Metrics for sqrtexp (problem 3.4.4)

analyze1.0ms (0%)

Memory

2.8MiB live, 2.8MiB 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
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample893.0ms (11.5%)

Memory

56.2MiB live, 969.0MiB allocated

Samples

454.0ms	8 256×	0	valid
148.0ms	2 684×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 399.0ms

ival-expm1: 148.0ms (37.1% of total)

ival-mult: 86.0ms (21.6% of total)

ival-div: 74.0ms (18.6% of total)

ival-sqrt: 73.0ms (18.3% of total)

ival-true: 8.0ms (2% of total)

exact: 6.0ms (1.5% of total)

ival-assert: 4.0ms (1% of total)

Bogosity

preprocess496.0ms (6.4%)

Memory

-28.8MiB live, 415.3MiB allocated

Algorithm

2×	egg-herbie

Rules

15 394×	`accelerator-lowering-fma.f32`
15 394×	`accelerator-lowering-fma.f64`
2 850×	`--lowering--.f32`
2 850×	`--lowering--.f64`
2 458×	`-lowering-.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	19	41
1	44	39
2	70	39
3	113	39
4	192	20
5	340	18
6	672	18
7	2570	18
0	10	12
1	22	12
2	28	12
3	40	12
4	66	7
5	119	5
6	195	5
7	593	5
8	2904	5
9	6743	5
0	8156	5

Stop Event

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

Calls

Call 1

Inputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))

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

Call 2

Inputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1)))
(neg (sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1))))

Outputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (+ 1 (exp x)))
(sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1)))
(sqrt (+ 1 (exp (neg x))))
(neg (sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1))))
(neg (sqrt (+ 1 (exp (neg x)))))

explain135.0ms (1.7%)

Memory

15.3MiB live, 166.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
185	0	-	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
185	0	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
1	0	-	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	1	(-164.96388663335864)	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) x)`
0	0	-	-	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	185	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	185	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/o	1	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	1
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	1
↳	`(exp.f64 x)`	overflow	1
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	1
`exp.f64`	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	sensitivity	1	1

Confusion

	Predicted +	Predicted -
+	186	0
-	1	69

Precision

0.9946524064171123

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	186	0	0
-	1	1	68

Precision?

0.9893617021276596

Recall?

1.0

Freqs

test

number	freq
0	69
1	2
2	185

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

43.0ms

512×

valid

Compiler

Compiled 120 to 44 computations (63.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 8.0ms (27.9% of total)

ival-exp: 7.0ms (24.5% of total)

ival-expm1: 6.0ms (21% of total)

ival-div: 4.0ms (14% of total)

ival-sqrt: 3.0ms (10.5% of total)

exact: 1.0ms (3.5% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	29.6%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify450.0ms (5.8%)

Memory

7.8MiB live, 457.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	192	(-.f64 (exp.f64 x) #s(literal 1 binary64))
✓	cost-diff	192	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓	cost-diff	7104	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

Rules

15 394×	`accelerator-lowering-fma.f32`
15 394×	`accelerator-lowering-fma.f64`
2 850×	`--lowering--.f32`
2 850×	`--lowering--.f64`
2 458×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	22	45
2	28	45
3	40	45
4	66	35
5	119	31
6	195	31
7	593	31
8	2904	31
9	6743	31
0	8156	27

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(- (exp (* 2 x)) 1)
(exp (* 2 x))
(* 2 x)
2
x
1
(- (exp x) 1)
(exp x)

Outputs
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(exp (* 2 x))
(exp.f64 (+.f64 x x))
(* 2 x)
(+.f64 x x)
2
#s(literal 2 binary64)
x
1
#s(literal 1 binary64)
(- (exp x) 1)
(expm1.f64 x)
(exp x)
(exp.f64 x)

localize32.0ms (0.4%)

Memory

4.8MiB live, 43.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(exp.f64 (*.f64 #s(literal 2 binary64) x))
✓	accuracy	99.7%	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	accuracy	33.6%	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓	accuracy	33.4%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

19.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

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

ival-exp: 3.0ms (24.9% of total)

ival-expm1: 3.0ms (24.9% of total)

ival-div: 2.0ms (16.6% of total)

ival-mult: 2.0ms (16.6% of total)

ival-sqrt: 2.0ms (16.6% of total)

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

exact: 0.0ms (0% of total)

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

series57.0ms (0.7%)

Memory

-35.2MiB live, 3.3MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp x) 1)>
#<alt (* 2 x)>
#<alt (exp (* 2 x))>

Outputs
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 2 x)))>
#<alt (* x (+ 2 (* x (+ 2 (* 4/3 x)))))>
#<alt (* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt 1>
#<alt (+ 1 (* 2 x))>
#<alt (+ 1 (* x (+ 2 (* 2 x))))>
#<alt (+ 1 (* x (+ 2 (* x (+ 2 (* 4/3 x))))))>
#<alt (exp (* 2 x))>
#<alt (exp (* 2 x))>
#<alt (exp (* 2 x))>
#<alt (exp (* 2 x))>
#<alt (exp (* 2 x))>
#<alt (exp (* 2 x))>
#<alt (exp (* 2 x))>
#<alt (exp (* 2 x))>

Calls

15 calls:

Time	Variable		Point	Expression
53.0ms	x	@	0	(* 2 x)
1.0ms	x	@	inf	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
1.0ms	x	@	-inf	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
0.0ms	x	@	0	(- (exp (* 2 x)) 1)
0.0ms	x	@	0	(/ (- (exp (* 2 x)) 1) (- (exp x) 1))

rewrite365.0ms (4.7%)

Memory

46.9MiB live, 438.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 402×	`accelerator-lowering-fma.f32`
5 402×	`accelerator-lowering-fma.f64`
4 492×	`-lowering-.f32`
4 492×	`-lowering-.f64`
2 532×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	50	21
2	372	21
3	4517	21
0	8145	17

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 673

Calls

Call 1

Inputs
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(* 2 x)
(exp (* 2 x))

