Metrics for sqrtexp (problem 3.4.4)

analyze2.0ms (0%)

Memory

3.2MiB live, 3.2MiB 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)

sample886.0ms (11%)

Memory

38.6MiB live, 917.7MiB allocated

Samples

450.0ms	8 256×	0	valid
152.0ms	2 585×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 390.0ms

ival-expm1: 125.0ms (32% of total)

ival-div: 93.0ms (23.8% of total)

ival-sqrt: 78.0ms (20% of total)

ival-mult: 77.0ms (19.7% of total)

ival-true: 8.0ms (2.1% of total)

exact: 6.0ms (1.5% of total)

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

Bogosity

preprocess489.0ms (6%)

Memory

4.6MiB live, 409.8MiB 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)))))

explain136.0ms (1.7%)

Memory

3.0MiB live, 158.4MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	169	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	169	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

Confusion

	Predicted +	Predicted -
+	168	0
-	2	86

Precision

0.9882352941176471

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	168	0	0
-	2	1	85

Precision?

0.9824561403508771

Recall?

1.0

Freqs

test

number	freq
0	86
1	1
2	169

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

42.0ms

512×

valid

Compiler

Compiled 120 to 44 computations (63.3% saved)

Precisions

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

ival-exp: 7.0ms (28.1% of total)

ival-expm1: 6.0ms (24.1% of total)

ival-div: 4.0ms (16.1% of total)

ival-mult: 4.0ms (16.1% of total)

ival-sqrt: 3.0ms (12.1% of total)

exact: 1.0ms (4% 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
▶	35.5%	(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)

simplify448.0ms (5.5%)

Memory

25.7MiB live, 454.5MiB 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)

localize35.0ms (0.4%)

Memory

-17.9MiB live, 42.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
✓	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	38.6%	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓	accuracy	38.5%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

23.0ms

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 (24.4% of total)

ival-expm1: 3.0ms (24.4% of total)

ival-div: 2.0ms (16.3% of total)

ival-mult: 2.0ms (16.3% of total)

ival-sqrt: 2.0ms (16.3% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

6.0MiB live, 6.0MiB 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 (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>

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

Calls

15 calls:

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

rewrite372.0ms (4.6%)

Memory

-15.0MiB live, 409.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 562×	`accelerator-lowering-fma.f32`
4 562×	`accelerator-lowering-fma.f64`
3 484×	`-lowering-.f32`
3 484×	`-lowering-.f64`
2 734×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	56	22
2	421	22
3	4985	22
0	8093	18

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 711

Calls

Call 1

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

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

simplify418.0ms (5.2%)

Memory

28.1MiB live, 500.1MiB allocated

Algorithm

1×	egg-herbie

Rules

15 504×	`accelerator-lowering-fma.f32`
15 504×	`accelerator-lowering-fma.f64`
4 704×	`-lowering-.f32`
4 704×	`-lowering-.f64`
2 492×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	480
1	252	446
2	663	446
3	1429	440
4	2558	360
5	5941	325
0	8294	270

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

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)
(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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

eval98.0ms (1.2%)

Memory: 7.2MiB live, 203.8MiB allocated
Compiler: Compiled 18 171 to 2 478 computations (86.4% saved)

prune92.0ms (1.1%)

Memory

-15.1MiB live, 193.0MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	762	9	771
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	763	9	772

Accuracy

100.0%

Counts

772 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.7%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	67.7%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶	66.5%	(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
	66.4%	(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)))
▶	68.0%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
	99.6%	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
▶	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
	66.2%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
▶	72.5%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 160 to 116 computations (27.5% saved)

simplify35.0ms (0.4%)

Memory

-12.8MiB live, 65.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Program
✓	cost-diff	(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #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	(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

1 172×	`accelerator-lowering-fma.f32`
1 172×	`accelerator-lowering-fma.f64`
478×	`-lowering-.f32`
478×	`-lowering-.f64`
226×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	104
1	63	104
2	143	104
3	325	104
4	601	104
5	821	104
6	826	104
0	826	92

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 (+ (* x (+ (* x 1/2) 1)) 2))
(+ (* x (+ (* x 1/2) 1)) 2)
x
(+ (* x 1/2) 1)
1/2
1
2
(+ (* x (/ 1/2 (sqrt 2))) (sqrt 2))
x
(/ 1/2 (sqrt 2))
1/2
(sqrt 2)
2
(+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2))
(/ x (sqrt 2))
x
(sqrt 2)
2
(+ (* x (+ (* x 7/192) 3/16)) 1/2)
(+ (* x 7/192) 3/16)
7/192
3/16
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 (+ (* 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)
(+ (* x (/ 1/2 (sqrt 2))) (sqrt 2))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
x
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ (* x (+ (* x 7/192) 3/16)) 1/2)
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(+ (* x 7/192) 3/16)
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
7/192
#s(literal 7/192 binary64)
3/16
#s(literal 3/16 binary64)
1/2
#s(literal 1/2 binary64)

localize89.0ms (1.1%)

