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

analyze0.0ms (0%)

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 26 to 19 computations (26.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

ival-<=: 0.0ms (0% of total)

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

sample2.0s (27.6%)

Results

845.0ms	5219×	0	valid
595.0ms	2513×	1	valid
179.0ms	524×	2	valid

Precisions

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

ival-pow: 318.0ms (31.6% of total)

backward-pass: 246.0ms (24.4% of total)

ival-<=: 142.0ms (14.1% of total)

ival-sub: 139.0ms (13.8% of total)

ival-add: 107.0ms (10.6% of total)

const: 28.0ms (2.8% of total)

ival-and: 25.0ms (2.5% of total)

Bogosity

preprocess961.0ms (13.1%)

Algorithm

2×	egg-herbie

Rules

18770×	`accelerator-lowering-fma.f32`
18770×	`accelerator-lowering-fma.f64`
2836×	`-lowering-.f32`
2836×	`-lowering-.f64`
2498×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	64
1	51	56
2	160	54
3	594	42
4	1837	42
5	4350	42
6	5916	42
7	6544	42
8	6773	42
9	6887	42
10	6920	42
11	7264	42
12	7492	42
13	7888	42
14	7897	42
15	7897	42
16	7971	42
0	7	9
1	12	9
2	32	9
3	92	9
4	271	7
5	850	7
6	2361	7
7	4280	7
8	5913	7
9	6914	7
10	7339	7
11	7607	7
12	7613	7
13	7613	7
0	8048	6

Stop Event

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

Calls

Call 1

Inputs
(- (pow (+ x eps) 2) (pow x 2))

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

Call 2

Inputs
(- (pow (+ x eps) 2) (pow x 2))
(- (pow (+ (neg x) eps) 2) (pow (neg x) 2))
(- (pow (+ x (neg eps)) 2) (pow x 2))
(neg (- (pow (+ (neg x) eps) 2) (pow (neg x) 2)))
(neg (- (pow (+ x (neg eps)) 2) (pow x 2)))
(- (pow (+ eps x) 2) (pow eps 2))

Outputs
(- (pow (+ x eps) 2) (pow x 2))
(* eps (+ x (+ x eps)))
(- (pow (+ (neg x) eps) 2) (pow (neg x) 2))
(* eps (- eps (+ x x)))
(- (pow (+ x (neg eps)) 2) (pow x 2))
(* eps (- eps (+ x x)))
(neg (- (pow (+ (neg x) eps) 2) (pow (neg x) 2)))
(* eps (+ x (- x eps)))
(neg (- (pow (+ x (neg eps)) 2) (pow x 2)))
(* eps (+ x (- x eps)))
(- (pow (+ eps x) 2) (pow eps 2))
(* x (+ x (+ eps eps)))

explain130.0ms (1.8%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
75	0	-	-	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	-	`x`
0	76	(-1.1616475187807621e-243 1.3046300531144826e-76)	-	`(pow.f64 (+.f64 x eps) #s(literal 2 binary64))`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(pow.f64 x #s(literal 2 binary64))`
0	0	-	-	`eps`

Results

32.0ms	322×	0	valid
46.0ms	152×	1	valid
12.0ms	38×	2	valid

Compiler

Compiled 63 to 36 computations (42.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-pow: 31.0ms (61.8% of total)

backward-pass: 7.0ms (13.9% of total)

ival-sub: 6.0ms (12% of total)

ival-add: 5.0ms (10% of total)

const: 2.0ms (4% of total)

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))

Compiler

Compiled 9 to 6 computations (33.3% saved)

localize46.0ms (0.6%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 eps (*.f64 x #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))
✓	accuracy	100.0%	(+.f64 eps (*.f64 x #s(literal 2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))

Rules

30×	`-lowering-.f32`
30×	`-lowering-.f64`
18×	`*-commutative`
18×	`accelerator-lowering-fma.f32`
18×	`accelerator-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	14	18
2	24	18
3	28	18
0	28	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* eps (+ eps (* x 2)))
eps
(+ eps (* x 2))
(* x 2)
x
2

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

Results

25.0ms

256×

valid

Compiler

Compiled 21 to 13 computations (38.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 6.0ms (62.1% of total)

ival-add: 3.0ms (31.1% of total)

const: 1.0ms (10.4% of total)

backward-pass: 0.0ms (0% of total)

series6.0ms (0.1%)

