Metrics for Main:bigenough3 from C

analyze1.0ms (0%)

Memory

2.7MiB live, 2.7MiB 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
50%	50%	50%	0%	0%	0%	0%	2
66.7%	50%	25%	0%	0%	25%	0%	3
80%	50%	12.5%	0%	0%	37.5%	0%	4
88.9%	50%	6.2%	0%	0%	43.7%	0%	5
94.1%	50%	3.1%	0%	0%	46.9%	0%	6
97%	50%	1.6%	0%	0%	48.4%	0%	7
98.5%	50%	0.8%	0%	0%	49.2%	0%	8
99.2%	50%	0.4%	0%	0%	49.6%	0%	9
99.6%	50%	0.2%	0%	0%	49.8%	0%	10
99.8%	50%	0.1%	0%	0%	49.9%	0%	11
99.9%	50%	0%	0%	0%	49.9%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.0s (10.8%)

Memory

45.3MiB live, 1 257.6MiB allocated

Samples

496.0ms	3 951×	1	valid
266.0ms	4 305×	0	valid
0.0ms	8×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 589.0ms

ival-sqrt: 344.0ms (58.4% of total)

adjust: 106.0ms (18% of total)

ival-add: 67.0ms (11.4% of total)

ival-sub: 61.0ms (10.3% of total)

ival-true: 5.0ms (0.8% of total)

exact: 4.0ms (0.7% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

preprocess22.0ms (0.2%)

Memory

1.2MiB live, 38.6MiB allocated

Algorithm

1×	egg-herbie

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
46×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

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

explain105.0ms (1.1%)

Memory

-41.2MiB live, 143.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
142	-	-	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
0	-	-	`(+.f64 x #s(literal 1 binary64))`
0	-	-	`(sqrt.f64 x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`	cancellation	142	0

Confusion

	Predicted +	Predicted -
+	142	0
-	0	114

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	142	0	0
-	0	0	114

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	114
1	142

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

47.0ms	280×	1	valid
12.0ms	232×	0	valid

Compiler

Compiled 56 to 28 computations (50% saved)

Precisions

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

ival-sqrt: 11.0ms (44.1% of total)

adjust: 6.0ms (24.1% of total)

ival-add: 4.0ms (16% of total)

ival-sub: 4.0ms (16% of total)

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

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

exact: 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

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify12.0ms (0.1%)

Memory

-19.8MiB live, 20.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Rules

80×	`lower-fma.f64`
80×	`lower-fma.f32`
48×	`lower-*.f64`
48×	`lower-*.f32`
36×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(sqrt.f64 x)

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

localize28.0ms (0.3%)

Memory

16.1MiB live, 54.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	47.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

13.0ms	140×	1	valid
7.0ms	116×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-sqrt: 5.0ms (39.3% of total)

ival-add: 3.0ms (23.6% of total)

adjust: 2.0ms (15.7% of total)

ival-sub: 2.0ms (15.7% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0%)

Memory

8.6MiB live, 8.6MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))>
#<alt (sqrt.f64 (+.f64 x #s(literal 1 binary64)))>
#<alt (+.f64 x #s(literal 1 binary64))>
#<alt (sqrt.f64 x)>

Outputs
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>

Calls

12 calls:

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

rewrite546.0ms (5.8%)

Memory

-38.3MiB live, 585.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 090×	`lower-fma.f64`
5 090×	`lower-fma.f32`
3 260×	`lower-*.f64`
3 260×	`lower-*.f32`
2 676×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	43	16
2	290	16
3	3385	16
0	8686	16

Stop Event

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

Counts

4 → 357

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
(sqrt.f64 x)

Outputs
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x)))
(+.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(+.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))) (neg.f64 (/.f64 (.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(+.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) #s(literal -1 binary64)))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))) (/.f64 (.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))))
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))))
(-.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 0 binary64)) (sqrt.f64 x))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
(fma.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))) (neg.f64 (/.f64 (*.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))) (neg.f64 (/.f64 (*.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (/.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 x) #s(literal -1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
(fma.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))) (neg.f64 (/.f64 (.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 x)))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (sqrt.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x)))))) (neg.f64 (/.f64 (*.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))) (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 x)))
(fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (*.f64 #s(literal -1 binary64) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(fma.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (fma.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (+.f64 x (sqrt.f64 (fma.f64 x x x)))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))))) (fma.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (-.f64 (+.f64 x (sqrt.f64 (fma.f64 x x x))) (+.f64 x #s(literal 1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))) (neg.f64 (/.f64 (.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(fma.f64 (/.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (.f64 (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) (+.f64 x (-.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))) (+.f64 x (-.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))) (neg.f64 (/.f64 (*.f64 x (sqrt.f64 x)) (+.f64 x (+.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (fma.f64 x x x))))))))
(fma.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) (neg.f64 (/.f64 x (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))))
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(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))
(*.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(*.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (+.f64 x #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))))
(.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(*.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64))) (+.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x (.f64 x x) #s(literal -1 binary64))) (+.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 x (.f64 (.f64 x (.f64 x x)) (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (fma.f64 x (.f64 x (.f64 x x)) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x x)))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (*.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))) (+.f64 (fma.f64 x x #s(literal -1 binary64)) x))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))
(.f64 (exp.f64 (log1p.f64 (.f64 x (.f64 x x)))) (exp.f64 (neg.f64 (log1p.f64 (-.f64 (.f64 x x) x)))))
(*.f64 (exp.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64)))) (exp.f64 (neg.f64 (log.f64 (+.f64 x #s(literal -1 binary64))))))
(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (sqrt.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))))
(.f64 (sqrt.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))))
(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))))
(.f64 (sqrt.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(fabs.f64 (sqrt.f64 x))
(sqrt.f64 x)
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 (sqrt.f64 x)) #s(literal 1 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/8 binary64))
(pow.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 x)))))
(*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 x))) (sqrt.f64 (neg.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x)))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
(.f64 (sqrt.f64 (.f64 (neg.f64 (sqrt.f64 x)) #s(literal -1 binary64))) (sqrt.f64 (sqrt.f64 x)))

simplify478.0ms (5%)

