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 (32.9%)

Results

613.0ms	5205×	0	valid
570.0ms	2471×	1	valid
130.0ms	580×	2	valid

Precisions

Click to see histograms. Total time spent on operations: 887.0ms

ival-pow: 340.0ms (38.3% of total)

ival-add: 170.0ms (19.2% of total)

ival-<=: 169.0ms (19.1% of total)

backward-pass: 96.0ms (10.8% of total)

ival-sub: 62.0ms (7% of total)

ival-and: 26.0ms (2.9% of total)

const: 24.0ms (2.7% of total)

Bogosity

preprocess247.0ms (4.9%)

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
81	3	(-4.749188038435536e-32 -2.559205360068117e-292)	-	`(-.f64 (pow.f64 (+.f64 x eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	0	-	-	`x`
0	79	(-1.450332090754676e-239 2.12473056631316e-133)	-	`(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

29.0ms	158×	1	valid
26.0ms	308×	0	valid
11.0ms	46×	2	valid

Compiler

Compiled 63 to 23 computations (63.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-pow: 20.0ms (57.8% of total)

ival-add: 5.0ms (14.4% of total)

backward-pass: 4.0ms (11.6% of total)

ival-sub: 4.0ms (11.6% of total)

const: 1.0ms (2.9% 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
▶	72.3%	(-.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)

simplify180.0ms (3.6%)

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)

localize84.0ms (1.7%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(pow.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(pow.f64 (+.f64 x eps) #s(literal 2 binary64))
✓	accuracy	72.4%	(-.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

43.0ms	154×	0	valid
19.0ms	79×	1	valid
8.0ms	23×	2	valid

Compiler

Compiled 44 to 12 computations (72.7% saved)

Precisions

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

ival-sub: 13.0ms (40.7% of total)

ival-pow: 8.0ms (25% of total)

ival-mult: 5.0ms (15.7% of total)

backward-pass: 3.0ms (9.4% of total)

ival-add: 2.0ms (6.3% of total)

const: 1.0ms (3.1% of total)

series8.0ms (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
1.0ms	x	@	0	(- (pow (+ x eps) 2) (pow x 2))
1.0ms	x	@	0	(* eps (- eps (* x -2)))
0.0ms	eps	@	0	(* eps (- eps (* x -2)))
0.0ms	eps	@	inf	(* eps (- eps (* x -2)))
0.0ms	x	@	inf	(- (pow (+ x eps) 2) (pow x 2))

rewrite366.0ms (7.2%)

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))))

simplify195.0ms (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)

eval58.0ms (1.2%)

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

prune54.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	502	3	505
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	503	4	507

Accuracy

100.0%

Counts

507 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 eps eps) (.f64 #s(literal 2 binary64) (*.f64 eps x)))
✓	100.0%	(.f64 eps (-.f64 eps (.f64 x #s(literal -2 binary64))))
▶	62.8%	(.f64 eps (.f64 #s(literal 2 binary64) x))
▶	69.8%	(*.f64 eps eps)

Compiler

Compiled 32 to 21 computations (34.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Rules

30×	`-lowering-.f32`
30×	`-lowering-.f64`
18×	`fma-lowering-fma.f32`
18×	`fma-define`
18×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	20	34
2	25	34
3	32	33
4	35	33
0	35	33

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize49.0ms (1%)

Localize:

Found 7 expressions of interest:

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

Results

26.0ms

256×

valid

Compiler

Compiled 41 to 10 computations (75.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 9.0ms (82.2% of total)

ival-add: 1.0ms (9.1% of total)

const: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Counts

6 → 120

Calls

Call 1

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

Calls

30 calls:

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

rewrite226.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

3342×	`-lowering-.f32`
3342×	`-lowering-.f64`
1602×	`pow-lowering-pow.f64`
1602×	`pow-lowering-pow.f32`
1574×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	34	25
2	241	25
3	2921	25
0	8343	25

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 130

Calls

Call 1

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

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

simplify140.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1986×	`-lowering-.f32`
1986×	`-lowering-.f64`
1654×	`fnmadd-define`
1516×	`fma-define`
986×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	534
1	79	501
2	219	501
3	550	501
4	1695	501
5	3736	501
6	7925	501
0	8297	501

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

eval25.0ms (0.5%)

Compiler: Compiled 5329 to 319 computations (94% saved)

prune18.0ms (0.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	267	1	268
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	267	5	272

Accuracy

100.0%

Counts

272 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
✓	100.0%	(+.f64 (.f64 eps eps) (.f64 #s(literal 2 binary64) (*.f64 eps x)))
✓	100.0%	(.f64 eps (-.f64 eps (.f64 x #s(literal -2 binary64))))
✓	62.8%	(.f64 eps (.f64 #s(literal 2 binary64) x))
✓	69.8%	(*.f64 eps eps)

Compiler

Compiled 42 to 27 computations (35.7% saved)

simplify39.0ms (0.8%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(*.f64 eps #s(literal 2 binary64))
✓	cost-diff	6400	(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))

Rules

30×	`-lowering-.f32`
30×	`-lowering-.f64`
18×	`fma-lowering-fma.f32`
18×	`fma-define`
18×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	14	15
2	28	14
3	37	14
0	37	14

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize25.0ms (0.5%)

Localize:

Found 3 expressions of interest:

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

Results

17.0ms

256×

valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 6.0ms (53.8% of total)

compiled-spec: 4.0ms (35.9% of total)

ival-add: 1.0ms (9% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

3 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite226.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

3230×	`-lowering-.f32`
3230×	`-lowering-.f64`
1986×	`fma-lowering-fma.f32`
1986×	`fma-lowering-fma.f64`
1874×	`fmsub-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	28	12
2	233	11
3	2942	11
0	8170	11

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 112

Calls

Call 1

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

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

simplify127.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1986×	`-lowering-.f32`
1986×	`-lowering-.f64`
1654×	`fnmadd-define`
1516×	`fma-define`
986×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	222
1	79	189
2	219	189
3	550	189
4	1694	189
5	3725	189
6	7918	189
0	8290	189

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval23.0ms (0.4%)

Compiler: Compiled 4657 to 341 computations (92.7% saved)

prune16.0ms (0.3%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	160	5	165

Accuracy

100.0%

Counts

165 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
✓	100.0%	(+.f64 (.f64 eps eps) (.f64 #s(literal 2 binary64) (*.f64 eps x)))
✓	100.0%	(.f64 eps (-.f64 eps (.f64 x #s(literal -2 binary64))))
✓	62.8%	(.f64 eps (.f64 #s(literal 2 binary64) x))
✓	69.8%	(*.f64 eps eps)

Compiler

Compiled 85 to 46 computations (45.9% saved)

regimes8.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`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)

regimes5.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0.1%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	eps
1.0ms	x

Results

Accuracy	Segments	Branch
91.7%	3	`x`
87.9%	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
69.8%	1	`eps`
69.8%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch39.0ms (0.8%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
19.0ms	1.8849626150594896e-124	8.504750883039398e-120
17.0ms	-3.4667954362843456e-130	-4.1891868640133474e-132

Results

22.0ms	141×	1	valid
6.0ms	99×	0	valid

Compiler

Compiled 226 to 161 computations (28.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-pow: 8.0ms (48.1% of total)

ival-add: 4.0ms (24.1% of total)

ival-sub: 2.0ms (12% of total)

backward-pass: 2.0ms (12% of total)

const: 0.0ms (0% of total)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`*-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	18	35
1	31	35
2	43	35
3	49	35
4	53	35
5	54	35

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
(.f64 eps (-.f64 eps (.f64 x #s(literal -2 binary64))))
(if (<=.f64 x #s(literal -8491156056859499/24973988402527937851052777838345330445988785141319769206873255677002973910558124960962448824507935769278615448971252983163583805434306282450321408 binary64)) (.f64 eps (.f64 #s(literal 2 binary64) x)) (if (<=.f64 x #s(literal 1362822608054263/181709681073901722637330951972001133588410340171829515070372549795159822028349480831547762678440891390190630401566544483383650407153664 binary64)) (.f64 eps eps) (.f64 eps (*.f64 #s(literal 2 binary64) x))))
(*.f64 eps eps)

Outputs
(fma.f64 (.f64 eps #s(literal 2 binary64)) x (.f64 eps eps))
(.f64 eps (-.f64 eps (.f64 x #s(literal -2 binary64))))
(if (<=.f64 x #s(literal -8491156056859499/24973988402527937851052777838345330445988785141319769206873255677002973910558124960962448824507935769278615448971252983163583805434306282450321408 binary64)) (.f64 eps (.f64 #s(literal 2 binary64) x)) (if (<=.f64 x #s(literal 1362822608054263/181709681073901722637330951972001133588410340171829515070372549795159822028349480831547762678440891390190630401566544483383650407153664 binary64)) (.f64 eps eps) (.f64 eps (*.f64 #s(literal 2 binary64) x))))
(*.f64 eps eps)

soundness1.1s (21.3%)

Rules

4694×	`-lowering-.f32`
4694×	`-lowering-.f64`
3342×	`-lowering-.f32`
3342×	`-lowering-.f64`
2860×	`/-lowering-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	34	25
2	241	25
3	2921	25
0	8343	25
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
0	11	35
1	69	31
2	590	29
3	7881	29
0	8063	29

Stop Event

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

Compiler

Compiled 124 to 72 computations (41.9% saved)

preprocess27.0ms (0.5%)

Compiler: Compiled 104 to 50 computations (51.9% saved)

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

analyze0.0ms (0%)

sample1.7s (32.9%)

preprocess247.0ms (4.9%)

explain100.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify180.0ms (3.6%)

localize84.0ms (1.7%)

series8.0ms (0.2%)

rewrite366.0ms (7.2%)

simplify195.0ms (3.9%)

eval58.0ms (1.2%)

prune54.0ms (1.1%)

simplify5.0ms (0.1%)

localize49.0ms (1%)

series6.0ms (0.1%)

rewrite226.0ms (4.5%)

simplify140.0ms (2.8%)

eval25.0ms (0.5%)

prune18.0ms (0.4%)

simplify39.0ms (0.8%)

localize25.0ms (0.5%)

series1.0ms (0%)

rewrite226.0ms (4.5%)

simplify127.0ms (2.5%)

eval23.0ms (0.4%)

prune16.0ms (0.3%)

regimes8.0ms (0.2%)

regimes5.0ms (0.1%)

regimes6.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch39.0ms (0.8%)

simplify10.0ms (0.2%)

soundness1.1s (21.3%)

preprocess27.0ms (0.5%)

end0.0ms (0%)

Profiling