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

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

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

Algorithm

1×

Search

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

Compiler

Compiled 25 to 18 computations (28% saved)

sample1.7s (37.6%)

Memory

37.0MiB live, 2 113.8MiB allocated; 569ms collecting garbage

Samples

563.0ms	5 158×	0	valid
471.0ms	2 536×	1	valid
204.0ms	562×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 1.0s

ival-pow2: 389.0ms (38.5% of total)

ival-add: 170.0ms (16.8% of total)

ival-sub: 159.0ms (15.7% of total)

ival-<=: 140.0ms (13.8% of total)

adjust: 116.0ms (11.5% of total)

ival-and: 21.0ms (2.1% of total)

exact: 15.0ms (1.5% of total)

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

Bogosity

explain158.0ms (3.6%)

Memory

-14.1MiB live, 275.3MiB allocated; 37ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
71	-	-	`(-.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	71	0

Confusion

	Predicted +	Predicted -
+	71	0
-	0	185

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	71	0	0
-	0	0	185

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	185
1	71

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

23.0ms	164×	1	valid
21.0ms	320×	0	valid
5.0ms	28×	2	valid

Compiler

Compiled 59 to 25 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-pow2: 16.0ms (49.8% of total)

adjust: 6.0ms (18.7% of total)

ival-sub: 5.0ms (15.6% of total)

ival-add: 4.0ms (12.5% of total)

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

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

exact: 0.0ms (0% of total)

preprocess188.0ms (4.2%)

Memory

17.6MiB live, 204.9MiB allocated; 31ms collecting garbage

Algorithm

1×	egg-herbie

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

1.0MiB live, 1.0MiB 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)

simplify109.0ms (2.5%)

Memory

7.9MiB live, 138.6MiB allocated; 24ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 x #s(literal 2 binary64))
cost-diff	0	(+.f64 x eps)
cost-diff	0	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
cost-diff	3	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	23
0	11	23
1	16	23
2	44	23
3	157	23
4	570	21
5	1812	21
0	8588	20

Stop Event

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

Calls

Call 1

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

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

localize68.0ms (1.5%)

Memory

7.8MiB live, 62.8MiB allocated; 42ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0078125	(pow.f64 x #s(literal 2 binary64))
accuracy	0.03515625	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
accuracy	15.432710834864105	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

49.0ms	160×	0	valid
10.0ms	82×	1	valid
2.0ms	14×	2	valid

Compiler

Compiled 25 to 9 computations (64% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-pow2: 33.0ms (62.5% of total)

ival-add: 15.0ms (28.4% of total)

adjust: 3.0ms (5.7% of total)

ival-sub: 2.0ms (3.8% of total)

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

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

exact: 0.0ms (0% of total)

series11.0ms (0.2%)

Memory

-25.8MiB live, 19.4MiB allocated; 13ms collecting garbage

Counts

4 → 23

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
(+.f64 x eps)
(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)
(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
(* 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
7.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (+ x eps) (pow x 2))

simplify204.0ms (4.6%)

Memory

9.7MiB live, 242.3MiB allocated; 29ms collecting garbage

Algorithm

1×	egg-herbie

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)
(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
(* 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)
(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
(* 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)))

rewrite58.0ms (1.3%)

Memory

-1.4MiB live, 44.1MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
0	11	20
1	51	20
0	386	20

Stop Event

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

Counts

4 → 61

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

eval8.0ms (0.2%)

Memory: 12.4MiB live, 12.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 322 to 269 computations (79.7% saved)

prune4.0ms (0.1%)

Memory

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

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	5	78

Accuracy

100.0%

Counts

78 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.1%	(-.f64 #s(approx (pow (+ x eps) 2) (.f64 (.f64 (fma.f64 (/.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64)) #s(literal 1 binary64)) x) x)) (pow.f64 x #s(literal 2 binary64)))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	87.7%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64))))
▶	61.6%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
▶	73.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 174 to 120 computations (31% saved)

simplify170.0ms (3.8%)

