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

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

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

Algorithm

1×

Search

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

Compiler

Compiled 25 to 18 computations (28% saved)

sample1.5s (56.3%)

Memory

-35.4MiB live, 1 482.8MiB allocated; 938ms collecting garbage

Samples

703.0ms	5 079×	0	valid
335.0ms	2 570×	1	valid
126.0ms	607×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 599.0ms

ival-pow2: 348.0ms (58.1% of total)

adjust: 103.0ms (17.2% of total)

ival-add: 77.0ms (12.9% of total)

ival-sub: 69.0ms (11.5% of total)

ival-assert: 2.0ms (0.3% of total)

Bogosity

explain135.0ms (5.1%)

Memory

-9.9MiB live, 147.0MiB allocated; 19ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
72	1	(-3.297166978000901e-39 8.787745372503529e-285)	-	`(-.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	73	0

Confusion

	Predicted +	Predicted -
+	72	0
-	1	183

Precision

0.9863013698630136

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	72	0	0
-	1	0	183

Precision?

0.9863013698630136

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

24.0ms	42×	2	valid
20.0ms	158×	1	valid
19.0ms	312×	0	valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-pow2: 14.0ms (48.2% of total)

adjust: 6.0ms (20.7% of total)

ival-add: 4.0ms (13.8% of total)

ival-sub: 3.0ms (10.3% of total)

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

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

exact: 0.0ms (0% of total)

preprocess229.0ms (8.7%)

Memory

3.7MiB live, 325.5MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	64
1	34	60
2	118	60
3	553	58
4	1771	44
5	5314	44
0	7	9
0	11	9
1	16	9
2	44	9
3	157	9
4	570	7
5	1812	7
0	8588	6

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

2.8MiB live, 2.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.2%	(-.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)

series7.0ms (0.3%)

Memory

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

Counts

7 → 29

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
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (pow eps 2)))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* x (+ x (* 2 eps))) (pow eps 2))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ eps x))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* 2 (* eps x)) (pow x 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* eps (+ eps (* 2 x))) (pow x 2))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Calls

6 calls:

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

rewrite180.0ms (6.8%)

Memory

-20.6MiB live, 222.2MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	456
0	110	446
1	557	431
0	5462	412

Stop Event

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

Counts

36 → 120

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))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (pow eps 2)))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* x (+ x (* 2 eps))) (pow eps 2))))
#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (pow x 2) #s(hole binary64 (pow x 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (pow x 2)))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* 2 (/ eps x))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (+ (* 2 (/ eps x)) (/ (pow eps 2) (pow x 2)))))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow x 2) (+ 1 (* -1 (/ (+ (* -2 eps) (* -1 (/ (pow eps 2) x))) x))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* 2 (* eps x)) (pow x 2))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (+ (* eps (+ eps (* 2 x))) (pow x 2))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (+ (* 2 (/ x eps)) (/ (pow x 2) (pow eps 2)))))))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (pow (+ x eps) 2) #s(hole binary64 (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -2 x) (* -1 (/ (pow x 2) eps))) eps))))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

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

eval15.0ms (0.6%)

Memory: -10.6MiB live, 33.7MiB allocated; 5ms collecting garbage
Compiler: Compiled 2 157 to 390 computations (81.9% saved)

prune3.0ms (0.1%)

Memory

12.0MiB live, 12.1MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	3	120

Accuracy

100.0%

Counts

120 → 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))
▶	63.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	73.6%	#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))

▶

63.9%

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

▶

73.6%

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

Compiler

Compiled 44 to 31 computations (29.5% saved)

series13.0ms (0.5%)

Memory

-15.1MiB live, 30.8MiB allocated; 5ms collecting garbage

Counts

11 → 26

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (* eps x) 2) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) eps (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) x 2 (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps))
2.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* eps eps) eps (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) x 2 (- (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) eps (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) x 2 (- (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) eps (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) x 2 (- (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) eps (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) x 2 (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps))

rewrite154.0ms (5.8%)

Memory

-18.5MiB live, 142.7MiB allocated; 92ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	422
0	87	406
1	330	404
0	2588	398

Stop Event

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

Counts

37 → 152

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)
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(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (* eps x) 2) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* eps x) #s(hole binary64 (* eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 eps))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (+ eps (* 2 x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* 2 x)))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* x (+ 2 (/ eps x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 2)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (* (+ (* 2 x) eps) eps) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* eps (+ 1 (* 2 (/ x eps))))))
#s(approx (+ (* 2 x) eps) #s(hole binary64 (* -1 (* eps (- (* -2 (/ x eps)) 1)))))

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

eval14.0ms (0.5%)