Counts

3 → 60

Calls

Call 1

Inputs
#<alt (* eps (+ eps (* x 2)))>
#<alt (* x 2)>
#<alt (+ eps (* x 2))>

Outputs
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(* eps (+ eps (* x 2)))
0.0ms	eps	@	0	(* eps (+ eps (* x 2)))
0.0ms	eps	@	inf	(* eps (+ eps (* x 2)))
0.0ms	x	@	inf	(* eps (+ eps (* x 2)))
0.0ms	eps	@	-inf	(* eps (+ eps (* x 2)))

rewrite894.0ms (12.2%)

Algorithm

1×	batch-egg-rewrite

Rules

8430×	`accelerator-lowering-fma.f32`
8430×	`accelerator-lowering-fma.f64`
4454×	`/-lowering-/.f32`
4454×	`/-lowering-/.f64`
3752×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	25	15
2	195	15
3	1813	15
0	8239	13

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 243

Calls

Call 1

Inputs
(* eps (+ eps (* x 2)))
(* x 2)
(+ eps (* x 2))

Outputs
(+.f64 (.f64 eps eps) (.f64 eps (*.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (*.f64 eps eps))
(+.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) (neg.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 eps eps) (.f64 x x))) (.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(-.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) (/.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 eps eps) (.f64 x x))) (.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(-.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 eps eps) (.f64 x x))) (-.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 eps eps))) (/.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (-.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (*.f64 eps eps))))
(fma.f64 eps eps (.f64 eps (.f64 x #s(literal 2 binary64))))
(fma.f64 eps (.f64 x #s(literal 2 binary64)) (.f64 eps eps))
(fma.f64 x (.f64 eps #s(literal 2 binary64)) (.f64 eps eps))
(fma.f64 #s(literal 2 binary64) (.f64 eps x) (.f64 eps eps))
(fma.f64 (.f64 x #s(literal 2 binary64)) eps (.f64 eps eps))
(fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) (neg.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 eps eps) (.f64 x x))) (.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
(fma.f64 (.f64 eps x) #s(literal 2 binary64) (.f64 eps eps))
(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (+.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (-.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 eps eps)))))
(/.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (+.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 eps eps) (.f64 x x))) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 eps eps) (.f64 x x))) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 x #s(literal 2 binary64))))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 eps eps)) (-.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 eps eps) (.f64 x x))) (.f64 (.f64 eps eps) (.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (neg.f64 (.f64 eps eps)) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64))))) (.f64 eps (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -8 binary64)) (.f64 eps (.f64 eps eps))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (.f64 x #s(literal 2 binary64))) (.f64 eps (+.f64 (neg.f64 (.f64 eps eps)) (.f64 x (*.f64 x #s(literal 4 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) (.f64 eps (-.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (neg.f64 (.f64 eps eps)) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64))))) (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -8 binary64)) (.f64 eps (.f64 eps eps))) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) eps) (.f64 x #s(literal 2 binary64))) (.f64 (+.f64 (neg.f64 (.f64 eps eps)) (.f64 x (*.f64 x #s(literal 4 binary64)))) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) (.f64 (-.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (*.f64 eps eps)) eps)))
(/.f64 (.f64 (.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) (.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (+.f64 (.f64 eps eps) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64))))))
(/.f64 (.f64 eps (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal -4 binary64)))) (-.f64 eps (*.f64 x #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (-.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 eps eps))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (neg.f64 (+.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 eps eps) (.f64 x x))) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 x #s(literal 2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))))) (-.f64 #s(literal 0 binary64) (.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))) (-.f64 (neg.f64 (.f64 eps eps)) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 eps (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal -4 binary64))))) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 x #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 4 binary64) (.f64 (.f64 eps eps) (.f64 x x))) (.f64 (.f64 eps eps) (.f64 eps eps))) (-.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 eps eps)))
(/.f64 (.f64 eps (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -8 binary64)) (.f64 eps (.f64 eps eps)))) (-.f64 (neg.f64 (.f64 eps eps)) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64))))))
(/.f64 (.f64 eps (+.f64 (neg.f64 (.f64 eps eps)) (.f64 x (.f64 x #s(literal 4 binary64))))) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 x #s(literal 2 binary64))))
(/.f64 (.f64 eps (-.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 eps eps))) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -8 binary64)) (.f64 eps (.f64 eps eps))) eps) (-.f64 (neg.f64 (.f64 eps eps)) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64))))))
(/.f64 (.f64 (+.f64 (neg.f64 (.f64 eps eps)) (.f64 x (.f64 x #s(literal 4 binary64)))) eps) (+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 x #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 eps eps)) eps) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))
(/.f64 (/.f64 (.f64 eps (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal -4 binary64)))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal -4 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 x #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 #s(literal 4 binary64) (.f64 (.f64 eps eps) (.f64 x x))))) (.f64 (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (-.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 eps eps)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))))) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 eps (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
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(.f64 #s(literal 1 binary64) (+.f64 eps (.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64)))))) (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal -4 binary64))))
(.f64 (-.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps)))
(.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -64 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 eps eps) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64))))) (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal -8 binary64))))))
(.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -64 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 eps (.f64 x #s(literal 2 binary64))) (+.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (+.f64 (.f64 eps eps) (.f64 x (*.f64 x #s(literal 4 binary64)))))))))
(.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -64 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal -8 binary64))) (+.f64 (.f64 eps eps) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64))))))))
(.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -64 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 4 binary64)))))) (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 #s(literal 16 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 eps (.f64 x #s(literal 2 binary64))) (+.f64 (.f64 eps eps) (.f64 x (*.f64 x #s(literal 4 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 #s(literal 16 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 4 binary64)))) (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 eps (.f64 x #s(literal 2 binary64)))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 x #s(literal 2 binary64)))))))
(.f64 (-.f64 (.f64 (.f64 eps eps) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 eps (.f64 x #s(literal 2 binary64))) (-.f64 eps (*.f64 x #s(literal 2 binary64))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x #s(literal 2 binary64)) eps))))
(.f64 (-.f64 (.f64 (/.f64 (.f64 eps eps) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (.f64 (/.f64 (.f64 eps eps) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (/.f64 (.f64 eps eps) (-.f64 eps (.f64 x #s(literal 2 binary64)))))) (.f64 (/.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x #s(literal 4 binary64))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (/.f64 (.f64 eps eps) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (/.f64 (.f64 eps eps) (-.f64 eps (.f64 x #s(literal 2 binary64))))) (+.f64 (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x #s(literal 4 binary64))))) (/.f64 (/.f64 (.f64 eps eps) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 x (*.f64 x #s(literal 4 binary64)))))))))
(.f64 (-.f64 (.f64 (/.f64 (.f64 eps eps) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (/.f64 (.f64 eps eps) (-.f64 eps (.f64 x #s(literal 2 binary64))))) (/.f64 (/.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 eps (.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x #s(literal 4 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 eps eps) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (-.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 512 binary64))) (+.f64 (.f64 eps eps) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps)))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -64 binary64))) (+.f64 (.f64 eps eps) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64)))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (*.f64 x x)) #s(literal -8 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -64 binary64))) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 4 binary64))))))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 #s(literal 16 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 eps (.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 4 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) (.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))) (+.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64)))) (-.f64 (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64)))) (*.f64 eps eps)))))
(.f64 (/.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) (-.f64 (.f64 x #s(literal 2 binary64)) eps))))) (-.f64 (.f64 eps eps) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (*.f64 eps #s(literal 2 binary64))))))
(.f64 (/.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal -4 binary64))) (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal -8 binary64)))) (+.f64 (.f64 eps eps) (.f64 x (+.f64 (.f64 x #s(literal 4 binary64)) (*.f64 eps #s(literal 2 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 eps eps) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64))))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 512 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 eps (.f64 eps eps)))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 eps eps) (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 eps #s(literal 2 binary64))))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -64 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (*.f64 x x)) #s(literal -8 binary64)))))
(.f64 (pow.f64 (/.f64 (-.f64 eps (.f64 x #s(literal 2 binary64))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -64 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 4 binary64))))))))
(.f64 (pow.f64 (/.f64 (-.f64 eps (.f64 x #s(literal 2 binary64))) (-.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 #s(literal 16 binary64) (.f64 (.f64 x x) (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal 4 binary64))))))

