 (sqrt.f64 (+.f64 eps x))) 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 #s(literal 2 binary64) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)) eps)
(fma.f64 (pow.f64 (sqrt.f64 (+.f64 eps x)) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (+.f64 eps x)) #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (+.f64 eps x))
(fma.f64 #s(literal -2 binary64) x eps)
(fma.f64 (sqrt.f64 (+.f64 eps x)) (sqrt.f64 (+.f64 eps x)) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 8 binary64)) eps)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) eps)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) eps)
(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 #s(literal -2 binary64) x)) eps)
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)) eps)
(fma.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)) eps)
(fma.f64 (sqrt.f64 x) (neg.f64 (sqrt.f64 x)) (neg.f64 (-.f64 x eps)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 eps x))
(fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64)) eps)
(fma.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 #s(literal -2 binary64) x) eps)
(fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)) eps)
(fma.f64 #s(literal 512 binary64) (pow.f64 x #s(literal 9 binary64)) eps)
(fma.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 512 binary64) eps)
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 16 binary64) eps)
(fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 64 binary64) eps)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64) eps)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal -2 binary64) x) eps)
(fma.f64 #s(literal 4 binary64) (*.f64 #s(literal -2 binary64) x) eps)
(fma.f64 #s(literal 4 binary64) (*.f64 x x) eps)
(fma.f64 #s(literal 4 binary64) x eps)
(fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) eps)
(fma.f64 #s(literal 8 binary64) (*.f64 #s(literal -2 binary64) x) eps)
(fma.f64 (*.f64 #s(literal -2 binary64) x) (pow.f64 x #s(literal 3 binary64)) eps)
(fma.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 4 binary64) eps)
(fma.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 8 binary64) eps)
(fma.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x) eps)
(fma.f64 (.f64 #s(literal -2 binary64) x) (.f64 x x) eps)
(fma.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 2 binary64) eps)
(fma.f64 (*.f64 #s(literal -2 binary64) x) x eps)
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 4 binary64)) eps)
(fma.f64 (neg.f64 x) #s(literal 2 binary64) eps)
(fma.f64 (.f64 x x) (.f64 x #s(literal 8 binary64)) eps)
(fma.f64 (*.f64 x x) #s(literal 4 binary64) eps)
(fma.f64 (.f64 x x) (.f64 #s(literal -2 binary64) x) eps)
(fma.f64 (*.f64 x x) #s(literal 2 binary64) eps)
(fma.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)) eps)
(fma.f64 #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) x) eps)
(fma.f64 #s(literal 2 binary64) (neg.f64 x) eps)
(fma.f64 #s(literal 2 binary64) (*.f64 x x) eps)
(fma.f64 #s(literal 2 binary64) x eps)
(fma.f64 x (.f64 (.f64 x x) #s(literal 8 binary64)) eps)
(fma.f64 x #s(literal -2 binary64) eps)
(fma.f64 x #s(literal 4 binary64) eps)
(fma.f64 x (*.f64 #s(literal -2 binary64) x) eps)
(fma.f64 x #s(literal 2 binary64) eps)
(-.f64 (+.f64 x (/.f64 (.f64 x x) (-.f64 x eps))) (/.f64 (.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (.f64 eps eps) (fma.f64 #s(literal -2 binary64) x eps)) (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x eps)))
(-.f64 (-.f64 eps x) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (-.f64 (/.f64 (.f64 eps eps) (-.f64 x eps)) x))
(-.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x eps)) (/.f64 (.f64 (neg.f64 eps) eps) (fma.f64 #s(literal -2 binary64) x eps)))
(-.f64 (*.f64 #s(literal -2 binary64) x) (neg.f64 eps))
(-.f64 (+.f64 eps x) (neg.f64 x))
(-.f64 eps (*.f64 #s(literal -2 binary64) x))
(-.f64 x (neg.f64 (+.f64 eps x)))
(+.f64 (+.f64 x (/.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 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))) x))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))) (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))))
(+.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))))
(+.f64 (/.f64 (.f64 #s(literal -2 binary64) x) (fma.f64 #s(literal -2 binary64) x eps)) (/.f64 (.f64 (neg.f64 eps) eps) (fma.f64 #s(literal -2 binary64) x (neg.f64 eps))))
(+.f64 (*.f64 #s(literal -2 binary64) x) eps)
(+.f64 (neg.f64 x) (neg.f64 (-.f64 x eps)))
(+.f64 (+.f64 eps x) x)
(+.f64 eps (*.f64 #s(literal -2 binary64) x))
(+.f64 x (+.f64 eps x))

eval55.0ms (1%)

