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)

sample1.3s (50.9%)

Memory

3.7MiB live, 1 020.4MiB allocated; 1.0s collecting garbage

Samples

411.0ms	2 508×	1	valid
357.0ms	593×	2	valid
236.0ms	5 155×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 784.0ms

ival-pow2: 342.0ms (43.6% of total)

adjust: 340.0ms (43.4% of total)

ival-add!: 60.0ms (7.7% of total)

ival-sub!: 43.0ms (5.5% of total)

Bogosity

explain109.0ms (4.4%)

Memory

29.5MiB live, 178.6MiB allocated; 18ms collecting garbage

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	cancellation	67	0

Confusion

	Predicted +	Predicted -
+	67	0
-	0	189

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	67	0	0
-	0	0	189

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	189
1	67

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

33.0ms	330×	0	valid
15.0ms	148×	1	valid
5.0ms	34×	2	valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

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

ival-pow2: 30.0ms (79.7% of total)

adjust: 4.0ms (10.6% of total)

ival-add!: 2.0ms (5.3% of total)

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

preprocess41.0ms (1.7%)

Memory

-33.2MiB live, 12.7MiB allocated; 5ms 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
▶	77.5%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

series6.0ms (0.2%)

Memory

9.3MiB live, 9.3MiB 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))

rewrite211.0ms (8.6%)