Outputs
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)) (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)))
(+.f64 (.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64)))) (exp.f64 (+.f64 x x))) (.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(+.f64 (.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64)))) (exp.f64 (+.f64 x x))))
(+.f64 (.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64)))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64)))) (exp.f64 x)))
(+.f64 (.f64 (exp.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64))))) (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64))))))
(+.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64))))) (.f64 (exp.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64))))))
(+.f64 (.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64))))) (.f64 (exp.f64 x) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64))))))
(exp.f64 (log1p.f64 (exp.f64 x)))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(-.f64 #s(literal 0 binary64) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal -1 binary64)))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(-.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (/.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(-.f64 (/.f64 (/.f64 (exp.f64 (fma.f64 x #s(literal 6 binary64) #s(literal 0 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)))))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)))))) (expm1.f64 x)))
(-.f64 (/.f64 (/.f64 (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (expm1.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (fma.f64 (exp.f64 x) #s(literal -1 binary64) #s(literal -1 binary64)))
(-.f64 (/.f64 (exp.f64 (fma.f64 x #s(literal 6 binary64) #s(literal 0 binary64))) (.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64))))))) (/.f64 #s(literal 1 binary64) (.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64))))))))
(-.f64 (/.f64 (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64))) (.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (expm1.f64 x) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(-.f64 (/.f64 (*.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (/.f64 (expm1.f64 x) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 (exp.f64 (fma.f64 x #s(literal 6 binary64) #s(literal 0 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (.f64 (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -3 binary64)) (fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))) (*.f64 (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))))))
(-.f64 (/.f64 (.f64 (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64)))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) #s(literal 1 binary64)))
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(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 (fma.f64 x #s(literal 6 binary64) #s(literal 0 binary64))) (expm1.f64 x))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64))))))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64))) (+.f64 (exp.f64 (fma.f64 x #s(literal 6 binary64) #s(literal 0 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 3 binary64)))) (fma.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (+.f64 x x))) (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64)))))
(*.f64 (/.f64 (expm1.f64 (fma.f64 x #s(literal 3 binary64) #s(literal 0 binary64))) (-.f64 (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)))) (-.f64 (expm1.f64 (+.f64 x x)) (exp.f64 x)))
(log.f64 (exp.f64 (+.f64 x x)))
(+.f64 x x)
(+.f64 (+.f64 x x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (+.f64 x x))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64))) (log.f64 (.f64 (exp.f64 (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(+.f64 (log.f64 (.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))))) (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 #s(literal 2 binary64) x #s(literal 0 binary64))
(fma.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)) (log.f64 (.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(fma.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64))) #s(literal 0 binary64))
(fma.f64 x #s(literal 2 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64) (log.f64 (.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 4 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64) #s(literal 0 binary64))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64) #s(literal 0 binary64))
(/.f64 (fma.f64 (.f64 x x) x (.f64 (.f64 x x) x)) (fma.f64 x x (-.f64 (.f64 x x) (*.f64 x x))))
(/.f64 (-.f64 (.f64 x x) (.f64 x x)) (-.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))))
(*.f64 x #s(literal 2 binary64))
(.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 4 binary64))
(.f64 (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
(.f64 (fma.f64 x #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64))) #s(literal 2 binary64))
(exp.f64 (+.f64 x x))
(exp.f64 (*.f64 (+.f64 x x) #s(literal 1 binary64)))
(exp.f64 (.f64 #s(literal 2 binary64) (fma.f64 x #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64)))))
(exp.f64 (.f64 #s(literal 4 binary64) (.f64 x #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))
(pow.f64 (exp.f64 x) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (fma.f64 x #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64))))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 1 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 (fma.f64 x #s(literal 1/2 binary64) (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(pow.f64 (exp.f64 (fma.f64 x #s(literal 4 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 #s(literal 4 binary64)) (*.f64 x #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 #s(literal 4 binary64)) (.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(pow.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(*.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))
(*.f64 (exp.f64 x) (exp.f64 x))
(.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (exp.f64 (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 1/2 binary64)))))
(.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) (.f64 (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64))))) (exp.f64 (.f64 #s(literal 2 binary64) (.f64 x #s(literal 1/2 binary64)))))

simplify494.0ms (6.4%)

Memory

13.2MiB live, 599.4MiB allocated

Algorithm

1×	egg-herbie

Rules

14 886×	`accelerator-lowering-fma.f32`
14 886×	`accelerator-lowering-fma.f64`
3 150×	`--lowering--.f32`
3 150×	`--lowering--.f64`
2 574×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	360
1	155	360
2	336	360
3	754	360
4	1207	320
5	1539	304
6	2137	304
7	3095	304
8	4622	304
0	8209	249

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
1
(+ 1 (* 2 x))
(+ 1 (* x (+ 2 (* 2 x))))
(+ 1 (* x (+ 2 (* x (+ 2 (* 4/3 x))))))
(exp (* 2 x))
(exp (* 2 x))
(exp (* 2 x))
(exp (* 2 x))
(exp (* 2 x))
(exp (* 2 x))
(exp (* 2 x))
(exp (* 2 x))

Outputs
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(* 2 x)
(+.f64 x x)
(* x (+ 2 (* 2 x)))
(*.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 4/3 binary64) #s(literal 2 binary64)) #s(literal 2 binary64)))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 2/3 binary64) #s(literal 4/3 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
(- (exp (* 2 x)) 1)
(expm1.f64 (+.f64 x x))
x
(* x (+ 1 (* 1/2 x)))
(*.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
(* 2 x)
(+.f64 x x)
1
#s(literal 1 binary64)
(+ 1 (* 2 x))
(fma.f64 #s(literal 2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 2 (* 2 x))))
(fma.f64 x (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 2 (* x (+ 2 (* 4/3 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 4/3 binary64) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))
(exp (* 2 x))
(exp.f64 (+.f64 x x))
(exp (* 2 x))
(exp.f64 (+.f64 x x))
(exp (* 2 x))
(exp.f64 (+.f64 x x))
(exp (* 2 x))
(exp.f64 (+.f64 x x))
(exp (* 2 x))
(exp.f64 (+.f64 x x))
(exp (* 2 x))
(exp.f64 (+.f64 x x))
(exp (* 2 x))
(exp.f64 (+.f64 x x))
(exp (* 2 x))
(exp.f64 (+.f64 x x))

eval96.0ms (1.2%)

Memory: -30.2MiB live, 179.3MiB allocated
Compiler: Compiled 17 842 to 2 432 computations (86.4% saved)

prune87.0ms (1.1%)

Memory

5.7MiB live, 202.5MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	728	5	733
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	729	5	734

Accuracy

100.0%

Counts

734 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	72.3%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶	73.7%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	72.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
▶	77.0%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 70 to 56 computations (20% saved)

simplify15.0ms (0.2%)

Memory

-5.2MiB live, 34.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Program
✓	cost-diff	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	cost-diff	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	cost-diff	(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	cost-diff	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	cost-diff	(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	cost-diff	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	cost-diff	(+.f64 #s(literal 2 binary64) x)
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	(exp.f64 x)
✓	cost-diff	(-.f64 (exp.f64 x) #s(literal -1 binary64))
✓	cost-diff	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))

Rules

400×	`accelerator-lowering-fma.f32`
400×	`accelerator-lowering-fma.f64`
134×	`-lowering-.f32`
134×	`-lowering-.f64`
132×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	99
1	54	99
2	100	99
3	186	99
4	232	99
5	239	99
0	239	85

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (- (exp x) -1))
(- (exp x) -1)
(exp x)
x
-1
(sqrt 2)
2
(sqrt (+ 2 x))
(+ 2 x)
2
x
(sqrt (+ (* x (+ (* x 1/2) 1)) 2))
(+ (* x (+ (* x 1/2) 1)) 2)
x
(+ (* x 1/2) 1)
1/2
1
2
(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
(+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)
x
(+ (* x (+ (* x 1/6) 1/2)) 1)
(+ (* x 1/6) 1/2)
1/6
1/2
1
2