Memory: 19.1MiB live, 120.5MiB allocated
Compiler: Compiled 11 756 to 1 422 computations (87.9% saved)

prune11.0ms (0.2%)

Memory

-13.6MiB live, 33.0MiB allocated

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	459	4	463
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	461	6	467

Accuracy

100.0%

Counts

467 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps x) eps (*.f64 eps x)))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	99.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
▶	64.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	73.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 97 to 65 computations (33% saved)

simplify226.0ms (4%)

Memory

32.1MiB live, 264.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	129
0	31	125
1	60	125
2	134	125
3	337	125
4	836	117
5	2056	117
6	6320	117
0	8299	106

Stop Event

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

Calls

Call 1

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

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

localize166.0ms (2.9%)

Memory

4.3MiB live, 145.5MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 eps x)
accuracy	0.0	(*.f64 eps x)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps x) eps (*.f64 eps x)))
accuracy	0.03125	(fma.f64 (+.f64 eps x) eps (*.f64 eps x))
accuracy	0.0	(*.f64 eps x)
accuracy	0.0	(*.f64 eps eps)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps)))
accuracy	0.02734375	(fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps))
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	0.0234375	(*.f64 (+.f64 (+.f64 eps x) x) eps)
accuracy	0.0625	(+.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	23.02081118439844	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))

Samples

113.0ms	78×	1	valid
34.0ms	169×	0	valid
3.0ms	9×	2	valid

Compiler

Compiled 101 to 20 computations (80.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-pow2: 33.0ms (48% of total)

ival-sub: 12.0ms (17.5% of total)

ival-mult: 12.0ms (17.5% of total)

ival-add: 7.0ms (10.2% of total)

adjust: 4.0ms (5.8% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.3%)

Memory

-29.3MiB live, 16.0MiB allocated

Counts

13 → 22

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	((- (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 x) 2) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps x) (* eps eps) (+ (* (+ eps x) eps) (* eps x)) (- (pow (+ x eps) 2) (pow x 2)))
2.0ms	x	@	0	((- (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 x) 2) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps x) (* eps eps) (+ (* (+ eps x) eps) (* eps x)) (- (pow (+ x eps) 2) (pow x 2)))
2.0ms	eps	@	-inf	((- (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 x) 2) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps x) (* eps eps) (+ (* (+ eps x) eps) (* eps x)) (- (pow (+ x eps) 2) (pow x 2)))
1.0ms	eps	@	inf	((- (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 x) 2) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps x) (* eps eps) (+ (* (+ eps x) eps) (* eps x)) (- (pow (+ x eps) 2) (pow x 2)))
1.0ms	x	@	inf	((- (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 x) 2) (* eps eps)) (- (pow (+ x eps) 2) (pow x 2)) (* eps x) (* eps eps) (+ (* (+ eps x) eps) (* eps x)) (- (pow (+ x eps) 2) (pow x 2)))

simplify98.0ms (1.7%)

Memory

-5.5MiB live, 144.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	104
1	164	94
2	438	94
3	1372	94
4	3913	94
5	6502	94
0	8135	84

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 20

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

rewrite231.0ms (4.1%)

Memory

32.8MiB live, 217.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	113
0	31	109
1	139	109
2	1076	109
0	8274	102

Stop Event

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

Counts

13 → 733

Calls

Call 1

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

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

eval53.0ms (0.9%)

Memory: 11.7MiB live, 97.5MiB allocated
Compiler: Compiled 15 668 to 1 697 computations (89.2% saved)

prune11.0ms (0.2%)

Memory

-34.8MiB live, 25.1MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	453	1	454
Fresh	0	0	0
Picked	1	3	4
Done	0	2	2
Total	454	6	460

Accuracy

100.0%

Counts

460 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps x) eps (*.f64 eps x)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	99.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
▶	64.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	73.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 97 to 64 computations (34% saved)

simplify299.0ms (5.3%)

Memory

0.4MiB live, 241.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
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	10	25
0	12	25
1	19	25
2	50	25
3	168	25
4	525	23
5	1636	23
6	5452	23
0	8165	22

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

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

localize142.0ms (2.5%)

