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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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 (25.5%)

Memory

60.2MiB live, 1 917.4MiB allocated

Samples

425.0ms	5 218×	0	valid
389.0ms	2 560×	1	valid
174.0ms	478×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 700.0ms

ival-pow2: 301.0ms (43% of total)

ival-<=: 130.0ms (18.6% of total)

ival-add: 92.0ms (13.1% of total)

ival-sub: 68.0ms (9.7% of total)

adjust: 67.0ms (9.6% of total)

ival-and: 22.0ms (3.1% of total)

exact: 17.0ms (2.4% of total)

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

Bogosity

explain108.0ms (2%)

Memory

-26.2MiB live, 131.2MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	cancellation	73	0

Confusion

	Predicted +	Predicted -
+	73	0
-	0	183

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	73	0	0
-	0	0	183

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	183
1	73

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

23.0ms	156×	1	valid
19.0ms	328×	0	valid
5.0ms	28×	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 (54.5% of total)

ival-add: 4.0ms (15.6% of total)

adjust: 3.0ms (11.7% of total)

ival-sub: 3.0ms (11.7% of total)

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

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

exact: 0.0ms (0% of total)

preprocess252.0ms (4.7%)

Memory

2.8MiB live, 152.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	47	47
2	182	45
3	797	35
4	2770	35
5	5134	35
6	7371	35
0	7	9
0	11	9
1	18	9
2	48	9
3	189	9
4	843	7
5	3805	7
6	5846	7
7	7793	7
0	8048	6

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.8%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify142.0ms (2.7%)

Memory

13.1MiB live, 97.0MiB 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	18	23
2	48	23
3	189	23
4	843	21
5	3805	21
6	5846	21
7	7793	21
0	8048	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)

localize30.0ms (0.6%)

Memory

9.6MiB live, 45.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 2 binary64))
accuracy	0	(+.f64 x eps)
accuracy	0.015625	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	15.459955814570678	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

13.0ms	164×	0	valid
9.0ms	78×	1	valid
2.0ms	14×	2	valid

Compiler

Compiled 48 to 16 computations (66.7% saved)

Precisions

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

ival-pow2: 7.0ms (44.9% of total)

ival-add: 5.0ms (32.1% of total)

adjust: 2.0ms (12.8% of total)

ival-sub: 2.0ms (12.8% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB 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
1.0ms	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	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow x 2) (pow (+ x eps) 2) (+ x eps))

simplify177.0ms (3.3%)

Memory

-11.0MiB live, 187.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	161
1	242	151
2	839	151
3	3594	143
0	8964	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)

rewrite199.0ms (3.7%)

Memory

2.5MiB live, 163.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	53	20
2	404	20
3	6082	20
0	8311	20

Stop Event

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

Counts

4 → 445

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 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (+.f64 eps 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 (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 (fma.f64 #s(literal -1 binary64) (+.f64 eps x) (neg.f64 x)) (-.f64 (neg.f64 (+.f64 eps x)) (neg.f64 x)))
(*.f64 (fma.f64 #s(literal -1 binary64) (+.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 (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)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))))
(.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (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))))))
(*.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 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 (+.f64 eps x) #s(literal 2 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 x #s(literal 6 binary64)) (pow.f64 (+.f64 eps 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 (+.f64 eps x) x) #s(literal 6 binary64)) (pow.f64 x #s(literal 12 binary64))) (pow.f64 (+.f64 eps x) #s(literal 12 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 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))))
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(/.f64 (neg.f64 (fma.f64 (neg.f64 x) x (*.f64 eps eps))) (neg.f64 (neg.f64 (-.f64 x eps))))
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(/.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 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 (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 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 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 (.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 (fma.f64 (.f64 eps eps) (fma.f64 eps eps (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.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 (-.f64 eps x) (+.f64 eps x)) (-.f64 eps x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.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 #s(literal 1 binary64) (/.f64 (-.f64 eps x) (*.f64 (-.f64 eps x) (+.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (fabs.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps 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)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(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) (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) (/.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 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) 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 (sqrt.f64 x) (sqrt.f64 x) eps)
(fma.f64 (neg.f64 x) (/.f64 (neg.f64 x) (-.f64 x eps)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(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 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (/.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 binary64)) (pow.f64 (fma.f64 (-.f64 eps x) eps (.f64 x x)) #s(literal -1 binary64)) (/.f64 (pow.f64 eps #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 (.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(fma.f64 (.f64 x x) (pow.f64 (-.f64 x eps) #s(literal -1 binary64)) (/.f64 (.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(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)) (neg.f64 (*.f64 eps (/.f64 eps (-.f64 x eps)))))
(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 (cosh.f64 (log.f64 (+.f64 eps x))) (sinh.f64 (neg.f64 (log.f64 (+.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 (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))) (neg.f64 (.f64 eps (/.f64 eps (-.f64 x eps)))))
(+.f64 (.f64 x (/.f64 x (-.f64 x eps))) (/.f64 (.f64 (neg.f64 eps) eps) (-.f64 x eps)))
(+.f64 eps x)
(+.f64 x eps)

