Metrics for x / (x^2 + 1)

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample523.0ms (7.9%)

Memory

31.2MiB live, 638.6MiB allocated

Samples

318.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 184.0ms

ival-mult: 71.0ms (38.6% of total)

ival-div: 59.0ms (32.1% of total)

ival-add: 41.0ms (22.3% of total)

ival-true: 5.0ms (2.7% of total)

exact: 5.0ms (2.7% of total)

ival-assert: 3.0ms (1.6% of total)

Bogosity

preprocess19.0ms (0.3%)

Memory

26.3MiB live, 26.3MiB allocated

Algorithm

2×	egg-herbie

Rules

46×	`associate-l`
42×	`times-frac`
30×	`unsub-neg`
28×	`distribute-lft-neg-in`
26×	`distribute-neg-frac2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	28	22
2	64	21
3	130	21
4	234	21
5	332	21
6	345	21
7	347	21
8	351	21
0	5	7
1	8	7
0	8	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

Inputs
(/ x (+ (* x x) 1))
(/ (neg x) (+ (* (neg x) (neg x)) 1))
(neg (/ (neg x) (+ (* (neg x) (neg x)) 1)))

Outputs
(/ x (+ (* x x) 1))
(/ x (+ 1 (* x x)))
(/ (neg x) (+ (* (neg x) (neg x)) 1))
(/ x (- -1 (* x x)))
(neg (/ (neg x) (+ (* (neg x) (neg x)) 1)))
(/ x (+ 1 (* x x)))

Symmetry

(negabs x)

explain80.0ms (1.2%)

Memory

-26.9MiB live, 103.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
59	-	-	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`	n/o	59	0
↳	`(*.f64 x x)`	overflow	59
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	59

Confusion

	Predicted +	Predicted -
+	59	0
-	0	197

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	59	0	0
-	0	0	197

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	197
1	59

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

21.0ms

512×

valid

Compiler

Compiled 54 to 24 computations (55.6% saved)

Precisions

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

ival-mult: 4.0ms (37.5% of total)

ival-div: 3.0ms (28.1% of total)

ival-add: 2.0ms (18.8% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.5%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify3.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`/-lowering-/.f32`
2×	`/-lowering-/.f64`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
1	8	17
0	8	15

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize19.0ms (0.3%)

Memory

-5.7MiB live, 30.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (*.f64 x x) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	78.5%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

13.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 2.0ms (38.1% of total)

ival-mult: 2.0ms (38.1% of total)

ival-add: 1.0ms (19.1% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

3.8MiB live, 3.8MiB allocated

Counts

3 → 36

Calls

Call 1

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

Outputs
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<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)>

Calls

9 calls:

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

rewrite521.0ms (7.9%)

Memory

21.3MiB live, 446.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 942×	`/-lowering-/.f32`
4 942×	`/-lowering-/.f64`
4 762×	`accelerator-lowering-fma.f32`
4 762×	`accelerator-lowering-fma.f64`
3 572×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
1	30	15
2	199	15
3	1759	15
0	8554	13

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 327

Calls

Call 1

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

Outputs
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(+.f64 #s(literal 1 binary64) (neg.f64 (*.f64 x (neg.f64 x))))
(+.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
(+.f64 (neg.f64 (*.f64 x (neg.f64 x))) #s(literal 1 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64))))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal -1 binary64) (*.f64 x x)))
(-.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal 1 binary64)))
(-.f64 (/.f64 (*.f64 x (neg.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)))) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))) (-.f64 #s(literal -1 binary64) (.f64 x x)))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))) (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal -1 binary64) (.f64 x x)))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))) #s(literal -1 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 1 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))))) (fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))))) (/.f64 (/.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))))) (fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))))))
(-.f64 (/.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))))
(fma.f64 x x #s(literal 1 binary64))
(fma.f64 x (/.f64 (.f64 x (.f64 x x)) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (*.f64 x x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) #s(literal 1 binary64))
(fma.f64 (.f64 x (.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (neg.f64 (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))))
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(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 x (-.f64 #s(literal -1 binary64) (.f64 x x))) #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (/.f64 x (-.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 x (-.f64 #s(literal -1 binary64) (.f64 x x))) (.f64 (/.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 x (-.f64 #s(literal -1 binary64) (*.f64 x x)))))))
(pow.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal -1 binary64))
(pow.f64 (pow.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))) #s(literal -1 binary64))
(*.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)))
(*.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64))))
(.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 x (-.f64 #s(literal -1 binary64) (.f64 x x))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) (neg.f64 x))
(*.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64))) (.f64 x (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (.f64 x (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64))) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 x (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (.f64 x (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)) #s(literal 1 binary64))))
(.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))))
(.f64 (.f64 x (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))))))
(.f64 (.f64 x (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)))))
(.f64 (.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
(.f64 (.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (pow.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))
(.f64 (.f64 (/.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64))) (fma.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))))))
(.f64 (.f64 (/.f64 x (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64))) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)) (.f64 x x))))
(.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 (neg.f64 x) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))))
(.f64 (/.f64 x (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 x) #s(literal 2 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))

