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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 25 to 18 computations (28% saved)

sample1.4s (31.6%)

Memory

43.7MiB live, 1 361.6MiB allocated

Samples

503.0ms	5 253×	0	valid
386.0ms	2 453×	1	valid
95.0ms	550×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 746.0ms

ival-pow2: 354.0ms (47.4% of total)

ival-<=: 112.0ms (15% of total)

ival-sub: 106.0ms (14.2% of total)

ival-add: 69.0ms (9.2% of total)

adjust: 67.0ms (9% of total)

ival-and: 20.0ms (2.7% of total)

exact: 16.0ms (2.1% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

explain145.0ms (3.3%)

Memory

-41.3MiB live, 89.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
76	1	(-1.7471011280491282e-56 8.489633308829737e-268)	-	`(-.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	77	0

Confusion

	Predicted +	Predicted -
+	76	0
-	1	179

Precision

0.987012987012987

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	76	0	0
-	1	0	179

Precision?

0.987012987012987

Recall?

1.0

Freqs

test

number	freq
0	179
1	77

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

20.0ms	170×	1	valid
18.0ms	310×	0	valid
5.0ms	32×	2	valid

Compiler

Compiled 82 to 32 computations (61% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-pow2: 14.0ms (53.7% of total)

adjust: 4.0ms (15.3% of total)

ival-add: 4.0ms (15.3% of total)

ival-sub: 3.0ms (11.5% of total)

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

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

exact: 0.0ms (0% of total)

preprocess486.0ms (11.1%)

Memory

-29.3MiB live, 284.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	45	47
2	149	45
3	549	35
4	1721	35
5	3972	35
6	5466	35
7	6180	35
8	6408	35
9	6514	35
10	6535	35
11	6535	35
12	6535	35
13	6535	35
14	6626	35
15	6954	35
16	7748	35
0	7	9
0	11	9
1	16	9
2	36	9
3	91	9
4	271	7
5	855	7
6	2424	7
7	4630	7
8	6290	7
9	7277	7
10	7703	7
11	7971	7
12	7977	7
13	7977	7
0	8284	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

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	73.8%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify184.0ms (4.2%)

Memory

34.8MiB live, 190.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 x eps)
cost-diff	0	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
cost-diff	6144	(pow.f64 x #s(literal 2 binary64))
cost-diff	6464	(-.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	36	23
3	91	23
4	271	21
5	855	21
6	2424	21
7	4630	21
8	6290	21
9	7277	21
10	7703	21
11	7971	21
12	7977	21
13	7977	21
0	8284	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)

localize29.0ms (0.7%)

Memory

4.9MiB live, 43.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(pow.f64 x #s(literal 2 binary64))
accuracy	0.0	(+.f64 x eps)
accuracy	0.029628759768442016	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	16.75022032184157	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

11.0ms	85×	1	valid
9.0ms	155×	0	valid
3.0ms	16×	2	valid

Compiler

Compiled 48 to 16 computations (66.7% saved)

Precisions

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

ival-pow2: 6.0ms (42.7% of total)

ival-add: 4.0ms (28.4% of total)

adjust: 2.0ms (14.2% of total)

ival-sub: 2.0ms (14.2% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

-30.2MiB live, 7.8MiB 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 x #s(literal 2 binary64))
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(+.f64 x eps)

Outputs
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(pow x 2)
(+ (* x (+ x (* 2 eps))) (pow eps 2))
eps
(+ eps x)
(* 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
3.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))
1.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))

simplify127.0ms (2.9%)

Memory

26.2MiB live, 152.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	161
1	214	151
2	570	151
3	1819	143
4	4177	143
5	7344	143
0	8016	124

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 21

Calls

Call 1

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

rewrite155.0ms (3.5%)

Memory

-0.2MiB live, 193.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	52	20
2	371	20
3	5134	20
0	8154	20