Memory

27.3MiB live, 164.4MiB allocated; 25ms 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 #s(literal 1 binary64) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 (+.f64 eps x) x)))) (neg.f64 (fma.f64 #s(literal 1 binary64) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 x x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 #s(literal 1 binary64) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (pow.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (.f64 (fma.f64 #s(literal 1 binary64) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (.f64 (fma.f64 #s(literal 2 binary64) x eps) (-.f64 (+.f64 eps x) x))) (fma.f64 #s(literal 1 binary64) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1 binary64) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (pow.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64))))
(fma.f64 (neg.f64 (+.f64 eps x)) (neg.f64 (+.f64 eps x)) (.f64 (.f64 #s(literal -1 binary64) x) x))
(fma.f64 (fabs.f64 (+.f64 eps x)) (fabs.f64 (+.f64 eps x)) (.f64 (.f64 #s(literal -1 binary64) x) x))
(fma.f64 (exp.f64 (log.f64 (+.f64 eps x))) (exp.f64 (log.f64 (+.f64 eps x))) (.f64 (.f64 #s(literal -1 binary64) x) x))
(fma.f64 (+.f64 eps x) (+.f64 eps x) (.f64 (.f64 #s(literal -1 binary64) x) x))
(-.f64 (/.f64 (pow.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)) (fma.f64 #s(literal 1 binary64) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))) (/.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 #s(literal 1 binary64) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1 binary64) (.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (pow.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (fma.f64 (.f64 x x) (fma.f64 #s(literal 1 binary64) (*.f64 x x) (pow.f64 (+.f64 eps x) #s(literal 2 binary64))) (pow.f64 (pow.f64 (+.f64 eps x) #s(literal 2 binary64)) #s(literal 2 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 (.f64 #s(literal -1 binary64) 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 #s(literal 1 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1 binary64) eps) eps)) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (.f64 (fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1 binary64) x) 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 (fabs.f64 x) (fabs.f64 x) (*.f64 eps (-.f64 eps x))))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (+.f64 eps x)) (fma.f64 (fabs.f64 eps) (fabs.f64 eps) (*.f64 x (-.f64 x eps))))
(/.f64 (.f64 (+.f64 eps x) (fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1 binary64) eps) eps))) (-.f64 x eps))
(/.f64 (.f64 (+.f64 eps x) (fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1 binary64) x) x))) (-.f64 eps x))
(/.f64 (.f64 (+.f64 eps x) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 eps (-.f64 eps x))))
(/.f64 (.f64 (+.f64 eps x) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (fma.f64 (fabs.f64 eps) (fabs.f64 eps) (*.f64 x (-.f64 x eps))))
(/.f64 (.f64 (fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1 binary64) eps) eps)) (fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1 binary64) eps) eps))) (.f64 (-.f64 x eps) (-.f64 x eps)))
(/.f64 (.f64 (fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1 binary64) eps) eps)) (fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1 binary64) x) x))) (.f64 (-.f64 x eps) (-.f64 eps x)))
(/.f64 (.f64 (fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1 binary64) eps) eps)) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (.f64 (-.f64 x eps) (fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 eps (-.f64 eps x)))))
(/.f64 (.f64 (fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1 binary64) eps) eps)) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (.f64 (-.f64 x eps) (fma.f64 (fabs.f64 eps) (fabs.f64 eps) (*.f64 x (-.f64 x eps)))))
(/.f64 (.f64 (fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1 binary64) x) x)) (fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1 binary64) eps) eps))) (.f64 (-.f64 eps x) (-.f64 x eps)))
(/.f64 (.f64 (fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1 binary64) x) x)) (fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1 binary64) x) x))) (.f64 (-.f64 eps x) (-.f64 eps x)))
(/.f64 (.f64 (fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1 binary64) x) x)) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (.f64 (-.f64 eps x) (fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 eps (-.f64 eps x)))))
(/.f64 (.f64 (fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1 binary64) x) x)) (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (.f64 (-.f64 eps x) (fma.f64 (fabs.f64 eps) (fabs.f64 eps) (*.f64 x (-.f64 x eps)))))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1 binary64) eps) eps))) (.f64 (fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 eps (-.f64 eps x))) (-.f64 x eps)))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (.f64 #s(literal -1 binary64) eps) eps))) (.f64 (fma.f64 (fabs.f64 eps) (fabs.f64 eps) (*.f64 x (-.f64 x eps))) (-.f64 x eps)))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1 binary64) x) x))) (.f64 (fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 eps (-.f64 eps x))) (-.f64 eps x)))
(/.f64 (.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (.f64 #s(literal -1 binary64) x) x))) (.f64 (fma.f64 (fabs.f64 eps) (fabs.f64 eps) (*.f64 x (-.f64 x 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 (fabs.f64 x) (fabs.f64 x) (.f64 eps (-.f64 eps x))) (fma.f64 (fabs.f64 x) (fabs.f64 x) (.f64 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 (fabs.f64 x) (fabs.f64 x) (.f64 eps (-.f64 eps x))) (fma.f64 (fabs.f64 eps) (fabs.f64 eps) (.f64 x (-.f64 x 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 (fabs.f64 eps) (fabs.f64 eps) (.f64 x (-.f64 x eps))) (fma.f64 (fabs.f64 x) (fabs.f64 x) (.f64 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 (fabs.f64 eps) (fabs.f64 eps) (.f64 x (-.f64 x eps))) (fma.f64 (fabs.f64 eps) (fabs.f64 eps) (.f64 x (-.f64 x 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 #s(literal 1 binary64) (.f64 x x) (.f64 (*.f64 #s(literal -1 binary64) eps) eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (*.f64 #s(literal -1 binary64) x) x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 (fabs.f64 x) (fabs.f64 x) (.f64 eps (-.f64 eps x)))))
(/.f64 (neg.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 (fabs.f64 eps) (fabs.f64 eps) (.f64 x (-.f64 x eps)))))
(/.f64 (fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 (*.f64 #s(literal -1 binary64) eps) eps)) (-.f64 x eps))
(/.f64 (fma.f64 #s(literal 1 binary64) (.f64 eps eps) (.f64 (*.f64 #s(literal -1 binary64) x) x)) (-.f64 eps x))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 (fabs.f64 x) (fabs.f64 x) (.f64 eps (-.f64 eps x))))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 x x) x)) (fma.f64 (fabs.f64 eps) (fabs.f64 eps) (.f64 x (-.f64 x 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 (fabs.f64 x) (fabs.f64 x) (.f64 eps (-.f64 eps x)))) (/.f64 (.f64 (.f64 eps eps) eps) (fma.f64 (fabs.f64 x) (fabs.f64 x) (.f64 eps (-.f64 eps x)))))
(+.f64 (/.f64 (.f64 (.f64 eps eps) eps) (fma.f64 (fabs.f64 eps) (fabs.f64 eps) (.f64 x (-.f64 x eps)))) (/.f64 (.f64 (.f64 x x) x) (fma.f64 (fabs.f64 eps) (fabs.f64 eps) (.f64 x (-.f64 x 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 (.f64 #s(literal -1 binary64) x) (*.f64 #s(literal -1 binary64) 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 (.f64 #s(literal -1 binary64) 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 #s(literal 1 binary64) (.f64 eps eps) (.f64 (fma.f64 #s(literal 2 binary64) eps x) x)))
#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 1 binary64) (/.f64 (.f64 eps eps) x) (*.f64 #s(literal 2 binary64) eps)) x))
#s(approx (pow (+ x eps) 2) (*.f64 x x))
#s(approx (pow (+ x eps) 2) (.f64 (.f64 (fma.f64 (*.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64)) x) x))
#s(approx (pow (+ x eps) 2) (.f64 (.f64 (fma.f64 (fma.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (/.f64 eps x) #s(literal 2 binary64))) #s(literal 1 binary64) #s(literal 1 binary64)) x) x))
#s(approx (+ x eps) x)
#s(approx (+ x eps) (*.f64 (fma.f64 (/.f64 eps x) #s(literal 1 binary64) #s(literal 1 binary64)) x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 (fma.f64 #s(literal -2 binary64) eps (.f64 #s(literal -1 binary64) (/.f64 (.f64 eps eps) x))) x) #s(literal -1 binary64)))
#s(approx (pow (+ x eps) 2) (.f64 (.f64 (fma.f64 (fma.f64 (pow.f64 (/.f64 eps x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (/.f64 eps x) #s(literal 2 binary64))) #s(literal 1 binary64) #s(literal 1 binary64)) x) x))
#s(approx (+ x eps) (.f64 (.f64 (fma.f64 (*.f64 #s(literal -1 binary64) (/.f64 eps x)) #s(literal 1 binary64) #s(literal -1 binary64)) 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 #s(literal 1 binary64) (.f64 eps eps) (.f64 (fma.f64 #s(literal 2 binary64) eps x) x)))
#s(approx eps eps)
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 (fma.f64 (*.f64 (/.f64 x eps) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64)) eps) eps))
#s(approx (pow (+ x eps) 2) (.f64 (.f64 (fma.f64 (*.f64 (/.f64 x eps) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64)) eps) eps))
#s(approx (pow (+ x eps) 2) (.f64 (.f64 (fma.f64 (fma.f64 (pow.f64 (/.f64 x eps) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (/.f64 x eps) #s(literal 2 binary64))) #s(literal 1 binary64) #s(literal 1 binary64)) eps) eps))
#s(approx (+ x eps) (*.f64 (fma.f64 (/.f64 x eps) #s(literal 1 binary64) #s(literal 1 binary64)) eps))
#s(approx (pow (+ x eps) 2) (.f64 (.f64 (fma.f64 (fma.f64 (pow.f64 (/.f64 x eps) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (/.f64 x eps) #s(literal 2 binary64))) #s(literal 1 binary64) #s(literal 1 binary64)) eps) eps))
#s(approx (+ x eps) (.f64 (.f64 (fma.f64 (*.f64 (/.f64 x eps) #s(literal -1 binary64)) #s(literal 1 binary64) #s(literal -1 binary64)) eps) #s(literal -1 binary64)))