simplify778.0ms (11.8%)

Memory

-5.4MiB live, 485.9MiB allocated

Algorithm

1×	egg-herbie

Rules

12 662×	`accelerator-lowering-fma.f32`
12 662×	`accelerator-lowering-fma.f64`
2 988×	`-lowering-.f32`
2 988×	`-lowering-.f64`
1 640×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	226
1	131	224
2	312	216
3	888	212
4	2381	210
5	5550	210
6	7627	210
0	8047	197

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(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)

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

eval45.0ms (0.7%)

Memory: -11.2MiB live, 102.6MiB allocated
Compiler: Compiled 12 302 to 1 051 computations (91.5% saved)

prune42.0ms (0.6%)

Memory

37.7MiB live, 113.1MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	357	6	363
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	358	6	364

Accuracy

100.0%

Counts

364 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.7%	(fma.f64 (*.f64 x x) (neg.f64 x) x)
	66.4%	(/.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64)))
▶	78.5%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	78.4%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
▶	48.7%	(/.f64 #s(literal 1 binary64) x)
▶	53.6%	x

Compiler

Compiled 92 to 48 computations (47.8% saved)

simplify442.0ms (6.7%)

Memory

-21.7MiB live, 736.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
✓	cost-diff	192	(/.f64 (fma.f64 x x #s(literal 1 binary64)) x)
✓	cost-diff	512	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
✓	cost-diff	0	(neg.f64 x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 (*.f64 x x) (neg.f64 x) x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
✓	cost-diff	0	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))

Rules

16 736×	`accelerator-lowering-fma.f32`
16 736×	`accelerator-lowering-fma.f64`
4 562×	`-lowering-.f32`
4 562×	`-lowering-.f64`
1 600×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	55
1	25	54
2	43	52
3	70	52
4	128	52
5	195	52
6	292	52
7	559	52
8	1026	52
9	2009	50
10	3049	50
11	4362	50
12	5178	50
13	5715	50
14	6354	50
15	6959	50
0	8368	46

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ x (+ (* x x) 1))
x
(+ (* x x) 1)
1
x
(/ 1 x)
1
x
(+ (* (* x x) (neg x)) x)
(* x x)
x
(neg x)
(/ 1 (/ (+ (* x x) 1) x))
1
(/ (+ (* x x) 1) x)
(+ (* x x) 1)
x

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

localize229.0ms (3.5%)

Memory

5.1MiB live, 81.0MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x x #s(literal 1 binary64))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x #s(literal 1 binary64)) x))
✓	accuracy	78.6%	(/.f64 (fma.f64 x x #s(literal 1 binary64)) x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	99.9%	(fma.f64 (*.f64 x x) (neg.f64 x) x)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(fma.f64 x x #s(literal 1 binary64))
✓	accuracy	78.5%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))

Samples

172.0ms

256×

valid

Compiler

Compiled 53 to 13 computations (75.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 163.0ms

ival-mult: 153.0ms (93.7% of total)

ival-div: 6.0ms (3.7% of total)

ival-add: 3.0ms (1.8% of total)

ival-neg: 1.0ms (0.6% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Counts

8 → 96

Calls

Call 1

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

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ 1 (pow x 2))))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* -1 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1))>
#<alt (* -1 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1 (/ 1 (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 x 2)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt x>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>

Calls

24 calls:

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

rewrite253.0ms (3.8%)

Memory

-13.8MiB live, 542.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 682×	`accelerator-lowering-fma.f32`
3 682×	`accelerator-lowering-fma.f64`
2 148×	`-lowering-.f32`
2 148×	`-lowering-.f64`
1 604×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	69	39
2	507	39
3	4793	36
0	9635	33