Outputs
(sqrt (- (exp x) -1))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(- (exp x) -1)
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
x
-1
#s(literal -1 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(sqrt (+ 2 x))
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)
x
(sqrt (+ (* x (+ (* x 1/2) 1)) 2))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(+ (* x (+ (* x 1/2) 1)) 2)
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(+ (* x 1/2) 1)
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
1
#s(literal 1 binary64)
2
#s(literal 2 binary64)
(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
x
(+ (* x (+ (* x 1/6) 1/2)) 1)
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ (* x 1/6) 1/2)
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
1/6
#s(literal 1/6 binary64)
1/2
#s(literal 1/2 binary64)
1
#s(literal 1 binary64)
2
#s(literal 2 binary64)

localize115.0ms (1.5%)

Memory

-6.4MiB live, 147.4MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(-.f64 (exp.f64 x) #s(literal -1 binary64))

Samples

35.0ms	187×	0	valid
15.0ms	69×	0	invalid

Compiler

Compiled 87 to 26 computations (70.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 13.0ms (34.7% of total)

ival-sqrt: 10.0ms (26.7% of total)

ival-add: 7.0ms (18.7% of total)

const: 4.0ms (10.7% of total)

ival-exp: 2.0ms (5.3% of total)

ival-sub: 1.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series11.0ms (0.1%)

Memory

17.4MiB live, 17.4MiB allocated

Counts

13 → 144

Calls

Call 1

Inputs
#<alt (sqrt (- (exp x) -1))>
#<alt (- (exp x) -1)>
#<alt (exp x)>
#<alt (sqrt 2)>
#<alt (sqrt (+ 2 x))>
#<alt (+ 2 x)>
#<alt (sqrt (+ (* x (+ (* x 1/2) 1)) 2))>
#<alt (+ (* x (+ (* x 1/2) 1)) 2)>
#<alt (+ (* x 1/2) 1)>
#<alt (sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))>
#<alt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)>
#<alt (+ (* x (+ (* x 1/6) 1/2)) 1)>
#<alt (+ (* x 1/6) 1/2)>

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

Calls

36 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
1.0ms	x	@	-inf	(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
1.0ms	x	@	-inf	(sqrt (+ 2 x))
1.0ms	x	@	0	(exp x)
1.0ms	x	@	inf	(sqrt (+ (* x (+ (* x 1/2) 1)) 2))

rewrite336.0ms (4.3%)

Memory

-10.9MiB live, 456.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 428×	`accelerator-lowering-fma.f32`
4 428×	`accelerator-lowering-fma.f64`
4 328×	`-lowering-.f32`
4 328×	`-lowering-.f64`
4 210×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	85
1	142	85
2	1122	85
0	8240	71

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 442

Calls

Call 1

Inputs
(sqrt (- (exp x) -1))
(- (exp x) -1)
(exp x)
(sqrt 2)
(sqrt (+ 2 x))
(+ 2 x)
(sqrt (+ (* x (+ (* x 1/2) 1)) 2))
(+ (* x (+ (* x 1/2) 1)) 2)
(+ (* x 1/2) 1)
(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
(+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2)
(+ (* x (+ (* x 1/6) 1/2)) 1)
(+ (* x 1/6) 1/2)

Outputs
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 (+.f64 x x)))))
(/.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (sqrt.f64 (+.f64 (neg.f64 (exp.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (+.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (+.f64 x x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1/4 binary64))
(.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(.f64 (sqrt.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(*.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (expm1.f64 x))))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (exp.f64 x))))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (exp.f64 x)) #s(literal -1 binary64)))
(+.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(-.f64 (exp.f64 x) #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (neg.f64 (exp.f64 x)))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(neg.f64 (/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 (+.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 (+.f64 (neg.f64 (exp.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (expm1.f64 (+.f64 x x))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (-.f64 (.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64))) (.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (-.f64 (.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (.f64 (expm1.f64 x) #s(literal 1 binary64))) (*.f64 (expm1.f64 x) (expm1.f64 x)))
(/.f64 (.f64 (+.f64 (exp.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (+.f64 (+.f64 x x) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (expm1.f64 x)))
(/.f64 (.f64 (expm1.f64 (+.f64 (+.f64 x x) (+.f64 x x))) #s(literal 1 binary64)) (.f64 (+.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64)) (expm1.f64 x)))
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(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(neg.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal -1/12 binary64))))))
(neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/36 binary64) (.f64 x #s(literal -1/12 binary64)))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/36 binary64) (*.f64 x x)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (+.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal -1/12 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/36 binary64) (.f64 x #s(literal -1/12 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal -1/12 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/36 binary64) (.f64 x #s(literal -1/12 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64)))
(/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/36 binary64) (.f64 x x))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/10077696 binary64) #s(literal 1/512 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/46656 binary64) (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64)))) (+.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal -1/12 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/46656 binary64) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal -1/8 binary64)) (+.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/46656 binary64) #s(literal -1/64 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) #s(literal 1/144 binary64)))) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64) #s(literal -1/16 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal -1/12 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)))) (neg.f64 (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/36 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (fma.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (.f64 (/.f64 (.f64 (*.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))) (.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal -1/2 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 x x) #s(literal 1/36 binary64) (*.f64 x #s(literal -1/12 binary64))))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/12 binary64))))))
(.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) #s(literal 1/36 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/6 binary64) #s(literal 1/2 binary64))))
(.f64 (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal -1/36 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))

simplify404.0ms (5.2%)

Memory

10.2MiB live, 558.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 602×	`accelerator-lowering-fma.f32`
11 602×	`accelerator-lowering-fma.f64`
5 042×	`-lowering-.f32`
5 042×	`-lowering-.f64`
3 340×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	277	1514
1	881	1294
2	2969	1264
0	8377	1149

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* -1/8 (/ x (pow (sqrt 2) 3))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt 2) 5))) (* 1/8 (/ 1 (pow (sqrt 2) 3))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal 1/16 binary64) (/.f64 x (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (sqrt (/ 1 (pow x 3)))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (* -1/2 (sqrt (/ 1 (pow x 5)))))))
(.f64 x (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* x (+ (sqrt (/ 1 x)) (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 7))))))))
(.f64 x (+.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) (fma.f64 #s(literal 1/2 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 (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(-.f64 #s(literal 0 binary64) (.f64 x (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (fma.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 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)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (-.f64 #s(literal 0 binary64) x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (*.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/4 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(+.f64 (fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/4 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -3/4 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))
(* -1 (* x (sqrt 1/2)))
(-.f64 #s(literal 0 binary64) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 #s(literal 0 binary64) (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 3/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(.f64 (.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(.f64 (.f64 x x) (fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (/.f64 x #s(literal 1/6 binary64)) #s(literal -1/16 binary64) #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/6 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (.f64 x (.f64 x x)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(.f64 x (.f64 x (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (/.f64 x #s(literal 1/6 binary64)) #s(literal -1/16 binary64) #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))) x) (.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/6 (pow x 3))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/6 (pow x 3))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(.f64 (.f64 x (.f64 x x)) (fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal -2 binary64) (.f64 x x))) x) #s(literal 1/6 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 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))

eval99.0ms (1.3%)

Memory: -12.3MiB live, 139.1MiB allocated
Compiler: Compiled 14 244 to 1 909 computations (86.6% saved)

prune74.0ms (1%)

Memory

0.8MiB live, 120.4MiB allocated

Pruning

15 alts after pruning (10 fresh and 5 done)

