Metrics for sqrtexp (problem 3.4.4)

analyze224.0ms (2.9%)

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
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
50%	50%	50%	0%	0%	0%	0%	4
50%	50%	50%	0%	0%	0%	0%	5
50%	50%	50%	0%	0%	0%	0%	6
53.1%	53.1%	46.9%	0%	0%	0%	0%	7
53.1%	53.1%	46.9%	0%	0%	0%	0%	8
53.9%	53.9%	46.1%	0%	0%	0%	0%	9
54.1%	54.1%	45.9%	0%	0%	0%	0%	10
54.2%	54.2%	45.8%	0%	0%	0%	0%	11
54.2%	54.2%	45.7%	0%	0%	0%	0%	12

Compiler

Compiled 14 to 11 computations (21.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-exp: 26.0ms (31.3% of total)

ival-sub: 19.0ms (22.8% of total)

ival-mult: 17.0ms (20.4% of total)

ival-sqrt: 12.0ms (14.4% of total)

ival-div: 6.0ms (7.2% of total)

const: 3.0ms (3.6% of total)

backward-pass: 1.0ms (1.2% of total)

sample2.7s (34.3%)

Results

1.5s	5316×	1	valid
482.0ms	2940×	0	valid
255.0ms	2695×	0	unsamplable

Precisions

Click to see histograms. Total time spent on operations: 1.8s

ival-exp: 772.0ms (42.9% of total)

ival-mult: 404.0ms (22.5% of total)

ival-sub: 259.0ms (14.4% of total)

ival-sqrt: 124.0ms (6.9% of total)

ival-div: 107.0ms (5.9% of total)

backward-pass: 104.0ms (5.8% of total)

const: 29.0ms (1.6% of total)

Bogosity

preprocess179.0ms (2.3%)

Algorithm

2×	egg-herbie

Rules

1390×	`sum3-define`
1276×	`sum4-define`
1274×	`fmsub-define`
1242×	`fnmsub-define`
1104×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	29
1	48	27
2	77	27
3	123	27
4	207	27
5	345	27
6	569	27
7	1232	27
8	3439	27
9	7988	27
0	10	8
1	24	8
2	31	8
3	44	8
4	63	8
5	96	8
6	149	8
7	271	8
8	606	8
9	1557	8
10	2233	8
11	2410	8
12	2438	8
0	2438	8

Stop Event

1×	iter limit
1×	saturated
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 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.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 (/ (expm1 (+ x x)) (expm1 x)))
(sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1)))
(sqrt (/ (expm1 (* x -2)) (expm1 (neg x))))
(neg (sqrt (/ (- (exp (* 2 (neg x))) 1) (- (exp (neg x)) 1))))
(neg (sqrt (/ (expm1 (* x -2)) (expm1 (neg x)))))

explain260.0ms (3.4%)

FPErrors

Click to see full error table

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

Results

184.0ms	348×	1	valid
22.0ms	164×	0	valid

Compiler

Compiled 107 to 32 computations (70.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 138.0ms

ival-exp: 96.0ms (69.4% of total)

ival-sub: 11.0ms (8% of total)

backward-pass: 11.0ms (8% of total)

ival-mult: 7.0ms (5.1% of total)

ival-sqrt: 6.0ms (4.3% of total)

ival-div: 5.0ms (3.6% of total)

const: 2.0ms (1.4% of total)

eval0.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	(expm1.f64 (*.f64 #s(literal 2 binary64) x))
✓	cost-diff	(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
✓	cost-diff	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))

Rules

698×	`fnmadd-define`
428×	`fmsub-define`
422×	`fma-define`
420×	`fnmsub-define`
392×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	24	26
2	31	26
3	44	26
4	63	26
5	96	26
6	149	26
7	271	26
8	606	26
9	1557	26
10	2233	26
11	2410	26
12	2438	26
0	2438	26

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize130.0ms (1.7%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
✓	accuracy	100.0%	(expm1.f64 (*.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(expm1.f64 x)
✓	accuracy	99.4%	(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))

Results

71.0ms	176×	1	valid
41.0ms	80×	0	valid

Compiler

Compiled 28 to 8 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 125.0ms

compiled-spec: 40.0ms (32.1% of total)

ival-div: 34.0ms (27.3% of total)

ival-exp: 29.0ms (23.3% of total)

ival-sqrt: 6.0ms (4.8% of total)

backward-pass: 6.0ms (4.8% of total)

ival-sub: 5.0ms (4% of total)

ival-mult: 4.0ms (3.2% of total)

const: 1.0ms (0.8% of total)

series5.0ms (0.1%)

Counts

5 → 60

Calls

Call 1

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

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 (/ (- (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)))>
#<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 (* 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 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

15 calls:

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

rewrite263.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2478×	`fma-lowering-fma.f32`
2478×	`fma-lowering-fma.f64`
1780×	`prod-diff`
1440×	`+-lowering-+.f64`
1440×	`+-lowering-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	35	24
2	116	24
3	576	24
4	3351	24
0	8211	24