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 780

Calls

Call 1

Inputs
(/ x (+ (* x x) 1))
(+ (* x x) 1)
(/ 1 x)
(+ (* (* x x) (neg x)) x)
(* x x)
(neg x)
(/ 1 (/ (+ (* x x) 1) x))
(/ (+ (* x x) 1) x)

Outputs
(+.f64 #s(literal 0 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) #s(literal 0 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(+.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(+.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (.f64 x (.f64 x (*.f64 x x)))))
(+.f64 (.f64 (/.f64 x (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (.f64 x x)) (.f64 (/.f64 x (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64)))))
(+.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64)))))
(+.f64 (.f64 (.f64 x x) (/.f64 x (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)))) (.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)))))
(exp.f64 (neg.f64 (log.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 (neg.f64 (log.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1 binary64) (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64) (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (log.f64 x) (.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64) (.f64 (log.f64 x) #s(literal 1 binary64))))
(exp.f64 (fma.f64 (log1p.f64 (.f64 x x)) #s(literal -1 binary64) (.f64 (neg.f64 (log.f64 x)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log1p.f64 (*.f64 x x)) #s(literal -1 binary64) (log.f64 x)))
(exp.f64 (fma.f64 (log.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64) (*.f64 (log.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(fma.f64 (.f64 x x) (/.f64 x (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)))))
(fma.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) #s(literal 0 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(fma.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)) (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (.f64 x (.f64 x (.f64 x x)))))
(fma.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (.f64 x (.f64 x (.f64 x x))) (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(fma.f64 (/.f64 x (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (.f64 x x) (.f64 (/.f64 x (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(/.f64 x (fma.f64 x x #s(literal -1 binary64)))
(/.f64 x (*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 x (*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (.f64 x x) (fma.f64 x (.f64 x x) x))
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x x) x) (.f64 x x)))
(/.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(/.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x (.f64 x x) x)))
(/.f64 (.f64 x (.f64 x x)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)))
(/.f64 (fma.f64 x (.f64 x x) x) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64))))
(/.f64 (/.f64 x (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x (.f64 x x) x)) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64)))
(/.f64 (.f64 x (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64))))) (.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))))))))
(/.f64 (.f64 x (.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)) (neg.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))) (.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) (neg.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)))))
(/.f64 (.f64 x (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64))))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))) (+.f64 #s(literal 0 binary64) (fma.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (*.f64 #s(literal 0 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 x (.f64 x x))) (.f64 x x))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 x x)) x)
(/.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64))))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (.f64 (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))) (.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)) (neg.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))) (neg.f64 (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64))))
(/.f64 (.f64 (/.f64 x (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 x (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)))
(/.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))) (.f64 x x))
(/.f64 (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))) x)
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(pow.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(pow.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 (fma.f64 x (.f64 x x) x) (.f64 x x)) #s(literal -1 binary64))
(pow.f64 (*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1/2 binary64))
(*.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 x (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)))
(*.f64 x (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)))
(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)))
(.f64 x (/.f64 x (fma.f64 x (.f64 x x) x)))
(.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) x)))
(*.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))
(*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 x x #s(literal 1 binary64))))
(.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)) (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
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(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) x)
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(/.f64 (sqrt.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) x)
(/.f64 (.f64 #s(literal -1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) x)) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) x)) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (neg.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))))) (sqrt.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))) (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (/.f64 x (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))) (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (/.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))
(pow.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) #s(literal -2 binary64))
(pow.f64 (*.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (.f64 x (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (.f64 x x) x) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)) (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64)) x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x (/.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (/.f64 x (fma.f64 x x #s(literal 1 binary64)))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x x) x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(*.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 #s(literal -1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))) x))
(.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64)))))
(.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) (/.f64 #s(literal -1 binary64) (.f64 x (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64)))))
(.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) x)))
(.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) x))
(.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64)))))
(.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) x)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) x) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) x) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) #s(literal 1 binary64)))
(.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))) x))
(.f64 (/.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) x))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))) x))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))
(.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))))
(.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))
(.f64 (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (sqrt.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x))))
(.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))))
(.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x (.f64 x x))) (.f64 x x))
(.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) x)
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x (.f64 x x))) (.f64 x x))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)) x)
(.f64 (/.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) x) (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (.f64 x (.f64 x x)) #s(literal 1 binary64))))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))
(.f64 (/.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal 1 binary64)) x) (.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64)) (neg.f64 (fma.f64 x (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))))) (neg.f64 (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (+.f64 x (/.f64 #s(literal 1 binary64) x))) (fma.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) (fma.f64 x (fma.f64 x (*.f64 x x) x) #s(literal 1 binary64)))

simplify412.0ms (6.2%)