	Pruned	Kept	Total
New	576	10	586
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	576	15	591

Accuracy

100.0%

Counts

591 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	72.5%	(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	73.5%	(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	3.1%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
▶	72.3%	(sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (+.f64 x #s(literal 2 binary64))))
▶	73.7%	(sqrt.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64))))
✓	72.3%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	73.7%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	72.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
	2.6%	(sqrt.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
▶	4.1%	(sqrt.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
▶	3.6%	(sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
	2.4%	(sqrt.f64 (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))
▶	2.6%	(sqrt.f64 x)
✓	77.0%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 245 to 168 computations (31.4% saved)

simplify15.0ms (0.2%)

Memory

20.9MiB live, 20.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (+.f64 x #s(literal 2 binary64))))
✓	cost-diff	128	(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (+.f64 x #s(literal 2 binary64)))
✓	cost-diff	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
✓	cost-diff	0	(sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
✓	cost-diff	0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
✓	cost-diff	0	(sqrt.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(+.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(sqrt.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64))))
✓	cost-diff	128	(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))

Rules

400×	`accelerator-lowering-fma.f32`
400×	`accelerator-lowering-fma.f64`
134×	`-lowering-.f32`
134×	`-lowering-.f64`
128×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	130
1	56	130
2	93	130
3	204	130
4	245	130
5	254	130
0	254	112

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ (* (* x x) 1/2) (+ x 2)))
(+ (* (* x x) 1/2) (+ x 2))
(* x x)
x
1/2
(+ x 2)
2
(sqrt x)
x
(sqrt (* x (+ (* 1/2 x) 1)))
(* x (+ (* 1/2 x) 1))
x
(+ (* 1/2 x) 1)
1/2
1
(sqrt (* x (* x (+ (* x 1/6) 1/2))))
(* x (* x (+ (* x 1/6) 1/2)))
x
(* x (+ (* x 1/6) 1/2))
(+ (* x 1/6) 1/2)
1/6
1/2
(sqrt (+ (* (+ (* x 1/6) 1/2) (* x x)) (+ x 2)))
(+ (* (+ (* x 1/6) 1/2) (* x x)) (+ x 2))
(+ (* x 1/6) 1/2)
x
1/6
1/2
(* x x)
(+ x 2)
2

Outputs
(sqrt (+ (* (* x x) 1/2) (+ x 2)))
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(+ (* (* x x) 1/2) (+ x 2))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* x x)
(*.f64 x x)
x
1/2
#s(literal 1/2 binary64)
(+ x 2)
(+.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(sqrt x)
(sqrt.f64 x)
x
(sqrt (* x (+ (* 1/2 x) 1)))
(sqrt.f64 (*.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
(* x (+ (* 1/2 x) 1))
(*.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
x
(+ (* 1/2 x) 1)
(fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
1
#s(literal 1 binary64)
(sqrt (* x (* x (+ (* x 1/6) 1/2))))
(sqrt.f64 (.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(* x (* x (+ (* x 1/6) 1/2)))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
x
(* x (+ (* x 1/6) 1/2))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(+ (* x 1/6) 1/2)
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
1/6
#s(literal 1/6 binary64)
1/2
#s(literal 1/2 binary64)
(sqrt (+ (* (+ (* x 1/6) 1/2) (* x x)) (+ x 2)))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(+ (* (+ (* x 1/6) 1/2) (* x x)) (+ x 2))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ (* x 1/6) 1/2)
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
x
1/6
#s(literal 1/6 binary64)
1/2
#s(literal 1/2 binary64)
(* x x)
(*.f64 x x)
(+ x 2)
(+.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)

localize105.0ms (1.4%)

Memory

-7.5MiB live, 110.2MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (+.f64 x #s(literal 2 binary64))))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
✓	accuracy	81.7%	(sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
✓	accuracy	100.0%	(*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64))))
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))

Samples

27.0ms	158×	0	invalid
21.0ms	98×	0	valid

Compiler

Compiled 118 to 25 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 15.0ms (45.3% of total)

ival-sqrt: 8.0ms (24.1% of total)

ival-add: 6.0ms (18.1% of total)

const: 4.0ms (12.1% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.1%)

Memory

-21.4MiB live, 16.8MiB allocated

Counts

14 → 168

Calls

Call 1

Inputs
#<alt (+ (* (* x x) 1/2) (+ x 2))>
#<alt (sqrt (+ (* (* x x) 1/2) (+ x 2)))>
#<alt (* x x)>
#<alt (+ x 2)>
#<alt (sqrt x)>
#<alt (sqrt (* x (+ (* 1/2 x) 1)))>
#<alt (* x (+ (* 1/2 x) 1))>
#<alt (+ (* 1/2 x) 1)>
#<alt (sqrt (* x (* x (+ (* x 1/6) 1/2))))>
#<alt (* x (* x (+ (* x 1/6) 1/2)))>
#<alt (* x (+ (* x 1/6) 1/2))>
#<alt (+ (* x 1/6) 1/2)>
#<alt (+ (* (+ (* x 1/6) 1/2) (* x x)) (+ x 2))>
#<alt (sqrt (+ (* (+ (* x 1/6) 1/2) (* x x)) (+ x 2)))>

Outputs
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt (+ 2 x)>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 1 (* 2 (/ 1 x))))>
#<alt (* x (+ 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 (sqrt x)>
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))>
#<alt (* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))>
#<alt (* -1 (* x (* (sqrt -1) (sqrt -1/2))))>
#<alt (* -1 (* x (+ (* -1/2 (/ (sqrt -1) (* x (sqrt -1/2)))) (* (sqrt -1) (sqrt -1/2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (sqrt -1) (* x (pow (sqrt -1/2) 3)))) (* 1/2 (/ (sqrt -1) (sqrt -1/2)))) x)) (* (sqrt -1) (sqrt -1/2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (sqrt -1) (pow (sqrt -1/2) 3))) (* -1/16 (/ (sqrt -1) (* x (pow (sqrt -1/2) 5))))) x)) (* 1/2 (/ (sqrt -1) (sqrt -1/2)))) x)) (* (sqrt -1) (sqrt -1/2)))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>

Calls

42 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(sqrt (* x (* x (+ (* x 1/6) 1/2))))
1.0ms	x	@	inf	(sqrt (* x (* x (+ (* x 1/6) 1/2))))
1.0ms	x	@	0	(sqrt (* x (* x (+ (* x 1/6) 1/2))))
0.0ms	x	@	-inf	(sqrt (* x (+ (* 1/2 x) 1)))
0.0ms	x	@	-inf	(sqrt x)

rewrite387.0ms (5%)

Memory

13.8MiB live, 610.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 872×	`/-lowering-/.f32`
4 872×	`/-lowering-/.f64`
4 762×	`-lowering-.f32`
4 762×	`-lowering-.f64`
3 984×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	105
1	129	105
2	978	103
0	8195	86