Memory

21.4MiB live, 566.5MiB allocated

Algorithm

1×	egg-herbie

Rules

17 328×	`lower-fma.f64`
17 328×	`lower-fma.f32`
3 884×	`lower-*.f64`
3 884×	`lower-*.f32`
2 664×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	498
1	299	446
2	802	442
3	2251	434
4	4609	434
0	8184	398

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 46

Calls

Call 1

Inputs
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -5/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal 5/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
1
#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)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)

eval57.0ms (0.6%)

Memory: -5.6MiB live, 111.7MiB allocated
Compiler: Compiled 8 780 to 1 381 computations (84.3% saved)

prune59.0ms (0.6%)

Memory

17.2MiB live, 141.9MiB allocated

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	393	10	403
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	393	11	404

Accuracy

100.0%

Counts

404 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	45.1%	(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	46.8%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	55.5%	(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	48.1%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
	48.1%	(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
	46.8%	(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
✓	47.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	3.5%	(-.f64 (sqrt.f64 x) (sqrt.f64 x))
▶	44.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	46.8%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))
▶	58.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 270 to 166 computations (38.5% saved)

simplify203.0ms (2.1%)

Memory

7.9MiB live, 123.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	cost-diff	(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
✓	cost-diff	(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Rules

2 104×	`lower-fma.f32`
2 096×	`lower-fma.f64`
808×	`lower-*.f32`
804×	`lower-*.f64`
712×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	103
0	30	103
1	53	103
2	82	103
3	149	103
4	289	103
5	581	103
6	1097	103
7	1495	103
8	1653	103
9	1774	103
10	1854	103
11	2309	103
12	2965	103
13	3301	103
14	3372	103
15	3403	103
16	3408	103
17	3410	103
0	3410	103

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
x
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
x
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
x
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
#s(literal -1/8 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(sqrt.f64 x)
#s(literal 1/2 binary64)

Outputs
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
x
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
x
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
x
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
#s(literal -1/8 binary64)
#s(literal 1/2 binary64)
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
#s(literal 1 binary64)
(sqrt.f64 x)
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(literal -1/8 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(literal 1/2 binary64)

localize80.0ms (0.8%)

Memory

-12.6MiB live, 144.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.6%	(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	accuracy	100.0%	(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Samples

42.0ms

256×

valid

Compiler

Compiled 111 to 21 computations (81.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 11.0ms (39.4% of total)

ival-sqrt: 7.0ms (25.1% of total)

ival-div: 4.0ms (14.3% of total)

ival-add: 4.0ms (14.3% of total)

ival-sub: 1.0ms (3.6% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.1%)

Memory

15.5MiB live, 15.5MiB allocated

Counts

10 → 120

Calls

Call 1

Inputs
#<alt (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))>
#<alt (sqrt.f64 (/.f64 #s(literal 1 binary64) x))>
#<alt (/.f64 #s(literal 1 binary64) x)>
#<alt (-.f64 #s(literal 1 binary64) (sqrt.f64 x))>
#<alt (sqrt.f64 x)>
#<alt (fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))>
#<alt (fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))>
#<alt (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))>
#<alt (/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)>
#<alt (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))>

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

Calls

30 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
1.0ms	x	@	-inf	(* 1/2 (sqrt (/ 1 x)))
0.0ms	x	@	0	(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)
0.0ms	x	@	-inf	(+ (* x (+ (* x -1/8) 1/2)) (- 1 (sqrt x)))
0.0ms	x	@	inf	(/ (+ (* -1/8 (sqrt (/ 1 x))) (* (sqrt x) 1/2)) x)

rewrite445.0ms (4.7%)

Memory

23.5MiB live, 655.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

11 848×	`lower-fma.f32`
11 840×	`lower-fma.f64`
4 858×	`lower-*.f32`
4 854×	`lower-*.f64`
3 472×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	62
0	30	62
1	131	57
2	1007	57
0	8937	55

Stop Event

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

Counts

10 → 565

Calls

Call 1

Inputs
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(sqrt.f64 x)
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))