Memory

2.8MiB live, 571.7MiB allocated

Algorithm

1×	egg-herbie

Rules

15 262×	`accelerator-lowering-fma.f32`
15 262×	`accelerator-lowering-fma.f64`
3 538×	`-lowering-.f32`
3 538×	`-lowering-.f64`
1 794×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	573
1	156	539
2	370	526
3	1200	500
4	4475	500
0	8316	475

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* -1 (pow x 2))))
(* -1 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* (pow x 3) (- (/ 1 (pow x 2)) 1))
(* -1 (pow x 3))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1 (/ 1 (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 x 2)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/ 1 x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))

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

eval111.0ms (1.7%)

Memory: 36.8MiB live, 299.2MiB allocated
Compiler: Compiled 19 052 to 1 649 computations (91.3% saved)

prune173.0ms (2.6%)

Memory

3.1MiB live, 271.7MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	985	2	987
Fresh	1	0	1
Picked	1	4	5
Done	0	0	0
Total	987	6	993

Accuracy

100.0%

Counts

993 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.7%	(fma.f64 (*.f64 x x) (neg.f64 x) x)
▶	45.0%	(/.f64 (.f64 x x) (fma.f64 x (.f64 x x) x))
✓	78.5%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	99.8%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))
✓	48.7%	(/.f64 #s(literal 1 binary64) x)
✓	53.6%	x

Compiler

Compiled 40 to 21 computations (47.5% saved)

simplify526.0ms (8%)

Memory

5.4MiB live, 496.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x (*.f64 x x) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	640	(/.f64 (.f64 x x) (fma.f64 x (.f64 x x) x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(+.f64 (/.f64 #s(literal 1 binary64) x) x)
✓	cost-diff	512	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))

Rules

8 448×	`-lowering-.f32`
8 448×	`-lowering-.f64`
4 206×	`accelerator-lowering-fma.f32`
4 206×	`accelerator-lowering-fma.f64`
3 950×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	18	33
2	21	33
3	29	33
4	46	33
5	46	33
6	122	33
7	413	33
8	1219	33
9	1605	33
10	2143	33
11	2989	33
12	3987	33
13	4386	33
14	4583	33
15	4735	33
16	4890	33
17	5049	33
18	6279	33
19	6869	33
20	7103	33
21	7251	33
22	7395	33
23	7537	33
24	7605	33
25	7639	33
26	7657	33
27	7836	33
28	7872	33
0	8749	31

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize29.0ms (0.4%)

Memory

1.5MiB live, 81.0MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(fma.f64 x (*.f64 x x) x)
✓	accuracy	45.4%	(/.f64 (.f64 x x) (fma.f64 x (.f64 x x) x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal 1 binary64) x) x)
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))

Samples

19.0ms

256×

valid

Compiler

Compiled 39 to 11 computations (71.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-div: 6.0ms (50.7% of total)

ival-mult: 3.0ms (25.4% of total)

ival-add: 2.0ms (16.9% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

-33.0MiB live, 5.5MiB allocated

Counts

6 → 72

Calls

Call 1

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

Outputs
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt (/ (+ 1 (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt x>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (* x (+ 1 (/ 1 (pow x 2))))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt x>
#<alt (* x (+ 1 (* -1 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)>
#<alt (/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) 1) x))>
#<alt (* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))>
#<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 x>
#<alt (* x (+ 1 (pow x 2)))>
#<alt (* x (+ 1 (pow x 2)))>
#<alt (* x (+ 1 (pow x 2)))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1 (/ 1 (pow x 2))))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1 (/ 1 (pow x 2))))>

Calls

18 calls:

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

rewrite292.0ms (4.4%)

Memory

22.5MiB live, 453.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 208×	`accelerator-lowering-fma.f32`
4 208×	`accelerator-lowering-fma.f64`
2 654×	`-lowering-.f32`
2 654×	`-lowering-.f64`
2 322×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	61	30
2	458	30
0	4640	28