eval34.0ms (1.4%)

Memory: -17.1MiB live, 26.4MiB allocated; 7ms collecting garbage
Compiler: Compiled 2 468 to 400 computations (83.8% saved)

prune97.0ms (3.9%)

Memory

37.2MiB live, 80.6MiB allocated; 6ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	118	2	120

Accuracy

100.0%

Counts

120 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.5%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 eps eps) x) (*.f64 #s(literal 2 binary64) eps)) x))

Status

Accuracy

Program

✓

77.5%

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

▶

100.0%

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

Compiler

Compiled 31 to 22 computations (29% saved)

series14.0ms (0.6%)

Memory

-27.7MiB live, 15.4MiB allocated; 5ms collecting garbage

Counts

10 → 25

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) x) (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) 1 (/ (* eps eps) x) (* eps eps) eps x (* 2 eps) 2)
3.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) x) (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) 1 (/ (* eps eps) x) (* eps eps) eps x (* 2 eps) 2)
2.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) x) (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) 1 (/ (* eps eps) x) (* eps eps) eps x (* 2 eps) 2)
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) x) (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) 1 (/ (* eps eps) x) (* eps eps) eps x (* 2 eps) 2)
1.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) x) (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) 1 (/ (* eps eps) x) (* eps eps) eps x (* 2 eps) 2)

rewrite100.0ms (4.1%)

Memory

11.8MiB live, 123.0MiB allocated; 33ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	487
0	83	429
1	343	415
0	2689	408