Outputs
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (sqrt.f64 x)))
(*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64))
(.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
(fabs.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 x)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (neg.f64 x))))
(pow.f64 x #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 x))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) x)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 x))))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 1/2 binary64)))
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(+.f64 (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(+.f64 (neg.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))
(-.f64 #s(literal 0 binary64) (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (*.f64 x #s(literal 1/4 binary64)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))) (/.f64 (/.f64 #s(literal 1/64 binary64) x) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))))
(fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/8 binary64) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(fma.f64 (sqrt.f64 x) #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(fma.f64 (/.f64 #s(literal 1/64 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))
(neg.f64 (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/16 binary64) (sqrt.f64 x)))) (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (-.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/64 binary64) x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (fma.f64 x #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/64 binary64) x))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/16 binary64) (sqrt.f64 x)))))
(/.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (neg.f64 (neg.f64 (fma.f64 x #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/64 binary64) x))))))
(/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64))) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))
(/.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64))) (neg.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (neg.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x))))) (neg.f64 (fma.f64 x #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/64 binary64) x)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x))))) (neg.f64 (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/16 binary64) (sqrt.f64 x))))))
(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64)))) (+.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (neg.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/64 binary64) x)) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (.f64 x #s(literal 1/4 binary64)))) (.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))))) (fma.f64 x #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/64 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))))) (neg.f64 (neg.f64 (fma.f64 x #s(literal 1/4 binary64) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/64 binary64) x))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64))))) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64))))) (neg.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (neg.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/64 binary64) x))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (/.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (fma.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))))))
(/.f64 (-.f64 (.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (/.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))) (.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))))) (+.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (fma.f64 (sqrt.f64 x) #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/64 binary64) x)))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/16 binary64) (sqrt.f64 x))))))
(.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (sqrt.f64 x)) (/.f64 #s(literal -1/512 binary64) (.f64 x (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x #s(literal 1/4 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/64 binary64) x))))))
(.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) x) (.f64 x #s(literal -1/4 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)) (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))))
(.f64 (-.f64 (.f64 x #s(literal 1/4 binary64)) (/.f64 #s(literal 1/64 binary64) x)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 x)))))

simplify324.0ms (3.4%)

Memory

-63.6MiB live, 413.7MiB allocated

Algorithm

1×	egg-herbie

Rules

8 602×	`lower-fma.f64`
8 602×	`lower-fma.f32`
3 052×	`lower-*.f64`
3 052×	`lower-*.f32`
1 754×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	86	1009
1	224	892
2	577	880
3	1438	858
4	2806	858
5	5157	858
0	8154	807

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 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)
(- 1 (sqrt x))
(- 1 (sqrt x))
(- 1 (sqrt x))
(- 1 (sqrt x))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
1/2
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(* -1/8 x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* -1/8 x)
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))

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

eval128.0ms (1.3%)

Memory: 20.6MiB live, 294.5MiB allocated
Compiler: Compiled 19 471 to 1 782 computations (90.8% saved)

prune155.0ms (1.6%)

Memory

0.7MiB live, 277.6MiB allocated

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	949	7	956
Fresh	2	3	5
Picked	2	3	5
Done	0	1	1
Total	953	14	967

Accuracy

100.0%

Counts

967 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	46.8%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	3.2%	(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
▶	48.1%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
	48.1%	(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
▶	58.0%	(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
▶	57.9%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	47.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	45.1%	(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))
	46.8%	(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
✓	44.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	46.8%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))
▶	1.8%	(.f64 x (.f64 x #s(literal -1/8 binary64)))
✓	58.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	1.7%	(neg.f64 (sqrt.f64 x))

Compiler

Compiled 270 to 166 computations (38.5% saved)

simplify468.0ms (4.9%)

Memory

-28.2MiB live, 457.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
✓	cost-diff	384	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(neg.f64 (sqrt.f64 x))
✓	cost-diff	0	(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
✓	cost-diff	0	(*.f64 x #s(literal -1/8 binary64))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal -1/8 binary64)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)

Rules

12 706×	`lower-fma.f32`
12 704×	`lower-fma.f64`
2 604×	`lower--.f32`
2 602×	`lower--.f64`
2 036×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	84
0	33	88
1	54	88
2	76	76
3	115	76
4	156	76
5	230	76
6	346	76
7	590	76
8	1002	76
9	1802	76
10	4291	76
11	6510	76
12	7483	76
13	7706	76
14	7877	76
15	7950	76
0	8578	76

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
(.f64 x (.f64 x #s(literal -1/8 binary64)))
x
(*.f64 x #s(literal -1/8 binary64))
#s(literal -1/8 binary64)
(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
x
#s(literal 1/2 binary64)
(neg.f64 (sqrt.f64 x))
(sqrt.f64 x)
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(+.f64 x (-.f64 #s(literal 1 binary64) x))
x
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
(sqrt.f64 x)

Outputs
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(.f64 #s(literal -1/8 binary64) (.f64 x x))
x
(*.f64 x #s(literal -1/8 binary64))
#s(literal -1/8 binary64)
(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
(-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
x
#s(literal 1/2 binary64)
(neg.f64 (sqrt.f64 x))
(sqrt.f64 x)
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
#s(literal 1/2 binary64)
(sqrt.f64 x)
x
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(+.f64 x (-.f64 #s(literal 1 binary64) x))
#s(literal 1 binary64)
x
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
(sqrt.f64 x)

localize113.0ms (1.2%)

Memory

19.6MiB live, 135.6MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	accuracy	99.7%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
✓	accuracy	47.8%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(neg.f64 (sqrt.f64 x))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal -1/8 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/8 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)