eval74.0ms (1.4%)

Memory: -0.7MiB live, 82.2MiB allocated
Compiler: Compiled 11 846 to 1 368 computations (88.5% saved)

prune7.0ms (0.1%)

Memory

-17.3MiB live, 21.4MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	449	3	452
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	450	3	453

Accuracy

100.0%

Counts

453 → 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))
▶	63.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	73.7%	#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))

▶

63.2%

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

▶

73.7%

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

Compiler

Compiled 44 to 31 computations (29.5% saved)

simplify131.0ms (2.5%)

Memory

22.2MiB live, 102.4MiB 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: 3 (0.0ms)

Iter	Nodes	Cost
0	15	72
0	21	72
1	41	72
2	106	72
3	365	63
4	1400	63
5	3504	63
6	5293	63
7	7068	63
0	8044	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

localize89.0ms (1.7%)

Memory

-22.5MiB live, 51.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 #s(literal 2 binary64) x eps)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
accuracy	0.0078125	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
accuracy	0	(*.f64 eps x)
accuracy	0.015625	(.f64 (.f64 eps x) #s(literal 2 binary64))
accuracy	23.549413349457495	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0	(*.f64 eps eps)
accuracy	16.843808851347625	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Samples

56.0ms	78×	1	valid
17.0ms	164×	0	valid
3.0ms	14×	2	valid

Compiler

Compiled 131 to 31 computations (76.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

adjust: 44.0ms (68.7% of total)

ival-mult: 7.0ms (10.9% of total)

ival-pow2: 7.0ms (10.9% of total)

ival-add: 3.0ms (4.7% of total)

ival-sub: 2.0ms (3.1% 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

13.3MiB live, 13.3MiB 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	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps))

simplify139.0ms (2.6%)

Memory

4.2MiB live, 89.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	85
1	131	75
2	391	75
3	1301	75
4	3787	75
5	6362	75
0	8056	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)

rewrite318.0ms (6%)

Memory

-150.6MiB live, 195.7MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	65
0	21	65
1	86	65
2	617	62
0	8841	62