Stop Event

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

Counts

6 → 591

Calls

Call 1

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

Outputs
(+.f64 (.f64 (/.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (/.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x)))) (.f64 x (-.f64 x (.f64 x (.f64 x x))))))
(+.f64 (.f64 (/.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x)))) (.f64 x (-.f64 x (.f64 x (.f64 x x))))) (.f64 (/.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))
(+.f64 (.f64 (/.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (.f64 x (fma.f64 x x #s(literal -1 binary64)))) (.f64 x (.f64 x x))) (.f64 (/.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (.f64 x (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 x)))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) (fma.f64 x x #s(literal -1 binary64))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (fma.f64 x x #s(literal -1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (neg.f64 x) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (neg.f64 x) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (neg.f64 x)))
(+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x))))) (.f64 (.f64 x (-.f64 x (.f64 x (.f64 x x)))) (/.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x))))))
(+.f64 (.f64 (.f64 x (-.f64 x (.f64 x (.f64 x x)))) (/.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (/.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x))))))
(+.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (.f64 x (fma.f64 x x #s(literal -1 binary64))))) (.f64 (neg.f64 x) (/.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (.f64 x (fma.f64 x x #s(literal -1 binary64))))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(+.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (neg.f64 x) (/.f64 #s(literal 1 binary64) (.f64 x x))))) (.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (fma.f64 x (neg.f64 x) (/.f64 #s(literal 1 binary64) (.f64 x x))))))
(exp.f64 (*.f64 #s(literal -1 binary64) (log.f64 (+.f64 x (/.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64)))))
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(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (neg.f64 x))) (neg.f64 (/.f64 x (fma.f64 x x #s(literal 1 binary64)))))
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(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (fma.f64 x (neg.f64 x) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (fma.f64 x (neg.f64 x) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
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(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))
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(/.f64 (neg.f64 (.f64 x (-.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))))) (neg.f64 (-.f64 x (.f64 x (*.f64 x x)))))
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(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x x #s(literal -1 binary64)))) (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (fma.f64 x x #s(literal -1 binary64))))) (.f64 (/.f64 (.f64 x x) (.f64 x (fma.f64 x x #s(literal -1 binary64)))) (/.f64 (.f64 x x) (.f64 x (fma.f64 x x #s(literal -1 binary64)))))) (fma.f64 (.f64 x x) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (fma.f64 x x #s(literal -1 binary64)))) (/.f64 (.f64 x x) (*.f64 x (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 (.f64 (fma.f64 x (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (pow.f64 x #s(literal 27 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x x #s(literal -1 binary64))))))) (fma.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (*.f64 x x))))))))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x x #s(literal -1 binary64))))))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (*.f64 x x))))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x x #s(literal -1 binary64))))) (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (.f64 x (.f64 x x))) x)))))
(/.f64 (.f64 (.f64 (.f64 x (fma.f64 x (.f64 x (.f64 x (.f64 x x))) x)) (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x x #s(literal -1 binary64))))) (.f64 x (fma.f64 x (.f64 x (.f64 x (*.f64 x x))) x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x x) x)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) x))
(*.f64 x (fma.f64 x x #s(literal 1 binary64)))
(.f64 (fma.f64 x (.f64 x x) x) #s(literal 1 binary64))
(.f64 (fma.f64 x (.f64 x x) x) (/.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (.f64 x (fma.f64 x x #s(literal -1 binary64)))))
(.f64 (fma.f64 x (.f64 x x) x) (.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 x x #s(literal -1 binary64))))))
(.f64 #s(literal -1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (neg.f64 x)))
(.f64 (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x x #s(literal -1 binary64)))))))
(.f64 (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x x #s(literal -1 binary64)))))) #s(literal 1 binary64)))
(.f64 (fma.f64 x x (.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x x #s(literal -1 binary64))))) (/.f64 (fma.f64 x (.f64 x x) x) (fma.f64 x x (.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x x #s(literal -1 binary64)))))))
(.f64 (fma.f64 x x (.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x x #s(literal -1 binary64))))) (.f64 (fma.f64 x (.f64 x x) x) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (.f64 x (.f64 x x)) (*.f64 x (fma.f64 x x #s(literal -1 binary64))))))))
(.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x x #s(literal -1 binary64)))))
(.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x x #s(literal -1 binary64)))) #s(literal 1 binary64)))
(.f64 (neg.f64 (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x x #s(literal -1 binary64))))))))
(.f64 (neg.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (neg.f64 x)) x)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) x)
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x x #s(literal -1 binary64)))))) (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x x #s(literal -1 binary64)))) (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))))
(.f64 (.f64 x (-.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 x (.f64 x x)))))
(.f64 (/.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64)))) (fma.f64 x (.f64 x x) x))
(.f64 (/.f64 (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x))) (fma.f64 (.f64 x (-.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 (-.f64 x (.f64 x (.f64 x x))) (-.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 x (-.f64 x (.f64 x (.f64 x x)))) (-.f64 (.f64 x (-.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x)))))))))
(.f64 (/.f64 (.f64 (fma.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 x (.f64 x x))) (.f64 (fma.f64 x x (.f64 (.f64 x (.f64 x x)) (.f64 x (fma.f64 x x #s(literal -1 binary64))))) (.f64 x (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (-.f64 x (.f64 x (.f64 x x))))))) (.f64 x (-.f64 (.f64 x (.f64 x (.f64 x (.f64 x x)))) (-.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -1 binary64))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))) (fma.f64 x (fma.f64 x (.f64 x x) x) (.f64 x (.f64 x (.f64 x (.f64 x (*.f64 x x)))))))