Samples

43.0ms	128×	1	valid
17.0ms	128×	0	valid

Compiler

Compiled 87 to 21 computations (75.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 6.0ms (21.7% of total)

ival-div: 5.0ms (18.1% of total)

ival-add: 5.0ms (18.1% of total)

adjust: 4.0ms (14.4% of total)

ival-sqrt: 4.0ms (14.4% of total)

ival-sub: 2.0ms (7.2% of total)

ival-neg: 1.0ms (3.6% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

17.1MiB live, 17.1MiB allocated

Counts

13 → 156

Calls

Call 1

Inputs
#<alt (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)>
#<alt (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))>
#<alt (sqrt.f64 x)>
#<alt (.f64 x (.f64 x #s(literal -1/8 binary64)))>
#<alt (*.f64 x #s(literal -1/8 binary64))>
#<alt (fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))>
#<alt (neg.f64 (sqrt.f64 x))>
#<alt (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))>
#<alt (+.f64 x (-.f64 #s(literal 1 binary64) x))>
#<alt (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))>
#<alt (-.f64 #s(literal 1 binary64) x)>
#<alt (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))>
#<alt (sqrt.f64 (+.f64 x #s(literal 1 binary64)))>

Outputs
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1/8 x)>
#<alt (* -1 (sqrt x))>
#<alt (- (* 1/2 x) (sqrt x))>
#<alt (- (* 1/2 x) (sqrt x))>
#<alt (- (* 1/2 x) (sqrt x))>
#<alt (* x (- 1/2 (sqrt (/ 1 x))))>
#<alt (* x (- 1/2 (sqrt (/ 1 x))))>
#<alt (* x (- 1/2 (sqrt (/ 1 x))))>
#<alt (* x (- 1/2 (sqrt (/ 1 x))))>
#<alt (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (* -1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* -1 (sqrt x))>
#<alt (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))>
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))>
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))>
#<alt (* 2 (sqrt x))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>

Calls

39 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))
1.0ms	x	@	-inf	(/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))
1.0ms	x	@	-inf	(/ 1/2 (sqrt x))
1.0ms	x	@	0	(/ (+ x (- 1 x)) (+ (sqrt (+ x 1)) (sqrt x)))
0.0ms	x	@	0	(* x (* x -1/8))

rewrite423.0ms (4.5%)

Memory

-28.8MiB live, 528.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 954×	`lower-fma.f32`
8 952×	`lower-fma.f64`
3 174×	`lower-*.f32`
3 168×	`lower-*.f64`
2 242×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	65
0	33	72
1	130	60
2	916	51
0	10713	51

Stop Event

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

Counts

13 → 1 262

Calls

Call 1

Inputs
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(sqrt.f64 x)
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(*.f64 x #s(literal -1/8 binary64))
(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
(neg.f64 (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(+.f64 x (-.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) x)
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))

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

simplify838.0ms (8.9%)

Memory

15.1MiB live, 779.7MiB allocated

Algorithm

1×	egg-herbie

Rules

18 268×	`lower-fma.f64`
18 268×	`lower-fma.f32`
5 074×	`lower-*.f64`
5 074×	`lower-*.f32`
2 450×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	200	1282
1	573	1184
2	1780	1177
3	5134	1170
0	8139	1117

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

Inputs
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1/8 x)
(* -1 (sqrt x))
(- (* 1/2 x) (sqrt x))
(- (* 1/2 x) (sqrt x))
(- (* 1/2 x) (sqrt x))
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (sqrt x))
(* -1 (sqrt x))
(* -1 (sqrt x))
(* -1 (sqrt x))
(* -1 (sqrt x))
(* -1 (sqrt x))
(* -1 (sqrt x))
(* -1 (sqrt x))
(* (sqrt x) (pow (sqrt -1) 2))
(* (sqrt x) (pow (sqrt -1) 2))
(* (sqrt x) (pow (sqrt -1) 2))
(* (sqrt x) (pow (sqrt -1) 2))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
1
1
1
1
1
1
1
1
1
1
1
1
(/ 1 (+ 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(* 2 (sqrt x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))

Outputs
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* -1/8 (pow x 2))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(- (* 1/2 x) (sqrt x))
(-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
(- (* 1/2 x) (sqrt x))
(-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
(- (* 1/2 x) (sqrt x))
(-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* -1 (sqrt x))
(neg.f64 (sqrt.f64 x))
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(* (sqrt x) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 x))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
(/ 1 (+ 1 (sqrt x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 x (/.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 x (fma.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))))) (/.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 x (fma.f64 x (-.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))))) (.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x))))) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))))) (/.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)
(/.f64 (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (fma.f64 #s(literal -5/128 binary64) (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 x #s(literal 6 binary64))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) x)
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 x) (/.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64)) (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))))))) x)
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (sqrt x))
(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x (sqrt.f64 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(+.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
(.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))

eval764.0ms (8.1%)

Memory: 21.6MiB live, 412.9MiB allocated
Compiler: Compiled 36 555 to 2 777 computations (92.4% saved)

prune420.0ms (4.4%)

Memory

-2.6MiB live, 352.8MiB allocated

Pruning

14 alts after pruning (7 fresh and 7 done)

	Pruned	Kept	Total
New	1 576	4	1 580
Fresh	2	3	5
Picked	2	3	5
Done	0	4	4
Total	1 580	14	1 594