Memory

-29.2MiB live, 116.7MiB allocated; 21ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 (fma.f64 (/.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64)) #s(literal 1 binary64)) x) x)
cost-diff	0	#s(approx (pow (+ x eps) 2) (.f64 (.f64 (fma.f64 (/.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64)) #s(literal 1 binary64)) x) x))
cost-diff	0	(-.f64 #s(approx (pow (+ x eps) 2) (.f64 (.f64 (fma.f64 (/.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64)) #s(literal 1 binary64)) x) x)) (pow.f64 x #s(literal 2 binary64)))
cost-diff	4	(*.f64 (fma.f64 (/.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64)) #s(literal 1 binary64)) x)
cost-diff	0	(-.f64 (/.f64 eps x) #s(literal -2 binary64))
cost-diff	0	(*.f64 eps x)
cost-diff	0	(.f64 (.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64)))
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64))))
cost-diff	0	(*.f64 eps x)
cost-diff	0	(.f64 (.f64 eps x) #s(literal 2 binary64))
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
cost-diff	0	(*.f64 eps eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
cost-diff	0	(fma.f64 #s(literal 2 binary64) x eps)
cost-diff	0	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	210
0	42	210
1	70	210
2	162	210
3	483	198
4	1963	186
5	7541	186
0	8179	182

Stop Event

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

Calls

Call 1

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

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

localize72.0ms (1.6%)

Memory

28.1MiB live, 72.4MiB allocated; 6ms collecting garbage

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.1484375	(.f64 (.f64 (fma.f64 (/.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64)) #s(literal 1 binary64)) x) x)
accuracy	0.221035009768442	(fma.f64 (/.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64)) #s(literal 1 binary64))
accuracy	7.276942089014971	(*.f64 (fma.f64 (/.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64)) #s(literal 1 binary64)) x)
accuracy	15.432710834864105	(-.f64 #s(approx (pow (+ x eps) 2) (.f64 (.f64 (fma.f64 (/.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64)) #s(literal 1 binary64)) x) x)) (pow.f64 x #s(literal 2 binary64)))
accuracy	0.0	(-.f64 (/.f64 eps x) #s(literal -2 binary64))
accuracy	0.0	(*.f64 eps x)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64))))
accuracy	7.857368283904903	(.f64 (.f64 eps x) (-.f64 (/.f64 eps x) #s(literal -2 binary64)))
accuracy	0.0	(*.f64 eps x)
accuracy	0.02734375	(.f64 (.f64 eps x) #s(literal 2 binary64))
accuracy	24.567163023785216	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps x) #s(literal 2 binary64)))
accuracy	0.0	(*.f64 eps eps)
accuracy	16.76688540741772	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))
accuracy	0.0	(fma.f64 #s(literal 2 binary64) x eps)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
accuracy	0.01171875	(*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps)

Samples

26.0ms	82×	1	valid
25.0ms	160×	0	valid
6.0ms	14×	2	valid

Compiler

Compiled 160 to 24 computations (85% saved)

Precisions

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

ival-mult: 12.0ms (31.9% of total)

ival-pow2: 9.0ms (23.9% of total)

adjust: 7.0ms (18.6% of total)

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

ival-sub: 3.0ms (8% of total)

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

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

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

exact: 0.0ms (0% of total)

series36.0ms (0.8%)