Memory

21.1MiB live, 170.0MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.9%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	99.8%	(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
✓	accuracy	99.3%	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.8%	(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	98.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 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	86.1%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	accuracy	100.0%	(-.f64 (exp.f64 x) #s(literal -1 binary64))

Samples

49.0ms	242×	0	valid
6.0ms	8×	1	valid
2.0ms	5×	2	valid
1.0ms	1×	5	exit

Compiler

Compiled 94 to 28 computations (70.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 13.0ms (32% of total)

const: 7.0ms (17.3% of total)

ival-add: 7.0ms (17.3% of total)

ival-sqrt: 5.0ms (12.3% of total)

ival-div: 3.0ms (7.4% of total)

ival-exp: 2.0ms (4.9% of total)

adjust: 1.0ms (2.5% of total)

exact: 1.0ms (2.5% of total)

ival-sub: 1.0ms (2.5% of total)

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

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

series15.0ms (0.2%)

Memory

-15.6MiB live, 27.9MiB allocated

Counts

13 → 132

Calls

Call 1

Inputs
#<alt (sqrt (- (exp x) -1))>
#<alt (- (exp x) -1)>
#<alt (exp x)>
#<alt (sqrt 2)>
#<alt (sqrt (+ (* x (+ (* x 1/2) 1)) 2))>
#<alt (+ (* x (+ (* x 1/2) 1)) 2)>
#<alt (+ (* x 1/2) 1)>
#<alt (+ (* x (/ 1/2 (sqrt 2))) (sqrt 2))>
#<alt (/ 1/2 (sqrt 2))>
#<alt (+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (+ (* x (+ (* x 7/192) 3/16)) 1/2)>
#<alt (+ (* x 7/192) 3/16)>

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 (+ (* 1/2 (/ (* 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) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (* 1/2 (/ x (sqrt 2)))>
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))>
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))>
#<alt (* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))>
#<alt (* 1/2 (/ x (sqrt 2)))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt 1/2>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (+ 1/2 (* x (+ 3/16 (* 7/192 x))))>
#<alt (+ 1/2 (* x (+ 3/16 (* 7/192 x))))>
#<alt (* 7/192 (pow x 2))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* 7/192 (pow x 2))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt 3/16>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>

Calls

33 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	(/ x (sqrt 2))
1.0ms	x	@	0	(+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2))
1.0ms	x	@	inf	(sqrt (- (exp x) -1))
1.0ms	x	@	inf	(sqrt (+ (* x (+ (* x 1/2) 1)) 2))
0.0ms	x	@	inf	(+ (* x (/ 1/2 (sqrt 2))) (sqrt 2))

rewrite397.0ms (4.9%)

Memory

-8.7MiB live, 536.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 414×	`accelerator-lowering-fma.f32`
4 414×	`accelerator-lowering-fma.f64`
4 324×	`/-lowering-/.f32`
4 324×	`/-lowering-/.f64`
3 476×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	85
1	168	84
2	1405	83
0	8278	71

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 496

Calls

Call 1

Inputs
(sqrt (- (exp x) -1))
(- (exp x) -1)
(exp x)
(sqrt 2)
(sqrt (+ (* x (+ (* x 1/2) 1)) 2))
(+ (* x (+ (* x 1/2) 1)) 2)
(+ (* x 1/2) 1)
(+ (* x (/ 1/2 (sqrt 2))) (sqrt 2))
(/ 1/2 (sqrt 2))
(+ (* (/ x (sqrt 2)) (+ (* x (+ (* x 7/192) 3/16)) 1/2)) (sqrt 2))
(/ x (sqrt 2))
(+ (* x (+ (* x 7/192) 3/16)) 1/2)
(+ (* x 7/192) 3/16)

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)))))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (.f64 x #s(literal 7/1024 binary64)))) (fma.f64 (.f64 x (*.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64))) (-.f64 #s(literal 9/256 binary64) (.f64 (*.f64 x x) #s(literal 49/36864 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (+.f64 #s(literal 9/256 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (-.f64 #s(literal 0 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (+.f64 #s(literal 9/256 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(/.f64 (-.f64 #s(literal 9/256 binary64) (.f64 (.f64 x x) #s(literal 49/36864 binary64))) (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) #s(literal 9/256 binary64))) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (.f64 x #s(literal 7/1024 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 9/256 binary64) (.f64 (.f64 x x) #s(literal 49/36864 binary64)))) (neg.f64 (-.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (fma.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (.f64 (/.f64 (.f64 (*.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) (.f64 (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 9/256 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 9/256 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 49/36864 binary64)) (.f64 x #s(literal 7/1024 binary64))))))
(.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal 7/1024 binary64))))))
(.f64 (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(.f64 (-.f64 #s(literal 9/256 binary64) (.f64 (.f64 x x) #s(literal 49/36864 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64)))))

simplify455.0ms (5.6%)