Accuracy

100.0%

Counts

1 594 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	46.8%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	5.4%	(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
✓	3.2%	(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
	48.1%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (/.f64 (sqrt.f64 x) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	48.1%	(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	58.0%	(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
▶	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
✓	57.9%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	47.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	45.1%	(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))
▶	46.8%	(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
✓	44.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
▶	3.8%	(.f64 x (.f64 #s(literal 1/8 binary64) x))
✓	58.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 219 to 140 computations (36.1% saved)

simplify91.0ms (1%)

Memory

5.6MiB live, 84.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))
✓	cost-diff	(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))
✓	cost-diff	(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
✓	cost-diff	(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
✓	cost-diff	(*.f64 #s(literal 1/8 binary64) x)
✓	cost-diff	(.f64 x (.f64 #s(literal 1/8 binary64) x))
✓	cost-diff	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))

Rules

1 656×	`lower-fma.f32`
1 648×	`lower-fma.f64`
456×	`lower-*.f32`
452×	`lower-*.f64`
444×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	91
0	35	91
1	59	91
2	99	91
3	209	91
4	493	91
5	869	91
6	1413	91
7	1738	91
8	1819	91
9	1862	91
10	1893	91
11	1909	91
12	1915	91
13	1916	91
0	1916	91

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
#s(literal 1 binary64)
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
x
(sqrt.f64 x)
(.f64 x (.f64 #s(literal 1/8 binary64) x))
x
(*.f64 #s(literal 1/8 binary64) x)
#s(literal 1/8 binary64)
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
x
#s(literal 1/2 binary64)
(sqrt.f64 x)
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
#s(literal 1 binary64)
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
x
#s(literal -1/2 binary64)
(sqrt.f64 x)
(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))
#s(literal 1 binary64)
(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))
x
(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))
#s(literal 1/8 binary64)
#s(literal -1/2 binary64)
(sqrt.f64 x)

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
#s(literal 1 binary64)
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
x
(sqrt.f64 x)
(.f64 x (.f64 #s(literal 1/8 binary64) x))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
x
(*.f64 #s(literal 1/8 binary64) x)
(*.f64 x #s(literal 1/8 binary64))
#s(literal 1/8 binary64)
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
x
#s(literal 1/2 binary64)
(sqrt.f64 x)
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
#s(literal 1 binary64)
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
x
#s(literal -1/2 binary64)
(sqrt.f64 x)
(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
#s(literal 1 binary64)
(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))
x
(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))
#s(literal 1/8 binary64)
#s(literal -1/2 binary64)
(sqrt.f64 x)

localize69.0ms (0.7%)

Memory

-42.4MiB live, 130.5MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(.f64 x (.f64 #s(literal 1/8 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/8 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))

Samples

41.0ms

256×

valid

Compiler

Compiled 101 to 24 computations (76.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-add: 8.0ms (30.3% of total)

ival-mult: 8.0ms (30.3% of total)

ival-sqrt: 6.0ms (22.7% of total)

ival-div: 2.0ms (7.6% of total)

ival-sub: 2.0ms (7.6% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0%)

Memory

8.9MiB live, 8.9MiB allocated

Counts

13 → 156

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))>
#<alt (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))>
#<alt (sqrt.f64 (+.f64 x #s(literal 1 binary64)))>
#<alt (+.f64 x #s(literal 1 binary64))>
#<alt (.f64 x (.f64 #s(literal 1/8 binary64) x))>
#<alt (*.f64 #s(literal 1/8 binary64) x)>
#<alt (fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))>
#<alt (sqrt.f64 x)>
#<alt (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))>
#<alt (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))>
#<alt (-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))>
#<alt (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))>
#<alt (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))>

Outputs
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))>
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))>
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))>
#<alt (* 2 (sqrt x))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (* 1/8 x)>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 x))>
#<alt (+ (sqrt x) (* 1/2 x))>
#<alt (+ (sqrt x) (* 1/2 x))>
#<alt (* x (+ 1/2 (sqrt (/ 1 x))))>
#<alt (* x (+ 1/2 (sqrt (/ 1 x))))>
#<alt (* x (+ 1/2 (sqrt (/ 1 x))))>
#<alt (* x (+ 1/2 (sqrt (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (* x (- 1/2 (sqrt (/ 1 x))))>
#<alt (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))>
#<alt (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))>
#<alt (* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))>
#<alt (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* -1/2 x))>
#<alt (+ (sqrt x) (* -1/2 x))>
#<alt (+ (sqrt x) (* -1/2 x))>
#<alt (* x (- (sqrt (/ 1 x)) 1/2))>
#<alt (* x (- (sqrt (/ 1 x)) 1/2))>
#<alt (* x (- (sqrt (/ 1 x)) 1/2))>
#<alt (* x (- (sqrt (/ 1 x)) 1/2))>
#<alt (* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 1/2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))>
#<alt (* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))>
#<alt (* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* -1/2 x))>
#<alt (+ (sqrt x) (* x (- (* 1/8 x) 1/2)))>
#<alt (+ (sqrt x) (* x (- (* 1/8 x) 1/2)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (- (+ 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (+ 1/8 (* -1 (/ (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x))))>
#<alt (* (pow x 2) (+ 1/8 (* -1 (/ (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x))))>
#<alt (* (pow x 2) (+ 1/8 (* -1 (/ (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x))))>
#<alt -1/2>
#<alt (- (* 1/8 x) 1/2)>
#<alt (- (* 1/8 x) 1/2)>
#<alt (- (* 1/8 x) 1/2)>
#<alt (* 1/8 x)>
#<alt (* x (- 1/8 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1/8 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1/8 (* 1/2 (/ 1 x))))>
#<alt (* 1/8 x)>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1/8)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1/8)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1/8)))>