Memory

-19.5MiB live, 33.4MiB allocated; 14ms collecting garbage

Counts

16 → 52

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) (- (/ eps x) -2)) (- (/ eps x) -2) (* (+ (* (/ eps x) (- (/ eps x) -2)) 1) x) (- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (* (* (+ (* (/ eps x) (- (/ eps x) -2)) 1) x) x) (+ (* (/ eps x) (- (/ eps x) -2)) 1))
3.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) (- (/ eps x) -2)) (- (/ eps x) -2) (* (+ (* (/ eps x) (- (/ eps x) -2)) 1) x) (- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (* (* (+ (* (/ eps x) (- (/ eps x) -2)) 1) x) x) (+ (* (/ eps x) (- (/ eps x) -2)) 1))
2.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) (- (/ eps x) -2)) (- (/ eps x) -2) (* (+ (* (/ eps x) (- (/ eps x) -2)) 1) x) (- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (* (* (+ (* (/ eps x) (- (/ eps x) -2)) 1) x) x) (+ (* (/ eps x) (- (/ eps x) -2)) 1))
2.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) (- (/ eps x) -2)) (- (/ eps x) -2) (* (+ (* (/ eps x) (- (/ eps x) -2)) 1) x) (- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (* (* (+ (* (/ eps x) (- (/ eps x) -2)) 1) x) x) (+ (* (/ eps x) (- (/ eps x) -2)) 1))
2.0ms	eps	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (+ (* 2 x) eps) eps) (+ (* 2 x) eps) (- (pow (+ x eps) 2) (pow x 2)) (* eps eps) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) 2) (* eps x) (- (pow (+ x eps) 2) (pow x 2)) (* (* eps x) (- (/ eps x) -2)) (- (/ eps x) -2) (* (+ (* (/ eps x) (- (/ eps x) -2)) 1) x) (- (pow (+ x eps) 2) (pow x 2)) (pow (+ x eps) 2) (* (* (+ (* (/ eps x) (- (/ eps x) -2)) 1) x) x) (+ (* (/ eps x) (- (/ eps x) -2)) 1))

simplify142.0ms (3.2%)

Memory

37.9MiB live, 125.9MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	448
1	410	430
2	1552	364
3	7361	364
0	9311	325

Stop Event

1×	iter limit
1×	node limit

Counts

52 → 50

Calls

Call 1

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

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

rewrite51.0ms (1.1%)

Memory

-3.2MiB live, 41.1MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	178
0	42	178
1	154	178
0	1113	178

Stop Event

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

Counts

16 → 146

Calls

Call 1

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

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

eval76.0ms (1.7%)

Memory: -7.5MiB live, 54.3MiB allocated; 17ms collecting garbage
Compiler: Compiled 4 847 to 678 computations (86% saved)

prune8.0ms (0.2%)

Memory

-31.2MiB live, 13.8MiB allocated; 4ms collecting garbage

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	177	3	180
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	180	5	185

Accuracy

100.0%

Counts

185 → 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 eps eps (.f64 (.f64 #s(literal 2 binary64) x) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
▶	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
▶	61.6%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))
✓	73.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 79 to 54 computations (31.6% saved)

simplify119.0ms (2.7%)

Memory

30.3MiB live, 170.7MiB allocated; 23ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal 2 binary64) x)
cost-diff	0	(.f64 (.f64 #s(literal 2 binary64) x) eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (.f64 (.f64 #s(literal 2 binary64) x) eps)))
cost-diff	2	(fma.f64 eps eps (.f64 (.f64 #s(literal 2 binary64) x) eps))
cost-diff	0	(+.f64 eps x)
cost-diff	0	(*.f64 (+.f64 (+.f64 eps x) x) eps)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
cost-diff	1	(+.f64 (+.f64 eps x) x)
cost-diff	0	(*.f64 eps #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	97
0	27	95
1	53	95
2	147	95
3	417	95
4	1049	89
5	3603	89
0	8317	81

Stop Event

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

Calls

Call 1

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

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

localize61.0ms (1.4%)

Memory

8.5MiB live, 53.0MiB allocated; 8ms collecting garbage

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0	(.f64 (.f64 #s(literal 2 binary64) x) eps)
accuracy	0.0	(*.f64 #s(literal 2 binary64) x)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (.f64 (.f64 #s(literal 2 binary64) x) eps)))
accuracy	0.0078125	(fma.f64 eps eps (.f64 (.f64 #s(literal 2 binary64) x) eps))
accuracy	0.0	(+.f64 eps x)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
accuracy	0.01171875	(*.f64 (+.f64 (+.f64 eps x) x) eps)
accuracy	0.0390625	(+.f64 (+.f64 eps x) x)
accuracy	0.0	(.f64 (.f64 eps #s(literal 2 binary64)) x)
accuracy	0.0	(*.f64 eps #s(literal 2 binary64))
accuracy	24.567163023785216	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (.f64 (.f64 eps #s(literal 2 binary64)) x))

