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)

sample1.7s (34.5%)

Results

692.0ms	5179×	0	valid
482.0ms	2496×	1	valid
185.0ms	581×	2	valid

Precisions

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

ival-pow: 471.0ms (46.7% of total)

ival-<=: 157.0ms (15.6% of total)

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

ival-sub: 116.0ms (11.5% of total)

backward-pass: 76.0ms (7.5% of total)

ival-and: 26.0ms (2.6% of total)

const: 25.0ms (2.5% of total)

Bogosity

preprocess201.0ms (4.1%)

Algorithm

2×	egg-herbie

Rules

1814×	`+-lowering-+.f64`
1814×	`+-lowering-+.f32`
1748×	`fmsub-define`
1686×	`fma-lowering-fma.f32`
1686×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	64
1	51	44
2	178	42
3	704	40
4	4141	36
5	7959	36
0	7	9
1	12	7
2	36	7
3	107	7
4	504	6
5	1631	6
6	3488	6
0	8225	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))

explain100.0ms (2%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
71	1	(-6.383406445992407e-154 7.805330606816623e-165)	-	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	-	`x`
0	84	(-1.0045429318214748e-72 3.103230587079105e-70)	-	`(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

34.0ms	150×	1	valid
24.0ms	326×	0	valid
9.0ms	36×	2	valid

Compiler

Compiled 63 to 23 computations (63.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-pow: 16.0ms (41.3% of total)

ival-sub: 13.0ms (33.5% of total)

ival-add: 5.0ms (12.9% of total)

backward-pass: 4.0ms (10.3% of total)

const: 1.0ms (2.6% 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
▶	75.6%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
▶	100.0%	(.f64 eps (-.f64 eps (.f64 x #s(literal -2 binary64))))

Compiler

Compiled 20 to 13 computations (35% saved)

simplify143.0ms (2.9%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	6208	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
✓	cost-diff	6336	(pow.f64 x #s(literal 2 binary64))
✓	cost-diff	12800	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 x #s(literal -2 binary64))
✓	cost-diff	0	(-.f64 eps (*.f64 x #s(literal -2 binary64)))
✓	cost-diff	0	(.f64 eps (-.f64 eps (.f64 x #s(literal -2 binary64))))

Rules

2542×	`+-lowering-+.f64`
2542×	`+-lowering-+.f32`
1740×	`sum4-define`
1458×	`fma-define`
1436×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	23	37
2	61	34
3	173	34
4	667	34
5	3101	34
6	7838	34
0	8398	34

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

localize60.0ms (1.2%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	99.9%	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
✓	accuracy	75.7%	(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
✓	accuracy	100.0%	(-.f64 eps (*.f64 x #s(literal -2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -2 binary64))
✓	accuracy	100.0%	(.f64 eps (-.f64 eps (.f64 x #s(literal -2 binary64))))

Results

20.0ms	163×	0	valid
20.0ms	75×	1	valid
6.0ms	18×	2	valid

Compiler

Compiled 44 to 12 computations (72.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-pow: 8.0ms (32.5% of total)

ival-mult: 7.0ms (28.5% of total)

ival-sub: 4.0ms (16.3% of total)

backward-pass: 3.0ms (12.2% of total)

ival-add: 2.0ms (8.1% of total)

const: 1.0ms (4.1% of total)

series9.0ms (0.2%)

Counts

7 → 144

Calls

Call 1

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

Calls

36 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	0	(* eps (- eps (* x -2)))
1.0ms	x	@	0	(- (pow (+ x eps) 2) (pow x 2))
1.0ms	eps	@	inf	(* eps (- eps (* x -2)))
1.0ms	x	@	0	(* eps (- eps (* x -2)))
0.0ms	x	@	inf	(* eps (- eps (* x -2)))

rewrite312.0ms (6.3%)

Algorithm

1×	batch-egg-rewrite

Rules

4694×	`-lowering-.f32`
4694×	`-lowering-.f64`
2860×	`/-lowering-/.f32`
2860×	`/-lowering-/.f64`
1528×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	69	31
2	590	29
3	7881	29
0	8063	29

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 361

Calls

Call 1

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

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

simplify193.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

2012×	`-lowering-.f32`
2012×	`-lowering-.f64`
1976×	`fnmsub-define`
1856×	`fma-lowering-fma.f32`
1856×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	726
1	268	615
2	775	615
3	2483	606
4	6209	606
0	8649	606

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

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

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

eval57.0ms (1.2%)

Compiler: Compiled 15861 to 1260 computations (92.1% saved)

prune48.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	500	5	505
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	501	6	507

Accuracy

100.0%

Counts

507 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
▶	100.0%	(+.f64 (.f64 eps eps) (.f64 #s(literal 2 binary64) (*.f64 eps x)))
▶	99.8%	(.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal -4 binary64))) (/.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64)))))
✓	100.0%	(.f64 eps (-.f64 eps (.f64 x #s(literal -2 binary64))))
▶	61.9%	(.f64 eps (.f64 #s(literal 2 binary64) x))
▶	72.8%	(*.f64 eps eps)