simplify263.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

4690×	`-lowering-.f32`
4690×	`-lowering-.f64`
2808×	`accelerator-lowering-fma.f32`
2808×	`accelerator-lowering-fma.f64`
1156×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	288
1	121	288
2	289	288
3	747	288
4	1881	288
5	3577	288
6	5308	288
7	6364	288
8	6949	288
0	8104	252

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

eval76.0ms (1%)

Compiler: Compiled 9797 to 4415 computations (54.9% saved)

prune40.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	300	3	303
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	300	4	304

Accuracy

100.0%

Counts

304 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
▶	67.4%	(.f64 x (.f64 #s(literal 2 binary64) eps))
✓	100.0%	(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))
▶	72.5%	(*.f64 eps eps)

Compiler

Compiled 32 to 22 computations (31.3% saved)

localize103.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 eps (*.f64 x #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))
✓	cost-diff	128	(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) eps)
✓	cost-diff	0	(.f64 x (.f64 #s(literal 2 binary64) eps))
✓	cost-diff	0	(*.f64 eps eps)
✓	accuracy	100.0%	(+.f64 eps (*.f64 x #s(literal 2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))
✓	accuracy	99.8%	(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
✓	accuracy	100.0%	(.f64 x (.f64 #s(literal 2 binary64) eps))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) eps)
✓	accuracy	100.0%	(*.f64 eps eps)