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 557

Calls

Call 1

Inputs
(+ (* (* x x) 1/2) (+ x 2))
(sqrt (+ (* (* x x) 1/2) (+ x 2)))
(* x x)
(+ x 2)
(sqrt x)
(sqrt (* x (+ (* 1/2 x) 1)))
(* x (+ (* 1/2 x) 1))
(+ (* 1/2 x) 1)
(sqrt (* x (* x (+ (* x 1/6) 1/2))))
(* x (* x (+ (* x 1/6) 1/2)))
(* x (+ (* x 1/6) 1/2))
(+ (* x 1/6) 1/2)
(+ (* (+ (* x 1/6) 1/2) (* x x)) (+ x 2))
(sqrt (+ (* (+ (* x 1/6) 1/2) (* x x)) (+ x 2)))

Outputs
(+.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) (+.f64 x #s(literal 2 binary64)))
(+.f64 #s(literal 2 binary64) (*.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))))
(+.f64 (+.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(+.f64 (*.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal 2 binary64))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal -2 binary64)) x)) (neg.f64 (/.f64 (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) (-.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -2 binary64)) x))))
(+.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) x)
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal -2 binary64)) x)) (/.f64 (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) (-.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -2 binary64)) x)))
(-.f64 (/.f64 (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) (-.f64 (+.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x #s(literal 1/2 binary64))))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (+.f64 x #s(literal 2 binary64)) (.f64 x (*.f64 x #s(literal 1/2 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (*.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64))))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) (+.f64 x #s(literal 2 binary64)))
(fma.f64 x #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) (+.f64 x #s(literal 2 binary64)))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 x #s(literal 1/2 binary64)) x (+.f64 x #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) x (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1 binary64) (+.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 (fma.f64 x (.f64 x x) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 #s(literal 4 binary64) (.f64 x #s(literal 2 binary64))))) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 x (.f64 x x) #s(literal 8 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (-.f64 (.f64 x x) (.f64 x #s(literal 2 binary64))))) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal -2 binary64)) x)) (neg.f64 (/.f64 (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) (-.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -2 binary64)) x))))
(fma.f64 (fma.f64 x x #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -2 binary64))) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 x x) #s(literal 8 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 x x (-.f64 #s(literal 4 binary64) (.f64 x #s(literal 2 binary64)))))) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(fma.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal -4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x #s(literal -2 binary64)))) (.f64 x (.f64 x #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x)))) #s(literal 2 binary64))
(fma.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x (*.f64 x #s(literal 1/2 binary64))) x)) #s(literal 2 binary64))
(fma.f64 (-.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x)) (.f64 x (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x (fma.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(fma.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) #s(literal 2 binary64))
(fma.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)) #s(literal 1 binary64)) x) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal 1 binary64)) (*.f64 x #s(literal 1/2 binary64)))) #s(literal 2 binary64))
(fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/2 binary64) #s(literal -1 binary64))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64)) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))))) (fma.f64 (+.f64 x #s(literal 2 binary64)) (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal 2 binary64)))) (fma.f64 (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (.f64 (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) #s(literal 8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (-.f64 (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal -2 binary64)) (fma.f64 (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal -4 binary64))))
(/.f64 (fma.f64 (+.f64 x #s(literal 2 binary64)) (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (+.f64 x #s(literal 2 binary64)) (-.f64 (+.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64)))))
(/.f64 (fma.f64 (+.f64 x #s(literal 2 binary64)) (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64)) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64)))))))
(/.f64 (.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal -2 binary64)) x)) (-.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -2 binary64)) x))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (+.f64 x #s(literal 2 binary64)) (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (-.f64 #s(literal 0 binary64) (fma.f64 (+.f64 x #s(literal 2 binary64)) (-.f64 (+.f64 x #s(literal 2 binary64)) (.f64 x (.f64 x #s(literal 1/2 binary64)))) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (+.f64 x #s(literal 2 binary64)) (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) (.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (neg.f64 (fma.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64)) (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64))))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 (fma.f64 x (.f64 x #s(literal 1/2 binary64)) #s(literal -2 binary64)) x))) (-.f64 #s(literal 0 binary64) (-.f64 (fma.f64 x (*.f64 x #s(literal 1/2 binary64)) #s(literal -2 binary64)) x)))
(/.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (.f64 (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))) #s(literal 8 binary64)) (fma.f64 (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) (-.f64 #s(literal 4 binary64) (.f64 (.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64))) #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (+.f64 x #s(literal 2 binary64)) (+.f64 x #s(literal 2 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (-.f64 (+.f64 x #s(literal 2 binary64)) (.f64 x (*.f64 x #s(literal 1/2 binary64)))))
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(*.f64 (pow.f64 (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x #s(literal 2 binary64)) #s(literal 1/4 binary64)))

simplify746.0ms (9.6%)

Memory

-4.9MiB live, 848.9MiB allocated

Algorithm

1×	egg-herbie

Rules

15 884×	`accelerator-lowering-fma.f32`
15 884×	`accelerator-lowering-fma.f64`
5 972×	`-lowering-.f32`
5 972×	`-lowering-.f64`
3 956×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	343	1902
1	1102	1708
2	3697	1664
0	8508	1539

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
2
(+ 2 x)
(+ 2 x)
(+ 2 x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 1 (* 2 (/ 1 x))))
(* x (+ 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)))
(sqrt x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))
(* -1 (* x (* (sqrt -1) (sqrt -1/2))))
(* -1 (* x (+ (* -1/2 (/ (sqrt -1) (* x (sqrt -1/2)))) (* (sqrt -1) (sqrt -1/2)))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (sqrt -1) (* x (pow (sqrt -1/2) 3)))) (* 1/2 (/ (sqrt -1) (sqrt -1/2)))) x)) (* (sqrt -1) (sqrt -1/2)))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (/ (sqrt -1) (pow (sqrt -1/2) 3))) (* -1/16 (/ (sqrt -1) (* x (pow (sqrt -1/2) 5))))) x)) (* 1/2 (/ (sqrt -1) (sqrt -1/2)))) x)) (* (sqrt -1) (sqrt -1/2)))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* 1/2 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))