Compiler

Compiled 115 to 76 computations (33.9% saved)

simplify31.0ms (0.6%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Rules

456×	`-lowering-.f32`
456×	`-lowering-.f64`
242×	`fma-define`
228×	`times-frac`
196×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	110
1	51	99
2	81	99
3	141	99
4	224	99
5	361	99
6	447	99
7	555	99
8	656	99
9	697	99
10	699	99
0	699	99

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize94.0ms (1.9%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal -4 binary64)))
✓	accuracy	100.0%	(.f64 (.f64 x x) #s(literal -4 binary64))
✓	accuracy	100.0%	(/.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64))))
✓	accuracy	99.8%	(.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal -4 binary64))) (/.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64)))))
✓	accuracy	100.0%	(+.f64 eps (*.f64 x #s(literal 2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))
✓	accuracy	99.7%	(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
✓	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)
✓	accuracy	100.0%	(*.f64 eps x)
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(+.f64 (.f64 eps eps) (.f64 #s(literal 2 binary64) (*.f64 eps x)))
✓	accuracy	100.0%	(.f64 #s(literal 2 binary64) (.f64 eps x))

Results

64.0ms

256×

valid

Compiler

Compiled 125 to 24 computations (80.8% saved)

Precisions

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

ival-mult: 20.0ms (63.1% of total)

ival-div: 5.0ms (15.8% of total)

ival-add: 5.0ms (15.8% of total)

const: 1.0ms (3.2% of total)

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

series20.0ms (0.4%)

Counts

14 → 288

Calls

Call 1

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

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

Calls

72 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(* (+ (* eps eps) (* (* x x) -4)) (/ eps (+ eps (* x -2))))
1.0ms	x	@	inf	(+ (* eps eps) (* 2 (* eps x)))
1.0ms	eps	@	0	(* (+ (* eps eps) (* (* x x) -4)) (/ eps (+ eps (* x -2))))
1.0ms	x	@	inf	(* (+ (* eps eps) (* (* x x) -4)) (/ eps (+ eps (* x -2))))
1.0ms	eps	@	-inf	(* (+ (* eps eps) (* (* x x) -4)) (/ eps (+ eps (* x -2))))

rewrite319.0ms (6.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3216×	`-lowering-.f32`
3216×	`-lowering-.f64`
2320×	`/-lowering-/.f32`
2320×	`/-lowering-/.f64`
1858×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	74
1	117	64
2	1051	64
0	8856	64