Samples

19.0ms	82×	1	valid
18.0ms	160×	0	valid
5.0ms	14×	2	valid

Compiler

Compiled 77 to 18 computations (76.6% saved)

Precisions

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

ival-mult: 9.0ms (31% of total)

ival-pow2: 7.0ms (24.1% of total)

adjust: 6.0ms (20.7% of total)

ival-add: 5.0ms (17.2% of total)

ival-sub: 2.0ms (6.9% of total)

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

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

exact: 0.0ms (0% of total)

series31.0ms (0.7%)

Memory

-33.4MiB live, 11.3MiB allocated; 11ms collecting garbage

Counts

11 → 21

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
25.0ms	eps	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* 2 x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))
1.0ms	x	@	-inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* 2 x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))
1.0ms	x	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* 2 x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))
1.0ms	eps	@	inf	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* 2 x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))
1.0ms	x	@	0	((- (pow (+ x eps) 2) (pow x 2)) (* (* eps 2) x) (* eps 2) (+ (+ eps x) x) (- (pow (+ x eps) 2) (pow x 2)) (* (+ (+ eps x) x) eps) (+ eps x) (+ (* eps eps) (* (* 2 x) eps)) (- (pow (+ x eps) 2) (pow x 2)) (* (* 2 x) eps) (* 2 x))

simplify129.0ms (2.9%)

Memory

5.5MiB live, 151.4MiB allocated; 18ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	101
1	164	91
2	471	91
3	1562	91
4	6780	91
0	8197	81

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

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

rewrite55.0ms (1.2%)

Memory

35.9MiB live, 35.9MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	89
0	27	87
1	120	87
0	951	82

Stop Event

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

Counts

11 → 195

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

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

eval43.0ms (1%)

Memory: -19.7MiB live, 26.4MiB allocated; 3ms collecting garbage
Compiler: Compiled 3 070 to 489 computations (84.1% saved)

prune4.0ms (0.1%)

Memory

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

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	0	0	0
Picked	2	1	3
Done	0	2	2
Total	132	5	137

Accuracy

100.0%

Counts

137 → 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 eps eps (*.f64 (+.f64 x x) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
▶	61.6%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	73.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 79 to 52 computations (34.2% saved)

simplify137.0ms (3.1%)

Memory

8.6MiB live, 108.5MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	61
0	20	59
1	39	59
2	116	59
3	347	59
4	962	55
5	3054	55
0	8168	51

Stop Event

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

Calls

Call 1

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

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

localize92.0ms (2.1%)

Memory

-20.9MiB live, 66.9MiB allocated; 12ms collecting garbage

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x x)
accuracy	0.0	(*.f64 (+.f64 x x) eps)
accuracy	0.0	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 (+.f64 x x) eps)))
accuracy	0.0078125	(fma.f64 eps eps (*.f64 (+.f64 x x) eps))
accuracy	0.0	(+.f64 eps eps)
accuracy	0.0	(*.f64 (+.f64 eps eps) x)
accuracy	24.567163023785216	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))

Samples

59.0ms	160×	0	valid
20.0ms	82×	1	valid
4.0ms	14×	2	valid

Compiler

Compiled 49 to 14 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-pow2: 51.0ms (70% of total)

ival-add: 11.0ms (15.1% of total)

ival-mult: 5.0ms (6.9% of total)

adjust: 4.0ms (5.5% of total)

ival-sub: 2.0ms (2.7% of total)

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

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

series6.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated; 0ms collecting garbage

Counts

7 → 9

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

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

Calls

6 calls:

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

simplify214.0ms (4.8%)

Memory

-38.7MiB live, 98.4MiB allocated; 62ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	59
1	89	49
2	309	49
3	1132	49
4	4795	49
0	8238	44

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 9

Calls

Call 1

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

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

rewrite27.0ms (0.6%)

Memory

-18.4MiB live, 24.9MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	57
0	20	55
0	98	55

Stop Event

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

Counts

7 → 25

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

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

eval3.0ms (0.1%)

