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 18 computations (30.8% 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)

sample1.6s (28%)

Results

597.0ms	5111×	0	valid
422.0ms	2540×	1	valid
182.0ms	605×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 776.0ms

ival-pow: 364.0ms (46.9% of total)

ival-<=: 144.0ms (18.5% of total)

ival-add: 87.0ms (11.2% of total)

backward-pass: 67.0ms (8.6% of total)

ival-sub: 65.0ms (8.4% of total)

const: 25.0ms (3.2% of total)

ival-and: 25.0ms (3.2% of total)

Bogosity

preprocess438.0ms (7.7%)

Algorithm

2×	egg-herbie

Rules

1988×	`+-lowering-+.f64`
1988×	`+-lowering-+.f32`
1748×	`fmsub-define`
1742×	`fma-lowering-fma.f32`
1742×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	64
1	51	56
2	172	50
3	698	40
4	4126	36
5	7934	36
0	7	9
1	12	9
2	34	8
3	112	8
4	511	6
5	1634	6
6	3534	6
0	8284	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 (sum3 x eps x))
(- (pow (+ (neg x) eps) 2) (pow (neg x) 2))
(* eps (fma x -2 eps))
(- (pow (+ x (neg eps)) 2) (pow x 2))
(* eps (fma x -2 eps))
(neg (- (pow (+ (neg x) eps) 2) (pow (neg x) 2)))
(* eps (fnmsub x -2 eps))
(neg (- (pow (+ x (neg eps)) 2) (pow x 2)))
(* eps (fnmsub x -2 eps))
(- (pow (+ eps x) 2) (pow eps 2))
(* x (sum3 x eps eps))

explain145.0ms (2.5%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
79	0	-	-	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	-	`x`
0	80	(2.0917665383194544e-159 -3.6473381022625494e-262)	-	`(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

55.0ms	48×	2	valid
34.0ms	140×	1	valid
24.0ms	324×	0	valid

Compiler

Compiled 63 to 23 computations (63.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 79.0ms

ival-pow: 65.0ms (82.5% of total)

ival-add: 5.0ms (6.3% of total)

backward-pass: 4.0ms (5.1% of total)

ival-sub: 4.0ms (5.1% of total)

const: 1.0ms (1.3% 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)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	14	16
2	28	16
3	40	16
0	40	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)

localize32.0ms (0.6%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	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))))

Results

25.0ms

256×

valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 14.0ms (89.1% of total)

ival-add: 1.0ms (6.4% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Counts

3 → 60

Calls

Call 1

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

Calls

15 calls:

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

rewrite382.0ms (6.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3084×	`-lowering-.f32`
3084×	`-lowering-.f64`
2746×	`/-lowering-/.f32`
2746×	`/-lowering-/.f64`
1486×	`sum5-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	25	13
2	213	13
3	2257	13
0	9046	13

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 195

Calls

Call 1

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

simplify175.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1886×	`fnmsub-define`
1856×	`sum4-define`
1704×	`fma-lowering-fma.f32`
1704×	`fmm-def`
1704×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	288
1	128	252
2	331	252
3	870	252
4	2492	252
5	6116	252
0	8495	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)
(+ 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)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)

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

eval28.0ms (0.5%)

Compiler: Compiled 7360 to 677 computations (90.8% saved)

prune26.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	251	4	255
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	251	5	256

Accuracy

100.0%

Counts

256 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (*.f64 eps eps))
▶	99.7%	(.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal -4 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (.f64 x #s(literal 2 binary64)))) eps))
✓	100.0%	(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))
▶	61.6%	(.f64 eps (.f64 #s(literal 2 binary64) x))
▶	70.6%	(*.f64 eps eps)

Compiler

Compiled 53 to 35 computations (34% saved)

simplify175.0ms (3.1%)

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(*.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(.f64 eps (.f64 x #s(literal 2 binary64)))
✓	cost-diff	128	(+.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (*.f64 eps eps))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal -4 binary64)))
✓	cost-diff	128	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (.f64 x #s(literal 2 binary64)))) eps)
✓	cost-diff	128	(.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal -4 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (.f64 x #s(literal 2 binary64)))) eps))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	(.f64 eps (.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(*.f64 eps eps)

Rules

1800×	`-lowering-.f32`
1800×	`-lowering-.f64`
1400×	`fma-lowering-fma.f32`
1400×	`fma-lowering-fma.f64`
1356×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	99
1	46	96
2	105	92
3	235	92
4	506	92
5	976	92
6	2883	92
7	5322	92
0	8013	92