Stop Event

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

Counts

8 → 370

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 (.f64 (neg.f64 eps) #s(literal -1 binary64)) eps)
(*.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)))
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 eps) eps))
(.f64 #s(literal 1 binary64) (.f64 eps eps))
(*.f64 (neg.f64 eps) (neg.f64 eps))
(*.f64 eps eps)
(pow.f64 (exp.f64 (log.f64 eps)) #s(literal 2 binary64))
(pow.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/2 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)))
(-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 eps) eps))
(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 (neg.f64 (.f64 #s(literal 2 binary64) eps)) x)
(.f64 (neg.f64 (.f64 eps #s(literal 2 binary64))) x)
(.f64 (.f64 #s(literal 2 binary64) eps) (neg.f64 x))
(.f64 (.f64 #s(literal 2 binary64) eps) x)
(.f64 (.f64 eps #s(literal 2 binary64)) (neg.f64 x))
(.f64 (.f64 eps #s(literal 2 binary64)) x)
(.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 #s(literal -1 binary64) (.f64 #s(literal -2 binary64) (*.f64 eps x)))
(.f64 (.f64 (neg.f64 x) eps) #s(literal 2 binary64))
(.f64 (neg.f64 x) (.f64 #s(literal 2 binary64) eps))
(.f64 (neg.f64 x) (.f64 eps #s(literal 2 binary64)))
(.f64 (neg.f64 eps) (.f64 #s(literal -2 binary64) x))
(.f64 (.f64 #s(literal -2 binary64) x) (neg.f64 eps))
(.f64 (.f64 #s(literal -2 binary64) x) eps)
(.f64 (.f64 eps x) #s(literal -2 binary64))
(.f64 (.f64 eps x) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (neg.f64 x) eps))
(.f64 #s(literal 2 binary64) (.f64 eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(.f64 x (neg.f64 (.f64 #s(literal 2 binary64) eps)))
(.f64 x (neg.f64 (.f64 eps #s(literal 2 binary64))))
(.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 #s(literal 0 binary64) eps) #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 #s(literal -1 binary64) (.f64 eps x) (.f64 (neg.f64 x) eps))
(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 #s(literal 0 binary64) (.f64 #s(literal -2 binary64) (.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)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))
(.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps)) eps)) (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)))
(.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)) (.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))) eps)) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)))
(.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)) (.f64 eps (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps)))) (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)))
(.f64 (/.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)) (.f64 eps (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 (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps)) eps) (neg.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 (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps)) eps) (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps))) (fma.f64 #s(literal -2 binary64) x eps))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))) eps) (-.f64 (.f64 #s(literal -2 binary64) x) (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)))) (neg.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))))
(.f64 (/.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))) eps) (fma.f64 #s(literal -2 binary64) x (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 3 binary64)))) (fma.f64 #s(literal -2 binary64) x (.f64 (.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 (/.f64 (.f64 eps (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps))) (neg.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 (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps))) (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps))) (fma.f64 #s(literal -2 binary64) x eps))
(.f64 (/.f64 (.f64 eps (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64)))) (-.f64 (.f64 #s(literal -2 binary64) x) (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)))) (neg.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))))
(.f64 (/.f64 (.f64 eps (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 #s(literal -2 binary64) x (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 3 binary64)))) (fma.f64 #s(literal -2 binary64) x (.f64 (.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 (.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 (neg.f64 eps) eps)) eps) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -2 binary64) x eps)))
(.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))) eps) (pow.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)) #s(literal -1 binary64)))
(.f64 (.f64 eps (fma.f64 #s(literal -2 binary64) x (*.f64 (neg.f64 eps) eps))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -2 binary64) x eps)))
(.f64 (.f64 eps (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (*.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 (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)) (.f64 (*.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2 binary64)))))
(.f64 (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps)) (*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -2 binary64) x eps)) eps))
(.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 #s(literal -2 binary64) x (*.f64 (fma.f64 #s(literal -2 binary64) x eps) 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 (pow.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)) (fma.f64 #s(literal -2 binary64) x eps)) eps)
(/.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)) eps) (fma.f64 #s(literal -2 binary64) x eps))
(/.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (.f64 eps eps)) eps) (fma.f64 #s(literal -2 binary64) x eps))
(/.f64 (.f64 (neg.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64)))) eps) (neg.f64 (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))))
(/.f64 (.f64 eps (fma.f64 #s(literal -2 binary64) x (.f64 eps eps))) (fma.f64 #s(literal -2 binary64) x eps))
(/.f64 (.f64 eps (neg.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))))
(/.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 #s(literal -2 binary64) (.f64 eps x)) (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2 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 (neg.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64))) (neg.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)))
(/.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))))) (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps)) eps)) (fma.f64 #s(literal -2 binary64) x eps))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))) eps)) (neg.f64 (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps))))
(/.f64 (neg.f64 (.f64 eps (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps)))) (fma.f64 #s(literal -2 binary64) x eps))
(/.f64 (neg.f64 (.f64 eps (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))))
(/.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps)) eps) (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)))
(/.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))) eps) (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)))
(/.f64 (.f64 eps (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps))) (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)))
(/.f64 (.f64 eps (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 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)) (.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 (pow.f64 eps #s(literal 3 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 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps) #s(literal 2 binary64)) (.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) x) #s(literal 2 binary64))) (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)) (.f64 (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps)) eps)))
(/.f64 #s(literal 1 binary64) (/.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 (pow.f64 eps #s(literal 3 binary64))) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) x (neg.f64 eps)) (.f64 eps (fma.f64 #s(literal -2 binary64) x (.f64 (neg.f64 eps) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) x (.f64 (fma.f64 #s(literal -2 binary64) x eps) eps)) (.f64 eps (fma.f64 #s(literal -2 binary64) x (pow.f64 eps #s(literal 3 binary64))))))
(/.f64 eps (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -2 binary64) x eps)))
(neg.f64 (fma.f64 (neg.f64 eps) eps (.f64 #s(literal -2 binary64) (.f64 eps x))))
(fma.f64 (.f64 eps (sqrt.f64 (+.f64 eps x))) (sqrt.f64 (+.f64 eps x)) (.f64 eps x))
(fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 eps eps))
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(fma.f64 (.f64 eps (sqrt.f64 x)) (sqrt.f64 x) (.f64 (+.f64 eps x) eps))
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(+.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)) (neg.f64 (/.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 (neg.f64 eps))))
(+.f64 (neg.f64 x) (fma.f64 #s(literal -1 binary64) x eps))
(+.f64 (*.f64 #s(literal -2 binary64) x) eps)
(+.f64 (+.f64 eps x) x)
(+.f64 eps (*.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64)))
(+.f64 eps (*.f64 #s(literal -2 binary64) x))
(+.f64 x (+.f64 eps x))