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 856

Calls

Call 1

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

Outputs
(+.f64 (.f64 eps eps) (.f64 eps (*.f64 #s(literal 2 binary64) x)))
(+.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))
(+.f64 (.f64 eps (.f64 #s(literal 2 binary64) x)) (*.f64 eps eps))
(+.f64 (.f64 eps (.f64 #s(literal 2 binary64) x)) (*.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) eps)))
(+.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64)))))))
(+.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 x (*.f64 x #s(literal -4 binary64)))))
(+.f64 (.f64 (/.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64)))) (.f64 x (.f64 x #s(literal -4 binary64)))) (.f64 (/.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64)))) (*.f64 eps eps)))
(+.f64 (.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) (+.f64 (.f64 eps (.f64 #s(literal 2 binary64) x)) (.f64 eps (.f64 x #s(literal -2 binary64)))))
(+.f64 (.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) (fma.f64 #s(literal 2 binary64) (.f64 eps x) (.f64 eps (*.f64 x #s(literal -2 binary64)))))
(+.f64 (.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) (fma.f64 (-.f64 #s(literal 0 binary64) eps) (.f64 x #s(literal -2 binary64)) (.f64 eps (*.f64 x #s(literal -2 binary64)))))
(+.f64 (.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) (fma.f64 (-.f64 #s(literal 0 binary64) x) (.f64 eps #s(literal -2 binary64)) (.f64 eps (*.f64 x #s(literal -2 binary64)))))
(+.f64 (/.f64 (.f64 eps eps) (/.f64 (+.f64 eps (.f64 x #s(literal -2 binary64))) eps)) (/.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (/.f64 (+.f64 eps (*.f64 x #s(literal -2 binary64))) eps)))
(+.f64 (/.f64 (.f64 x (.f64 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 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) eps)) (.f64 eps (*.f64 #s(literal 2 binary64) x)))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 eps eps)) (.f64 #s(literal 1 binary64) (.f64 eps (*.f64 #s(literal 2 binary64) x))))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 eps (.f64 #s(literal 2 binary64) x))) (.f64 #s(literal 1 binary64) (*.f64 eps eps)))
(+.f64 (.f64 (.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x))))) (+.f64 eps (.f64 #s(literal 2 binary64) x))) (.f64 eps eps)) (.f64 (.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x))))) (+.f64 eps (.f64 #s(literal 2 binary64) x))) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x)))))
(+.f64 (.f64 (.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x))))) (+.f64 eps (.f64 #s(literal 2 binary64) x))) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x))))) (+.f64 eps (.f64 #s(literal 2 binary64) x))) (.f64 eps eps)))
(+.f64 (.f64 (.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) (/.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))) eps) (.f64 (.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) (/.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))) (*.f64 #s(literal 2 binary64) x)))
(+.f64 (.f64 (.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) (/.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))) (.f64 #s(literal 2 binary64) x)) (.f64 (.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) (/.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))) eps))
(+.f64 (.f64 (.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (.f64 eps eps))
(+.f64 (.f64 (.f64 eps eps) (.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x))))) (+.f64 eps (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x))) (.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x))))) (+.f64 eps (.f64 #s(literal 2 binary64) x)))))
(+.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x))) (.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x))))) (+.f64 eps (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps eps) (.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x))))) (+.f64 eps (.f64 #s(literal 2 binary64) x)))))
(+.f64 (.f64 eps (.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) (/.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 #s(literal 2 binary64) x) (.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) (/.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))
(+.f64 (.f64 (.f64 #s(literal 2 binary64) x) (.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) (/.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))))) (.f64 eps (.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) (/.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))
(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 #s(literal 2 binary64) x))) eps)) #s(literal -1 binary64)))
(-.f64 (.f64 eps eps) (.f64 eps (*.f64 x #s(literal -2 binary64))))
(-.f64 #s(literal 0 binary64) (.f64 eps (-.f64 (.f64 x #s(literal -2 binary64)) eps)))
(-.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64))))) (/.f64 (.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (+.f64 eps (.f64 #s(literal 2 binary64) x)))) (.f64 eps (-.f64 (*.f64 x #s(literal -2 binary64)) eps)))
(-.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))) (.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 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64))))) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64))))) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) (/.f64 (+.f64 eps (.f64 x #s(literal -2 binary64))) eps)) (/.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) (/.f64 (+.f64 eps (*.f64 x #s(literal -2 binary64))) eps)))
(fma.f64 eps eps (.f64 eps (.f64 #s(literal 2 binary64) 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 x (.f64 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 eps x) #s(literal 2 binary64) (.f64 eps eps))
(fma.f64 (.f64 #s(literal 2 binary64) x) eps (.f64 eps eps))
(fma.f64 (.f64 x (.f64 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 eps (+.f64 eps (.f64 x #s(literal -2 binary64)))) (.f64 eps eps) (.f64 (/.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64)))) (.f64 x (.f64 x #s(literal -4 binary64)))))
(fma.f64 (/.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64)))) (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 (/.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64)))) (.f64 eps eps)))
(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
(neg.f64 (.f64 eps (-.f64 (.f64 x #s(literal -2 binary64)) eps)))
(neg.f64 (.f64 (/.f64 eps (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (+.f64 (.f64 eps eps) (.f64 x (*.f64 x #s(literal -4 binary64))))))
(neg.f64 (.f64 (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64)))) (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(neg.f64 (/.f64 (+.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))))
(neg.f64 (/.f64 (.f64 (.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) (.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64))))) (-.f64 #s(literal 0 binary64) (.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64)))))))
(neg.f64 (/.f64 (.f64 eps (-.f64 (.f64 x #s(literal -2 binary64)) eps)) #s(literal 1 binary64)))
(neg.f64 (/.f64 (.f64 eps (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64))))) (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x))) eps)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))))) (+.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))))))
(neg.f64 (/.f64 (.f64 (.f64 eps (-.f64 (.f64 x #s(literal -2 binary64)) eps)) (.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64))))) (.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64))))))
(neg.f64 (/.f64 (.f64 eps (-.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 eps eps))) (+.f64 eps (*.f64 x #s(literal -2 binary64)))))
(/.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 #s(literal 2 binary64) x))) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 (.f64 eps eps) (.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64)))))) (+.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (-.f64 (.f64 #s(literal 2 binary64) x) eps))) (.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (.f64 (.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) (.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 eps eps)))) (+.f64 eps (.f64 x #s(literal -2 binary64)))) (.f64 (+.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -64 binary64)))) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 eps eps)))) (/.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64))))) (+.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -64 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 eps eps)))) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (.f64 (+.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -64 binary64)))) (-.f64 #s(literal 0 binary64) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 eps (.f64 x #s(literal -2 binary64)))) (.f64 (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 16 binary64)))) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))) (/.f64 (+.f64 eps (.f64 x #s(literal -2 binary64))) eps)) (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (.f64 (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 16 binary64)))) (-.f64 #s(literal 0 binary64) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 eps (.f64 x #s(literal -2 binary64))) (+.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 eps eps))))) (.f64 eps (+.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal -64 binary64)))))))