Rules

34×	`-lowering-.f32`
34×	`-lowering-.f64`
22×	`/-lowering-/.f32`
22×	`/-lowering-/.f64`
18×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	20	37
2	33	37
3	46	37
4	52	37
5	52	37
0	52	34

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

Results

42.0ms

256×

valid

Compiler

Compiled 46 to 28 computations (39.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-mult: 13.0ms (56.7% of total)

ival-div: 5.0ms (21.8% of total)

ival-add: 4.0ms (17.4% of total)

const: 1.0ms (4.4% of total)

backward-pass: 0.0ms (0% of total)

series14.0ms (0.2%)

Counts

7 → 132

Calls

Call 1

Inputs
#<alt (* eps eps)>
#<alt (* 2 eps)>
#<alt (* x (* 2 eps))>
#<alt (/ eps (/ 1 (+ eps (* x 2))))>
#<alt (/ 1 (+ eps (* x 2)))>
#<alt (* x 2)>
#<alt (+ eps (* x 2))>

Outputs
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (* eps (+ eps (* 2 x)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (* (pow eps 2) (+ 1 (* 2 (/ x eps))))>
#<alt (pow eps 2)>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (+ (* 2 (* eps x)) (pow eps 2))>
#<alt (* 2 (* eps x))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* x (+ (* 2 eps) (/ (pow eps 2) x)))>
#<alt (* 2 (* eps x))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (/ 1/2 x)>
#<alt (+ (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x)))>
#<alt (+ (* eps (- (* 1/8 (/ eps (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))>
#<alt (+ (* eps (- (* eps (+ (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 3))))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))>
#<alt (/ 1 eps)>
#<alt (/ (+ 1 (* -2 (/ x eps))) eps)>
#<alt (/ (- (+ 1 (* 4 (/ (pow x 2) (pow eps 2)))) (* 2 (/ x eps))) eps)>
#<alt (/ (- (+ 1 (* -8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* 2 (/ x eps)))) eps)>
#<alt (/ 1 eps)>
#<alt (* -1 (/ (- (* 2 (/ x eps)) 1) eps))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 4 (/ (pow x 2) eps)) (* 2 x)) eps)) 1) eps))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* 4 (pow x 2))) eps)) (* 2 x)) eps)) 1) eps))>
#<alt (/ 1 eps)>
#<alt (+ (* -2 (/ x (pow eps 2))) (/ 1 eps))>
#<alt (+ (* x (- (* 4 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))>
#<alt (+ (* x (- (* x (+ (* -8 (/ x (pow eps 4))) (* 4 (/ 1 (pow eps 3))))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* -1/4 (/ eps x))) x)>
#<alt (/ (- (+ 1/2 (* 1/8 (/ (pow eps 2) (pow x 2)))) (* 1/4 (/ eps x))) x)>
#<alt (/ (- (+ 1/2 (* -1/16 (/ (pow eps 3) (pow x 3)))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/4 (/ eps x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow eps 2) x)) (* 1/4 eps)) x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow eps 3) x)) (* 1/8 (pow eps 2))) x)) (* 1/4 eps)) x)) 1/2) x))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>

Calls

33 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/ 1 (+ eps (* x 2)))
1.0ms	eps	@	0	(* eps eps)
1.0ms	eps	@	0	(* x (* 2 eps))
0.0ms	x	@	inf	(* x (* 2 eps))
0.0ms	x	@	0	(* x (* 2 eps))

rewrite651.0ms (8.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4656×	`-lowering-.f32`
4656×	`-lowering-.f64`
4026×	`accelerator-lowering-fma.f32`
4026×	`accelerator-lowering-fma.f64`
3076×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	48	33
2	290	33
3	2834	33
0	8363	30

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 500

Calls

Call 1

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

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

simplify814.0ms (11.1%)

Algorithm

1×	egg-herbie

Rules

13562×	`accelerator-lowering-fma.f32`
13562×	`accelerator-lowering-fma.f64`
4498×	`-lowering-.f32`
4498×	`-lowering-.f64`
2046×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	173	842
1	511	836
2	1303	814
3	3925	788
0	8194	716