Memory

-11.1MiB live, 465.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10 586×	`accelerator-lowering-fma.f32`
10 586×	`accelerator-lowering-fma.f64`
3 958×	`-lowering-.f32`
3 958×	`-lowering-.f64`
2 708×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	196	1199
1	652	1039
2	2116	953
3	6397	949
0	8336	866

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

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 (+ (* 1/2 (/ (* 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) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(* 1/2 (/ x (sqrt 2)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(* x (+ (* 1/2 (/ 1 (sqrt 2))) (/ (sqrt 2) x)))
(* 1/2 (/ x (sqrt 2)))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2))))))
(* -1 (* x (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))

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

eval100.0ms (1.2%)

Memory: 15.2MiB live, 199.2MiB allocated
Compiler: Compiled 16 643 to 1 741 computations (89.5% saved)

prune78.0ms (1%)

Memory

10.6MiB live, 174.6MiB allocated

Pruning

15 alts after pruning (11 fresh and 4 done)

	Pruned	Kept	Total
New	676	8	684
Fresh	1	3	4
Picked	1	4	5
Done	0	0	0
Total	678	15	693

Accuracy

100.0%

Counts

693 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	66.7%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	66.7%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	66.0%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
	66.6%	(fma.f64 (.f64 (fma.f64 x (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal -1/4 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
	2.6%	(/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
▶	3.1%	(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
	2.9%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
▶	66.4%	(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)))
✓	68.0%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
▶	99.6%	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
▶	66.2%	(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
▶	66.2%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
	4.0%	(sqrt.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
✓	72.5%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 307 to 211 computations (31.3% saved)

simplify418.0ms (5.2%)

Memory

9.3MiB live, 530.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
✓	cost-diff	0	(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
✓	cost-diff	0	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))
✓	cost-diff	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))
✓	cost-diff	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)))
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	cost-diff	192	(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(expm1.f64 (+.f64 x x))
✓	cost-diff	0	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓	cost-diff	7104	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))

Rules

13 134×	`accelerator-lowering-fma.f32`
13 134×	`accelerator-lowering-fma.f64`
2 880×	`--lowering--.f32`
2 880×	`--lowering--.f64`
2 694×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	142
1	80	142
2	196	142
3	454	132
4	672	128
5	963	128
6	1599	128
7	3973	128
0	8614	112

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1)))
(/ (- (exp (+ x x)) 1) (- (exp x) 1))
(- (exp (+ x x)) 1)
(+ x x)
x
(- (exp x) 1)
(sqrt (+ 2 x))
(+ 2 x)
2
x
(sqrt (- (+ x 1) -1))
(- (+ x 1) -1)
(+ x 1)
x
1
-1
(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
(* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)))
x
(* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))
(/ x (sqrt 2))
(sqrt 2)
2
(+ (* x 7/192) 3/16)
7/192
3/16

Outputs
(sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ (- (exp (+ x x)) 1) (- (exp x) 1))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(- (exp (+ x x)) 1)
(expm1.f64 (+.f64 x x))
(+ x x)
(+.f64 x x)
x
(- (exp x) 1)
(expm1.f64 x)
(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 1) -1))
(sqrt.f64 (+.f64 x #s(literal 2 binary64)))
(- (+ x 1) -1)
(+.f64 x #s(literal 2 binary64))
(+ x 1)
(+.f64 x #s(literal 1 binary64))
x
1
#s(literal 1 binary64)
-1
#s(literal -1 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)
(* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)))
(.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 (.f64 x x) (sqrt.f64 #s(literal 2 binary64))))
x
(* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ (* x 7/192) 3/16)
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
7/192
#s(literal 7/192 binary64)
3/16
#s(literal 3/16 binary64)

localize265.0ms (3.3%)

Memory

-23.6MiB live, 130.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
✓	accuracy	99.7%	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
✓	accuracy	99.6%	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 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%	(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%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	accuracy	100.0%	(-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(expm1.f64 (+.f64 x x))
✓	accuracy	100.0%	(expm1.f64 x)
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓	accuracy	99.7%	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))

Samples

37.0ms	172×	0	valid
19.0ms	83×	0	invalid
1.0ms	1×	5	exit

Compiler

Compiled 124 to 33 computations (73.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 9.0ms (22.1% of total)

ival-sqrt: 8.0ms (19.6% of total)

ival-add: 8.0ms (19.6% of total)

const: 7.0ms (17.2% of total)

ival-div: 4.0ms (9.8% of total)

ival-expm1: 3.0ms (7.4% of total)

exact: 1.0ms (2.5% of total)

ival-sub: 1.0ms (2.5% of total)

adjust: 0.0ms (0% of total)