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(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64)))))) (neg.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) (.f64 x (.f64 x #s(literal -4 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (.f64 eps (.f64 eps (.f64 eps eps))))) (neg.f64 (-.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 eps eps))))
(/.f64 (+.f64 (pow.f64 (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64)))) #s(literal 3 binary64)) (pow.f64 (+.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 3 binary64))) (+.f64 (.f64 (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64)))) (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64))))) (-.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64)))) (.f64 (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64)))) (+.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 (*.f64 x x) #s(literal 4 binary64)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))))) (+.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))))) (.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal 4 binary64))))))))
(/.f64 (-.f64 (.f64 (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64)))) (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64))))) (.f64 (+.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 (.f64 x x) #s(literal 4 binary64))))) (-.f64 (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64)))) (+.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (.f64 (*.f64 x x) #s(literal 4 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))))) (+.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (+.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal 4 binary64))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (.f64 x (*.f64 x #s(literal -4 binary64))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64)))))
(.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) (+.f64 eps (*.f64 x #s(literal -2 binary64))))
(.f64 (+.f64 eps (.f64 x #s(literal -2 binary64))) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(.f64 (+.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -64 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 x (.f64 x #s(literal -4 binary64))) (*.f64 eps eps))))))
(.f64 (+.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -64 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (.f64 (.f64 eps eps) (+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal 4 binary64)))))))
(.f64 (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64)))) #s(literal 1 binary64))
(.f64 (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal 4 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -64 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (*.f64 eps eps)))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 eps eps)) (.f64 x (*.f64 x #s(literal -4 binary64))))))
(.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 16 binary64))) (.f64 eps (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (.f64 x #s(literal -4 binary64))) (*.f64 eps eps))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) #s(literal 4 binary64)))
(neg.f64 (.f64 (.f64 x x) #s(literal 4 binary64)))
(.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal -2 binary64))))
(.f64 #s(literal 2 binary64) (neg.f64 (.f64 x (*.f64 #s(literal 2 binary64) x))))
(.f64 x (.f64 x #s(literal -4 binary64)))
(.f64 x (neg.f64 (.f64 #s(literal -2 binary64) (*.f64 x #s(literal -2 binary64)))))
(.f64 x (neg.f64 (.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x))))
(.f64 (.f64 #s(literal 2 binary64) x) (*.f64 x #s(literal -2 binary64)))
(.f64 (.f64 x x) #s(literal -4 binary64))
(.f64 #s(literal -4 binary64) (.f64 x x))
(.f64 #s(literal -2 binary64) (.f64 x (*.f64 #s(literal 2 binary64) x)))
(.f64 #s(literal -2 binary64) (neg.f64 (.f64 x (*.f64 x #s(literal -2 binary64)))))
(.f64 (.f64 x #s(literal -2 binary64)) (*.f64 #s(literal 2 binary64) x))
(.f64 #s(literal -1 binary64) (.f64 (*.f64 x x) #s(literal 4 binary64)))
(.f64 (.f64 x #s(literal -4 binary64)) x)
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal -2 binary64) (*.f64 x #s(literal -2 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x)))
(.f64 #s(literal 4 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 4 binary64))
(.f64 (.f64 (*.f64 x #s(literal -2 binary64)) x) #s(literal 2 binary64))
(.f64 (.f64 (*.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64)) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) x) x) #s(literal -2 binary64))
(.f64 (neg.f64 (.f64 (*.f64 x #s(literal -2 binary64)) x)) #s(literal -2 binary64))
(.f64 (neg.f64 (.f64 (*.f64 x #s(literal -2 binary64)) #s(literal -2 binary64))) x)
(.f64 (neg.f64 (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 2 binary64))) x)
(.f64 (neg.f64 (.f64 (*.f64 #s(literal 2 binary64) x) x)) #s(literal 2 binary64))
(+.f64 (.f64 (/.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))))) (.f64 eps eps)) (.f64 (/.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))))) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x)))))
(+.f64 (.f64 (/.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))))) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x)))) (.f64 (/.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))))) (.f64 eps eps)))
(+.f64 (.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64))))) eps) (.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64))))) (*.f64 #s(literal 2 binary64) x)))
(+.f64 (.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64))))) (.f64 #s(literal 2 binary64) x)) (.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 x (*.f64 x #s(literal -4 binary64))))) eps))
(+.f64 (.f64 (.f64 eps eps) (/.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))))) (.f64 (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x))) (/.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))))))
(+.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x))) (/.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))))) (.f64 (.f64 eps eps) (/.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))))))
(+.f64 (.f64 eps (/.f64 eps (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64)))))) (.f64 (.f64 #s(literal 2 binary64) x) (/.f64 eps (+.f64 (.f64 eps eps) (.f64 x (*.f64 x #s(literal -4 binary64)))))))
(+.f64 (.f64 (.f64 #s(literal 2 binary64) x) (/.f64 eps (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64)))))) (.f64 eps (/.f64 eps (+.f64 (.f64 eps eps) (.f64 x (*.f64 x #s(literal -4 binary64)))))))
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 eps (.f64 x #s(literal -2 binary64))) eps)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (.f64 #s(literal 2 binary64) x) eps)) (/.f64 eps (-.f64 (.f64 #s(literal 2 binary64) x) eps)))
(neg.f64 (/.f64 eps (-.f64 (*.f64 #s(literal 2 binary64) x) eps)))
(neg.f64 (.f64 #s(literal 1 binary64) (/.f64 eps (-.f64 (.f64 #s(literal 2 binary64) x) eps))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (+.f64 eps (*.f64 x #s(literal -2 binary64))) eps)))
(/.f64 eps (+.f64 eps (*.f64 x #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps (*.f64 x #s(literal -2 binary64))) eps))
(/.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal 2 binary64) x) eps) eps))
(/.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 (*.f64 #s(literal 2 binary64) x) eps))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x #s(literal -2 binary64)))) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 #s(literal 2 binary64) x))))
(pow.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal -2 binary64))) eps) #s(literal -1 binary64))
(.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 x #s(literal -2 binary64)))))
(.f64 #s(literal 1 binary64) (/.f64 eps (+.f64 eps (.f64 x #s(literal -2 binary64)))))
(.f64 #s(literal -1 binary64) (/.f64 eps (-.f64 (.f64 #s(literal 2 binary64) x) eps)))
(.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 2 binary64) x) eps)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 x #s(literal -2 binary64)))) eps)
(.f64 (/.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x)))))
(.f64 (/.f64 eps (+.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 eps (.f64 #s(literal 2 binary64) x)))))))
(.f64 (/.f64 eps (+.f64 (.f64 eps eps) (.f64 x (.f64 x #s(literal -4 binary64))))) (+.f64 eps (*.f64 #s(literal 2 binary64) x)))
(.f64 (pow.f64 (/.f64 (+.f64 eps (.f64 x #s(literal -2 binary64))) eps) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal -2 binary64))) eps) #s(literal -1/2 binary64)))