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* eps eps)
eps
(* eps (* 2 x))
eps
(* 2 x)
2
x
(* (+ (* eps eps) (* (* x x) -4)) (* (/ 1 (- eps (* x 2))) eps))
(+ (* eps eps) (* (* x x) -4))
(* eps eps)
eps
(* (* x x) -4)
(* x x)
x
-4
(* (/ 1 (- eps (* x 2))) eps)
(/ 1 (- eps (* x 2)))
1
(- eps (* x 2))
(* x 2)
2
(+ (* eps (* x 2)) (* eps eps))
(* eps (* x 2))
eps
(* x 2)
x
2
(* eps eps)

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

localize125.0ms (2.2%)

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(.f64 eps (.f64 x #s(literal 2 binary64)))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(+.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (*.f64 eps eps))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (-.f64 eps (*.f64 x #s(literal 2 binary64))))
✓	accuracy	99.9%	(.f64 (.f64 x x) #s(literal -4 binary64))
✓	accuracy	99.9%	(.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal -4 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (.f64 x #s(literal 2 binary64)))) eps))
✓	accuracy	99.7%	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (.f64 x #s(literal 2 binary64)))) eps)
✓	accuracy	100.0%	(.f64 eps (.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(*.f64 eps eps)

Results

100.0ms

256×

valid

Compiler

Compiled 109 to 19 computations (82.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-mult: 57.0ms (87.1% of total)

ival-div: 3.0ms (4.6% of total)

ival-sub: 2.0ms (3.1% of total)

ival-add: 2.0ms (3.1% of total)

const: 1.0ms (1.5% of total)

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

series16.0ms (0.3%)

Counts

11 → 216

Calls

Call 1

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

Calls

54 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	0	(* (+ (* eps eps) (* (* x x) -4)) (* (/ 1 (- eps (* x 2))) eps))
2.0ms	eps	@	inf	(* (+ (* eps eps) (* (* x x) -4)) (* (/ 1 (- eps (* x 2))) eps))
1.0ms	eps	@	0	(* eps eps)
1.0ms	x	@	inf	(* (+ (* eps eps) (* (* x x) -4)) (* (/ 1 (- eps (* x 2))) eps))
1.0ms	x	@	0	(* (+ (* eps eps) (* (* x x) -4)) (* (/ 1 (- eps (* x 2))) eps))

rewrite330.0ms (5.8%)

Algorithm

1×	batch-egg-rewrite

Rules

5454×	`-lowering-.f32`
5454×	`-lowering-.f64`
2284×	`/-lowering-/.f32`
2284×	`/-lowering-/.f64`
1682×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	80
1	89	77
2	754	55
0	9231	55

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 606

Calls

Call 1

Inputs
(* eps eps)
(* eps (* 2 x))
(* 2 x)
(* (+ (* eps eps) (* (* x x) -4)) (* (/ 1 (- eps (* x 2))) eps))
(* (/ 1 (- eps (* x 2))) eps)
(+ (* eps eps) (* (* x x) -4))
(+ (* eps (* x 2)) (* eps eps))
(* eps (* x 2))
(* x 2)
(* (* x x) -4)
(/ 1 (- eps (* x 2)))

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

simplify322.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

4334×	`-lowering-.f32`
4334×	`-lowering-.f64`
1904×	`fnmsub-define`
1450×	`fma-lowering-fma.f32`
1450×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	239	1725
1	795	1634
2	2257	1588
3	7238	1586
0	8780	1586

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

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

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 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 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 (* 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 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x eps)))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x eps)))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x eps)))))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x eps)))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x eps)))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) (/.f64 x eps)))))
(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 x (.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(.f64 x (.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(.f64 x (.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
(* 2 (* eps x))
(.f64 eps (.f64 #s(literal 2 binary64) x))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(.f64 x (.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(.f64 x (.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
(* -1 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(.f64 x (.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps (- (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x))))
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eval98.0ms (1.7%)

Compiler: Compiled 26135 to 1518 computations (94.2% saved)

prune65.0ms (1.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	887	1	888
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	888	5	893

Accuracy

100.0%

Counts

893 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(+.f64 (.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)))) (*.f64 eps eps))
✓	100.0%	(+.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (*.f64 eps eps))
✓	100.0%	(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))
✓	61.6%	(.f64 eps (.f64 #s(literal 2 binary64) x))
✓	70.6%	(*.f64 eps eps)

Compiler

Compiled 47 to 31 computations (34% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x)))
✓	cost-diff	256	(.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))))
✓	cost-diff	384	(+.f64 (.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)))) (*.f64 eps eps))

Rules

78×	`-lowering-.f32`
78×	`-lowering-.f64`
48×	`fma-define`
48×	`/-lowering-/.f32`
48×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	30	27
2	63	27
3	113	27
4	139	27
5	154	27
6	154	27
0	154	27

