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

0.4MiB live, 0.4MiB 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)

sample929.0ms (63.1%)

Memory

43.8MiB live, 958.9MiB allocated; 236ms collecting garbage

Samples

267.0ms	2 560×	1	valid
249.0ms	5 103×	0	valid
127.0ms	593×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 438.0ms

ival-pow2: 298.0ms (68.1% of total)

adjust: 69.0ms (15.8% of total)

ival-add!: 37.0ms (8.5% of total)

ival-sub!: 34.0ms (7.8% of total)

Bogosity

preprocess42.0ms (2.8%)

Memory

1.7MiB live, 43.9MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	64
1	34	60
2	118	60
3	553	58
4	1771	44
5	5314	44

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	79.9%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Compiler

Compiled 16 to 14 computations (12.5% saved)

series6.0ms (0.4%)

Memory

11.6MiB live, 11.6MiB 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	eps	@	-inf	((- (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	x	@	0	((- (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))

rewrite162.0ms (11%)

Memory

6.8MiB live, 154.1MiB allocated; 22ms 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 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 x x)) (.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 (+.f64 eps x) x)))) (neg.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 x x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)))) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x)) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))))
(/.f64 (.f64 (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 x x)) (.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 (+.f64 eps x) x))) (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 x x)))
(/.f64 (-.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))) (fma.f64 (.f64 x x) (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x)) (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 (+.f64 eps x) (+.f64 eps x) (.f64 x x))) (/.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 (+.f64 eps x) #s(literal 6 binary64)) (fma.f64 (.f64 x x) (fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 x x)) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 (+.f64 eps x) (+.f64 eps x) (*.f64 x x)) (pow.f64 (+.f64 eps x) #s(literal 4 binary64)))))
(-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x x))
(+.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.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 (*.f64 (+.f64 eps x) (+.f64 eps x)) #s(literal 1 binary64))
(pow.f64 (+.f64 eps x) #s(literal 2 binary64))
(/.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (+.f64 eps x)) (-.f64 eps x))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (+.f64 eps x)) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (+.f64 eps x)) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (-.f64 x eps))) (-.f64 x eps))
(/.f64 (.f64 (+.f64 eps x) (.f64 (+.f64 eps x) (-.f64 eps x))) (-.f64 eps x))
(/.f64 (.f64 (+.f64 eps x) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (.f64 (+.f64 eps x) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))
(/.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (+.f64 eps x) (-.f64 x eps))) (.f64 (-.f64 x eps) (-.f64 x eps)))
(/.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (.f64 (+.f64 eps x) (-.f64 eps x))) (.f64 (-.f64 x eps) (-.f64 eps x)))
(/.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (.f64 (-.f64 x eps) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 x eps)) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (.f64 (-.f64 x eps) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (.f64 (+.f64 eps x) (-.f64 x eps))) (.f64 (-.f64 eps x) (-.f64 x 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 (.f64 (+.f64 eps x) (-.f64 eps x)) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (.f64 (-.f64 eps x) (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (.f64 (-.f64 eps x) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (.f64 (+.f64 eps x) (-.f64 x eps))) (.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (-.f64 x eps)))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (.f64 (+.f64 eps x) (-.f64 x eps))) (.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (-.f64 x eps)))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (.f64 (+.f64 eps x) (-.f64 eps x))) (.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x)) (-.f64 eps x)))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (.f64 (+.f64 eps x) (-.f64 eps x))) (.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)) (-.f64 eps x)))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x)) (fma.f64 x (-.f64 x eps) (.f64 eps eps))))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (.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 (*.f64 (+.f64 eps x) (-.f64 x eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (*.f64 (+.f64 eps x) (-.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(/.f64 (neg.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps))))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 x eps)) (-.f64 x eps))
(/.f64 (*.f64 (+.f64 eps x) (-.f64 eps x)) (-.f64 eps x))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 eps (-.f64 eps x) (.f64 x x)))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (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 (.f64 (.f64 x x) x) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (.f64 (.f64 eps eps) eps) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(+.f64 (/.f64 (.f64 (.f64 eps eps) eps) (fma.f64 x (-.f64 x eps) (.f64 eps eps))) (/.f64 (.f64 (.f64 x x) x) (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 x x) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 eps (/.f64 eps x) (+.f64 eps eps)) 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 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal -2 binary64) eps) (/.f64 (.f64 eps eps) x)) x)) 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 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal -2 binary64) eps) (/.f64 (.f64 eps eps) x)) x)) x) x))
#s(approx (+ x eps) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.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 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal -2 binary64) x) (.f64 x (/.f64 x eps))) eps)) eps) eps))
#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (pow (+ x eps) 2) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal -2 binary64) x) (.f64 x (/.f64 x eps))) eps)) eps) eps))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval10.0ms (0.7%)

Memory: 18.0MiB live, 18.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 964 to 392 computations (59.3% saved)

prune51.0ms (3.5%)

Memory

-37.1MiB live, 9.1MiB allocated; 4ms collecting garbage

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	6	113

Accuracy

100.0%

Counts

113 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	79.9%	(-.f64 (.f64 (+.f64 eps x) (+.f64 eps x)) (.f64 x x))
	79.9%	(-.f64 #s(approx (pow (+ x eps) 2) (fma.f64 (fma.f64 #s(literal 2 binary64) eps x) x (*.f64 eps eps))) (pow.f64 x #s(literal 2 binary64)))
▶	99.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 eps (/.f64 eps x) (+.f64 eps eps)) x))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	66.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
▶	77.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 124 to 120 computations (3.2% saved)

series16.0ms (1.1%)