eval44.0ms (0.8%)

Memory: 8.0MiB live, 82.4MiB allocated
Compiler: Compiled 9 438 to 1 266 computations (86.6% saved)

prune11.0ms (0.2%)

Memory

-22.2MiB live, 22.7MiB allocated

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	373	2	375
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	374	4	378

Accuracy

100.0%

Counts

378 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 x eps (*.f64 (+.f64 eps x) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	63.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	73.7%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 62 to 42 computations (32.3% saved)

simplify132.0ms (2.5%)

Memory

24.7MiB live, 100.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	(+.f64 eps x)
cost-diff	0	(*.f64 (+.f64 eps x) eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 x eps (*.f64 (+.f64 eps x) eps)))
cost-diff	192	(fma.f64 x eps (*.f64 (+.f64 eps x) eps))
cost-diff	0	(*.f64 eps #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	62
0	20	60
1	40	60
2	100	60
3	316	60
4	1380	56
5	5104	56
6	7948	56
0	8075	52

Stop Event

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

Calls

Call 1

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

localize57.0ms (1.1%)

Memory

17.7MiB live, 55.0MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 eps x)
accuracy	0	(*.f64 (+.f64 eps x) eps)
accuracy	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 x eps (*.f64 (+.f64 eps x) eps)))
accuracy	0.01171875	(fma.f64 x eps (*.f64 (+.f64 eps x) eps))
accuracy	0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
accuracy	0	(*.f64 eps #s(literal 2 binary64))
accuracy	23.549413349457495	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))

Samples

29.0ms	78×	1	valid
16.0ms	164×	0	valid
3.0ms	14×	2	valid

Compiler

Compiled 112 to 30 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 22.0ms (58% of total)

ival-pow2: 7.0ms (18.5% of total)

ival-add: 4.0ms (10.6% of total)

adjust: 3.0ms (7.9% of total)

ival-sub: 2.0ms (5.3% of total)

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

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

exact: 0.0ms (0% of total)

series28.0ms (0.5%)

Memory

-11.4MiB live, 29.9MiB allocated

Counts

7 → 21

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
23.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* x eps) (* (+ eps x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (+ eps x) eps) (+ eps x))
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* x eps) (* (+ eps x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (+ eps x) eps) (+ eps x))
1.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* x eps) (* (+ eps x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (+ eps x) eps) (+ eps x))
1.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* x eps) (* (+ eps x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (+ eps x) eps) (+ eps x))
1.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (* x eps) (* (+ eps x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (+ eps x) eps) (+ eps x))

simplify120.0ms (2.2%)

Memory

-2.6MiB live, 71.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	101
1	172	91
2	484	91
3	1548	91
4	3584	91
5	5876	91
6	7557	91
0	8152	86

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 19

Calls

Call 1

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

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

rewrite280.0ms (5.2%)

Memory

2.7MiB live, 200.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	57
0	20	55
1	96	55
2	787	55
0	8953	53

Stop Event

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

Counts

7 → 406

Calls

Call 1

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

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

eval99.0ms (1.8%)

Memory: -14.9MiB live, 106.6MiB allocated
Compiler: Compiled 13 159 to 1 521 computations (88.4% saved)

prune7.0ms (0.1%)

Memory

17.0MiB live, 17.0MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	411	1	412
Fresh	0	0	0
Picked	1	1	2
Done	0	2	2
Total	412	4	416

Accuracy

100.0%

Counts

416 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 x eps (*.f64 (+.f64 eps x) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	63.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	73.7%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 62 to 41 computations (33.9% saved)

simplify136.0ms (2.5%)