Stop Event

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

Counts

35 → 205

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 x (-.f64 (/.f64 eps x) #s(literal -2 binary64))) eps))
(.f64 (.f64 x (-.f64 (/.f64 eps x) #s(literal -2 binary64))) eps)
(.f64 (-.f64 (/.f64 eps x) #s(literal -2 binary64)) (.f64 eps x))
(.f64 (.f64 (-.f64 (/.f64 eps x) #s(literal -2 binary64)) eps) x)
(.f64 (.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64)))
(.f64 eps (.f64 (-.f64 (/.f64 eps x) #s(literal -2 binary64)) x))
(.f64 x (.f64 (-.f64 (/.f64 eps x) #s(literal -2 binary64)) eps))
(/.f64 (.f64 (.f64 (.f64 eps (-.f64 #s(literal -2 binary64) (/.f64 eps x))) (fma.f64 #s(literal -2 binary64) eps (.f64 (/.f64 eps x) eps))) x) (*.f64 eps (-.f64 #s(literal 2 binary64) (/.f64 eps x))))
(/.f64 (.f64 (.f64 (.f64 (-.f64 (/.f64 eps x) #s(literal -2 binary64)) eps) (fma.f64 (.f64 (/.f64 eps x) eps) #s(literal 1 binary64) (.f64 #s(literal -2 binary64) eps))) x) (fma.f64 (.f64 (/.f64 eps x) eps) #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) eps)))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 eps eps) eps) (pow.f64 (.f64 (/.f64 eps x) eps) #s(literal 3 binary64))) x) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) #s(literal 2 binary64)) eps (.f64 (.f64 (/.f64 eps x) eps) (fma.f64 (.f64 (/.f64 eps x) eps) #s(literal 1 binary64) (.f64 #s(literal -2 binary64) eps)))))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 eps eps) eps) (pow.f64 (.f64 (/.f64 eps x) eps) #s(literal 3 binary64))) x) (fma.f64 (.f64 (.f64 (/.f64 eps x) eps) eps) (/.f64 eps x) (.f64 (.f64 #s(literal 2 binary64) eps) (*.f64 eps (-.f64 #s(literal 2 binary64) (/.f64 eps x))))))
(/.f64 (.f64 x (.f64 (.f64 eps (-.f64 #s(literal -2 binary64) (/.f64 eps x))) (fma.f64 #s(literal -2 binary64) eps (.f64 (/.f64 eps x) eps)))) (*.f64 eps (-.f64 #s(literal 2 binary64) (/.f64 eps x))))
(/.f64 (.f64 x (.f64 (.f64 (-.f64 (/.f64 eps x) #s(literal -2 binary64)) eps) (fma.f64 (.f64 (/.f64 eps x) eps) #s(literal 1 binary64) (.f64 #s(literal -2 binary64) eps)))) (fma.f64 (.f64 (/.f64 eps x) eps) #s(literal 1 binary64) (*.f64 #s(literal -2 binary64) eps)))
(/.f64 (.f64 x (fma.f64 #s(literal 8 binary64) (.f64 (.f64 eps eps) eps) (pow.f64 (.f64 (/.f64 eps x) eps) #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) #s(literal 2 binary64)) eps (.f64 (.f64 (/.f64 eps x) eps) (fma.f64 (.f64 (/.f64 eps x) eps) #s(literal 1 binary64) (.f64 #s(literal -2 binary64) eps)))))
(/.f64 (.f64 x (fma.f64 #s(literal 8 binary64) (.f64 (.f64 eps eps) eps) (pow.f64 (.f64 (/.f64 eps x) eps) #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 (/.f64 eps x) eps) eps) (/.f64 eps x) (.f64 (.f64 #s(literal 2 binary64) eps) (*.f64 eps (-.f64 #s(literal 2 binary64) (/.f64 eps x))))))
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(*.f64 eps #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 eps eps))
(/.f64 (fma.f64 (.f64 eps eps) eps (.f64 (.f64 eps eps) eps)) (fma.f64 (.f64 (fabs.f64 eps) #s(literal 1 binary64)) (.f64 (fabs.f64 eps) #s(literal 1 binary64)) (-.f64 (.f64 eps eps) (*.f64 eps eps))))
(fma.f64 #s(literal 1 binary64) eps (*.f64 #s(literal 1 binary64) eps))
(fma.f64 eps #s(literal 1 binary64) (*.f64 eps #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) eps) (.f64 #s(literal 1 binary64) eps))
(+.f64 (.f64 eps #s(literal 1 binary64)) (.f64 eps #s(literal 1 binary64)))
(+.f64 eps eps)
#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)) (fma.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 eps eps)))
#s(approx (* (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) x) (*.f64 eps eps))
#s(approx (* (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) x) (fma.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 eps eps)))
#s(approx (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) (*.f64 (/.f64 eps x) eps))
#s(approx (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) (/.f64 (fma.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 eps eps)) x))
#s(approx (/ (* eps eps) x) (*.f64 (/.f64 eps x) eps))
#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 (.f64 x (-.f64 (/.f64 eps x) #s(literal -2 binary64))) eps))
#s(approx (* (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) x) (.f64 (.f64 eps x) #s(literal 2 binary64)))
#s(approx (* (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) x) (.f64 (.f64 x (-.f64 (/.f64 eps x) #s(literal -2 binary64))) eps))
#s(approx (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) (*.f64 #s(literal 2 binary64) eps))
#s(approx (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) (*.f64 (-.f64 (/.f64 eps x) #s(literal -2 binary64)) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 #s(literal -1 binary64) x) (*.f64 eps (-.f64 #s(literal -2 binary64) (/.f64 eps x)))))
#s(approx (* (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) x) (.f64 (.f64 #s(literal -1 binary64) x) (*.f64 eps (-.f64 #s(literal -2 binary64) (/.f64 eps x)))))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 eps eps)))
#s(approx (* (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) x) (fma.f64 (.f64 (.f64 eps x) #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 eps eps)))
#s(approx (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) (*.f64 (-.f64 (/.f64 eps x) #s(literal -2 binary64)) eps))
#s(approx (* eps eps) (*.f64 eps eps))
#s(approx eps eps)
#s(approx (* 2 eps) (*.f64 #s(literal 2 binary64) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 (fma.f64 (*.f64 (/.f64 x eps) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64)) eps) eps))
#s(approx (* (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) x) (.f64 (.f64 (fma.f64 (*.f64 (/.f64 x eps) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64)) eps) eps))
#s(approx (+ (* 1 (/ (* eps eps) x)) (* 2 eps)) (.f64 (.f64 (fma.f64 (*.f64 (pow.f64 eps #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))) eps) eps))