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

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

series13.0ms (0.2%)

Memory

30.2MiB live, 30.2MiB allocated

Counts

18 → 204

Calls

Call 1

Inputs
#<alt (/ (- (exp (+ x x)) 1) (- (exp x) 1))>
#<alt (sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1)))>
#<alt (- (exp (+ x x)) 1)>
#<alt (+ x x)>
#<alt (sqrt (+ 2 x))>
#<alt (+ 2 x)>
#<alt (- (+ x 1) -1)>
#<alt (sqrt (- (+ x 1) -1))>
#<alt (+ x 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)>
#<alt (* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)))>
#<alt (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))>
#<alt (/ x (sqrt 2))>
#<alt (sqrt 2)>
#<alt (- (exp x) 1)>

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 (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (sqrt (/ (- (exp (neg (* -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 (neg (* -2 x))) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt (- (exp (neg (* -2 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 (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 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 (+ (* -1/8 (/ 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 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (sqrt 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))))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* 3/16 (/ x (sqrt 2)))>
#<alt (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* 7/192 (/ (pow x 2) (sqrt 2)))>
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<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)>

Calls

51 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)))
1.0ms	x	@	-inf	(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
1.0ms	x	@	-inf	(sqrt (+ 2 x))
1.0ms	x	@	inf	(sqrt (+ (* x (+ (* x (+ (* x 1/6) 1/2)) 1)) 2))
1.0ms	x	@	inf	(sqrt (+ 2 x))

rewrite383.0ms (4.7%)

Memory

-12.5MiB live, 692.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 132×	`/-lowering-/.f32`
4 132×	`/-lowering-/.f64`
3 590×	`accelerator-lowering-fma.f32`
3 590×	`accelerator-lowering-fma.f64`
3 064×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	124
1	209	110
2	1774	106
0	9494	91

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 1 038

Calls

Call 1

Inputs
(/ (- (exp (+ x x)) 1) (- (exp x) 1))
(sqrt (/ (- (exp (+ x x)) 1) (- (exp x) 1)))
(- (exp (+ x x)) 1)
(+ x x)
(sqrt (+ 2 x))
(+ 2 x)
(- (+ x 1) -1)
(sqrt (- (+ x 1) -1))
(+ x 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)
(* x (* (/ x (sqrt 2)) (+ (* x 7/192) 3/16)))
(* (/ x (sqrt 2)) (+ (* x 7/192) 3/16))
(/ x (sqrt 2))
(sqrt 2)
(- (exp x) 1)

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

simplify668.0ms (8.3%)

Memory

-3.5MiB live, 417.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12 486×	`accelerator-lowering-fma.f32`
12 486×	`accelerator-lowering-fma.f64`
5 022×	`-lowering-.f32`
5 022×	`-lowering-.f64`
3 174×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	270	2007
1	846	1851
2	2577	1765
3	5606	1737
0	8200	1522

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

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 (neg (* -2 x))) 1) (- (exp x) 1))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt (/ (- (exp (neg (* -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 (neg (* -2 x))) 1)
(- (exp (neg (* -2 x))) 1)
(- (exp (neg (* -2 x))) 1)
(- (exp (neg (* -2 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)
(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))))
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 (+ (* -1/8 (/ 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)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(sqrt 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))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* (pow x 2) (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2)))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
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)

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 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.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 (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 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 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 x x) #s(literal 7/192 binary64) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(sqrt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.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 (neg (* -2 x))) 1)
(expm1.f64 (+.f64 x x))
(- (exp (neg (* -2 x))) 1)
(expm1.f64 (+.f64 x x))
(- (exp (neg (* -2 x))) 1)
(expm1.f64 (+.f64 x x))
(- (exp (neg (* -2 x))) 1)
(expm1.f64 (+.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)
(* 2 x)
(+.f64 x 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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal -1/16 binary64) #s(literal 1/2 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 x (/.f64 #s(literal 1/16 binary64) (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 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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)))))))
(* 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
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#s(literal 2 binary64)
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#s(literal 2 binary64)
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#s(literal 1 binary64)
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(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 (.f64 x x) #s(literal 7/192 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
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)

eval199.0ms (2.5%)

Memory: 5.8MiB live, 269.6MiB allocated
Compiler: Compiled 24 152 to 3 384 computations (86% saved)

prune134.0ms (1.7%)

Memory

-6.7MiB live, 282.6MiB allocated

Pruning

20 alts after pruning (11 fresh and 9 done)

	Pruned	Kept	Total
New	1 237	5	1 242
Fresh	0	6	6
Picked	0	5	5
Done	0	4	4
Total	1 237	20	1 257