Memory

-19.7MiB live, 104.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	-128	(+.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	21	25
2	59	25
3	209	25
4	830	23
5	3768	23
6	5815	23
7	7790	23
0	8045	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

localize33.0ms (0.6%)

Memory

3.8MiB live, 42.0MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 eps eps)
accuracy	0	(*.f64 (+.f64 eps eps) x)
accuracy	23.549413349457495	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))

Samples

14.0ms	164×	0	valid
10.0ms	78×	1	valid
3.0ms	14×	2	valid

Compiler

Compiled 46 to 20 computations (56.5% saved)

Precisions

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

ival-pow2: 7.0ms (42.9% of total)

ival-add: 3.0ms (18.4% of total)

adjust: 2.0ms (12.3% of total)

ival-mult: 2.0ms (12.3% of total)

ival-sub: 2.0ms (12.3% of total)

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

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

series4.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB 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))

simplify130.0ms (2.4%)

Memory

4.5MiB live, 124.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	56
1	89	46
2	283	46
3	940	46
4	2729	46
5	5835	46
6	7804	46
0	8029	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)

rewrite41.0ms (0.8%)

Memory

-7.5MiB live, 30.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
0	12	23
1	62	23
0	492	23

Stop Event

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

Counts

3 → 24

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 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (pow.f64 eps #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps #s(literal 0 binary64))))
(*.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 1 binary64) (/.f64 (fma.f64 eps eps #s(literal 0 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 eps #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) eps))
(/.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)

eval3.0ms (0.1%)

Memory: 3.6MiB live, 3.6MiB allocated
Compiler: Compiled 507 to 96 computations (81.1% saved)

prune3.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	28	4	32

Accuracy

100.0%

Counts

32 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 x eps (*.f64 (+.f64 eps x) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	63.2%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	73.7%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 163 to 71 computations (56.4% saved)

regimes8.0ms (0.2%)

Memory

11.2MiB live, 11.2MiB allocated

Counts

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

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	`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)

regimes9.0ms (0.2%)

Memory

-26.4MiB live, 12.6MiB 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:

5.0ms	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
93.1%	3	`x`
90.3%	3	`eps`
97.9%	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)

regimes4.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB 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
73.7%	1	`eps`
73.7%	1	`x`
73.7%	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

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	6.6146e-320

Compiler

Compiled 12 to 12 computations (0% saved)

simplify43.0ms (0.8%)

Memory

-8.2MiB live, 38.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	69
1	27	69
2	31	69
3	36	69
4	50	69
5	69	69
6	82	69
7	96	69

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

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

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

soundness1.1s (19.8%)

Memory

5.4MiB live, 475.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
0	21	65
1	86	65
2	617	62
0	8841	62
0	14	57
0	20	55
1	96	55
2	787	55
0	8953	53
0	69	161
1	242	151
2	839	151
3	3594	143
0	8964	124

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 110 to 58 computations (47.3% saved)

preprocess50.0ms (0.9%)

Memory: 6.1MiB live, 44.5MiB 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 (25.5%)

explain108.0ms (2%)

preprocess252.0ms (4.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify142.0ms (2.7%)

localize30.0ms (0.6%)

series5.0ms (0.1%)

simplify177.0ms (3.3%)

rewrite199.0ms (3.7%)

eval74.0ms (1.4%)

prune7.0ms (0.1%)

simplify131.0ms (2.5%)

localize89.0ms (1.7%)

series9.0ms (0.2%)

simplify139.0ms (2.6%)

rewrite318.0ms (6%)

eval44.0ms (0.8%)

prune11.0ms (0.2%)

simplify132.0ms (2.5%)

localize57.0ms (1.1%)

series28.0ms (0.5%)

simplify120.0ms (2.2%)

rewrite280.0ms (5.2%)

eval99.0ms (1.8%)

prune7.0ms (0.1%)

simplify136.0ms (2.5%)

localize33.0ms (0.6%)

series4.0ms (0.1%)

simplify130.0ms (2.4%)

rewrite41.0ms (0.8%)

eval3.0ms (0.1%)

prune3.0ms (0.1%)

regimes8.0ms (0.2%)

regimes9.0ms (0.2%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

simplify43.0ms (0.8%)

soundness1.1s (19.8%)

preprocess50.0ms (0.9%)

end0.0ms (0%)

Profiling