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

start0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 25 to 18 computations (28% saved)

sample2.0s (56.2%)

Memory

50.7MiB live, 2 428.2MiB allocated; 594ms collecting garbage

Samples

655.0ms	5 176×	0	valid
632.0ms	2 498×	1	valid
181.0ms	582×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-<=: 309.0ms (27.1% of total)

ival-add: 280.0ms (24.6% of total)

ival-pow2: 270.0ms (23.7% of total)

adjust: 126.0ms (11.1% of total)

ival-sub: 107.0ms (9.4% of total)

ival-and: 25.0ms (2.2% of total)

exact: 19.0ms (1.7% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain182.0ms (5.1%)

Memory

-14.9MiB live, 266.7MiB allocated; 68ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
72	-	-	`(-.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	72	0

Confusion

	Predicted +	Predicted -
+	72	0
-	0	184

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	72	0	0
-	0	0	184

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	184
1	72

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

29.0ms	146×	1	valid
23.0ms	314×	0	valid
10.0ms	52×	2	valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-pow2: 27.0ms (63.2% of total)

adjust: 7.0ms (16.4% of total)

ival-add: 4.0ms (9.4% of total)

ival-sub: 4.0ms (9.4% of total)

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

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

exact: 0.0ms (0% of total)

preprocess154.0ms (4.3%)

Memory

48.9MiB live, 185.2MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	30	51
2	110	51
3	486	49
4	1521	37
5	4312	37
0	7	9
0	11	9
1	16	9
2	44	9
3	157	9
4	570	7
5	1812	7
0	8588	6

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

series40.0ms (1.1%)

Memory

-37.4MiB live, 9.3MiB allocated; 2ms collecting garbage

Counts

7 → 23

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

Calls

6 calls:

Time	Variable		Point	Expression
35.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) x eps 2 (pow x 2))
1.0ms	x	@	-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	@	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))

simplify231.0ms (6.5%)

Memory

21.2MiB live, 205.9MiB allocated; 69ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	215
1	239	203
2	874	191
3	3924	183
0	8175	172

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 21

Calls

Call 1

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

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

rewrite64.0ms (1.8%)

Memory

9.6MiB live, 72.4MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	11	23
1	51	23
0	386	23

Stop Event

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

Counts

7 → 63

Calls

Call 1

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

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

eval16.0ms (0.4%)

Memory: -20.7MiB live, 23.3MiB allocated; 9ms collecting garbage
Compiler: Compiled 1 353 to 265 computations (80.4% saved)

prune3.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	4	82

Accuracy

100.0%

Counts

82 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	89.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64))))
▶	64.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	73.1%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 63 to 44 computations (30.2% saved)

series16.0ms (0.4%)

Memory

-12.4MiB live, 33.1MiB allocated; 5ms collecting garbage

Counts

16 → 21

Calls

Call 1

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

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

Calls

6 calls:

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

simplify105.0ms (2.9%)

Memory

25.7MiB live, 170.3MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	111
1	148	101
2	482	95
3	1760	95
4	6392	95
0	8162	85

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 19

Calls

Call 1

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

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

rewrite50.0ms (1.4%)

Memory

-15.0MiB live, 31.2MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	105
0	29	105
1	110	105
0	759	105

Stop Event

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

Counts

16 → 103

Calls

Call 1

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

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

eval11.0ms (0.3%)

Memory: 19.3MiB live, 19.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 504 to 333 computations (86.7% saved)

prune8.0ms (0.2%)

Memory

-32.9MiB live, 13.4MiB allocated; 3ms collecting garbage

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	0	0	0
Picked	2	2	4
Done	0	0	0
Total	123	4	127

Accuracy

100.0%

Counts

127 → 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 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	64.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	73.1%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 62 to 43 computations (30.6% saved)

series6.0ms (0.2%)

Memory

11.2MiB live, 11.2MiB allocated; 0ms collecting garbage

Counts

10 → 11

Calls

Call 1

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

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

Calls

6 calls:

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

simplify112.0ms (3.2%)

Memory

8.6MiB live, 103.3MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	61
1	89	51
2	306	51
3	1148	51
4	4818	51
0	8224	46

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 9

Calls

Call 1

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

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

rewrite79.0ms (2.2%)

Memory

-18.6MiB live, 26.6MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	58
0	20	58
1	87	56
0	653	54