simplify649.0ms (9.8%)

Memory

27.5MiB live, 782.4MiB allocated

Algorithm

1×	egg-herbie

Rules

19 126×	`accelerator-lowering-fma.f32`
19 126×	`accelerator-lowering-fma.f64`
2 904×	`-lowering-.f32`
2 904×	`-lowering-.f64`
2 168×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	486
1	148	452
2	340	448
3	951	422
4	4379	422
5	7576	422
0	8340	406

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/ 1 x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
(/ (+ 1 (pow x 2)) x)
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
x
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(* x (+ 1 (/ 1 (pow x 2))))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/ 1 x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(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)
x
(* x (+ 1 (pow x 2)))
(* x (+ 1 (pow x 2)))
(* x (+ 1 (pow x 2)))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1 (/ 1 (pow x 2))))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1 (/ 1 (pow x 2))))
(* (pow x 3) (+ 1 (/ 1 (pow x 2))))

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

eval74.0ms (1.1%)

Memory: 1.6MiB live, 151.2MiB allocated
Compiler: Compiled 18 317 to 1 265 computations (93.1% saved)

prune62.0ms (0.9%)

Memory

-52.4MiB live, 136.5MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	692	0	692
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	692	6	698

Accuracy

100.0%

Counts

698 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.7%	(fma.f64 (*.f64 x x) (neg.f64 x) x)
✓	45.0%	(/.f64 (.f64 x x) (fma.f64 x (.f64 x x) x))
✓	78.5%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	99.8%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))
✓	48.7%	(/.f64 #s(literal 1 binary64) x)
✓	53.6%	x

Compiler

Compiled 105 to 42 computations (60% saved)

regimes7.0ms (0.1%)

Memory

14.7MiB live, 14.7MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	x
3.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes5.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
x
(/.f64 #s(literal 1 binary64) x)
(fma.f64 (*.f64 x x) (neg.f64 x) x)
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Outputs
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) x)

Calls

2 calls:

2.0ms	x
2.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
100.0%	2	`x`
99.9%	2	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes5.0ms (0.1%)

Memory

-32.5MiB live, 9.1MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs
x
(/.f64 #s(literal 1 binary64) x)
(fma.f64 (*.f64 x x) (neg.f64 x) x)

Outputs
(fma.f64 (*.f64 x x) (neg.f64 x) x)
(/.f64 #s(literal 1 binary64) x)

Calls

2 calls:

3.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
2.0ms	x

Results

Accuracy	Segments	Branch
81.8%	4	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
98.8%	2	`x`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes2.0ms (0%)

Memory

4.3MiB live, 4.3MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
98.5%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

7.2MiB live, 7.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

2 calls:

1.0ms	x
1.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
53.6%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
53.6%	1	`x`

Compiler

Compiled 10 to 6 computations (40% saved)

bsearch10.0ms (0.1%)

Memory

21.4MiB live, 21.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
9.0ms	622.9669813358317	55796284622.38148