eval23.0ms (0.9%)

Memory: 12.6MiB live, 57.7MiB allocated; 4ms collecting garbage
Compiler: Compiled 5 579 to 821 computations (85.3% saved)

prune321.0ms (13.1%)

Memory

5.6MiB live, 418.5MiB allocated; 67ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	206	3	209

Accuracy

100.0%

Counts

209 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.5%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
▶	99.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 (*.f64 (/.f64 eps x) eps) x)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 eps eps) x) (*.f64 #s(literal 2 binary64) eps)) x))

Status

Accuracy

Program

✓

77.5%

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

▶

99.8%

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

✓

100.0%

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

Compiler

Compiled 53 to 36 computations (32.1% saved)

series15.0ms (0.6%)

Memory

-35.0MiB live, 20.0MiB allocated; 11ms collecting garbage

Counts

9 → 20

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) (* 2 x) 2 x eps (* (* (/ eps x) eps) x) (* (/ eps x) eps) (/ eps x))
2.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) (* 2 x) 2 x eps (* (* (/ eps x) eps) x) (* (/ eps x) eps) (/ eps x))
2.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) (* 2 x) 2 x eps (* (* (/ eps x) eps) x) (* (/ eps x) eps) (/ eps x))
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) (* 2 x) 2 x eps (* (* (/ eps x) eps) x) (* (/ eps x) eps) (/ eps x))
1.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) (* 2 x) 2 x eps (* (* (/ eps x) eps) x) (* (/ eps x) eps) (/ eps x))

rewrite72.0ms (2.9%)

Memory

13.7MiB live, 104.4MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	380
0	69	363
1	271	339
0	1992	333