Accuracy

100.0%

Counts

1 257 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	66.7%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶	66.7%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	66.0%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
	66.6%	(fma.f64 (.f64 (fma.f64 x (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal -1/4 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
▶	4.2%	(/.f64 (.f64 (.f64 x x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	2.6%	(/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
✓	3.1%	(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
	2.9%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	66.4%	(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)))
✓	68.0%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	99.6%	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓	66.2%	(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	66.2%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
	2.3%	(sqrt.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
▶	4.0%	(sqrt.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
▶	3.4%	(sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
	2.2%	(sqrt.f64 (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
▶	2.3%	(sqrt.f64 x)
✓	72.5%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 346 to 237 computations (31.5% saved)

simplify189.0ms (2.3%)

Memory

-2.4MiB live, 193.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Program
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) #s(literal 3/16 binary64))
✓	cost-diff	(/.f64 (.f64 (.f64 x x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
✓	cost-diff	(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
✓	cost-diff	(.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))))
✓	cost-diff	(sqrt.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))))
✓	cost-diff	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
✓	cost-diff	(*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
✓	cost-diff	(sqrt.f64 (*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(fma.f64 x (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 1/2 binary64))
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
✓	cost-diff	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))

Rules

2 544×	`accelerator-lowering-fma.f32`
2 544×	`accelerator-lowering-fma.f64`
1 616×	`-lowering-.f32`
1 616×	`-lowering-.f64`
1 314×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	164
1	80	164
2	173	164
3	355	164
4	528	164
5	906	164
6	1255	164
7	2314	164
8	3037	164
9	3256	164
10	3297	164
11	3331	164
12	3370	164
13	3376	164
14	3376	164
15	3390	164
16	3408	164
17	3907	164
18	4097	164
19	4097	164
20	4097	164
21	4108	164
22	4120	164
23	4120	164
24	4122	164
25	4125	164
26	4205	164
27	4205	164
0	4205	146

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* (/ x (sqrt 2)) (+ (* x (/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))) 1/2)) (sqrt 2))
(/ x (sqrt 2))
x
(sqrt 2)
2
(+ (* x (/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))) 1/2)
(/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))
(+ (* (* x x) 49/36864) -9/256)
(* x x)
49/36864
-9/256
(+ (* x 7/192) -3/16)
7/192
-3/16
1/2
(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
(/ (* (* x x) 3/16) (sqrt 2))
(* (* x x) 3/16)
(* x x)
x
3/16
(sqrt 2)
2

Outputs
(+ (* (/ x (sqrt 2)) (+ (* x (/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))) 1/2)) (sqrt 2))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 x (*.f64 x #s(literal 49/36864 binary64)) #s(literal -9/256 binary64)) (/.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ (* x (/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))) 1/2)
(fma.f64 (fma.f64 x (*.f64 x #s(literal 49/36864 binary64)) #s(literal -9/256 binary64)) (/.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 1/2 binary64))
(/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))
(/.f64 (fma.f64 x (*.f64 x #s(literal 49/36864 binary64)) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))
(+ (* (* x x) 49/36864) -9/256)
(fma.f64 x (*.f64 x #s(literal 49/36864 binary64)) #s(literal -9/256 binary64))
(* x x)
(*.f64 x x)
49/36864
#s(literal 49/36864 binary64)
-9/256
#s(literal -9/256 binary64)
(+ (* x 7/192) -3/16)
(fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))
7/192
#s(literal 7/192 binary64)
-3/16
#s(literal -3/16 binary64)
1/2
#s(literal 1/2 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)
(/ (* (* x x) 3/16) (sqrt 2))
(.f64 #s(literal 3/16 binary64) (.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(* (* x x) 3/16)
(.f64 x (.f64 x #s(literal 3/16 binary64)))
(* x x)
(*.f64 x x)
x
3/16
#s(literal 3/16 binary64)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)

localize107.0ms (1.3%)

Memory

11.9MiB live, 167.4MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	99.9%	(.f64 (.f64 x x) #s(literal 3/16 binary64))
✓	accuracy	99.9%	(/.f64 (.f64 (.f64 x x) #s(literal 3/16 binary64)) (sqrt.f64 #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 (.f64 x (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	85.3%	(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%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))
✓	accuracy	99.8%	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))

Samples

51.0ms	171×	0	invalid
20.0ms	84×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 148 to 36 computations (75.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-mult: 16.0ms (33% of total)

const: 9.0ms (18.6% of total)

ival-sqrt: 8.0ms (16.5% of total)

ival-div: 7.0ms (14.4% of total)

ival-add: 7.0ms (14.4% of total)

exact: 1.0ms (2.1% of total)

adjust: 0.0ms (0% of total)