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize39.0ms (0.7%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(+.f64 (.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)))) (*.f64 eps eps))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x)))

Results

27.0ms

256×

valid

Compiler

Compiled 47 to 11 computations (76.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 9.0ms (61% of total)

ival-div: 4.0ms (27.1% of total)

ival-add: 1.0ms (6.8% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

6 → 96

Calls

Call 1

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

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 (* 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 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 (/ 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 (* 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 (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)>

Calls

24 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	@	0	(+ (* eps (/ 1 (/ 1 (* 2 x)))) (* eps eps))
0.0ms	x	@	-inf	(+ (* eps (/ 1 (/ 1 (* 2 x)))) (* eps eps))

rewrite201.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2828×	`-lowering-.f32`
2828×	`-lowering-.f64`
1370×	`/-lowering-/.f32`
1370×	`/-lowering-/.f64`
1176×	`sum5-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	59	23
2	376	23
3	4317	23
0	8079	23

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 245

Calls

Call 1

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

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

simplify151.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

2004×	`-lowering-.f32`
2004×	`-lowering-.f64`
1654×	`fnmadd-define`
1518×	`fma-define`
986×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	414
1	81	396
2	220	396
3	550	396
4	1694	396
5	3724	396
6	7941	396
0	8293	396

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

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 (* 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 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 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)
(/ 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)
(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)

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

eval35.0ms (0.6%)

Compiler: Compiled 6314 to 807 computations (87.2% saved)

prune31.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	340	1	341
Fresh	0	0	0
Picked	1	0	1
Done	1	3	4
Total	342	4	346

Accuracy

100.0%

Counts

346 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(-.f64 (*.f64 eps eps) (/.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
✓	100.0%	(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))
✓	61.6%	(.f64 eps (.f64 #s(literal 2 binary64) x))
✓	70.6%	(*.f64 eps eps)

Compiler

Compiled 32 to 21 computations (34.4% saved)

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

1222×	`fnmadd-define`
1196×	`fma-define`
874×	`sum3-define`
872×	`sum5-define`
712×	`fmsub-define`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	7	22
1	13	22
2	30	22
3	70	21
4	135	21
5	245	20
6	495	20
7	903	20
8	1600	20
9	3503	20
10	4371	20
11	4432	20
12	4457	20
0	4457	20

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize27.0ms (0.5%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal -1/2 binary64) x)
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(-.f64 (*.f64 eps eps) (/.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
✓	accuracy	99.7%	(/.f64 eps (/.f64 #s(literal -1/2 binary64) x))

Results

18.0ms

256×

valid

Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 4.0ms (51.7% of total)

ival-mult: 2.0ms (25.9% of total)

ival-sub: 1.0ms (12.9% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Counts

4 → 72

Calls

Call 1

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

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

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(- (* eps eps) (/ eps (/ -1/2 x)))
0.0ms	x	@	0	(/ -1/2 x)
0.0ms	eps	@	0	(- (* eps eps) (/ eps (/ -1/2 x)))
0.0ms	x	@	0	(- (* eps eps) (/ eps (/ -1/2 x)))
0.0ms	eps	@	0	(/ eps (/ -1/2 x))

rewrite235.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2796×	`-lowering-.f32`
2796×	`-lowering-.f64`
1914×	`/-lowering-/.f32`
1914×	`/-lowering-/.f64`
1878×	`fnmadd-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	44	18
2	383	18
3	4870	17
0	8339	17

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 173

Calls

Call 1

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

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

simplify97.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1634×	`sum5-define`
1370×	`sum3-define`
1182×	`fnmsub-define`
1158×	`fmsub-define`
1020×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	342
1	77	342
2	186	324
3	553	324
4	2042	324
5	4888	324
0	8021	324

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

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

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

eval25.0ms (0.4%)

Compiler: Compiled 5386 to 504 computations (90.6% saved)

prune25.0ms (0.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	245	4	249

Accuracy

100.0%

Counts

249 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(-.f64 (*.f64 eps eps) (/.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
✓	100.0%	(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))
✓	61.6%	(.f64 eps (.f64 #s(literal 2 binary64) x))
✓	70.6%	(*.f64 eps eps)

Compiler

Compiled 108 to 53 computations (50.9% saved)

regimes11.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

Inputs
(*.f64 eps eps)
(.f64 eps (.f64 #s(literal 2 binary64) x))
(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 eps (.f64 x #s(literal 2 binary64))) (*.f64 eps eps))
(-.f64 (*.f64 eps eps) (/.f64 eps (/.f64 #s(literal -1/2 binary64) x)))
(+.f64 (.f64 eps (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)))) (*.f64 eps eps))
(.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal -4 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 eps (.f64 x #s(literal 2 binary64)))) eps))
(-.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:

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

Results

Accuracy	Segments	Branch
100.0%	1	`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 11 computations (35.3% saved)

regimes3.0ms (0.1%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	eps
1.0ms	x

Results

Accuracy	Segments	Branch
94.3%	3	`x`
87.3%	3	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 eps eps)

Outputs
(*.f64 eps eps)

Calls

2 calls:

1.0ms	x
1.0ms	eps

Results

Accuracy	Segments	Branch
70.6%	1	`eps`
70.6%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch36.0ms (0.6%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
20.0ms	2.9101490955063213e-102	1.5237030174186917e-99
14.0ms	-5.1418197050272095e-111	-9.199514008106935e-112

Results

21.0ms	166×	1	valid
5.0ms	58×	0	valid

Compiler

Compiled 212 to 151 computations (28.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-pow: 8.0ms (53.8% of total)

ival-add: 2.0ms (13.4% of total)

ival-sub: 2.0ms (13.4% of total)

backward-pass: 2.0ms (13.4% of total)

const: 0.0ms (0% of total)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`if-if-or-not_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
1	22	27

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 x #s(literal -5144601971513231/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) x)) (if (<=.f64 x #s(literal 5201064817924071/78804012392788958424558080200287227610159478540930893335896586808491443542994421222828532509769831281613255980613632 binary64)) (*.f64 eps eps) (*.f64 eps (*.f64 #s(literal 2 binary64) x))))

(*.f64 eps eps)

Outputs
(.f64 eps (+.f64 eps (.f64 x #s(literal 2 binary64))))
(if (<=.f64 x #s(literal -5144601971513231/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152 binary64)) (.f64 eps (.f64 #s(literal 2 binary64) x)) (if (<=.f64 x #s(literal 5201064817924071/78804012392788958424558080200287227610159478540930893335896586808491443542994421222828532509769831281613255980613632 binary64)) (.f64 eps eps) (.f64 eps (*.f64 #s(literal 2 binary64) x))))
(if (<=.f64 x #s(literal -5144601971513231/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152 binary64)) (.f64 eps (.f64 x #s(literal 2 binary64))) (if (<=.f64 x #s(literal 5201064817924071/78804012392788958424558080200287227610159478540930893335896586808491443542994421222828532509769831281613255980613632 binary64)) (.f64 eps eps) (.f64 eps (*.f64 x #s(literal 2 binary64)))))
(*.f64 eps eps)

soundness708.0ms (12.4%)

Rules

1988×	`+-lowering-+.f64`
1988×	`+-lowering-+.f32`
1886×	`fnmsub-define`
1856×	`sum4-define`
1748×	`fmsub-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	288
1	128	252
2	331	252
3	870	252
4	2492	252
5	6116	252
0	8495	252
0	7	9
1	12	9
2	34	8
3	112	8
4	511	6
5	1634	6
6	3534	6
0	8284	6

Stop Event

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

Compiler

Compiled 86 to 49 computations (43% saved)

preprocess24.0ms (0.4%)

Compiler: Compiled 88 to 42 computations (52.3% saved)

analyze0.0ms (0%)

sample1.6s (28%)

preprocess438.0ms (7.7%)

explain145.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize32.0ms (0.6%)

series4.0ms (0.1%)

rewrite382.0ms (6.7%)

simplify175.0ms (3.1%)

eval28.0ms (0.5%)

prune26.0ms (0.5%)

simplify175.0ms (3.1%)

localize125.0ms (2.2%)

series16.0ms (0.3%)

rewrite330.0ms (5.8%)

simplify322.0ms (5.6%)

eval98.0ms (1.7%)

prune65.0ms (1.1%)

simplify9.0ms (0.2%)

localize39.0ms (0.7%)

series2.0ms (0%)

rewrite201.0ms (3.5%)

simplify151.0ms (2.6%)

eval35.0ms (0.6%)

prune31.0ms (0.5%)

simplify63.0ms (1.1%)

localize27.0ms (0.5%)

series4.0ms (0.1%)

rewrite235.0ms (4.1%)

simplify97.0ms (1.7%)

eval25.0ms (0.4%)

prune25.0ms (0.4%)

regimes11.0ms (0.2%)

regimes3.0ms (0.1%)

regimes3.0ms (0%)

bsearch36.0ms (0.6%)

simplify11.0ms (0.2%)

soundness708.0ms (12.4%)

preprocess24.0ms (0.4%)

end0.0ms (0%)

Profiling