simplify274.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

5088×	`-lowering-.f32`
5088×	`-lowering-.f64`
1930×	`/-lowering-/.f32`
1930×	`/-lowering-/.f64`
1754×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	264	2130
1	897	1878
2	2528	1831
0	8381	1831

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 288

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

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 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) 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 (*.f64 #s(literal 2 binary64) x) eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) 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 #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))))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(.f64 x (.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
(* 2 (* eps x))
(.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 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(.f64 x (.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps 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 #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))
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* eps x)
(*.f64 eps x)
(* 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)
(* 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 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) 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 (*.f64 #s(literal 2 binary64) x) eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) 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 #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))))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(.f64 x (.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
(* 2 (* eps x))
(.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 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(.f64 x (.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(+ (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x)))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal -1/4 binary64)) x)) x)
(+ (* eps (- (* 1/8 (/ eps (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))
(+.f64 (/.f64 (/.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) x) (.f64 x x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps #s(literal -1/4 binary64)) x)) x))
(+ (* eps (- (* eps (+ (* -1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 3))))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))
(+.f64 (.f64 (.f64 eps eps) (+.f64 (/.f64 (.f64 eps #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps #s(literal -1/4 binary64)) x)) x))
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(/ (+ 1 (* -2 (/ x eps))) eps)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal -2 binary64)) eps)) eps)
(/ (- (+ 1 (* 4 (/ (pow x 2) (pow eps 2)))) (* 2 (/ x eps))) eps)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 4 binary64))) eps) (*.f64 x #s(literal -2 binary64))) eps)) eps)
(/ (- (+ 1 (* -8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* 2 (/ x eps)))) eps)
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x #s(literal -8 binary64)))) (.f64 eps (.f64 eps eps)))) (/.f64 (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 4 binary64))) eps) (.f64 x #s(literal -2 binary64))) eps)) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(* -1 (/ (- (* 2 (/ x eps)) 1) eps))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal -2 binary64)) eps)) eps)
(* -1 (/ (- (* -1 (/ (- (* 4 (/ (pow x 2) eps)) (* 2 x)) eps)) 1) eps))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 x (.f64 x #s(literal 4 binary64))) eps) (*.f64 x #s(literal -2 binary64))) eps)) eps)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* 4 (pow x 2))) eps)) (* 2 x)) eps)) 1) eps))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 #s(literal -8 binary64) (/.f64 (.f64 x (.f64 x x)) eps))) eps) (.f64 x #s(literal -2 binary64))) eps)) eps)
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
(+ (* -2 (/ x (pow eps 2))) (/ 1 eps))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal -2 binary64)) eps)) eps)
(+ (* x (- (* 4 (/ x (pow eps 3))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))
(+.f64 (/.f64 (.f64 x (/.f64 (.f64 x (/.f64 #s(literal 4 binary64) eps)) eps)) eps) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x #s(literal -2 binary64)) eps)) eps))
(+ (* x (- (* x (+ (* -8 (/ x (pow eps 4))) (* 4 (/ 1 (pow eps 3))))) (* 2 (/ 1 (pow eps 2))))) (/ 1 eps))
(+.f64 (.f64 (.f64 x x) (+.f64 (/.f64 (.f64 x #s(literal -8 binary64)) (pow.f64 eps #s(literal 4 binary64))) (/.f64 #s(literal 4 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x #s(literal -2 binary64)) eps)) eps))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* -1/4 (/ eps x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal -1/4 binary64)) x)) x)
(/ (- (+ 1/2 (* 1/8 (/ (pow eps 2) (pow x 2)))) (* 1/4 (/ eps x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) x) (*.f64 eps #s(literal -1/4 binary64))) x)) x)
(/ (- (+ 1/2 (* -1/16 (/ (pow eps 3) (pow x 3)))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) x)
(/.f64 (+.f64 (/.f64 (.f64 eps (.f64 eps (.f64 eps #s(literal -1/16 binary64)))) (.f64 x (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) x) (.f64 eps #s(literal -1/4 binary64))) x))) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/4 (/ eps x)) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps #s(literal -1/4 binary64)) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 1/8 (/ (pow eps 2) x)) (* 1/4 eps)) x)) 1/2) x))
(/.f64 (+.f64 (/.f64 (+.f64 (.f64 eps #s(literal 1/4 binary64)) (/.f64 (.f64 eps (*.f64 eps #s(literal -1/8 binary64))) x)) x) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ (pow eps 3) x)) (* 1/8 (pow eps 2))) x)) (* 1/4 eps)) x)) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 eps #s(literal -1/4 binary64)) (/.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (.f64 eps (.f64 eps eps)) x)) (.f64 eps (.f64 eps #s(literal -1/8 binary64)))) x)) x)) 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 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) x) eps)))
(* eps (+ 1 (* 2 (/ x eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) x) eps)))
(* eps (+ 1 (* 2 (/ x eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) x) eps)))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) x) eps)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) x) eps)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 2 binary64) x) eps)))
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 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal -2 binary64) (/.f64 eps x))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal -2 binary64) (/.f64 eps x))))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(-.f64 #s(literal 0 binary64) (*.f64 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)