Outputs
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (fma.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (fma.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (fma.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (fma.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x))) #s(literal 1 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 x (*.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1 binary64)) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/4 binary64) (.f64 (.f64 x x) (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (.f64 (.f64 x x) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -3/8 binary64) (.f64 x (.f64 x (.f64 x (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (sqrt 1/2)))
(*.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(-.f64 #s(literal 0 binary64) (fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (fma.f64 x (/.f64 #s(literal -3/4 binary64) (.f64 (.f64 x x) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(-.f64 (fma.f64 x (/.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 3/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) (.f64 x x)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 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)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(fma.f64 #s(literal 1/4 binary64) (sqrt.f64 (.f64 x (.f64 x x))) (sqrt.f64 x))
(+ (sqrt x) (* (pow x 2) (+ (* -1/32 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(fma.f64 (fma.f64 (.f64 x x) #s(literal -1/32 binary64) #s(literal 1 binary64)) (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 x x))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/32 (sqrt (/ 1 (pow x 3)))) (* 1/128 (sqrt (/ 1 x))))))))
(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/32 binary64) (.f64 x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(fma.f64 x (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (- (+ (sqrt 1/2) (/ 1/2 (* x (sqrt 1/2)))) (/ 1/8 (* (pow x 2) (pow (sqrt 1/2) 3)))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) (sqrt.f64 #s(literal 1/2 binary64)))))))
(* x (- (+ (sqrt 1/2) (+ (/ 1/2 (* x (sqrt 1/2))) (* 1/16 (/ 1 (* (pow x 3) (pow (sqrt 1/2) 5)))))) (* 1/8 (/ 1 (* (pow x 2) (pow (sqrt 1/2) 3))))))
(fma.f64 x (/.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (sqrt.f64 #s(literal 1/2 binary64)))) (fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (*.f64 x (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64)))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))))
(* -1 (* x (* (sqrt -1) (sqrt -1/2))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (-.f64 #s(literal 0 binary64) x) (sqrt.f64 #s(literal -1/2 binary64))))
(* -1 (* x (+ (* -1/2 (/ (sqrt -1) (* x (sqrt -1/2)))) (* (sqrt -1) (sqrt -1/2)))))
(-.f64 #s(literal 0 binary64) (fma.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/2 binary64))) (.f64 #s(literal 1 binary64) (/.f64 (*.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/2 binary64))))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (sqrt -1) (* x (pow (sqrt -1/2) 3)))) (* 1/2 (/ (sqrt -1) (sqrt -1/2)))) x)) (* (sqrt -1) (sqrt -1/2)))))
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(.f64 (.f64 x x) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(fma.f64 x (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/16 binary64) (/.f64 x #s(literal -1/6 binary64)) #s(literal 2 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))) (.f64 x x)) (.f64 (.f64 x x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))))

eval344.0ms (4.4%)

Memory: 6.6MiB live, 155.5MiB allocated
Compiler: Compiled 21 708 to 2 466 computations (88.6% saved)

prune103.0ms (1.3%)

Memory

-11.3MiB live, 186.8MiB allocated

Pruning

14 alts after pruning (7 fresh and 7 done)

	Pruned	Kept	Total
New	842	4	846
Fresh	2	3	5
Picked	3	2	5
Done	0	5	5
Total	847	14	861

Accuracy

100.0%

Counts

861 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	1.3%	(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/32 binary64) (.f64 x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x))
	72.5%	(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
▶	73.5%	(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
▶	2.8%	(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
▶	4.1%	(*.f64 x (fma.f64 #s(literal 1/12 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
▶	3.1%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
▶	2.6%	(sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
✓	73.7%	(sqrt.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64))))
✓	72.3%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	73.7%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	72.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	2.6%	(sqrt.f64 x)
✓	77.0%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 254 to 161 computations (36.6% saved)

simplify35.0ms (0.4%)

Memory

8.1MiB live, 48.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(fma.f64 #s(literal 1/12 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 x (fma.f64 #s(literal 1/12 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
✓	cost-diff	0	(sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
✓	cost-diff	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	0	(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
✓	cost-diff	0	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	1344	(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))

Rules

468×	`accelerator-lowering-fma.f32`
468×	`accelerator-lowering-fma.f64`
430×	`-lowering-.f32`
430×	`-lowering-.f64`
186×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	134
1	57	134
2	112	134
3	178	131
4	237	131
5	261	131
6	398	131
7	440	128
8	529	128
9	529	128
10	555	128
11	597	128
12	607	128
13	614	128
0	614	115

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* x (+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2)))) (sqrt 2))
x
(+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2)))
(/ 3/16 (sqrt 2))
3/16
(sqrt 2)
2
(/ 1/2 (sqrt 2))
1/2
(* x (sqrt 1/2))
x
(sqrt 1/2)
1/2
(* (sqrt (+ (* x 1/6) 1/2)) x)
(sqrt (+ (* x 1/6) 1/2))
(+ (* x 1/6) 1/2)
x
1/6
1/2
(sqrt (+ (* (+ (* x 1/6) 1/2) (* x x)) x))
(+ (* (+ (* x 1/6) 1/2) (* x x)) x)
(+ (* x 1/6) 1/2)
x
1/6
1/2
(* x x)
(* x (+ (* 1/12 (/ x (sqrt 1/2))) (sqrt 1/2)))
x
(+ (* 1/12 (/ x (sqrt 1/2))) (sqrt 1/2))
1/12
(/ x (sqrt 1/2))
(sqrt 1/2)
1/2

Outputs
(+ (* x (+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2)))) (sqrt 2))
(fma.f64 x (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
x
(+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2)))
(/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/ 3/16 (sqrt 2))
(/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))
3/16
#s(literal 3/16 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
x
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* (sqrt (+ (* x 1/6) 1/2)) x)
(*.f64 x (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
(sqrt (+ (* x 1/6) 1/2))
(sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(+ (* x 1/6) 1/2)
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
x
1/6
#s(literal 1/6 binary64)
1/2
#s(literal 1/2 binary64)
(sqrt (+ (* (+ (* x 1/6) 1/2) (* x x)) x))
(sqrt.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(+ (* (+ (* x 1/6) 1/2) (* x x)) x)
(*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(+ (* x 1/6) 1/2)
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
x
1/6
#s(literal 1/6 binary64)
1/2
#s(literal 1/2 binary64)
(* x x)
(*.f64 x x)
(* x (+ (* 1/12 (/ x (sqrt 1/2))) (sqrt 1/2)))
(*.f64 x (fma.f64 x (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
x
(+ (* 1/12 (/ x (sqrt 1/2))) (sqrt 1/2))
(fma.f64 x (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
1/12
#s(literal 1/12 binary64)
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)

localize94.0ms (1.2%)

Memory

-8.9MiB live, 156.3MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/12 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(*.f64 x (fma.f64 #s(literal 1/12 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
✓	accuracy	99.7%	(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x)
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓	accuracy	99.7%	(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	99.7%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
✓	accuracy	99.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))

Samples

36.0ms	158×	0	invalid
19.0ms	98×	0	valid

Compiler

Compiled 123 to 29 computations (76.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 15.0ms (39% of total)

ival-sqrt: 7.0ms (18.2% of total)

const: 6.0ms (15.6% of total)

ival-div: 5.0ms (13% of total)

ival-add: 5.0ms (13% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.2%)

Memory

23.0MiB live, 23.0MiB allocated

Counts

16 → 144

Calls

Call 1

Inputs
#<alt (+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2)))>
#<alt (+ (* x (+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2)))) (sqrt 2))>
#<alt (/ 3/16 (sqrt 2))>
#<alt (sqrt 2)>
#<alt (* x (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (* (sqrt (+ (* x 1/6) 1/2)) x)>
#<alt (sqrt (+ (* x 1/6) 1/2))>
#<alt (+ (* x 1/6) 1/2)>
#<alt (sqrt (+ (* (+ (* x 1/6) 1/2) (* x x)) x))>
#<alt (+ (* (+ (* x 1/6) 1/2) (* x x)) x)>
#<alt (* x x)>
#<alt (* x (+ (* 1/12 (/ x (sqrt 1/2))) (sqrt 1/2)))>
#<alt (+ (* 1/12 (/ x (sqrt 1/2))) (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ 1/2 (sqrt 2))>