Stop Event

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

Counts

29 → 109

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 (*.f64 (/.f64 eps x) eps) x)))
(fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 (*.f64 (/.f64 eps x) eps) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
eps
(.f64 (.f64 (/.f64 eps x) eps) x)
(*.f64 (/.f64 eps x) eps)
(/.f64 eps 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 (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) #s(hole binary64 (+ (* 2 (* eps x)) (pow eps 2))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (* (/ eps x) eps) x) #s(hole binary64 (pow eps 2)))
#s(approx (* (/ eps x) eps) #s(hole binary64 (/ (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 x) eps) x)) #s(hole binary64 (* 2 (* eps x))))
#s(approx (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) #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 (+ (* (* 2 x) eps) (* (* (/ eps x) 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 x) eps) x)) #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 (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) #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 1 binary64) (.f64 (/.f64 eps x) eps) (*.f64 #s(literal 2 binary64) eps)) x))
(.f64 (fma.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) eps) (*.f64 #s(literal 2 binary64) eps)) x)
(.f64 (.f64 eps x) (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(.f64 (.f64 eps x) (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(.f64 x (fma.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) eps) (*.f64 #s(literal 2 binary64) eps)))
(/.f64 (.f64 (fma.f64 #s(literal 8 binary64) (.f64 (.f64 eps eps) eps) (pow.f64 (.f64 (/.f64 eps x) eps) #s(literal 3 binary64))) x) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) #s(literal 2 binary64)) eps (-.f64 (pow.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) #s(literal 2 binary64)) (.f64 (.f64 (*.f64 #s(literal 2 binary64) eps) eps) (/.f64 eps x)))))
(/.f64 (.f64 (.f64 (fma.f64 #s(literal -2 binary64) eps (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps))) (fma.f64 #s(literal -2 binary64) eps (.f64 (/.f64 eps x) eps))) x) (fma.f64 #s(literal 2 binary64) eps (.f64 #s(literal -1 binary64) (*.f64 (/.f64 eps x) eps))))
(/.f64 (.f64 x (fma.f64 #s(literal 8 binary64) (.f64 (.f64 eps eps) eps) (pow.f64 (.f64 (/.f64 eps x) eps) #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 #s(literal 2 binary64) eps) #s(literal 2 binary64)) eps (-.f64 (pow.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) #s(literal 2 binary64)) (.f64 (.f64 (*.f64 #s(literal 2 binary64) eps) eps) (/.f64 eps x)))))
(/.f64 (.f64 x (.f64 (fma.f64 #s(literal -2 binary64) eps (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps))) (fma.f64 #s(literal -2 binary64) eps (.f64 (/.f64 eps x) eps)))) (fma.f64 #s(literal 2 binary64) eps (.f64 #s(literal -1 binary64) (*.f64 (/.f64 eps x) eps))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x) (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 eps x) (fma.f64 (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x) (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x) (.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (.f64 #s(literal -1 binary64) (*.f64 (/.f64 eps x) eps)) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x) (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x)))) (neg.f64 (.f64 (*.f64 eps x) (-.f64 #s(literal 2 binary64) (/.f64 eps x)))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 3/2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 3/2 binary64)) (.f64 (pow.f64 (/.f64 eps x) #s(literal 3 binary64)) (pow.f64 (.f64 eps x) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 #s(literal 2 binary64) eps)) x (.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (-.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps))))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x) (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x))) (.f64 (*.f64 eps x) (-.f64 #s(literal 2 binary64) (/.f64 eps x))))
(/.f64 (fma.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 3/2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 3/2 binary64)) (.f64 (pow.f64 (/.f64 eps x) #s(literal 3 binary64)) (pow.f64 (.f64 eps x) #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x) (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x) (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) x) (*.f64 (/.f64 eps x) eps)))))
(/.f64 (fma.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 3/2 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 3/2 binary64)) (.f64 (pow.f64 (/.f64 eps x) #s(literal 3 binary64)) (pow.f64 (.f64 eps x) #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 #s(literal 2 binary64) eps)) x (.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (-.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(fma.f64 (.f64 (/.f64 eps x) x) eps (.f64 (*.f64 #s(literal 2 binary64) x) eps))
(fma.f64 (.f64 x (/.f64 eps x)) eps (.f64 (*.f64 #s(literal 2 binary64) x) eps))
(fma.f64 (.f64 #s(literal 2 binary64) eps) x (.f64 (*.f64 (/.f64 eps x) x) eps))
(fma.f64 (.f64 (/.f64 eps x) eps) x (.f64 (*.f64 #s(literal 2 binary64) x) eps))
(fma.f64 (/.f64 eps x) (.f64 eps x) (.f64 (*.f64 #s(literal 2 binary64) x) eps))
(fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 (*.f64 (/.f64 eps x) x) eps))
(fma.f64 (.f64 eps x) (/.f64 eps x) (.f64 (*.f64 #s(literal 2 binary64) x) eps))
(fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 (*.f64 (/.f64 eps x) x) eps))
(fma.f64 #s(literal 2 binary64) (.f64 eps x) (.f64 (*.f64 (/.f64 eps x) x) eps))
(fma.f64 eps (.f64 (/.f64 eps x) x) (.f64 (*.f64 #s(literal 2 binary64) x) eps))
(fma.f64 eps (.f64 #s(literal 2 binary64) x) (.f64 (*.f64 (/.f64 eps x) x) eps))
(fma.f64 eps x (-.f64 (.f64 eps x) (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x)))