Stop Event

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

Counts

4 → 370

Calls

Call 1

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

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

eval76.0ms (1.7%)

Memory: 3.8MiB live, 49.5MiB allocated
Compiler: Compiled 9 295 to 1 147 computations (87.7% saved)

prune20.0ms (0.5%)

Memory

-16.6MiB live, 19.1MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	374	3	377
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	375	3	378

Accuracy

100.0%

Counts

378 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	68.6%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	72.3%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Status

Accuracy

Program

▶

100.0%

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

▶

68.6%

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

▶

72.3%

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

Compiler

Compiled 44 to 31 computations (29.5% saved)

simplify188.0ms (4.3%)

Memory

20.1MiB live, 138.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	72
0	21	72
1	33	72
2	63	72
3	117	69
4	261	63
5	835	63
6	2376	63
7	4551	63
8	6203	63
9	7193	63
10	7615	63
11	7883	63
12	7889	63
13	7889	63
0	8196	63

Stop Event

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

Calls

Call 1

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

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

localize66.0ms (1.5%)

Memory

-18.9MiB live, 95.6MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 #s(literal 2 binary64) x eps)
accuracy	0.0	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
accuracy	0.0	(*.f64 eps x)
accuracy	0.0234375	(.f64 (.f64 eps x) #s(literal 2 binary64))
accuracy	20.09000614972167	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0.0	(*.f64 eps eps)
accuracy	17.723731376871644	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Samples

17.0ms	155×	0	valid
15.0ms	85×	1	valid
4.0ms	16×	2	valid

Compiler

Compiled 131 to 31 computations (76.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 8.0ms (34% of total)

ival-pow2: 7.0ms (29.7% of total)

adjust: 3.0ms (12.7% of total)

ival-add: 3.0ms (12.7% of total)

ival-sub: 2.0ms (8.5% of total)

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

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

exact: 0.0ms (0% of total)

series9.0ms (0.2%)

Memory

15.4MiB live, 15.4MiB allocated

Counts

8 → 15

Calls

Call 1

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

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

Calls

6 calls:

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

simplify121.0ms (2.8%)

Memory

-29.7MiB live, 94.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	85
1	121	75
2	287	75
3	749	75
4	1911	75
5	3737	75
6	5497	75
7	6550	75
8	7132	75
0	8287	65

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 14

Calls

Call 1

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

rewrite191.0ms (4.4%)

Memory

11.8MiB live, 167.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
0	21	65
1	79	65
2	524	65
3	6756	65
0	8315	65

Stop Event

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

Counts

8 → 134

Calls

Call 1

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

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

eval15.0ms (0.3%)

Memory: 16.8MiB live, 16.8MiB allocated
Compiler: Compiled 4 092 to 535 computations (86.9% saved)

prune4.0ms (0.1%)

Memory

7.1MiB live, 7.1MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	138	3	141

Accuracy

100.0%

Counts

141 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

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

▶

68.6%

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

✓

72.3%

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

Compiler

Compiled 44 to 31 computations (29.5% saved)

simplify194.0ms (4.4%)

Memory

-15.1MiB live, 140.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
0	12	26
1	21	26
2	48	26
3	104	26
4	248	24
5	807	24
6	2401	24
7	4614	24
8	6260	24
9	7253	24
10	7679	24
11	7947	24
12	7953	24
13	7953	24
0	8260	23

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 #s(literal 2 binary64) x) eps))
(.f64 (.f64 #s(literal 2 binary64) x) eps)
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
eps

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

localize32.0ms (0.7%)

Memory

-3.4MiB live, 34.7MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(.f64 (.f64 #s(literal 2 binary64) x) eps)
accuracy	0.0	(*.f64 #s(literal 2 binary64) x)
accuracy	20.09000614972167	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 #s(literal 2 binary64) x) eps))

