Metrics for x / (x^2 + 1)

analyze0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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)

sample522.0ms (10.3%)

Memory

68.0MiB live, 675.1MiB allocated

Samples

326.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 180.0ms

ival-mult: 65.0ms (36.1% of total)

ival-div: 61.0ms (33.9% of total)

ival-add: 41.0ms (22.8% of total)

ival-true: 5.0ms (2.8% of total)

exact: 5.0ms (2.8% of total)

ival-assert: 3.0ms (1.7% of total)

Bogosity

preprocess74.0ms (1.5%)

Memory

-23.9MiB live, 28.0MiB allocated

Algorithm

1×	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	7	17
1	26	15
2	62	14
3	128	14
4	232	14
5	331	14
6	344	14
7	346	14
8	350	14
0	5	7
0	8	7
1	11	7
0	11	6

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Symmetry

(negabs x)

explain67.0ms (1.3%)

Memory

0.6MiB live, 112.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
58	-	-	`(/.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	58	0
↳	`(*.f64 x x)`	overflow	58
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	58

Confusion

	Predicted +	Predicted -
+	58	0
-	0	198

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	58	0	0
-	0	0	198

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	198
1	58

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

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 (35.6% of total)

ival-div: 3.0ms (26.7% of total)

ival-add: 3.0ms (26.7% 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	78.8%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify4.0ms (0.1%)

Memory

6.7MiB live, 6.7MiB 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×	`lower-+.f32`
2×	`lift-+.f64`
2×	`lift-/.f64`
2×	`lower-fma.f64`
2×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	8	17
1	11	17
0	11	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize20.0ms (0.4%)

Memory

-19.9MiB live, 24.8MiB 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	78.8%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

14.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 5.0ms (56.8% of total)

ival-div: 2.0ms (22.7% of total)

ival-add: 1.0ms (11.4% 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

2.1MiB live, 2.1MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (+.f64 (*.f64 x x) #s(literal 1 binary64))>
#<alt (/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))>
#<alt (*.f64 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))

rewrite534.0ms (10.5%)

Memory

23.2MiB live, 439.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 942×	`lower-/.f32`
4 940×	`lower-/.f64`
4 762×	`lower-fma.f64`
4 762×	`lower-fma.f32`
3 572×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	33	15
2	202	15
3	1766	15
0	8562	13

Stop Event

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

Counts

3 → 327

Calls

Call 1

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

simplify788.0ms (15.5%)

Memory

4.2MiB live, 497.5MiB allocated

Algorithm

1×	egg-herbie

Rules

12 662×	`lower-fma.f64`
12 662×	`lower-fma.f32`
2 988×	`lower-*.f64`
2 988×	`lower-*.f32`
1 640×	`lower-+.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 → 35

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)

eval44.0ms (0.9%)

Memory: -15.6MiB live, 98.0MiB allocated
Compiler: Compiled 12 301 to 1 050 computations (91.5% saved)

prune59.0ms (1.2%)

Memory

-15.4MiB live, 120.3MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	357	5	362
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	358	5	363

Accuracy

100.0%

Counts

363 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.8%	(fma.f64 (*.f64 x x) (neg.f64 x) x)
▶	78.8%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	55.6%	(/.f64 x #s(literal 1 binary64))
▶	47.5%	(/.f64 #s(literal 1 binary64) x)
▶	78.7%	(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)

Compiler

Compiled 64 to 38 computations (40.6% saved)

simplify743.0ms (14.6%)

Memory

33.7MiB live, 842.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))
✓	cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) (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	704	(/.f64 x #s(literal 1 binary64))
✓	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

25 088×	`lower-fma.f32`
25 084×	`lower-fma.f64`
6 300×	`lower-+.f64`
6 300×	`lower-+.f32`
2 504×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	55
0	21	51
1	36	51
2	68	49
3	131	49
4	160	49
5	230	49
6	327	49
7	602	49
8	1030	49
9	1747	49
10	2663	49
11	3479	49
12	4198	49
13	4395	49
14	4455	49
15	4467	49
16	4479	49
17	4487	49
18	4533	49
19	4533	49
0	8047	49

Stop Event

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

Calls

Call 1

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

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

localize50.0ms (1%)

Memory

-0.3MiB live, 114.7MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x x #s(literal 1 binary64))
✓	accuracy	98.9%	(/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64)))
✓	accuracy	80.0%	(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) (neg.f64 x) x)
✓	accuracy	100.0%	(/.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(fma.f64 x x #s(literal 1 binary64))
✓	accuracy	78.8%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))

Samples

34.0ms

256×

valid

Compiler

Compiled 57 to 14 computations (75.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 11.0ms (51.5% of total)

ival-div: 6.0ms (28.1% of total)

ival-add: 2.0ms (9.4% of total)

ival-neg: 1.0ms (4.7% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated

Counts

9 → 108

Calls

Call 1

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

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

Calls

27 calls:

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

rewrite246.0ms (4.8%)

Memory

-9.3MiB live, 478.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 260×	`lower-fma.f32`
4 256×	`lower-fma.f64`
2 074×	`lower-*.f32`
2 070×	`lower-*.f64`
1 480×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	42
0	21	37
1	80	35
2	566	35
3	5183	35
0	9839	35

Stop Event

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

Counts

9 → 744

Calls

Call 1

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

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

simplify571.0ms (11.2%)

Memory

12.0MiB live, 613.0MiB allocated

Algorithm

1×	egg-herbie

Rules

15 548×	`lower-fma.f64`
15 548×	`lower-fma.f32`
3 754×	`lower-*.f64`
3 754×	`lower-*.f32`
2 140×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	665
1	158	628
2	384	612
3	1262	600
4	4881	600
0	8466	564