Samples

5.0ms

128×

valid

Compiler

Compiled 115 to 81 computations (29.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-div: 1.0ms (40.3% of total)

ival-add: 1.0ms (40.3% of total)

ival-mult: 1.0ms (40.3% of total)

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

exact: 0.0ms (0% of total)

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

bsearch11.0ms (0.2%)

Memory

-19.8MiB live, 18.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.3895916939530971	622.9669813358317

Samples

5.0ms

128×

valid

Compiler

Compiled 123 to 81 computations (34.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-div: 1.0ms (40.3% of total)

ival-add: 1.0ms (40.3% of total)

ival-mult: 1.0ms (40.3% of total)

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

exact: 0.0ms (0% of total)

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

bsearch9.0ms (0.1%)

Memory

18.7MiB live, 18.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	0.3895916939530971	622.9669813358317

Samples

5.0ms

128×

valid

Compiler

Compiled 75 to 57 computations (24% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-div: 1.0ms (40.3% of total)

ival-add: 1.0ms (40.3% of total)

ival-mult: 1.0ms (40.3% of total)

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

exact: 0.0ms (0% of total)

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

simplify9.0ms (0.1%)

Memory

-21.7MiB live, 16.1MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	43
1	25	43
2	27	43
3	28	43

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))
(if (<=.f64 x #s(literal 100000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal 7656119366529843/9007199254740992 binary64)) (fma.f64 (*.f64 x x) (neg.f64 x) x) (/.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal 1 binary64)) x (/.f64 #s(literal 1 binary64) x))
x

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) x))
(/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 100000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal 7656119366529843/9007199254740992 binary64)) (fma.f64 (*.f64 x x) (neg.f64 x) x) (/.f64 #s(literal 1 binary64) x))
(if (<=.f64 x #s(literal 1 binary64)) x (/.f64 #s(literal 1 binary64) x))
x

soundness1.0s (15.2%)

Memory

20.2MiB live, 416.0MiB allocated

Rules

12 662×	`accelerator-lowering-fma.f32`
12 662×	`accelerator-lowering-fma.f64`
4 942×	`/-lowering-/.f32`
4 942×	`/-lowering-/.f64`
4 762×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	69	39
2	507	39
3	4793	36
0	9635	33
0	45	226
1	131	224
2	312	216
3	888	212
4	2381	210
5	5550	210
6	7627	210
0	8047	197
0	5	15
1	30	15
2	199	15
3	1759	15
0	8554	13

Stop Event

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

Compiler

Compiled 92 to 47 computations (48.9% saved)

preprocess249.0ms (3.8%)

Memory: -5.5MiB live, 187.8MiB allocated
Compiler: Compiled 176 to 88 computations (50% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	10	22
1	28	22
2	64	21
3	130	21
4	234	21
5	332	21
6	345	21
7	347	21
8	351	21
0	5	7
1	8	7
0	8	6

Iter	Nodes	Cost
0	10	22
1	28	22
2	64	21
3	130	21
4	234	21
5	332	21
6	345	21
7	347	21
8	351	21
0	5	7
1	8	7
0	8	6

analyze0.0ms (0%)

sample523.0ms (7.9%)

preprocess19.0ms (0.3%)

explain80.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize19.0ms (0.3%)

series2.0ms (0%)

rewrite521.0ms (7.9%)

simplify778.0ms (11.8%)

eval45.0ms (0.7%)

prune42.0ms (0.6%)

simplify442.0ms (6.7%)

localize229.0ms (3.5%)

series3.0ms (0%)

rewrite253.0ms (3.8%)

simplify412.0ms (6.2%)

eval111.0ms (1.7%)

prune173.0ms (2.6%)

simplify526.0ms (8%)

localize29.0ms (0.4%)

series3.0ms (0%)

rewrite292.0ms (4.4%)

simplify649.0ms (9.8%)

eval74.0ms (1.1%)

prune62.0ms (0.9%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes2.0ms (0%)

regimes3.0ms (0%)

bsearch10.0ms (0.1%)

bsearch11.0ms (0.2%)

bsearch9.0ms (0.1%)

simplify9.0ms (0.1%)

soundness1.0s (15.2%)

preprocess249.0ms (3.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	10	22
1	28	22
2	64	21
3	130	21
4	234	21
5	332	21
6	345	21
7	347	21
8	351	21
0	5	7
1	8	7
0	8	6