(* 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 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) 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 (*.f64 #s(literal 2 binary64) x) eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))))
(* (pow eps 2) (+ 1 (* 2 (/ x eps))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) 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 #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))))
(* x (+ (* 2 eps) (/ (pow eps 2) x)))
(.f64 x (.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
(* 2 (* eps x))
(.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 (* x (+ (* -2 eps) (* -1 (/ (pow eps 2) x)))))
(.f64 x (.f64 eps (+.f64 #s(literal 2 binary64) (/.f64 eps x))))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(+ (* -4 (pow x 2)) (pow eps 2))
(+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal -4 binary64)))
(+ (* -4 (pow x 2)) (pow eps 2))
(+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal -4 binary64)))
(+ (* -4 (pow x 2)) (pow eps 2))
(+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal -4 binary64)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) #s(literal -4 binary64)) (*.f64 eps eps))))
(* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) #s(literal -4 binary64)) (*.f64 eps eps))))
(* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) #s(literal -4 binary64)) (*.f64 eps eps))))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) #s(literal -4 binary64)) (*.f64 eps eps))))
(* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) #s(literal -4 binary64)) (*.f64 eps eps))))
(* (pow eps 2) (+ 1 (* -4 (/ (pow x 2) (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) #s(literal -4 binary64)) (*.f64 eps eps))))
(pow eps 2)
(*.f64 eps eps)
(+ (* -4 (pow x 2)) (pow eps 2))
(+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal -4 binary64)))
(+ (* -4 (pow x 2)) (pow eps 2))
(+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal -4 binary64)))
(+ (* -4 (pow x 2)) (pow eps 2))
(+.f64 (.f64 eps eps) (.f64 (*.f64 x x) #s(literal -4 binary64)))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))
(.f64 x (.f64 x (+.f64 #s(literal -4 binary64) (/.f64 (/.f64 (*.f64 eps eps) x) x))))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))
(.f64 x (.f64 x (+.f64 #s(literal -4 binary64) (/.f64 (/.f64 (*.f64 eps eps) x) x))))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))
(.f64 x (.f64 x (+.f64 #s(literal -4 binary64) (/.f64 (/.f64 (*.f64 eps eps) x) x))))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))
(.f64 x (.f64 x (+.f64 #s(literal -4 binary64) (/.f64 (/.f64 (*.f64 eps eps) x) x))))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))
(.f64 x (.f64 x (+.f64 #s(literal -4 binary64) (/.f64 (/.f64 (*.f64 eps eps) x) x))))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) 4))
(.f64 x (.f64 x (+.f64 #s(literal -4 binary64) (/.f64 (/.f64 (*.f64 eps eps) x) x))))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* -4 (pow x 2))
(.f64 (.f64 x x) #s(literal -4 binary64))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps (- (* -1/4 (/ eps (pow x 2))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (.f64 #s(literal -1/4 binary64) (/.f64 eps (*.f64 x x))) (/.f64 #s(literal -1/2 binary64) x)))
(* eps (- (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/4 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (/.f64 #s(literal -1/4 binary64) (.f64 x x)) (/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) 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))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 eps (+.f64 (/.f64 (.f64 eps #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/4 binary64) (*.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x)))
1
#s(literal 1 binary64)
(+ 1 (* 2 (/ x eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))
(- (+ 1 (* 4 (/ (pow x 2) (pow eps 2)))) (* -2 (/ x eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (/.f64 (.f64 x (*.f64 x #s(literal 4 binary64))) eps)) eps))
(- (+ 1 (* 8 (/ (pow x 3) (pow eps 3)))) (+ (* -4 (/ (pow x 2) (pow eps 2))) (* -2 (/ x eps))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (.f64 x (+.f64 (.f64 #s(literal 8 binary64) (/.f64 x (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 4 binary64) (.f64 eps eps)))))))
1
#s(literal 1 binary64)
(+ 1 (* 2 (/ x eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))
(+ 1 (* -1 (/ (- (* -4 (/ (pow x 2) eps)) (* 2 x)) eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (/.f64 (.f64 x (*.f64 x #s(literal 4 binary64))) eps)) eps))
(+ 1 (* -1 (/ (- (* -1 (/ (- (* 8 (/ (pow x 3) eps)) (* -4 (pow x 2))) eps)) (* 2 x)) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal -4 binary64)) (.f64 #s(literal -8 binary64) (/.f64 (.f64 x (.f64 x x)) eps))) eps) (.f64 x #s(literal -2 binary64))) eps))
1
#s(literal 1 binary64)
(+ 1 (* 2 (/ x eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal 2 binary64) x) eps))
(+ 1 (* x (+ (* 4 (/ x (pow eps 2))) (* 2 (/ 1 eps)))))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (/.f64 (.f64 x (*.f64 x #s(literal 4 binary64))) eps)) eps))
(+ 1 (* x (+ (* x (+ (* 8 (/ x (pow eps 3))) (* 4 (/ 1 (pow eps 2))))) (* 2 (/ 1 eps)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (/.f64 #s(literal 2 binary64) eps) (.f64 x (+.f64 (.f64 #s(literal 8 binary64) (/.f64 x (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 4 binary64) (.f64 eps eps)))))))
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(/ (+ (* -1/2 eps) (* -1/4 (/ (pow eps 2) x))) x)
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x)) x)
(/ (- (+ (* -1/2 eps) (* -1/8 (/ (pow eps 3) (pow x 2)))) (* 1/4 (/ (pow eps 2) x))) x)
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps (.f64 eps eps)) x)) (.f64 (.f64 eps eps) #s(literal -1/4 binary64))) 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)
(/.f64 (+.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 eps #s(literal 4 binary64))) (.f64 x (.f64 x x)))) (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 eps (.f64 eps eps)) x)) (.f64 (*.f64 eps eps) #s(literal -1/4 binary64))) x)) x)
(* -1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* -1 (/ (+ (* 1/4 (/ (pow eps 2) x)) (* 1/2 eps)) x))
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 (*.f64 eps eps) #s(literal -1/4 binary64)) x)) x)
(* -1 (/ (+ (* -1 (/ (- (* -1/8 (/ (pow eps 3) x)) (* 1/4 (pow eps 2))) x)) (* 1/2 eps)) x))
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 eps (.f64 eps eps)) x))) (-.f64 #s(literal 0 binary64) x))) 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))
(/.f64 (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal -1/4 binary64)) (/.f64 (+.f64 (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 1/16 binary64)) x) (.f64 eps (.f64 eps (*.f64 eps #s(literal 1/8 binary64))))) x)) x)) x)