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* 2 (* eps x))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(* eps (+ eps (* 2 x)))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(pow eps 2)
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(+ (* 2 (* eps x)) (pow eps 2))
(* 2 (* eps x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(* 2 (* eps x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(/ 1/2 x)
(+ (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x)))
(+ (* eps (- (* 1/8 (/ eps (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))
(+ (* eps (- (* eps (+ (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 3))))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))
(/ 1 eps)
(/ (+ 1 (* -2 (/ x eps))) eps)
(/ (- (+ 1 (* 4 (/ (pow x 2) (pow eps 2)))) (* 2 (/ x eps))) eps)
(/ (- (+ 1 (* -8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* 2 (/ x eps)))) eps)
(/ 1 eps)
(* -1 (/ (- (* 2 (/ x eps)) 1) eps))
(* -1 (/ (- (* -1 (/ (- (* 4 (/ (pow x 2) eps)) (* 2 x)) eps)) 1) eps))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* 4 (pow x 2))) eps)) (* 2 x)) eps)) 1) eps))
(/ 1 eps)
(+ (* -2 (/ x (pow eps 2))) (/ 1 eps))
(+ (* x (- (* 4 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))
(+ (* x (- (* x (+ (* -8 (/ x (pow eps 4))) (* 4 (/ 1 (pow eps 3))))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))
(/ 1/2 x)
(/ (+ 1/2 (* -1/4 (/ eps x))) x)
(/ (- (+ 1/2 (* 1/8 (/ (pow eps 2) (pow x 2)))) (* 1/4 (/ eps x))) x)
(/ (- (+ 1/2 (* -1/16 (/ (pow eps 3) (pow x 3)))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/4 (/ eps x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow eps 2) x)) (* 1/4 eps)) x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow eps 3) x)) (* 1/8 (pow eps 2))) x)) (* 1/4 eps)) x)) 1/2) x))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))

Outputs
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 eps)
(*.f64 eps #s(literal 2 binary64))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* eps (+ eps (* 2 x)))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(* eps (+ eps (* 2 x)))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(* eps (+ eps (* 2 x)))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(pow eps 2)
(*.f64 eps eps)
(+ (* 2 (* eps x)) (pow eps 2))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(+ (* 2 (* eps x)) (pow eps 2))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(+ (* 2 (* eps x)) (pow eps 2))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(+ (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x)))
(/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 eps x))) x)
(+ (* eps (- (* 1/8 (/ eps (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps (+.f64 #s(literal -1/4 binary64) (.f64 #s(literal 1/8 binary64) (/.f64 eps x)))) x)) x)
(+ (* eps (- (* eps (+ (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 3))))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))
(+.f64 (.f64 eps (/.f64 (.f64 eps (.f64 eps #s(literal -1/16 binary64))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps (+.f64 #s(literal -1/4 binary64) (*.f64 #s(literal 1/8 binary64) (/.f64 eps x)))) x)) x))
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ (+ 1 (* -2 (/ x eps))) eps)
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x eps))) eps)
(/ (- (+ 1 (* 4 (/ (pow x 2) (pow eps 2)))) (* 2 (/ x eps))) eps)
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x eps) (-.f64 #s(literal 2 binary64) (/.f64 (.f64 x #s(literal 4 binary64)) eps)))) eps)
(/ (- (+ 1 (* -8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* 2 (/ x eps)))) eps)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x #s(literal -2 binary64)) (.f64 (/.f64 (.f64 x x) eps) (+.f64 (/.f64 (.f64 x #s(literal 8 binary64)) eps) #s(literal -4 binary64)))) eps)) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(* -1 (/ (- (* 2 (/ x eps)) 1) eps))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x eps))) eps)
(* -1 (/ (- (* -1 (/ (- (* 4 (/ (pow x 2) eps)) (* 2 x)) eps)) 1) eps))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x eps) (-.f64 #s(literal 2 binary64) (/.f64 (.f64 x #s(literal 4 binary64)) eps)))) eps)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* 4 (pow x 2))) eps)) (* 2 x)) eps)) 1) eps))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x #s(literal -2 binary64)) (.f64 (/.f64 (.f64 x x) eps) (+.f64 (/.f64 (.f64 x #s(literal 8 binary64)) eps) #s(literal -4 binary64)))) eps)) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(+ (* -2 (/ x (pow eps 2))) (/ 1 eps))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x eps))) eps)
(+ (* x (- (* 4 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x eps) (-.f64 #s(literal 2 binary64) (/.f64 (.f64 x #s(literal 4 binary64)) eps)))) eps)
(+ (* x (- (* x (+ (* -8 (/ x (pow eps 4))) (* 4 (/ 1 (pow eps 3))))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))
(+.f64 (.f64 (/.f64 (.f64 x (.f64 x #s(literal -8 binary64))) (pow.f64 eps #s(literal 4 binary64))) x) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 x eps) (-.f64 #s(literal 2 binary64) (/.f64 (*.f64 x #s(literal 4 binary64)) eps)))) eps))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* -1/4 (/ eps x))) x)
(/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 eps x))) x)
(/ (- (+ 1/2 (* 1/8 (/ (pow eps 2) (pow x 2)))) (* 1/4 (/ eps x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps (+.f64 #s(literal -1/4 binary64) (.f64 #s(literal 1/8 binary64) (/.f64 eps x)))) x)) x)
(/ (- (+ 1/2 (* -1/16 (/ (pow eps 3) (pow x 3)))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 eps #s(literal -1/4 binary64)) (/.f64 (.f64 (.f64 eps eps) (+.f64 (.f64 (/.f64 eps x) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) x)) x)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/4 (/ eps x)) 1/2) x))
(/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/4 binary64) (/.f64 eps x))) x)
(* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow eps 2) x)) (* 1/4 eps)) x)) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps (+.f64 #s(literal -1/4 binary64) (.f64 #s(literal 1/8 binary64) (/.f64 eps x)))) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow eps 3) x)) (* 1/8 (pow eps 2))) x)) (* 1/4 eps)) x)) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 eps #s(literal -1/4 binary64)) (/.f64 (.f64 (.f64 eps eps) (+.f64 (.f64 (/.f64 eps x) #s(literal 1/16 binary64)) #s(literal -1/8 binary64))) x)) x)) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ eps (* 2 x))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(+ eps (* 2 x))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(+ eps (* 2 x))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* eps (+ 1 (* 2 (/ x eps))))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* eps (+ 1 (* 2 (/ x eps))))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
eps
(+ eps (* 2 x))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(+ eps (* 2 x))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(+ eps (* 2 x))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (/ eps x)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x (+ 2 (/ eps x)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* x (+ 2 (/ eps x)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(+.f64 eps (*.f64 #s(literal 2 binary64) x))