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

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

series12.0ms (0.2%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

16 → 180

Calls

Call 1

Inputs
#<alt (+ (* (/ x (sqrt 2)) (+ (* x (/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))) 1/2)) (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (sqrt 2)>
#<alt (+ (* x (/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))) 1/2)>
#<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 x) 3/16) (sqrt 2))>
#<alt (* (* x x) 3/16)>
#<alt (* x x)>
#<alt (/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))>

Outputs
#<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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))>
#<alt (* 7/192 (/ (pow x 3) (sqrt 2)))>
#<alt (* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt (/ x (sqrt 2))>
#<alt 1/2>
#<alt (+ 1/2 (* 3/16 x))>
#<alt (+ 1/2 (* x (+ 3/16 (* 7/192 x))))>
#<alt (+ 1/2 (* x (+ 3/16 (* 7/192 x))))>
#<alt (* 7/192 (pow x 2))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* 7/192 (pow x 2))>
#<alt (* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))>
#<alt (* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 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 (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (/ (pow x 2) (sqrt 2)))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (* 3/16 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 3/16>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (+ 3/16 (* 7/192 x))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* 7/192 x)>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>
#<alt (* x (+ 7/192 (* 3/16 (/ 1 x))))>

Calls

45 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt (* x (* x (+ (* x 1/6) 1/2))))
1.0ms	x	@	-inf	(sqrt (* x (* x (+ (* x 1/6) 1/2))))
1.0ms	x	@	inf	(+ (* (/ x (sqrt 2)) (+ (* x (/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))) 1/2)) (sqrt 2))
1.0ms	x	@	inf	(sqrt (* x (* x (+ (* x 1/6) 1/2))))
1.0ms	x	@	0	(/ (* (* x x) 3/16) (sqrt 2))

rewrite357.0ms (4.4%)

Memory

6.0MiB live, 486.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 716×	`/-lowering-/.f32`
4 716×	`/-lowering-/.f64`
4 660×	`accelerator-lowering-fma.f32`
4 660×	`accelerator-lowering-fma.f64`
3 828×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	130
1	185	106
2	1490	104
0	8321	91

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 543

Calls

Call 1

Inputs
(+ (* (/ x (sqrt 2)) (+ (* x (/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))) 1/2)) (sqrt 2))
(/ x (sqrt 2))
(sqrt 2)
(+ (* x (/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))) 1/2)
(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 x) 3/16) (sqrt 2))
(* (* x x) 3/16)
(* x x)
(/ (+ (* (* x x) 49/36864) -9/256) (+ (* x 7/192) -3/16))

Outputs
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(+.f64 (/.f64 (.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (-.f64 (/.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 2 binary64) (-.f64 (/.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 x (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (-.f64 (/.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (-.f64 (/.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 2 binary64) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 x (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 x (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 x (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1 binary64) (/.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (-.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal 1/4 binary64)) (.f64 x (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal 1/4 binary64)) (.f64 x (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 (.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 (/.f64 #s(literal 2 binary64) (-.f64 (/.f64 (.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (/.f64 #s(literal 1 binary64) x)) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) x))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (.f64 x (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
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(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal 81/65536 binary64)) (.f64 (.f64 x x) #s(literal -49/1048576 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 117649/50096498540544 binary64)) #s(literal -729/16777216 binary64))))
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(/.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal -81/65536 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal 27/4096 binary64))) (neg.f64 (fma.f64 x (.f64 x #s(literal 49/36864 binary64)) (+.f64 #s(literal 9/256 binary64) (.f64 x #s(literal -7/1024 binary64))))))
(/.f64 (neg.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 117649/50096498540544 binary64)) #s(literal -729/16777216 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal 81/65536 binary64)) (.f64 (.f64 x x) #s(literal -49/1048576 binary64)))))
(/.f64 (neg.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal -81/65536 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
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(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 117649/50096498540544 binary64)) #s(literal -729/16777216 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal 81/65536 binary64)) (.f64 (.f64 x x) #s(literal -49/1048576 binary64))))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 117649/50096498540544 binary64)) #s(literal -729/16777216 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal 81/65536 binary64)) (.f64 (.f64 x x) #s(literal -49/1048576 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)))
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(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal -81/65536 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))))
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(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 117649/50096498540544 binary64)) #s(literal -729/16777216 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal 81/65536 binary64)) (.f64 (*.f64 x x) #s(literal -49/1048576 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal -81/65536 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal -27/4096 binary64))) (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (.f64 x #s(literal -7/1024 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal -27/4096 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (.f64 x #s(literal -7/1024 binary64))))))
(.f64 (pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 117649/50096498540544 binary64)) #s(literal -729/16777216 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal 81/65536 binary64)) (.f64 (*.f64 x x) #s(literal -49/1048576 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal -81/65536 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 117649/50096498540544 binary64)) #s(literal -729/16777216 binary64)) (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal 81/65536 binary64)) (.f64 (.f64 x x) #s(literal -49/1048576 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 2401/1358954496 binary64) #s(literal -81/65536 binary64)) (fma.f64 (.f64 x (.f64 x x)) #s(literal 343/7077888 binary64) #s(literal -27/4096 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 49/36864 binary64) #s(literal 9/256 binary64)) (*.f64 x #s(literal -7/1024 binary64))))))

simplify629.0ms (7.8%)