eval129.0ms (2.6%)

Compiler: Compiled 31034 to 1574 computations (94.9% saved)

prune67.0ms (1.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1182	2	1184
Fresh	0	0	0
Picked	3	2	5
Done	0	1	1
Total	1185	5	1190

Accuracy

100.0%

Counts

1190 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 1 binary64) eps))
▶	72.7%	(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
✓	100.0%	(.f64 eps (-.f64 eps (.f64 x #s(literal -2 binary64))))
✓	61.9%	(.f64 eps (.f64 #s(literal 2 binary64) x))
✓	72.8%	(*.f64 eps eps)

Compiler

Compiled 39 to 27 computations (30.8% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Rules

34×	`-lowering-.f32`
34×	`-lowering-.f64`
24×	`fma-define`
24×	`/-lowering-/.f32`
24×	`/-lowering-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	18	26
2	25	25
3	37	25
4	51	25
5	68	25
6	70	25
0	70	25

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize37.0ms (0.7%)

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) eps)
✓	accuracy	100.0%	(+.f64 eps (*.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	99.7%	(/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 1 binary64) eps))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) eps)
✓	accuracy	99.8%	(/.f64 eps (/.f64 #s(literal 1 binary64) eps))

Results

24.0ms

256×

valid

Compiler

Compiled 37 to 10 computations (73% saved)

Precisions

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

ival-div: 6.0ms (58.2% of total)

ival-mult: 2.0ms (19.4% of total)

ival-add: 1.0ms (9.7% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

5 → 84

Calls

Call 1

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

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 (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<alt (/ 1 eps)>
#<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

21 calls:

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

rewrite226.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2538×	`-lowering-.f32`
2538×	`-lowering-.f64`
1650×	`/-lowering-/.f32`
1650×	`/-lowering-/.f64`
1326×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	49	17
2	334	17
3	4213	17
0	8043	17

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 271

Calls

Call 1

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

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

simplify144.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1856×	`sum4-define`
1854×	`fnmsub-define`
1664×	`fma-lowering-fma.f32`
1664×	`fma-lowering-fma.f64`
1644×	`fmm-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	348
1	130	297
2	334	297
3	874	297
4	2506	297
5	6119	297
0	8463	297

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

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

eval44.0ms (0.9%)

Compiler: Compiled 7187 to 682 computations (90.5% saved)

prune53.0ms (1.1%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	388	0	388
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	388	5	393