eval131.0ms (1.8%)

Compiler: Compiled 13067 to 7498 computations (42.6% saved)

prune140.0ms (1.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	630	2	632
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	630	6	636

Accuracy

100.0%

Counts

636 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
▶	72.4%	(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
▶	67.3%	(/.f64 eps (/.f64 #s(literal 1/2 binary64) x))
✓	67.4%	(.f64 x (.f64 #s(literal 2 binary64) eps))
✓	100.0%	(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))
✓	72.5%	(*.f64 eps eps)

Compiler

Compiled 46 to 32 computations (30.4% saved)

localize54.0ms (0.7%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) eps)
✓	cost-diff	128	(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(/.f64 eps (/.f64 #s(literal 1/2 binary64) x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) eps)
✓	accuracy	99.8%	(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	99.8%	(/.f64 eps (/.f64 #s(literal 1/2 binary64) x))

Rules

28×	`/-lowering-/.f32`
28×	`/-lowering-/.f64`
22×	`-lowering-.f32`
22×	`-lowering-.f64`
8×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	14	18
2	19	18
3	31	18
4	36	18
5	41	18
6	41	18
0	41	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ eps (/ 1/2 x))
eps
(/ 1/2 x)
1/2
x
(/ eps (/ 1 eps))
(/ 1 eps)
1

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

Results

26.0ms

256×

valid

Compiler

Compiled 24 to 15 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-div: 13.0ms (93% of total)

const: 1.0ms (7.2% of total)

backward-pass: 0.0ms (0% of total)

series5.0ms (0.1%)

Counts

4 → 60

Calls

Call 1

Inputs
#<alt (/ eps (/ 1/2 x))>
#<alt (/ 1/2 x)>
#<alt (/ eps (/ 1 eps))>
#<alt (/ 1 eps)>

Outputs
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (* 2 (* eps x))>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/ 1/2 x)
0.0ms	x	@	inf	(/ 1/2 x)
0.0ms	x	@	-inf	(/ 1/2 x)
0.0ms	eps	@	-inf	(/ 1 eps)
0.0ms	eps	@	0	(/ 1 eps)

rewrite215.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1876×	`-lowering-.f32`
1876×	`-lowering-.f64`
1338×	`/-lowering-/.f32`
1338×	`/-lowering-/.f64`
646×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	41	14
2	187	14
3	1053	14
0	5176	14

Stop Event

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

Counts

4 → 388

Calls

Call 1

Inputs
(/ eps (/ 1/2 x))
(/ 1/2 x)
(/ eps (/ 1 eps))
(/ 1 eps)

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

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

26×	`-lowering-.f32`
26×	`-lowering-.f64`
10×	`*-commutative`
6×	`associate-r`
6×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	228
1	17	228
2	24	228
3	26	228
0	26	228

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

Calls

Call 1

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

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

eval74.0ms (1%)