Memory

23.8MiB live, 23.8MiB allocated; 0ms collecting garbage

Counts

20 → 68

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) 2 x eps (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) (- (* (+ eps x) (+ eps x)) (* x x)) (* (+ eps x) (+ eps x)) (+ eps x) (* x x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* eps (/ eps x)) (+ eps eps)) x) (+ (* eps (/ eps x)) (+ eps eps)) (/ eps x) (+ eps eps))
3.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) 2 x eps (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) (- (* (+ eps x) (+ eps x)) (* x x)) (* (+ eps x) (+ eps x)) (+ eps x) (* x x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* eps (/ eps x)) (+ eps eps)) x) (+ (* eps (/ eps x)) (+ eps eps)) (/ eps x) (+ eps eps))
2.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) 2 x eps (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) (- (* (+ eps x) (+ eps x)) (* x x)) (* (+ eps x) (+ eps x)) (+ eps x) (* x x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* eps (/ eps x)) (+ eps eps)) x) (+ (* eps (/ eps x)) (+ eps eps)) (/ eps x) (+ eps eps))
2.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) 2 x eps (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) (- (* (+ eps x) (+ eps x)) (* x x)) (* (+ eps x) (+ eps x)) (+ eps x) (* x x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* eps (/ eps x)) (+ eps eps)) x) (+ (* eps (/ eps x)) (+ eps eps)) (/ eps x) (+ eps eps))
2.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) 2 x eps (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (+ x x) eps) (+ x x) (- (* (+ eps x) (+ eps x)) (* x x)) (* (+ eps x) (+ eps x)) (+ eps x) (* x x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (* eps (/ eps x)) (+ eps eps)) x) (+ (* eps (/ eps x)) (+ eps eps)) (/ eps x) (+ eps eps))

rewrite50.0ms (3.4%)

Memory

-15.2MiB live, 29.3MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	186	1209
0	202	1112
0	832	1087

Stop Event

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

Counts

88 → 163

Calls

Call 1

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

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

eval13.0ms (0.9%)

Memory: 19.6MiB live, 19.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 200 to 581 computations (51.6% saved)

prune6.0ms (0.4%)

Memory

9.1MiB live, 9.1MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	0	1
Picked	2	3	5
Done	0	0	0
Total	169	4	173

Accuracy

100.0%

Counts

173 → 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 eps eps (*.f64 (+.f64 x x) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	66.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
✓	77.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 41 to 41 computations (0% saved)

series6.0ms (0.4%)

Memory

7.2MiB live, 7.2MiB allocated; 0ms collecting garbage

Counts

6 → 18

Calls

Call 1

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

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

rewrite58.0ms (3.9%)

Memory

-9.4MiB live, 34.8MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	315
0	61	302
0	258	283

Stop Event

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

Counts

24 → 41

Calls

Call 1

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

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

eval3.0ms (0.2%)

Memory: 6.1MiB live, 6.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 266 to 138 computations (48.1% saved)

prune3.0ms (0.2%)

Memory

7.0MiB live, 7.0MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	35	4	39

Accuracy

100.0%

Counts

39 → 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 eps eps (*.f64 (+.f64 x x) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	66.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 x x) eps))
✓	77.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 95 to 76 computations (20% saved)

regimes16.0ms (1.1%)

Memory

-34.5MiB live, 17.0MiB allocated; 10ms collecting garbage

Counts

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

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

Calls

3 calls:

11.0ms	eps
2.0ms	x
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
100.0%	1	`(-.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 10 to 11 computations (-10% saved)

regimes4.0ms (0.3%)

Memory

11.3MiB live, 11.3MiB allocated; 0ms collecting garbage

Counts

3 → 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 (fma.f64 #s(literal 2 binary64) x eps) eps))

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x 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
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 10 to 11 computations (-10% saved)

regimes4.0ms (0.2%)

Memory

9.9MiB live, 9.9MiB allocated; 0ms collecting garbage

Counts

2 → 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))

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:

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
96.9%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
93.3%	3	`x`
87.2%	3	`eps`

Compiler

Compiled 10 to 11 computations (-10% saved)

regimes3.0ms (0.2%)

Memory

8.6MiB live, 8.6MiB 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
77.0%	1	`eps`
77.0%	1	`x`
77.0%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 10 to 11 computations (-10% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	2e-323

Compiler

Compiled 11 to 12 computations (-9.1% saved)

derivations63.0ms (4.3%)

Memory

-31.7MiB live, 56.3MiB allocated; 11ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 36 to 25 computations (30.6% saved)

preprocess26.0ms (1.7%)

Memory: 15.8MiB live, 61.4MiB allocated; 4ms collecting garbage
Compiler: Compiled 44 to 32 computations (27.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample929.0ms (63.1%)

preprocess42.0ms (2.8%)

series6.0ms (0.4%)

rewrite162.0ms (11%)

eval10.0ms (0.7%)

prune51.0ms (3.5%)

series16.0ms (1.1%)

rewrite50.0ms (3.4%)

eval13.0ms (0.9%)

prune6.0ms (0.4%)

series6.0ms (0.4%)

rewrite58.0ms (3.9%)

eval3.0ms (0.2%)

prune3.0ms (0.2%)

regimes16.0ms (1.1%)

regimes4.0ms (0.3%)

regimes4.0ms (0.2%)

regimes3.0ms (0.2%)

bsearch0.0ms (0%)

derivations63.0ms (4.3%)

preprocess26.0ms (1.7%)

end0.0ms (0%)

Profiling