(fma.f64 eps x (+.f64 (.f64 eps x) (.f64 (*.f64 (/.f64 eps x) x) eps)))
(fma.f64 x (.f64 #s(literal 2 binary64) eps) (.f64 (*.f64 (/.f64 eps x) x) eps))
(fma.f64 x (.f64 (/.f64 eps x) eps) (.f64 (*.f64 #s(literal 2 binary64) x) eps))
(fma.f64 x eps (-.f64 (.f64 eps x) (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x)))
(fma.f64 x eps (+.f64 (.f64 eps x) (.f64 (*.f64 (/.f64 eps x) x) eps)))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 2 binary64)) (.f64 (.f64 eps x) (-.f64 #s(literal 2 binary64) (/.f64 eps x)))) (/.f64 (.f64 (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x) (.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)) x)) (.f64 (*.f64 eps x) (-.f64 #s(literal 2 binary64) (/.f64 eps x)))))
(-.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (neg.f64 (/.f64 eps x)) (.f64 eps x)))
(-.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (.f64 #s(literal -1 binary64) (*.f64 (/.f64 eps x) eps)) x))
(-.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (.f64 (neg.f64 (.f64 eps x)) #s(literal 2 binary64)))
(-.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (.f64 (neg.f64 eps) (.f64 #s(literal 2 binary64) x)))
(-.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (.f64 (.f64 #s(literal -2 binary64) x) eps))
(+.f64 (fma.f64 (.f64 (/.f64 eps x) eps) x (.f64 eps x)) (*.f64 eps x))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) #s(literal 3 binary64)) (fma.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 #s(literal 2 binary64) eps)) x (.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (-.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (.f64 (.f64 #s(literal 2 binary64) x) eps))))) (/.f64 (.f64 (pow.f64 (/.f64 eps x) #s(literal 3 binary64)) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 #s(literal 2 binary64) eps)) x (.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (-.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (.f64 (.f64 #s(literal 2 binary64) x) eps))))))
(+.f64 (.f64 (.f64 #s(literal 2 binary64) x) eps) (.f64 (.f64 (/.f64 eps x) x) eps))
(+.f64 (.f64 eps x) (-.f64 (.f64 eps x) (.f64 (.f64 #s(literal -1 binary64) (*.f64 (/.f64 eps x) eps)) x)))
(+.f64 (.f64 eps x) (+.f64 (.f64 eps x) (.f64 (.f64 (/.f64 eps x) x) eps)))
(+.f64 (.f64 (.f64 (/.f64 eps x) x) eps) (.f64 (.f64 #s(literal 2 binary64) x) eps))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 x x) (.f64 x x)) (-.f64 x x))
(/.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 x x) x)) (fma.f64 (fabs.f64 x) (fabs.f64 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
(.f64 (.f64 (/.f64 eps x) x) eps)
(.f64 (.f64 x (/.f64 eps x)) eps)
(.f64 (.f64 (/.f64 eps x) eps) x)
(.f64 (/.f64 eps x) (.f64 eps x))
(.f64 (.f64 eps x) (/.f64 eps x))
(.f64 eps (.f64 (/.f64 eps x) x))
(.f64 x (.f64 (/.f64 eps x) eps))
(/.f64 (.f64 (.f64 eps eps) x) x)
(/.f64 (.f64 (neg.f64 eps) (.f64 eps x)) (*.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 eps (.f64 eps x)) x)
(/.f64 (.f64 (.f64 (neg.f64 eps) eps) x) (*.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 x (.f64 (neg.f64 eps) eps)) (*.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 x (.f64 eps eps)) x)
(.f64 (.f64 #s(literal 1 binary64) (/.f64 eps x)) eps)
(.f64 (.f64 #s(literal 1 binary64) eps) (/.f64 eps x))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) eps))
(.f64 (.f64 (/.f64 eps x) eps) #s(literal 1 binary64))
(*.f64 (/.f64 eps x) eps)
(*.f64 eps (/.f64 eps x))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (neg.f64 eps) eps)) (*.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 (/.f64 eps x) eps)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 (neg.f64 eps) eps)) (.f64 #s(literal 2 binary64) (.f64 #s(literal -1 binary64) x)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 eps eps)) (*.f64 #s(literal 2 binary64) x))
(/.f64 (.f64 (neg.f64 eps) eps) (.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 eps eps) (neg.f64 (.f64 #s(literal -1 binary64) x)))
(/.f64 (*.f64 eps eps) x)
(neg.f64 (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps)))
(/.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (*.f64 #s(literal -1 binary64) x)))
(/.f64 (neg.f64 eps) (*.f64 #s(literal -1 binary64) x))
(/.f64 eps x)
(neg.f64 (/.f64 (neg.f64 eps) x))
(neg.f64 (/.f64 eps (*.f64 #s(literal -1 binary64) 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 (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) (*.f64 eps eps))
#s(approx (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (* 2 x) (*.f64 #s(literal 2 binary64) x))
#s(approx x x)
#s(approx (* (* (/ eps x) eps) x) (*.f64 eps eps))
#s(approx (* (/ eps x) eps) (*.f64 (/.f64 eps x) eps))
#s(approx (/ eps x) (/.f64 eps x))
#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 (fma.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) eps) (*.f64 #s(literal 2 binary64) eps)) x))
#s(approx (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) (.f64 (.f64 #s(literal 2 binary64) x) eps))
#s(approx (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) (.f64 (fma.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) eps) (*.f64 #s(literal 2 binary64) eps)) x))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 (fma.f64 #s(literal -2 binary64) eps (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) eps))) x) #s(literal -1 binary64)))
#s(approx (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) (.f64 (.f64 (fma.f64 #s(literal -2 binary64) eps (.f64 #s(literal -1 binary64) (.f64 (/.f64 eps x) 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 (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) (*.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 (/.f64 x eps) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64)) eps) eps))
#s(approx (+ (* (* 2 x) eps) (* (* (/ eps x) eps) x)) (.f64 (.f64 (fma.f64 (*.f64 (/.f64 x eps) #s(literal 2 binary64)) #s(literal 1 binary64) #s(literal 1 binary64)) eps) eps))