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 93

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

eval156.0ms (3.1%)

Memory: 24.6MiB live, 280.5MiB allocated
Compiler: Compiled 17 375 to 1 512 computations (91.3% saved)

prune313.0ms (6.2%)

Memory

-3.6MiB live, 213.3MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	958	1	959
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	959	5	964

Accuracy

100.0%

Counts

964 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.8%	(fma.f64 (*.f64 x x) (neg.f64 x) x)
✓	78.8%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	47.5%	(/.f64 #s(literal 1 binary64) x)
✓	78.7%	(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
▶	55.6%	x

Compiler

Compiled 30 to 17 computations (43.3% saved)

simplify3.0ms (0.1%)

Memory

2.7MiB live, 2.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1
0	1	1

Stop Event

1×	saturated
1×	saturated
1×	saturated

Calls

Call 1

Inputs
x

Outputs
x

localize17.0ms (0.3%)

Memory

-30.9MiB live, 8.8MiB allocated

Samples

15.0ms

256×

valid

Compiler

Compiled 3 to 3 computations (0% saved)

Precisions

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

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

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

series0.0ms (0%)

Memory

0.0MiB live, 0.0MiB allocated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite7.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify2.0ms (0%)

Memory

2.8MiB live, 2.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune3.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	4	4
Total	5	5

Accuracy

100.0%

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.8%	(fma.f64 (*.f64 x x) (neg.f64 x) x)
✓	78.8%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	47.5%	(/.f64 #s(literal 1 binary64) x)
✓	78.7%	(*.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) x)
✓	55.6%	x

Compiler

Compiled 66 to 30 computations (54.5% saved)

regimes6.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	x
3.0ms	(/.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)

regimes4.0ms (0.1%)

Memory

7.1MiB live, 7.1MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
77.7%	2	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
99.6%	2	`x`

Compiler

Compiled 10 to 6 computations (40% saved)

regimes11.0ms (0.2%)

Memory

-30.7MiB live, 6.8MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.1%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB 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
55.6%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
55.6%	1	`x`

Compiler

Compiled 10 to 6 computations (40% saved)

bsearch5.0ms (0.1%)

Memory

12.9MiB live, 12.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
5.0ms	659085.4687709162	2387208926.1006274

Samples

3.0ms

64×

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

Precisions

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

ival-mult: 1.0ms (75.1% of total)

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

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

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

exact: 0.0ms (0% of total)

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

bsearch13.0ms (0.2%)

Memory

-8.5MiB live, 29.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.0002100055121570376	20000.38020972167

Samples

7.0ms

144×

valid

Compiler

Compiled 137 to 90 computations (34.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-div: 1.0ms (33.8% of total)

ival-add: 1.0ms (33.8% of total)

ival-mult: 1.0ms (33.8% of total)

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

exact: 0.0ms (0% of total)

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

bsearch4.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
4.0ms	0.0002100055121570376	20000.38020972167

Samples

2.0ms

48×

valid

Compiler

Compiled 83 to 63 computations (24.1% saved)

Precisions

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

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

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

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

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

exact: 0.0ms (0% of total)

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

simplify6.0ms (0.1%)

Memory

13.6MiB live, 13.6MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-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	16	36
1	22	36
2	24	36
3	25	36

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 200000000 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
(if (<=.f64 x #s(literal 200000000 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

soundness667.0ms (13.1%)

Memory

-8.2MiB live, 452.2MiB allocated

Rules

12 662×	`lower-fma.f64`
12 662×	`lower-fma.f32`
4 942×	`lower-/.f32`
4 940×	`lower-/.f64`
4 762×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
0	21	37
1	80	35
2	566	35
3	5183	35
0	9839	35
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
0	8	15
1	33	15
2	202	15
3	1766	15
0	8562	13

Stop Event

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

Compiler

Compiled 76 to 41 computations (46.1% saved)

preprocess137.0ms (2.7%)

Memory: 12.6MiB live, 242.7MiB allocated
Compiler: Compiled 134 to 68 computations (49.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	7	17
1	26	15
2	62	14
3	128	14
4	232	14
5	331	14
6	344	14
7	346	14
8	350	14
0	5	7
0	8	7
1	11	7
0	11	6

Iter	Nodes	Cost
0	7	17
1	26	15
2	62	14
3	128	14
4	232	14
5	331	14
6	344	14
7	346	14
8	350	14
0	5	7
0	8	7
1	11	7
0	11	6

analyze0.0ms (0%)

sample522.0ms (10.3%)

preprocess74.0ms (1.5%)

explain67.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize20.0ms (0.4%)

series2.0ms (0%)

rewrite534.0ms (10.5%)

simplify788.0ms (15.5%)

eval44.0ms (0.9%)

prune59.0ms (1.2%)

simplify743.0ms (14.6%)

localize50.0ms (1%)

series3.0ms (0.1%)

rewrite246.0ms (4.8%)

simplify571.0ms (11.2%)

eval156.0ms (3.1%)

prune313.0ms (6.2%)

simplify3.0ms (0.1%)

localize17.0ms (0.3%)

series0.0ms (0%)

rewrite7.0ms (0.1%)

simplify2.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

regimes11.0ms (0.2%)

regimes3.0ms (0.1%)

bsearch5.0ms (0.1%)

bsearch13.0ms (0.2%)

bsearch4.0ms (0.1%)

simplify6.0ms (0.1%)

soundness667.0ms (13.1%)

preprocess137.0ms (2.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	17
1	26	15
2	62	14
3	128	14
4	232	14
5	331	14
6	344	14
7	346	14
8	350	14
0	5	7
0	8	7
1	11	7
0	11	6