Calls

39 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(- 1 (+ (* x (+ (* x 1/8) -1/2)) (sqrt x)))
0.0ms	x	@	0	(* x (* 1/8 x))
0.0ms	x	@	0	(* 1/8 x)
0.0ms	x	@	inf	(* x (* 1/8 x))
0.0ms	x	@	inf	(- 1 (+ (* x (+ (* x 1/8) -1/2)) (sqrt x)))

rewrite284.0ms (3%)

Memory

30.7MiB live, 579.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 730×	`lower-fma.f32`
4 722×	`lower-fma.f64`
4 268×	`lower-/.f32`
4 266×	`lower-/.f64`
4 140×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	72
0	35	72
1	158	72
2	1312	72
0	8337	72

Stop Event

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

Counts

13 → 509

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(+.f64 x #s(literal 1 binary64))
(.f64 x (.f64 #s(literal 1/8 binary64) x))
(*.f64 #s(literal 1/8 binary64) x)
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
(sqrt.f64 x)
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))
(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))
(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))

Outputs
(exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64)))
(-.f64 (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (/.f64 (sqrt.f64 x) (-.f64 (+.f64 #s(literal 1 binary64) x) x)))
(-.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 x (sqrt.f64 x)))) (/.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 x (sqrt.f64 x)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))))
(/.f64 (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)))) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 x (sqrt.f64 x))))
(/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) x) x))
(/.f64 (neg.f64 (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))))) (neg.f64 (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 x (sqrt.f64 x)))))
(/.f64 (neg.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (neg.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x)))
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64))
(pow.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(.f64 (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 x (sqrt.f64 x)))))
(*.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) x)))
(*.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 x (sqrt.f64 x)))) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 x (sqrt.f64 x)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) x) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1 binary64) x) x)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64)))
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64))))
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simplify432.0ms (4.6%)

Memory

9.4MiB live, 595.7MiB allocated

Algorithm

1×	egg-herbie

Rules

17 388×	`lower-fma.f64`
17 388×	`lower-fma.f32`
4 444×	`lower-*.f64`
4 444×	`lower-*.f32`
2 876×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	242	1594
1	699	1475
2	2138	1450
3	6587	1427
0	8403	1331

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 154

Calls

Call 1

Inputs
(/ 1 (+ 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(* 2 (sqrt x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(* 1/8 x)
(sqrt x)
(+ (sqrt x) (* 1/2 x))
(+ (sqrt x) (* 1/2 x))
(+ (sqrt x) (* 1/2 x))
(* x (+ 1/2 (sqrt (/ 1 x))))
(* x (+ 1/2 (sqrt (/ 1 x))))
(* x (+ 1/2 (sqrt (/ 1 x))))
(* x (+ 1/2 (sqrt (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(* x (- 1/2 (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(sqrt x)
(+ (sqrt x) (* -1/2 x))
(+ (sqrt x) (* -1/2 x))
(+ (sqrt x) (* -1/2 x))
(* x (- (sqrt (/ 1 x)) 1/2))
(* x (- (sqrt (/ 1 x)) 1/2))
(* x (- (sqrt (/ 1 x)) 1/2))
(* x (- (sqrt (/ 1 x)) 1/2))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(sqrt x)
(+ (sqrt x) (* -1/2 x))
(+ (sqrt x) (* x (- (* 1/8 x) 1/2)))
(+ (sqrt x) (* x (- (* 1/8 x) 1/2)))
(* 1/8 (pow x 2))
(* (pow x 2) (- (+ 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))
(* 1/8 (pow x 2))
(* (pow x 2) (+ 1/8 (* -1 (/ (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x))))
(* (pow x 2) (+ 1/8 (* -1 (/ (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x))))
(* (pow x 2) (+ 1/8 (* -1 (/ (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x))))
-1/2
(- (* 1/8 x) 1/2)
(- (* 1/8 x) 1/2)
(- (* 1/8 x) 1/2)
(* 1/8 x)
(* x (- 1/8 (* 1/2 (/ 1 x))))
(* x (- 1/8 (* 1/2 (/ 1 x))))
(* x (- 1/8 (* 1/2 (/ 1 x))))
(* 1/8 x)
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/8)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/8)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/8)))