Outputs
#<alt (/ 1/2 (sqrt 2))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))))))>
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt x) (/ (sqrt -1) (pow (sqrt -1/6) 3))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* 1/12 (/ (pow x 2) (sqrt 1/2)))>
#<alt (* (pow x 2) (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))>
#<alt (* (pow x 2) (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))>
#<alt (* (pow x 2) (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))>
#<alt (* 1/12 (/ (pow x 2) (sqrt 1/2)))>
#<alt (* (pow x 2) (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))>
#<alt (* (pow x 2) (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))>
#<alt (* (pow x 2) (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))>
#<alt (* 1/12 (/ x (sqrt 1/2)))>
#<alt (* x (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))>
#<alt (* x (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))>
#<alt (* x (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))>
#<alt (* 1/12 (/ x (sqrt 1/2)))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/12 (/ 1 (sqrt 1/2))))))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/12 (/ 1 (sqrt 1/2))))))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/12 (/ 1 (sqrt 1/2))))))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>
#<alt (/ x (sqrt 1/2))>

Calls

36 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(+ (* x (+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2)))) (sqrt 2))
1.0ms	x	@	0	(+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2)))
1.0ms	x	@	-inf	(sqrt (+ (* x 1/6) 1/2))
1.0ms	x	@	0	(* x (+ (* 1/12 (/ x (sqrt 1/2))) (sqrt 1/2)))
1.0ms	x	@	-inf	(* (sqrt (+ (* x 1/6) 1/2)) x)

rewrite347.0ms (4.5%)

Memory

-12.6MiB live, 494.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 434×	`accelerator-lowering-fma.f32`
5 434×	`accelerator-lowering-fma.f64`
3 836×	`-lowering-.f32`
3 836×	`-lowering-.f64`
3 622×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	112
1	146	112
2	1232	109
0	8408	97

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 504

Calls

Call 1

Inputs
(+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2)))
(+ (* x (+ (* x (/ 3/16 (sqrt 2))) (/ 1/2 (sqrt 2)))) (sqrt 2))
(/ 3/16 (sqrt 2))
(sqrt 2)
(* x (sqrt 1/2))
(sqrt 1/2)
(* (sqrt (+ (* x 1/6) 1/2)) x)
(sqrt (+ (* x 1/6) 1/2))
(+ (* x 1/6) 1/2)
(sqrt (+ (* (+ (* x 1/6) 1/2) (* x x)) x))
(+ (* (+ (* x 1/6) 1/2) (* x x)) x)
(* x x)
(* x (+ (* 1/12 (/ x (sqrt 1/2))) (sqrt 1/2)))
(+ (* 1/12 (/ x (sqrt 1/2))) (sqrt 1/2))
(/ x (sqrt 1/2))
(/ 1/2 (sqrt 2))

Outputs
(+.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 9/512 binary64)) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(-.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 9/512 binary64)) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/8 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 9/512 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 3/16 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 (.f64 (.f64 x x) #s(literal 9/512 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 1/8 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x #s(literal 16/3 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 x #s(literal 3/16 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 (*.f64 x #s(literal -3/16 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/2 binary64)) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/4 binary64)) #s(literal -1 binary64)) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(fma.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 3/16 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 3/16 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) (/.f64 x (*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 16/3 binary64))))
(neg.f64 (/.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 27/4096 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) #s(literal 8 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) #s(literal 9/512 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x #s(literal 3/16 binary64)) #s(literal 1/4 binary64)))))))
(neg.f64 (/.f64 (fma.f64 (*.f64 x x) #s(literal 9/512 binary64) #s(literal -1/8 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 27/4096 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) #s(literal 8 binary64))) (fma.f64 (.f64 x x) #s(literal 9/512 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x #s(literal 3/16 binary64)) #s(literal 1/4 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 x x) #s(literal 9/512 binary64) #s(literal -1/8 binary64))) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 27/4096 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) #s(literal 8 binary64)) (fma.f64 (.f64 x x) #s(literal 9/512 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x #s(literal 3/16 binary64)) #s(literal 1/4 binary64)))))
(/.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 27/4096 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) #s(literal 8 binary64)) (+.f64 #s(literal 1/8 binary64) (fma.f64 (.f64 x x) #s(literal 9/512 binary64) (-.f64 #s(literal 0 binary64) (.f64 (*.f64 x #s(literal 3/16 binary64)) #s(literal 1/4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 9/512 binary64) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (fma.f64 (.f64 x x) #s(literal 9/512 binary64) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x #s(literal 3/16 binary64)) #s(literal 1/4 binary64))))) (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 27/4096 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/8 binary64))) #s(literal 8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 9/512 binary64) #s(literal -1/8 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fma.f64 (.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (fma.f64 (.f64 x #s(literal 3/16 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (fma.f64 (.f64 x #s(literal 3/16 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x #s(literal 3/16 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 4 binary64) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 3/16 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64))) (-.f64 #s(literal 1/8 binary64) (.f64 (*.f64 x x) #s(literal 9/512 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 9/512 binary64) #s(literal -1/8 binary64)) (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (fma.f64 x #s(literal 3/16 binary64) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 x x) #s(literal 9/512 binary64) #s(literal -1/8 binary64)))))
(/.f64 (fma.f64 (.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64))
(/.f64 (fma.f64 (.f64 x #s(literal 3/16 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))) #s(literal -2 binary64))
(/.f64 (fma.f64 (.f64 x #s(literal 3/16 binary64)) (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 4 binary64))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3/16 binary64)))) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x #s(literal 3/16 binary64)))) #s(literal -2 binary64))
(/.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 x #s(literal 3/16 binary64)))) #s(literal 4 binary64))
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(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/2 binary64)))

simplify482.0ms (6.2%)

Memory

37.0MiB live, 674.8MiB allocated

Algorithm

1×	egg-herbie

Rules

14 852×	`accelerator-lowering-fma.f32`
14 852×	`accelerator-lowering-fma.f64`
5 682×	`-lowering-.f32`
5 682×	`-lowering-.f64`
2 774×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	230	1786
1	745	1730
2	2369	1669
3	5506	1638
0	8345	1530

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt 1/6))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt x) (/ (sqrt -1) (pow (sqrt -1/6) 3))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* 1/12 (/ (pow x 2) (sqrt 1/2)))
(* (pow x 2) (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))
(* (pow x 2) (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))
(* (pow x 2) (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))
(* 1/12 (/ (pow x 2) (sqrt 1/2)))
(* (pow x 2) (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))
(* (pow x 2) (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))
(* (pow x 2) (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))
(* 1/12 (/ x (sqrt 1/2)))
(* x (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))
(* x (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))
(* x (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))
(* 1/12 (/ x (sqrt 1/2)))
(* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/12 (/ 1 (sqrt 1/2))))))
(* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/12 (/ 1 (sqrt 1/2))))))
(* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/12 (/ 1 (sqrt 1/2))))))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))
(/ x (sqrt 1/2))