Compiler: Compiled 4401 to 2824 computations (35.8% saved)

prune63.0ms (0.9%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	446	2	448
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	446	8	454

Accuracy

100.0%

Counts

454 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	41.3%	(/.f64 (*.f64 eps x) #s(literal -1/2 binary64))
✓	99.8%	(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
✓	72.4%	(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
✓	67.3%	(/.f64 eps (/.f64 #s(literal 1/2 binary64) x))
✓	67.4%	(.f64 x (.f64 #s(literal 2 binary64) eps))
✓	100.0%	(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))
✓	72.5%	(*.f64 eps eps)
▶	41.0%	(neg.f64 (*.f64 eps eps))

Compiler

Compiled 59 to 41 computations (30.5% saved)

localize71.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 eps x)
✓	cost-diff	0	(/.f64 (*.f64 eps x) #s(literal -1/2 binary64))
✓	cost-diff	-64	(neg.f64 (*.f64 eps eps))
✓	cost-diff	0	(*.f64 eps eps)
✓	accuracy	100.0%	(*.f64 eps x)
✓	accuracy	100.0%	(/.f64 (*.f64 eps x) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(neg.f64 (*.f64 eps eps))

Rules

28×	`+-lowering-+.f64`
28×	`+-lowering-+.f32`
26×	`-lowering-.f32`
26×	`-lowering-.f64`
26×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	17	18
2	24	18
3	31	18
4	38	18
5	46	18
6	54	18
7	70	18
8	76	18
9	77	18
0	77	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(neg (* eps eps))
(* eps eps)
eps
(/ (* eps x) -1/2)
(* eps x)
x
-1/2

Outputs
(neg (* eps eps))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(* eps eps)
(*.f64 eps eps)
eps
(/ (* eps x) -1/2)
(/.f64 (*.f64 eps x) #s(literal -1/2 binary64))
(* eps x)
(*.f64 eps x)
x
-1/2
#s(literal -1/2 binary64)

Results

44.0ms

256×

valid

Compiler

Compiled 22 to 9 computations (59.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-div: 19.0ms (69.9% of total)

ival-mult: 7.0ms (25.8% of total)

ival-neg: 1.0ms (3.7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series5.0ms (0.1%)

Counts

4 → 72

Calls

Call 1

Inputs
#<alt (neg (* eps eps))>
#<alt (* eps eps)>
#<alt (/ (* eps x) -1/2)>
#<alt (* eps x)>

Outputs
#<alt (* -1 (pow eps 2))>
#<alt (* -1 (pow eps 2))>
#<alt (* -1 (pow eps 2))>
#<alt (* -1 (pow eps 2))>
#<alt (* -1 (pow eps 2))>
#<alt (* -1 (pow eps 2))>
#<alt (* -1 (pow eps 2))>
#<alt (* -1 (pow eps 2))>
#<alt (* -1 (pow eps 2))>
#<alt (* -1 (pow eps 2))>
#<alt (* -1 (pow eps 2))>
#<alt (* -1 (pow eps 2))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* -2 (* eps x))>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>
#<alt (* eps x)>

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	eps	@	0	(/ (* eps x) -1/2)
0.0ms	x	@	0	(/ (* eps x) -1/2)
0.0ms	x	@	-inf	(* eps x)
0.0ms	eps	@	-inf	(* eps x)
0.0ms	eps	@	0	(neg (* eps eps))

rewrite240.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1530×	`-lowering-.f32`
1530×	`-lowering-.f64`
1470×	`accelerator-lowering-fma.f32`
1470×	`accelerator-lowering-fma.f64`
1310×	`/-lowering-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	29	16
2	91	16
3	436	16
4	3420	14
0	8597	14

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 364

Calls

Call 1

Inputs
(neg (* eps eps))
(* eps eps)
(/ (* eps x) -1/2)
(* eps x)

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

simplify20.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

38×	`-lowering-.f32`
38×	`-lowering-.f64`
34×	`accelerator-lowering-fma.f32`
34×	`accelerator-lowering-fma.f64`
28×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	276
1	16	276
2	32	276
3	36	276
4	39	276
5	46	276
6	54	276
7	62	276
8	79	276
9	85	276
0	85	276

Stop Event

1×	iter limit
1×	saturated

Counts

72 → 72

Calls

Call 1

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

Outputs
(* -1 (pow eps 2))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(* -1 (pow eps 2))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(* -1 (pow eps 2))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(* -1 (pow eps 2))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(* -1 (pow eps 2))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(* -1 (pow eps 2))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(* -1 (pow eps 2))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(* -1 (pow eps 2))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(* -1 (pow eps 2))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(* -1 (pow eps 2))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(* -1 (pow eps 2))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(* -1 (pow eps 2))
(*.f64 eps (-.f64 #s(literal 0 binary64) eps))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* -2 (* eps x))
(.f64 eps (.f64 #s(literal -2 binary64) x))
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)

eval127.0ms (1.7%)