Outputs
(/ 1 (+ 1 (sqrt x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 x (/.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 x (fma.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))))) (/.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(fma.f64 x (fma.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))) (fma.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x))))) (+.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))) (/.f64 #s(literal 1/8 binary64) (.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))) (neg.f64 x) (/.f64 #s(literal 1/4 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x))))))) (/.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 x (sqrt.f64 x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)
(/.f64 (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))) x)
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)
(/.f64 (fma.f64 #s(literal -5/128 binary64) (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x)
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))
(/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) x)
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))
(/.f64 (+.f64 (/.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) #s(literal 5/128 binary64)) (.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))))) x)
(+ 1 (sqrt x))
(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
(.f64 x (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/16 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 x (fma.f64 #s(literal -1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
1
#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)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
(+ (sqrt x) (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
(+ (sqrt x) (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
(* x (+ 1/2 (sqrt (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ 1/2 (sqrt (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ 1/2 (sqrt (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ 1/2 (sqrt (/ 1 x))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
(+ (sqrt x) (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
(+ (sqrt x) (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
(* x (- (sqrt (/ 1 x)) 1/2))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (sqrt (/ 1 x)) 1/2))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (sqrt (/ 1 x)) 1/2))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (sqrt (/ 1 x)) 1/2))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* -1/8 (pow x 2))
(.f64 #s(literal -1/8 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(.f64 x (fma.f64 x (-.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) #s(literal 1/2 binary64)))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(+.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (-.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) #s(literal 1/2 binary64))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(+.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (-.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) #s(literal 1/2 binary64))))
(* -1/8 (pow x 2))
(.f64 #s(literal -1/8 binary64) (.f64 x x))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))
(.f64 x (fma.f64 x (-.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) #s(literal 1/2 binary64)))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(+.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (-.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) #s(literal 1/2 binary64))))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(+.f64 #s(literal 1 binary64) (.f64 x (fma.f64 x (-.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) #s(literal 1/2 binary64))))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))
(+ (sqrt x) (* x (- (* 1/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))
(+ (sqrt x) (* x (- (* 1/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* (pow x 2) (- (+ 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))
(.f64 x (fma.f64 x (+.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) #s(literal -1/2 binary64)))
(* (pow x 2) (- (+ 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))
(.f64 x (fma.f64 x (+.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) #s(literal -1/2 binary64)))
(* (pow x 2) (- (+ 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (/ 1 x))))
(.f64 x (fma.f64 x (+.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) #s(literal -1/2 binary64)))
(* 1/8 (pow x 2))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(* (pow x 2) (+ 1/8 (* -1 (/ (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)))
(* (pow x 2) (+ 1/8 (* -1 (/ (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)))
(* (pow x 2) (+ 1/8 (* -1 (/ (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)))
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 x) 1/2)
(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))
(- (* 1/8 x) 1/2)
(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))
(- (* 1/8 x) 1/2)
(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* x (- 1/8 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))
(* x (- 1/8 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))
(* x (- 1/8 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))
(* 1/8 x)
(*.f64 x #s(literal 1/8 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/8)))
(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/8)))
(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/8)))
(fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))

eval100.0ms (1.1%)

Memory: -11.4MiB live, 195.4MiB allocated
Compiler: Compiled 15 213 to 1 854 computations (87.8% saved)

prune80.0ms (0.9%)

Memory

11.8MiB live, 168.7MiB allocated

Pruning

12 alts after pruning (3 fresh and 9 done)

	Pruned	Kept	Total
New	737	1	738
Fresh	0	2	2
Picked	2	3	5
Done	1	6	7
Total	740	12	752

Accuracy

100.0%

Counts

752 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	46.8%	(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	48.1%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (/.f64 (sqrt.f64 x) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	48.1%	(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
✓	58.0%	(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
✓	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
✓	57.9%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	47.4%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	45.1%	(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))
✓	46.8%	(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
✓	44.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	58.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	5.9%	(sqrt.f64 x)

Compiler

Compiled 324 to 135 computations (58.3% saved)

regimes14.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Counts

23 → 1

Calls

Call 1

Inputs
(sqrt.f64 x)
(.f64 x (.f64 #s(literal 1/8 binary64) x))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(neg.f64 (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(-.f64 (sqrt.f64 x) (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 x (/.f64 (sqrt.f64 x) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (.f64 (.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))) (+.f64 x (+.f64 x #s(literal 1 binary64))))
(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (fma.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (.f64 x (sqrt.f64 x)))) (+.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x x)))))

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

Calls

2 calls:

7.0ms	x
6.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes45.0ms (0.5%)

Memory

-27.9MiB live, 15.2MiB allocated

Counts

17 → 2

Calls

Call 1

Inputs
(sqrt.f64 x)
(.f64 x (.f64 #s(literal 1/8 binary64) x))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(neg.f64 (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(-.f64 (sqrt.f64 x) (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)

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

Calls

2 calls:

5.0ms	x
4.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.6%	2	`x`
99.6%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes10.0ms (0.1%)

Memory

15.3MiB live, 15.3MiB allocated

Counts

15 → 2

Calls

Call 1

Inputs
(sqrt.f64 x)
(.f64 x (.f64 #s(literal 1/8 binary64) x))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(neg.f64 (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(-.f64 (sqrt.f64 x) (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Outputs
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))

Calls

2 calls:

5.0ms	x
4.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.4%	2	`x`
99.4%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes35.0ms (0.4%)

Memory

-24.6MiB live, 14.5MiB allocated

Counts

14 → 2

Calls

Call 1

Inputs
(sqrt.f64 x)
(.f64 x (.f64 #s(literal 1/8 binary64) x))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(neg.f64 (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(-.f64 (sqrt.f64 x) (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))

Outputs
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x)))

Calls

2 calls:

31.0ms	x
4.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.4%	2	`x`
99.4%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes8.0ms (0.1%)

Memory

15.1MiB live, 15.1MiB allocated

Counts

12 → 2

Calls

Call 1

Inputs
(sqrt.f64 x)
(.f64 x (.f64 #s(literal 1/8 binary64) x))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(neg.f64 (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(-.f64 (sqrt.f64 x) (sqrt.f64 x))

Outputs
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))

Calls

2 calls:

4.0ms	x
3.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.3%	2	`x`
99.3%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.1%)