Outputs
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* 3/16 (/ x (sqrt 2)))
(*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(*.f64 x (fma.f64 x (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(*.f64 x (fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/144 binary64) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(*.f64 x (fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 1/3456 binary64) (pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/144 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(.f64 (.f64 x x) (fma.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 1/6 binary64)))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(.f64 (.f64 x x) (fma.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/128 binary64) (pow.f64 (sqrt.f64 #s(literal 1/6 binary64)) #s(literal 5 binary64))) (fma.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 1/6 binary64))))))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(.f64 (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (sqrt.f64 #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64))))
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(* x (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))
(fma.f64 x (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))
(fma.f64 x (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(* x (+ (* 1/12 (/ 1 (sqrt 1/2))) (/ (sqrt 1/2) x)))
(fma.f64 x (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(* 1/12 (/ x (sqrt 1/2)))
(/.f64 (*.f64 x #s(literal 1/12 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/12 (/ 1 (sqrt 1/2))))))
(fma.f64 x (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/12 (/ 1 (sqrt 1/2))))))
(fma.f64 x (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* x (- (* -1 (/ (sqrt 1/2) x)) (* 1/12 (/ 1 (sqrt 1/2))))))
(fma.f64 x (/.f64 #s(literal 1/12 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(/ x (sqrt 1/2))
(/.f64 x (sqrt.f64 #s(literal 1/2 binary64)))

eval177.0ms (2.3%)

Memory: -26.6MiB live, 98.7MiB allocated
Compiler: Compiled 17 882 to 2 009 computations (88.8% saved)

prune262.0ms (3.4%)

Memory

31.3MiB live, 145.0MiB allocated

Pruning

19 alts after pruning (9 fresh and 10 done)

	Pruned	Kept	Total
New	751	7	758
Fresh	0	2	2
Picked	2	3	5
Done	0	7	7
Total	753	19	772

Accuracy

100.0%

Counts

772 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	2.6%	(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1 binary64)) (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 x x))))
	73.5%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	1.3%	(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/32 binary64) (.f64 x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x))
	2.6%	(fma.f64 (.f64 x x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 5/96 binary64) x #s(literal 1/4 binary64))) (sqrt.f64 x))
	73.5%	(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
	72.5%	(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	4.1%	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
✓	2.8%	(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
	1.8%	(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
✓	3.1%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	4.3%	(.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
✓	2.6%	(sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
✓	73.7%	(sqrt.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64))))
✓	72.3%	(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	73.7%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	72.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	2.6%	(sqrt.f64 x)
✓	77.0%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 490 to 237 computations (51.6% saved)

regimes86.0ms (1.1%)

Memory

-13.5MiB live, 33.6MiB allocated

Counts

27 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
(sqrt.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64))))
(sqrt.f64 (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))
(sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (+.f64 x #s(literal 2 binary64))))
(.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(*.f64 x (fma.f64 #s(literal 1/12 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 5/96 binary64) x #s(literal 1/4 binary64))) (sqrt.f64 x))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1 binary64)) (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 x x))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/32 binary64) (.f64 x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x))
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

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

Calls

3 calls:

8.0ms

7.0ms

(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

6.0ms

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

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
100.0%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes23.0ms (0.3%)

Memory

-12.6MiB live, 26.1MiB allocated

Accuracy

Total -48.7b remaining (-330.1%)

Threshold costs -48.7b (-330.1%)

Counts

25 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
(sqrt.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 (*.f64 x x) #s(literal 1/2 binary64) (+.f64 x #s(literal 2 binary64))))
(sqrt.f64 (.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x))))
(sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
(sqrt.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) x))
(sqrt.f64 (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64)))
(sqrt.f64 (fma.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) (*.f64 x x) (+.f64 x #s(literal 2 binary64))))
(.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)))
(*.f64 x (fma.f64 #s(literal 1/12 binary64) (/.f64 x (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 5/96 binary64) x #s(literal 1/4 binary64))) (sqrt.f64 x))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1 binary64)) (sqrt.f64 x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 x x))))
(fma.f64 x (fma.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x (fma.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal -1/32 binary64) (.f64 x x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal 1/128 binary64) (*.f64 x x) #s(literal 1/4 binary64)))) (sqrt.f64 x))

Outputs
(sqrt.f64 #s(literal 2 binary64))

Calls

3 calls:

8.0ms

(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))

7.0ms

6.0ms

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

Results

Accuracy	Segments	Branch
77.0%	1	`x`
77.0%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
77.0%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`

Compiler

Compiled 27 to 20 computations (25.9% saved)

simplify7.0ms (0.1%)

Memory

8.6MiB live, 8.6MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	9	7
2	13	7
3	14	7
4	15	7

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 #s(literal 2 binary64))

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

soundness344.0ms (4.4%)

Memory

-18.7MiB live, 175.8MiB allocated

Rules

14 886×	`accelerator-lowering-fma.f32`
14 886×	`accelerator-lowering-fma.f64`
5 402×	`accelerator-lowering-fma.f32`
5 402×	`accelerator-lowering-fma.f64`
4 492×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	50	21
2	372	21
3	4517	21
0	8145	17
0	49	360
1	155	360
2	336	360
3	754	360
4	1207	320
5	1539	304
6	2137	304
7	3095	304
8	4622	304
0	8209	249

Stop Event

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

Compiler

Compiled 17 to 15 computations (11.8% saved)

preprocess22.0ms (0.3%)

Memory: 19.3MiB live, 56.6MiB allocated
Compiler: Compiled 42 to 34 computations (19% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	27	134
1	57	134
2	112	134
3	178	131
4	237	131
5	261	131
6	398	131
7	440	128
8	529	128
9	529	128
10	555	128
11	597	128
12	607	128
13	614	128
0	614	115

Iter	Nodes	Cost
0	27	134
1	57	134
2	112	134
3	178	131
4	237	131
5	261	131
6	398	131
7	440	128
8	529	128
9	529	128
10	555	128
11	597	128
12	607	128
13	614	128
0	614	115

analyze1.0ms (0%)

sample893.0ms (11.5%)

preprocess496.0ms (6.4%)

explain135.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify450.0ms (5.8%)

localize32.0ms (0.4%)

series57.0ms (0.7%)

rewrite365.0ms (4.7%)

simplify494.0ms (6.4%)

eval96.0ms (1.2%)

prune87.0ms (1.1%)

simplify15.0ms (0.2%)

localize115.0ms (1.5%)

series11.0ms (0.1%)

rewrite336.0ms (4.3%)

simplify404.0ms (5.2%)

eval99.0ms (1.3%)

prune74.0ms (1%)

simplify15.0ms (0.2%)

localize105.0ms (1.4%)

series11.0ms (0.1%)

rewrite387.0ms (5%)

simplify746.0ms (9.6%)

eval344.0ms (4.4%)

prune103.0ms (1.3%)

simplify35.0ms (0.4%)

localize94.0ms (1.2%)

series12.0ms (0.2%)

rewrite347.0ms (4.5%)

simplify482.0ms (6.2%)

eval177.0ms (2.3%)

prune262.0ms (3.4%)

regimes86.0ms (1.1%)

regimes23.0ms (0.3%)

simplify7.0ms (0.1%)

soundness344.0ms (4.4%)

preprocess22.0ms (0.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	27	134
1	57	134
2	112	134
3	178	131
4	237	131
5	261	131
6	398	131
7	440	128
8	529	128
9	529	128
10	555	128
11	597	128
12	607	128
13	614	128
0	614	115