eval11.0ms (0.5%)

Memory: 27.4MiB live, 27.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 3 206 to 410 computations (87.2% saved)

prune116.0ms (4.7%)

Memory

-48.9MiB live, 108.2MiB allocated; 27ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	114	3	117

Accuracy

100.0%

Counts

117 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.5%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
✓	99.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 (*.f64 (/.f64 eps x) eps) x)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 eps eps) x) (*.f64 #s(literal 2 binary64) eps)) x))

Status

Accuracy

Program

✓

77.5%

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

✓

99.8%

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

✓

100.0%

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

Compiler

Compiled 106 to 61 computations (42.5% saved)

regimes5.0ms (0.2%)

Memory

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

Accuracy

Total -14.5b remaining (-46479.6%)

Threshold costs -14.5b (-46479.6%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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 11 to 11 computations (0% saved)

derivations20.0ms (0.8%)

Memory

11.8MiB live, 11.8MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 22 to 15 computations (31.8% saved)

preprocess11.0ms (0.4%)

Memory: 12.2MiB live, 12.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 62 to 44 computations (29% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.3s (50.9%)

explain109.0ms (4.4%)

preprocess41.0ms (1.7%)

series6.0ms (0.2%)

rewrite211.0ms (8.6%)

eval34.0ms (1.4%)

prune97.0ms (3.9%)

series14.0ms (0.6%)

rewrite100.0ms (4.1%)

eval23.0ms (0.9%)

prune321.0ms (13.1%)

series15.0ms (0.6%)

rewrite72.0ms (2.9%)

eval11.0ms (0.5%)

prune116.0ms (4.7%)

regimes5.0ms (0.2%)

derivations20.0ms (0.8%)

preprocess11.0ms (0.4%)

end0.0ms (0%)

Profiling