Memory

15.6MiB live, 15.6MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
(sqrt.f64 x)
(.f64 x (.f64 #s(literal 1/8 binary64) x))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(neg.f64 (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
(-.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))

Outputs
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))

Calls

2 calls:

4.0ms	x
3.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
46.8%	1	`x`
46.8%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

-25.3MiB live, 13.2MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
(sqrt.f64 x)
(.f64 x (.f64 #s(literal 1/8 binary64) x))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(neg.f64 (sqrt.f64 x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (sqrt.f64 x))
(fma.f64 x #s(literal 1/2 binary64) (neg.f64 (sqrt.f64 x)))

Outputs
(sqrt.f64 x)
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))

Calls

2 calls:

3.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
3.0ms	x

Results

Accuracy	Segments	Branch
46.4%	2	`x`
46.4%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes4.0ms (0%)

Memory

9.8MiB live, 9.8MiB allocated

Accuracy

Total -2.9b remaining (-4.8%)

Threshold costs -2.9b (-4.8%)

Counts

4 → 1

Calls

Call 1

Inputs
(sqrt.f64 x)
(.f64 x (.f64 #s(literal 1/8 binary64) x))
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(neg.f64 (sqrt.f64 x))

Outputs
(sqrt.f64 x)

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
5.9%	1	`x`
5.9%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.4901161193847656e-8	0.0008899610141952508

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.004531390423167636	0.9983007552206349

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.004531390423167636	0.9983007552206349

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.004531390423167636	0.9983007552206349

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.004531390423167636	0.9983007552206349

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify8.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	128
1	43	128
2	54	128
3	60	128
4	63	128

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 3022314549036573/151115727451828646838272 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 5764607523034235/1152921504606846976 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 5764607523034235/1152921504606846976 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 5764607523034235/1152921504606846976 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 5764607523034235/1152921504606846976 binary64)) (sqrt.f64 x) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 x)

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 3022314549036573/151115727451828646838272 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 3022314549036573/151115727451828646838272 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 5764607523034235/1152921504606846976 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 5764607523034235/1152921504606846976 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 5764607523034235/1152921504606846976 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 5764607523034235/1152921504606846976 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (sqrt.f64 x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 5764607523034235/1152921504606846976 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 5764607523034235/1152921504606846976 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x))))
(-.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/2 binary64) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 5764607523034235/1152921504606846976 binary64)) (sqrt.f64 x) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 5764607523034235/1152921504606846976 binary64)) (sqrt.f64 x) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(sqrt.f64 x)

soundness1.5s (15.8%)

Memory

4.2MiB live, 1 029.0MiB allocated

Rules

17 388×	`lower-fma.f64`
17 388×	`lower-fma.f32`
17 328×	`lower-fma.f64`
17 328×	`lower-fma.f32`
11 848×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	65
0	33	72
1	130	60
2	916	51
0	10713	51
0	6	16
0	10	16
1	43	16
2	290	16
3	3385	16
0	8686	16
0	242	1594
1	699	1475
2	2138	1450
3	6587	1427
0	8403	1331
0	15	62
0	30	62
1	131	57
2	1007	57
0	8937	55
0	86	1009
1	224	892
2	577	880
3	1438	858
4	2806	858
5	5157	858
0	8154	807
0	113	498
1	299	446
2	802	442
3	2251	434
4	4609	434
0	8184	398

Stop Event

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

Compiler

Compiled 290 to 152 computations (47.6% saved)

preprocess61.0ms (0.6%)

Memory: 4.2MiB live, 160.7MiB allocated
Compiler: Compiled 294 to 86 computations (70.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18

analyze1.0ms (0%)

sample1.0s (10.8%)

preprocess22.0ms (0.2%)

explain105.0ms (1.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify12.0ms (0.1%)

localize28.0ms (0.3%)

series5.0ms (0%)

rewrite546.0ms (5.8%)

simplify478.0ms (5%)

eval57.0ms (0.6%)

prune59.0ms (0.6%)

simplify203.0ms (2.1%)

localize80.0ms (0.8%)

series8.0ms (0.1%)

rewrite445.0ms (4.7%)

simplify324.0ms (3.4%)

eval128.0ms (1.3%)

prune155.0ms (1.6%)

simplify468.0ms (4.9%)

localize113.0ms (1.2%)

series8.0ms (0.1%)

rewrite423.0ms (4.5%)

simplify838.0ms (8.9%)

eval764.0ms (8.1%)

prune420.0ms (4.4%)

simplify91.0ms (1%)

localize69.0ms (0.7%)

series5.0ms (0%)

rewrite284.0ms (3%)

simplify432.0ms (4.6%)

eval100.0ms (1.1%)

prune80.0ms (0.9%)

regimes14.0ms (0.1%)

regimes45.0ms (0.5%)

regimes10.0ms (0.1%)

regimes35.0ms (0.4%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

soundness1.5s (15.8%)

preprocess61.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	19
1	18	17
2	41	16
3	73	16
4	121	16
5	178	16
6	201	16
7	212	16
0	6	7
0	10	7
1	15	7
2	19	7
3	25	7
4	33	7
5	48	7
6	80	7
7	106	7
8	150	7
9	165	7
10	173	7
0	173	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	15	18
2	19	18
3	25	18
4	33	18
5	48	18
6	80	18
7	106	18
8	150	18
9	165	18
10	173	18
0	173	18