Compiler: Compiled 5634 to 1884 computations (66.6% saved)

prune66.0ms (0.9%)

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	436	0	436
Fresh	0	0	0
Picked	0	2	2
Done	0	6	6
Total	436	8	444

Accuracy

100.0%

Counts

444 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	41.3%	(/.f64 (*.f64 eps x) #s(literal -1/2 binary64))
✓	99.8%	(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
✓	72.4%	(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
✓	67.3%	(/.f64 eps (/.f64 #s(literal 1/2 binary64) x))
✓	67.4%	(.f64 x (.f64 #s(literal 2 binary64) eps))
✓	100.0%	(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))
✓	72.5%	(*.f64 eps eps)
✓	41.0%	(neg.f64 (*.f64 eps eps))

Compiler

Compiled 113 to 73 computations (35.4% saved)

regimes9.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	x
3.0ms	eps
1.0ms	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Results

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

Compiler

Compiled 17 to 12 computations (29.4% saved)

regimes13.0ms (0.2%)

Counts

6 → 3

Calls

Call 1

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

Outputs
(.f64 x (.f64 #s(literal 2 binary64) eps))
(*.f64 eps eps)
(.f64 x (.f64 #s(literal 2 binary64) eps))

Calls

2 calls:

7.0ms	x
6.0ms	eps

Results

Accuracy	Segments	Branch
94.3%	3	`x`
86.7%	3	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total -20.3b remaining (-115.6%)

Threshold costs -20.3b (-115.6%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 eps eps)
(neg.f64 (*.f64 eps eps))

Outputs
(*.f64 eps eps)

Calls

2 calls:

1.0ms	eps
1.0ms	x

Results

Accuracy	Segments	Branch
72.5%	1	`eps`
72.5%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch21.0ms (0.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
7.0ms	5.103582859867761e-89	6.255969761877536e-89
12.0ms	-1.8326294176484874e-103	-5.899851158799805e-104

Results

12.0ms	83×	1	valid
3.0ms	45×	0	valid

Compiler

Compiled 128 to 92 computations (28.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-pow: 5.0ms (50.8% of total)

backward-pass: 2.0ms (20.3% of total)

ival-add: 1.0ms (10.2% of total)

ival-sub: 1.0ms (10.2% of total)

const: 0.0ms (0% of total)

soundness1.0ms (0%)

Stop Event

1×

done

Compiler

Compiled 33 to 19 computations (42.4% saved)

preprocess28.0ms (0.4%)

Compiler: Compiled 88 to 54 computations (38.6% saved)

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

analyze0.0ms (0%)

sample2.0s (27.6%)

preprocess961.0ms (13.1%)

explain130.0ms (1.8%)

eval0.0ms (0%)

prune1.0ms (0%)

localize46.0ms (0.6%)

series6.0ms (0.1%)

rewrite894.0ms (12.2%)

simplify263.0ms (3.6%)

eval76.0ms (1%)

prune40.0ms (0.5%)

localize103.0ms (1.4%)

series14.0ms (0.2%)

rewrite651.0ms (8.9%)

simplify814.0ms (11.1%)

eval131.0ms (1.8%)

prune140.0ms (1.9%)

localize54.0ms (0.7%)

series5.0ms (0.1%)

rewrite215.0ms (2.9%)

simplify12.0ms (0.2%)

eval74.0ms (1%)

prune63.0ms (0.9%)

localize71.0ms (1%)

series5.0ms (0.1%)

rewrite240.0ms (3.3%)

simplify20.0ms (0.3%)

eval127.0ms (1.7%)

prune66.0ms (0.9%)

regimes9.0ms (0.1%)

regimes13.0ms (0.2%)

regimes3.0ms (0%)

bsearch21.0ms (0.3%)

soundness1.0ms (0%)

preprocess28.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	9	276
1	16	276
2	32	276
3	36	276
4	39	276
5	46	276
6	54	276
7	62	276
8	79	276
9	85	276
0	85	276

Iter	Nodes	Cost
0	9	276
1	16	276
2	32	276
3	36	276
4	39	276
5	46	276
6	54	276
7	62	276
8	79	276
9	85	276
0	85	276

Iter	Nodes	Cost
0	9	276
1	16	276
2	32	276
3	36	276
4	39	276
5	46	276
6	54	276
7	62	276
8	79	276
9	85	276
0	85	276