Memory

-20.2MiB live, 585.2MiB allocated

Algorithm

1×	egg-herbie

Rules

10 254×	`accelerator-lowering-fma.f32`
10 254×	`accelerator-lowering-fma.f64`
4 920×	`-lowering-.f32`
4 920×	`-lowering-.f64`
2 926×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	273	1535
1	832	1507
2	2398	1462
3	7039	1456
0	8287	1342

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(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 (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
(/ x (sqrt 2))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 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))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(* 3/16 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
3/16
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(+ 3/16 (* 7/192 x))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* x (+ 7/192 (* 3/16 (/ 1 x))))

Outputs
(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 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(fma.f64 x (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (.f64 x (.f64 x x)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (*.f64 x x)))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (.f64 #s(literal 7/192 binary64) (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))) x)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))) x)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 3/16 x))
(fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(* 7/192 (pow x 2))
(.f64 x (.f64 x #s(literal 7/192 binary64)))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(* 7/192 (pow x 2))
(.f64 x (.f64 x #s(literal 7/192 binary64)))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(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 (.f64 x x) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/32 binary64) #s(literal 1 binary64)) (sqrt.f64 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 (.f64 x x) (.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.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 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 x x))))))
(* 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 (sqrt.f64 #s(literal 1/2 binary64)) (.f64 x x))) (fma.f64 x (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 x (*.f64 x 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 #s(literal 0 binary64) (.f64 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 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/2 binary64)) #s(literal 0 binary64)) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 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)))))
(-.f64 #s(literal 0 binary64) (fma.f64 x (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/2 binary64)) #s(literal 0 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x (sqrt.f64 #s(literal -1/2 binary64)))) #s(literal -1/4 binary64) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1/2 binary64))) #s(literal 0 binary64))))))
(* -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)))))
(-.f64 #s(literal 0 binary64) (fma.f64 x (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/2 binary64)) #s(literal 0 binary64)) (+.f64 (/.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal -1/16 binary64) (.f64 x (pow.f64 (sqrt.f64 #s(literal -1/2 binary64)) #s(literal 5 binary64)))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/2 binary64)))) x) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1/2 binary64))))))
x
(* x (+ 1 (* 1/2 x)))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(* x (+ 1 (* 1/2 x)))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(* x (+ 1 (* 1/2 x)))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) 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 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(* (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)))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) 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 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
(* (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)))
(*.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 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))
(* 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 #s(literal 1/12 binary64) (/.f64 x (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 x (/.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))))
(* 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 #s(literal 1/3456 binary64) (/.f64 x (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 #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))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (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 #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) x)) (sqrt.f64 #s(literal 1/6 binary64)) (*.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 x (.f64 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 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)) (*.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)))))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(.f64 (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (sqrt.f64 #s(literal -1/6 binary64))) (sqrt.f64 #s(literal -1 binary64)))
(* (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 #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))))))
(* (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))))))
(.f64 (.f64 x x) (fma.f64 #s(literal 3/16 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1/6 binary64))) (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)))))))
(* (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)))))))
(.f64 (.f64 x x) (fma.f64 #s(literal 3/16 binary64) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1/6 binary64))) (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))) (fma.f64 (/.f64 (.f64 #s(literal 1/128 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (sqrt.f64 #s(literal -1/6 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/6 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/6 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 1/6 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/6 x)))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(* 1/6 (pow x 2))
(.f64 (.f64 x 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))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 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)))
(* 1/6 (pow x 2))
(.f64 (.f64 x 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))))
(*.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 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)))
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))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 x (.f64 x (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* 3/16 (pow x 2))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
(* 3/16 (pow x 2))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
(* 3/16 (pow x 2))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
(* 3/16 (pow x 2))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
(* 3/16 (pow x 2))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
(* 3/16 (pow x 2))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
(* 3/16 (pow x 2))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
(* 3/16 (pow x 2))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
(* 3/16 (pow x 2))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
(* 3/16 (pow x 2))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
(* 3/16 (pow x 2))
(.f64 x (.f64 x #s(literal 3/16 binary64)))
(* 3/16 (pow x 2))
(.f64 x (.f64 x #s(literal 3/16 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)
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(+ 3/16 (* 7/192 x))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* 7/192 x)
(*.f64 x #s(literal 7/192 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))

eval97.0ms (1.2%)