Memory

-0.8MiB live, 45.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 eps eps)
accuracy	0.0	(*.f64 (+.f64 eps eps) x)
accuracy	23.02081118439844	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))

Samples

125.0ms	169×	0	valid
10.0ms	78×	1	valid
2.0ms	9×	2	valid

Compiler

Compiled 21 to 10 computations (52.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 129.0ms

ival-pow2: 121.0ms (93.5% of total)

ival-add: 3.0ms (2.3% of total)

adjust: 2.0ms (1.5% of total)

ival-sub: 2.0ms (1.5% of total)

ival-mult: 2.0ms (1.5% of total)

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

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

series4.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

3 → 8

Calls

Call 1

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

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

Calls

6 calls:

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

simplify91.0ms (1.6%)

Memory

19.2MiB live, 117.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	56
1	89	46
2	281	46
3	942	46
4	2846	46
5	5640	46
0	8021	41

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 8

Calls

Call 1

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

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

rewrite148.0ms (2.6%)

Memory

-27.3MiB live, 18.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
0	12	23
1	60	23
0	443	23

Stop Event

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

Counts

3 → 20

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)

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)

eval2.0ms (0%)

Memory: 2.5MiB live, 2.5MiB allocated
Compiler: Compiled 425 to 80 computations (81.2% saved)

prune3.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	24	6	30

Accuracy

100.0%

Counts

30 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (+.f64 eps x) eps (*.f64 eps x)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	99.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
✓	64.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	73.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 252 to 102 computations (59.5% saved)

regimes9.0ms (0.2%)

Memory

16.2MiB live, 16.2MiB allocated

Counts

10 → 1

Calls

Call 1

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

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

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes6.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB allocated

Counts

5 → 1

Calls

Call 1

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

Results

Accuracy	Segments	Branch
99.9%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
99.9%	1	`x`
99.9%	1	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes10.0ms (0.2%)

Memory

-32.5MiB live, 14.0MiB allocated

Counts

4 → 2

Calls

Call 1

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

7.0ms	x
2.0ms	eps
1.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
95.7%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
91.7%	3	`x`
82.8%	3	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes3.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
73.9%	1	`eps`
73.9%	1	`x`
73.9%	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)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	2.088633e-318

Compiler

Compiled 12 to 12 computations (0% saved)

simplify50.0ms (0.9%)

Memory

9.4MiB live, 54.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	26	86
1	33	86
2	59	86
3	171	86
4	571	76
5	1730	76
6	5635	76

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))

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))

derivations563.0ms (9.9%)

Memory

-14.1MiB live, 366.9MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	113
0	31	109
1	139	109
2	1076	109
0	8274	102
0	19	98
0	28	98
1	115	98
2	782	94
0	9348	94
0	69	215
1	239	203
2	827	191
3	3630	191
0	8470	176

Stop Event

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

Compiler

Compiled 86 to 27 computations (68.6% saved)

preprocess24.0ms (0.4%)

Memory: 22.2MiB live, 22.2MiB allocated
Compiler: Compiled 190 to 68 computations (64.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.5s (27.2%)

explain131.0ms (2.3%)

preprocess241.0ms (4.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify239.0ms (4.2%)

localize67.0ms (1.2%)

series5.0ms (0.1%)

simplify287.0ms (5.1%)

rewrite212.0ms (3.7%)

eval71.0ms (1.2%)

prune36.0ms (0.6%)

simplify189.0ms (3.3%)

localize87.0ms (1.5%)

series12.0ms (0.2%)

simplify90.0ms (1.6%)

rewrite248.0ms (4.4%)

eval55.0ms (1%)

prune11.0ms (0.2%)

simplify226.0ms (4%)

localize166.0ms (2.9%)

series15.0ms (0.3%)

simplify98.0ms (1.7%)

rewrite231.0ms (4.1%)

eval53.0ms (0.9%)

prune11.0ms (0.2%)

simplify299.0ms (5.3%)

localize142.0ms (2.5%)

series4.0ms (0.1%)

simplify91.0ms (1.6%)

rewrite148.0ms (2.6%)

eval2.0ms (0%)

prune3.0ms (0.1%)

regimes9.0ms (0.2%)

regimes6.0ms (0.1%)

regimes10.0ms (0.2%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

simplify50.0ms (0.9%)

derivations563.0ms (9.9%)

preprocess24.0ms (0.4%)

end0.0ms (0%)

Profiling