Memory: 5.4MiB live, 5.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 627 to 107 computations (82.9% saved)

prune4.0ms (0.1%)

Memory

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

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	30	5	35

Accuracy

100.0%

Counts

35 → 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 eps eps (*.f64 (+.f64 x x) eps)))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
✓	100.0%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
✓	61.6%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 eps eps) x))
✓	73.8%	#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 eps eps))

Compiler

Compiled 258 to 101 computations (60.9% saved)

regimes10.0ms (0.2%)

Memory

20.9MiB live, 20.9MiB allocated; 0ms collecting garbage

Counts

11 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	eps
3.0ms	x
3.0ms	(-.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)

regimes11.0ms (0.2%)

Memory

-22.3MiB live, 19.3MiB allocated; 6ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	x
2.0ms	eps
2.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

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

Compiler

Compiled 11 to 11 computations (0% saved)

regimes6.0ms (0.1%)

Memory

16.4MiB live, 16.4MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

Outputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) 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
100.0%	1	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
100.0%	1	`x`
100.0%	1	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes5.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated; 0ms collecting garbage

Counts

4 → 2

Calls

Call 1

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

Results

Accuracy	Segments	Branch
97.8%	2	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
93.0%	3	`x`
87.7%	3	`eps`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes4.0ms (0.1%)

Memory

-36.4MiB live, 10.0MiB allocated; 2ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
73.8%	1	`eps`
73.8%	1	`x`
73.8%	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

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.040287216562815e-309	1.1926148418770364e-306

Compiler

Compiled 12 to 12 computations (0% saved)

simplify63.0ms (1.4%)

Memory

-3.1MiB live, 54.2MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	104
1	37	104
2	69	104
3	184	104
4	609	92
5	2084	92
6	7897	92

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (fma.f64 eps eps (*.f64 (+.f64 x x) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 404804506614621/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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)) (fma.f64 eps eps (*.f64 (+.f64 x x) eps)))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (fma.f64 #s(literal 2 binary64) x eps) eps))
#s(approx (- (pow (+ x eps) 2) (pow x 2)) (*.f64 (+.f64 (+.f64 eps x) x) eps))
(if (<=.f64 (-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 404804506614621/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784 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))

derivations351.0ms (7.9%)

Memory

13.7MiB live, 344.2MiB allocated; 39ms 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
0	27	178
0	42	178
1	154	178
0	1113	178
0	18	89
0	27	87
1	120	87
0	951	82

Stop Event

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

Compiler

Compiled 104 to 31 computations (70.2% saved)

preprocess35.0ms (0.8%)

Memory: -11.7MiB live, 42.6MiB allocated; 5ms collecting garbage
Compiler: Compiled 226 to 76 computations (66.4% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.7s (37.6%)

explain158.0ms (3.6%)

preprocess188.0ms (4.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify109.0ms (2.5%)

localize68.0ms (1.5%)

series11.0ms (0.2%)

simplify204.0ms (4.6%)

rewrite58.0ms (1.3%)

eval8.0ms (0.2%)

prune4.0ms (0.1%)

simplify170.0ms (3.8%)

localize72.0ms (1.6%)

series36.0ms (0.8%)

simplify142.0ms (3.2%)

rewrite51.0ms (1.1%)

eval76.0ms (1.7%)

prune8.0ms (0.2%)

simplify119.0ms (2.7%)

localize61.0ms (1.4%)

series31.0ms (0.7%)

simplify129.0ms (2.9%)

rewrite55.0ms (1.2%)

eval43.0ms (1%)

prune4.0ms (0.1%)

simplify137.0ms (3.1%)

localize92.0ms (2.1%)

series6.0ms (0.1%)

simplify214.0ms (4.8%)

rewrite27.0ms (0.6%)

eval3.0ms (0.1%)

prune4.0ms (0.1%)

regimes10.0ms (0.2%)

regimes11.0ms (0.2%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

simplify63.0ms (1.4%)

derivations351.0ms (7.9%)

preprocess35.0ms (0.8%)

end0.0ms (0%)

Profiling