Memory: 33.3MiB live, 33.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 3 403 to 462 computations (86.4% saved)

prune34.0ms (1.3%)

Memory

-25.9MiB live, 21.2MiB allocated; 2ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	158	3	161

Accuracy

100.0%

Counts

161 → 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))
▶	63.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 #s(literal 2 binary64) x) eps))
✓	73.6%	#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))

▶

63.9%

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

✓

73.6%

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

Compiler

Compiled 44 to 31 computations (29.5% saved)

series5.0ms (0.2%)

Memory

15.0MiB live, 15.0MiB allocated; 0ms collecting garbage

Counts

6 → 11

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)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (* 2 x) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (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) 2 x eps)
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x) 2 x eps)
1.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x) 2 x eps)
1.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x) 2 x eps)
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x) 2 x eps)

rewrite79.0ms (3%)

Memory

22.9MiB live, 109.3MiB allocated; 26ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	181
0	47	177
1	217	176
0	1750	172

Stop Event

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

Counts

17 → 41

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
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (* 2 x) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (pow eps 2) (+ 1 (* 2 (/ x eps))))))

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

eval18.0ms (0.7%)

Memory: -16.3MiB live, 15.6MiB allocated; 18ms collecting garbage
Compiler: Compiled 731 to 125 computations (82.9% saved)

prune2.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	39	3	42

Accuracy

100.0%

Counts

42 → 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))
▶	63.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
✓	73.6%	#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))

▶

63.9%

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

✓

73.6%

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

Compiler

Compiled 44 to 30 computations (31.8% saved)

series5.0ms (0.2%)

Memory

21.4MiB live, 21.4MiB allocated; 0ms collecting garbage

Counts

5 → 11

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (pow eps 2)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* (+ x x) eps) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* x (+ (* 2 eps) (/ (pow eps 2) x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* eps (+ eps (* 2 x)))))
#s(approx eps #s(hole binary64 eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) #s(hole binary64 (* (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)) (* (+ x x) eps) (+ x x) x eps)
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) x eps)
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) x eps)
1.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) x eps)
1.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) x eps)

rewrite50.0ms (1.9%)

Memory

-9.6MiB live, 78.4MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	180
0	48	178
0	225	173

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

16 → 21

Calls

Call 1

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

eval2.0ms (0.1%)

Memory: 5.7MiB live, 5.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 403 to 74 computations (81.6% saved)

prune2.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	23	3	26

Accuracy

100.0%

Counts

26 → 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))

✓

63.9%

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

✓

73.6%

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

Compiler

Compiled 127 to 56 computations (55.9% saved)

regimes36.0ms (1.4%)

Memory

-40.8MiB live, 24.6MiB allocated; 31ms collecting garbage

Counts

6 → 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 x x) 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:

31.0ms	x
2.0ms	eps
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes5.0ms (0.2%)

Memory

15.4MiB live, 15.4MiB allocated; 0ms collecting garbage

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.4%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
92.4%	3	`x`
88.7%	3	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes3.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated; 0ms collecting garbage

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
73.6%	1	`eps`
73.6%	1	`x`
73.6%	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

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	6.4e-323

Compiler

Compiled 12 to 12 computations (0% saved)

simplify62.0ms (2.4%)

Memory

-24.1MiB live, 72.5MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	69
1	29	69
2	60	69
3	179	69
4	604	61
5	2079	61
6	7844	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 x 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 x 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))

derivations74.0ms (2.8%)

Memory

31.0MiB live, 78.4MiB allocated; 2ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 69 to 23 computations (66.7% saved)

preprocess24.0ms (0.9%)

Memory: -1.4MiB live, 47.3MiB allocated; 7ms collecting garbage
Compiler: Compiled 156 to 60 computations (61.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.5s (56.3%)

explain135.0ms (5.1%)

preprocess229.0ms (8.7%)

eval0.0ms (0%)

prune1.0ms (0%)

series7.0ms (0.3%)

rewrite180.0ms (6.8%)

eval15.0ms (0.6%)

prune3.0ms (0.1%)

series13.0ms (0.5%)

rewrite154.0ms (5.8%)

eval14.0ms (0.5%)

prune34.0ms (1.3%)

series5.0ms (0.2%)

rewrite79.0ms (3%)

eval18.0ms (0.7%)

prune2.0ms (0.1%)

series5.0ms (0.2%)

rewrite50.0ms (1.9%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

regimes36.0ms (1.4%)

regimes5.0ms (0.2%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

simplify62.0ms (2.4%)

derivations74.0ms (2.8%)

preprocess24.0ms (0.9%)

end0.0ms (0%)

Profiling