Samples

12.0ms	85×	1	valid
10.0ms	155×	0	valid
3.0ms	16×	2	valid

Compiler

Compiled 48 to 22 computations (54.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-pow2: 8.0ms (46.2% of total)

ival-mult: 3.0ms (17.3% of total)

adjust: 2.0ms (11.5% of total)

ival-add: 2.0ms (11.5% of total)

ival-sub: 2.0ms (11.5% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

3 → 8

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))
1.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))
1.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))
0.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))
0.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))

simplify120.0ms (2.7%)

Memory

-2.5MiB live, 81.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	56
1	76	46
2	187	46
3	452	46
4	1323	46
5	2434	46
6	4600	46
7	7473	46
0	8063	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))
(* 2 x)
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* eps (+ eps (* 2 x)))
(* (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))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 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)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)

rewrite158.0ms (3.6%)

Memory

1.1MiB live, 118.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
0	12	23
1	56	23
2	381	23
3	5145	23
0	8155	23

Stop Event

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

Counts

3 → 13

Calls

Call 1

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

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

eval2.0ms (0%)

Memory: 1.8MiB live, 1.8MiB allocated
Compiler: Compiled 280 to 53 computations (81.1% saved)

prune3.0ms (0.1%)

Memory

3.5MiB live, 3.5MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	17	3	20

Accuracy

100.0%

Counts

20 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

100.0%

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

✓

68.6%

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

✓

72.3%

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

Compiler

Compiled 112 to 54 computations (51.8% saved)

regimes6.0ms (0.1%)

Memory

7.6MiB live, 7.6MiB 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 #s(literal 2 binary64) x) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
(-.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:

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

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes5.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Counts

3 → 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 #s(literal 2 binary64) x) eps))

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

Calls

3 calls:

2.0ms	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
94.9%	3	`x`
88.2%	3	`eps`
98.2%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes5.0ms (0.1%)

Memory

-28.8MiB live, 9.6MiB 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:

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

Results

Accuracy	Segments	Branch
72.3%	1	`eps`
72.3%	1	`x`
72.3%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	5e-324

Compiler

Compiled 12 to 12 computations (0% saved)

simplify74.0ms (1.7%)

Memory

5.7MiB live, 43.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	69
1	29	69
2	51	69
3	109	69
4	293	61
5	877	61
6	2425	61
7	4656	61
8	6456	61
9	7926	61

Stop Event

1×	node limit

Calls

Call 1

Inputs

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

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

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

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

soundness540.0ms (12.3%)

Memory

2.6MiB live, 241.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	161
1	214	151
2	570	151
3	1819	143
4	4177	143
5	7344	143
0	8016	124
0	15	65
0	21	65
1	79	65
2	524	65
3	6756	65
0	8315	65

Stop Event

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

Compiler

Compiled 95 to 47 computations (50.5% saved)

preprocess33.0ms (0.8%)

Memory: 9.5MiB live, 47.9MiB allocated
Compiler: Compiled 156 to 60 computations (61.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.4s (31.6%)

explain145.0ms (3.3%)

preprocess486.0ms (11.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify184.0ms (4.2%)

localize29.0ms (0.7%)

series6.0ms (0.1%)

simplify127.0ms (2.9%)

rewrite155.0ms (3.5%)

eval76.0ms (1.7%)

prune20.0ms (0.5%)

simplify188.0ms (4.3%)

localize66.0ms (1.5%)

series9.0ms (0.2%)

simplify121.0ms (2.8%)

rewrite191.0ms (4.4%)

eval15.0ms (0.3%)

prune4.0ms (0.1%)

simplify194.0ms (4.4%)

localize32.0ms (0.7%)

series4.0ms (0.1%)

simplify120.0ms (2.7%)

rewrite158.0ms (3.6%)

eval2.0ms (0%)

prune3.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

bsearch0.0ms (0%)

simplify74.0ms (1.7%)

soundness540.0ms (12.3%)

preprocess33.0ms (0.8%)

end0.0ms (0%)

Profiling