Stop Event

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

Counts

10 → 81

Calls

Call 1

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

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

eval9.0ms (0.2%)

Memory: 10.0MiB live, 10.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 887 to 249 computations (86.8% saved)

prune4.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	0	0
Picked	1	1	2
Done	0	2	2
Total	91	4	95

Accuracy

100.0%

Counts

95 → 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 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	64.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	73.1%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 62 to 42 computations (32.3% saved)

series4.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated; 0ms collecting garbage

Counts

5 → 10

Calls

Call 1

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

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

Calls

6 calls:

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

simplify110.0ms (3.1%)

Memory

13.7MiB live, 59.4MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	58
1	89	48
2	306	48
3	1148	48
4	4818	48
0	8224	43

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 8

Calls

Call 1

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

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

rewrite70.0ms (2%)

Memory

-36.5MiB live, 20.6MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	25
0	12	25
1	60	19
0	475	19

Stop Event

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

Counts

5 → 15

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 #s(literal 2 binary64) x))
(.f64 (.f64 #s(literal 2 binary64) x) eps)
(.f64 #s(literal 2 binary64) (.f64 eps x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (*.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 eps #s(literal 3 binary64))) x) (fma.f64 eps eps #s(literal 0 binary64)))
(/.f64 (*.f64 x #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (.f64 x (.f64 #s(literal 2 binary64) (pow.f64 eps #s(literal 3 binary64)))) (fma.f64 eps eps #s(literal 0 binary64)))
(fma.f64 eps x (*.f64 eps x))
(fma.f64 x eps (*.f64 eps x))
(+.f64 (.f64 eps x) (.f64 eps x))
#s(literal 2 binary64)
eps
x

eval2.0ms (0%)

Memory: 2.0MiB live, 2.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 319 to 57 computations (82.1% saved)

prune3.0ms (0.1%)

Memory

4.1MiB live, 4.1MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	19	5	24

Accuracy

100.0%

Counts

24 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	64.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
	4.9%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 x #s(literal 2 binary64)))
✓	73.1%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 208 to 87 computations (58.2% saved)

regimes8.0ms (0.2%)

Memory

9.4MiB live, 9.4MiB allocated; 0ms collecting garbage

Counts

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

Calls

3 calls:

3.0ms	eps
3.0ms	x
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
100.0%	1	`(-.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)

regimes6.0ms (0.2%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.5%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
94.1%	3	`x`
89.3%	3	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated; 0ms collecting garbage

Accuracy

Total -43.7b remaining (-253.7%)

Threshold costs -43.7b (-253.7%)

Counts

2 → 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 x #s(literal 2 binary64)))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
73.1%	1	`eps`
73.1%	1	`x`
73.1%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`

Compiler

Compiled 11 to 11 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	2.0682853795e-314

Compiler

Compiled 12 to 12 computations (0% saved)

simplify61.0ms (1.7%)

Memory

-30.4MiB live, 16.0MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

derivations183.0ms (5.1%)

Memory

2.2MiB live, 92.6MiB allocated; 10ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 69 to 23 computations (66.7% saved)

preprocess18.0ms (0.5%)

Memory: 29.1MiB live, 29.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 156 to 60 computations (61.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample2.0s (56.2%)

explain182.0ms (5.1%)

preprocess154.0ms (4.3%)

eval0.0ms (0%)

prune0.0ms (0%)

series40.0ms (1.1%)

simplify231.0ms (6.5%)

rewrite64.0ms (1.8%)

eval16.0ms (0.4%)

prune3.0ms (0.1%)

series16.0ms (0.4%)

simplify105.0ms (2.9%)

rewrite50.0ms (1.4%)

eval11.0ms (0.3%)

prune8.0ms (0.2%)

series6.0ms (0.2%)

simplify112.0ms (3.2%)

rewrite79.0ms (2.2%)

eval9.0ms (0.2%)

prune4.0ms (0.1%)

series4.0ms (0.1%)

simplify110.0ms (3.1%)

rewrite70.0ms (2%)

eval2.0ms (0%)

prune3.0ms (0.1%)

regimes8.0ms (0.2%)

regimes6.0ms (0.2%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

simplify61.0ms (1.7%)

derivations183.0ms (5.1%)

preprocess18.0ms (0.5%)

end0.0ms (0%)

Profiling