Memory: 29.4MiB live, 182.1MiB allocated
Compiler: Compiled 17 639 to 2 040 computations (88.4% saved)

prune114.0ms (1.4%)

Memory

-39.4MiB live, 135.9MiB allocated

Pruning

19 alts after pruning (8 fresh and 11 done)

	Pruned	Kept	Total
New	767	4	771
Fresh	2	4	6
Picked	3	2	5
Done	0	9	9
Total	772	19	791

Accuracy

100.0%

Counts

791 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	66.7%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
✓	66.7%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
	66.0%	(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
	66.6%	(fma.f64 (.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
	1.1%	(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.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%	(/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
	2.6%	(*.f64 (sqrt.f64 (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))) x)
	4.2%	(.f64 x (/.f64 (.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	3.1%	(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
	2.9%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	66.4%	(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)))
✓	68.0%	(sqrt.f64 (fma.f64 x (fma.f64 x #s(literal 1/2 binary64) #s(literal 1 binary64)) #s(literal 2 binary64)))
✓	99.6%	(sqrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓	66.2%	(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
✓	100.0%	(sqrt.f64 (-.f64 (exp.f64 x) #s(literal -1 binary64)))
✓	66.2%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
	2.3%	(sqrt.f64 (*.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
✓	2.3%	(sqrt.f64 x)
✓	72.5%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 526 to 255 computations (51.5% saved)

regimes25.0ms (0.3%)

Memory

-2.4MiB live, 34.3MiB 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)))
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(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 (.f64 x (.f64 #s(literal 1/6 binary64) (*.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 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)))
(.f64 x (/.f64 (.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 x x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 (fma.f64 x (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal -1/4 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.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 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(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:

10.0ms

6.0ms

(/.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)

regimes8.0ms (0.1%)

Memory

14.9MiB live, 14.9MiB allocated

Accuracy

Total -46.0b remaining (-261.1%)

Threshold costs -46b (-261.1%)

Counts

24 → 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)))
(sqrt.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(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 (.f64 x (.f64 #s(literal 1/6 binary64) (*.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 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)))
(.f64 x (/.f64 (.f64 x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 x x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 7/192 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 x (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))))
(fma.f64 x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x #s(literal 3/16 binary64) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 x (/.f64 (fma.f64 (*.f64 x x) #s(literal 49/36864 binary64) #s(literal -9/256 binary64)) (fma.f64 x #s(literal 7/192 binary64) #s(literal -3/16 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 (fma.f64 x (.f64 (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)))) #s(literal -1/4 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 (fma.f64 (.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) (*.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64))) #s(literal -1/4 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x #s(literal 7/192 binary64) #s(literal 3/16 binary64)) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.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

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
72.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB 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))

soundness270.0ms (3.3%)

Memory

-26.7MiB live, 168.8MiB allocated

Rules

15 504×	`accelerator-lowering-fma.f32`
15 504×	`accelerator-lowering-fma.f64`
4 704×	`-lowering-.f32`
4 704×	`-lowering-.f64`
4 562×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	56	22
2	421	22
3	4985	22
0	8093	18
0	77	480
1	252	446
2	663	446
3	1429	440
4	2558	360
5	5941	325
0	8294	270

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)

preprocess47.0ms (0.6%)

Memory: 16.7MiB live, 56.7MiB allocated
Compiler: Compiled 42 to 34 computations (19% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

sample886.0ms (11%)

preprocess489.0ms (6%)

explain136.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify448.0ms (5.5%)

localize35.0ms (0.4%)

series4.0ms (0.1%)

rewrite372.0ms (4.6%)

simplify418.0ms (5.2%)

eval98.0ms (1.2%)

prune92.0ms (1.1%)

simplify35.0ms (0.4%)

localize89.0ms (1.1%)

series15.0ms (0.2%)

rewrite397.0ms (4.9%)

simplify455.0ms (5.6%)

eval100.0ms (1.2%)

prune78.0ms (1%)

simplify418.0ms (5.2%)

localize265.0ms (3.3%)

series13.0ms (0.2%)

rewrite383.0ms (4.7%)

simplify668.0ms (8.3%)

eval199.0ms (2.5%)

prune134.0ms (1.7%)

simplify189.0ms (2.3%)

localize107.0ms (1.3%)

series12.0ms (0.2%)

rewrite357.0ms (4.4%)

simplify629.0ms (7.8%)

eval97.0ms (1.2%)

prune114.0ms (1.4%)

regimes25.0ms (0.3%)

regimes8.0ms (0.1%)

simplify7.0ms (0.1%)

soundness270.0ms (3.3%)

preprocess47.0ms (0.6%)

end0.0ms (0%)

Profiling