Accuracy

100.0%

Counts

393 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 1 binary64) eps))
✓	72.7%	(/.f64 eps (/.f64 #s(literal 1 binary64) eps))
✓	100.0%	(.f64 eps (-.f64 eps (.f64 x #s(literal -2 binary64))))
✓	61.9%	(.f64 eps (.f64 #s(literal 2 binary64) x))
✓	72.8%	(*.f64 eps eps)

Compiler

Compiled 114 to 60 computations (47.4% saved)

regimes10.0ms (0.2%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`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)

regimes7.0ms (0.1%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
92.2%	3	`x`
87.2%	3	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0.1%)

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
72.8%	1	`eps`
72.8%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch38.0ms (0.8%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
20.0ms	2.1278323130872135e-136	1.346261024110787e-134
15.0ms	-1.8571672432308776e-113	-2.9987309324156347e-115

Results

23.0ms	138×	1	valid
5.0ms	86×	0	valid

Compiler

Compiled 212 to 151 computations (28.8% saved)

Precisions

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

ival-pow: 8.0ms (56.4% of total)

ival-add: 2.0ms (14.1% of total)

ival-sub: 2.0ms (14.1% of total)

backward-pass: 2.0ms (14.1% of total)

const: 0.0ms (0% of total)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	28	27
2	40	27
3	46	27
4	50	27
5	51	27

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 x #s(literal -6065214955889283/346583711765101857447301773017885462929554634421977071896309947576827663475703202879996800763017447262173901370175446478621769728 binary64)) (*.f64 eps (*.f64 #s(literal 2 binary64) x)) (if (<=.f64 x #s(literal 5319259737831231/409173825987017733751648712103449894027080255755383098685411421012016724550584319360408761540738019643860835515945008876152157068235674131666065948672 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 -6065214955889283/346583711765101857447301773017885462929554634421977071896309947576827663475703202879996800763017447262173901370175446478621769728 binary64)) (.f64 eps (.f64 #s(literal 2 binary64) x)) (if (<=.f64 x #s(literal 5319259737831231/409173825987017733751648712103449894027080255755383098685411421012016724550584319360408761540738019643860835515945008876152157068235674131666065948672 binary64)) (.f64 eps eps) (.f64 eps (*.f64 #s(literal 2 binary64) x))))
(if (<=.f64 x #s(literal -6065214955889283/346583711765101857447301773017885462929554634421977071896309947576827663475703202879996800763017447262173901370175446478621769728 binary64)) (.f64 eps (.f64 x #s(literal 2 binary64))) (if (<=.f64 x #s(literal 5319259737831231/409173825987017733751648712103449894027080255755383098685411421012016724550584319360408761540738019643860835515945008876152157068235674131666065948672 binary64)) (.f64 eps eps) (.f64 eps (*.f64 x #s(literal 2 binary64)))))
(*.f64 eps eps)

soundness583.0ms (11.7%)

Rules

2012×	`-lowering-.f32`
2012×	`-lowering-.f64`
1976×	`fnmsub-define`
1856×	`fma-lowering-fma.f32`
1856×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	80	726
1	268	615
2	775	615
3	2483	606
4	6209	606
0	8649	606
0	7	9
1	12	7
2	36	7
3	107	7
4	504	6
5	1631	6
6	3488	6
0	8225	6

Stop Event

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

Compiler

Compiled 86 to 51 computations (40.7% saved)

preprocess33.0ms (0.7%)

Compiler: Compiled 88 to 46 computations (47.7% saved)

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

analyze0.0ms (0%)

sample1.7s (34.5%)

preprocess201.0ms (4.1%)

explain100.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify143.0ms (2.9%)

localize60.0ms (1.2%)

series9.0ms (0.2%)

rewrite312.0ms (6.3%)

simplify193.0ms (3.9%)

eval57.0ms (1.2%)

prune48.0ms (1%)

simplify31.0ms (0.6%)

localize94.0ms (1.9%)

series20.0ms (0.4%)

rewrite319.0ms (6.4%)

simplify274.0ms (5.5%)

eval129.0ms (2.6%)

prune67.0ms (1.4%)

simplify6.0ms (0.1%)

localize37.0ms (0.7%)

series1.0ms (0%)

rewrite226.0ms (4.5%)

simplify144.0ms (2.9%)

eval44.0ms (0.9%)

prune53.0ms (1.1%)

regimes10.0ms (0.2%)

regimes7.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch38.0ms (0.8%)

simplify9.0ms (0.2%)

soundness583.0ms (11.7%)

preprocess33.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	23	110
1	51	99
2	81	99
3	141	99
4	224	99
5	361	99
6	447	99
7	555	99
8	656	99
9	697	99
10	699	99
0	699	99

Iter	Nodes	Cost
0	23	110
1	51	99
2	81	99
3	141	99
4	224	99
5	361	99
6	447	99
7	555	99
8	656	99
9	697	99
10	699	99
0	699	99

Iter	Nodes	Cost
0	23	110
1	51	99
2	81	99
3	141	99
4	224	99
5	361	99
6	447	99
7	555	99
8	656	99
9	697	99
10	699	99
0	699	99