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 471

Calls

Call 1

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

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))))
(exp.f64 (.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))))) #s(literal -1 binary64)))
(exp.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)))) (*.f64 #s(literal 1/2 binary64) (log.f64 (expm1.f64 x)))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64)))) (neg.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(neg.f64 (neg.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))))
(neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 x))))))
(neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 x) (sqrt.f64 (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)) (pow.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1/2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64))))
(/.f64 (sqrt.f64 (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x)))) (expm1.f64 x))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 (expm1.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (sqrt.f64 (-.f64 (expm1.f64 x) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (sqrt.f64 (/.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 2 binary64) x)))))
(/.f64 (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (sqrt.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (exp.f64 (.f64 #s(literal 2 binary64) x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (/.f64 (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (expm1.f64 x))) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 (expm1.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (expm1.f64 x))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64))))
(/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) #s(literal -1 binary64)) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64)))
(pow.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))))
(.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 x))))
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 x))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 x))) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x))) (pow.f64 (expm1.f64 x) #s(literal -1/2 binary64)))
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(/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (exp.f64 (.f64 #s(literal 2 binary64) x))))
(/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (exp.f64 (*.f64 #s(literal 2 binary64) x)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (/.f64 (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (expm1.f64 x)) (expm1.f64 x))
(/.f64 (exp.f64 (log.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (expm1.f64 x))
(/.f64 (exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))))) (exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (exp.f64 (log.f64 #s(literal -1 binary64))) (exp.f64 (log.f64 (/.f64 (expm1.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))))))
(/.f64 (exp.f64 (log.f64 (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))))) (exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 (expm1.f64 x)))))
(/.f64 (+.f64 (expm1.f64 x) (.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))) (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (expm1.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 0 binary64) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) (expm1.f64 x)) (/.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 2 binary64) x))))
(/.f64 (+.f64 (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (exp.f64 (.f64 #s(literal 2 binary64) x))))
(/.f64 (+.f64 (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 (expm1.f64 x) (-.f64 #s(literal 0 binary64) (/.f64 (expm1.f64 x) (exp.f64 (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (.f64 (-.f64 #s(literal 0 binary64) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64))) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (exp.f64 (*.f64 #s(literal 2 binary64) x))))
(/.f64 (-.f64 (expm1.f64 x) (.f64 (-.f64 #s(literal 0 binary64) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal -1 binary64))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 2 binary64) x))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (expm1.f64 x)) (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (exp.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) (expm1.f64 x))) (*.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (expm1.f64 x) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (exp.f64 (.f64 #s(literal 2 binary64) x))))
(/.f64 (neg.f64 (+.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) (exp.f64 (.f64 #s(literal 2 binary64) x))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))))) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))
(/.f64 (neg.f64 (/.f64 (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (expm1.f64 x))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (/.f64 (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (exp.f64 (*.f64 #s(literal 2 binary64) x))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (/.f64 (.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (expm1.f64 x))) (expm1.f64 x))
(/.f64 (.f64 (-.f64 (expm1.f64 x) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64)) (/.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 2 binary64) x))))
(/.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (exp.f64 (*.f64 #s(literal 2 binary64) x))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))))) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x)))) (expm1.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (/.f64 (-.f64 (expm1.f64 x) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) (expm1.f64 x))
(/.f64 (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (/.f64 (/.f64 (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (expm1.f64 x)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 (expm1.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))))
(pow.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)) #s(literal 1 binary64))
(pow.f64 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))))
(.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 x)) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (expm1.f64 (.f64 #s(literal 2 binary64) x)))
(.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (/.f64 (.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (expm1.f64 x)))
(.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (exp.f64 (log.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)))))
(.f64 #s(literal -1 binary64) (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(.f64 (.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))
(.f64 (.f64 (expm1.f64 x) (expm1.f64 (.f64 #s(literal 2 binary64) x))) (.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (/.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))
(.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)) (pow.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 (.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64)))
(.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64))
(.f64 (-.f64 (expm1.f64 x) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) (exp.f64 (*.f64 #s(literal 2 binary64) x)))))
(.f64 (+.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (/.f64 (expm1.f64 x) (exp.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (exp.f64 (*.f64 #s(literal 2 binary64) x)))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))))
(.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))))
(.f64 (/.f64 (.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 (.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (expm1.f64 x) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) #s(literal -1 binary64)) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))
(.f64 (exp.f64 (log.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(.f64 (exp.f64 (log.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))) (exp.f64 (log.f64 (/.f64 #s(literal -1 binary64) (expm1.f64 x)))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 x))) (pow.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 2 binary64)))
(+.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))
(+.f64 #s(literal -1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal -1 binary64)))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))))
(-.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))))
(-.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)))
(fma.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))
(fma.f64 (exp.f64 x) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64))
(fma.f64 #s(literal -1 binary64) (/.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64)) #s(literal -1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64) #s(literal -1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (exp.f64 x)) (-.f64 #s(literal 0 binary64) (exp.f64 x)) #s(literal -1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (exp.f64 x)) (/.f64 (exp.f64 x) #s(literal -1 binary64)) #s(literal -1 binary64))
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) x))))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64))
(pow.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (expm1.f64 (.f64 #s(literal 2 binary64) x)))
(.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 #s(literal 2 binary64) x))))
(log.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)))
(+.f64 x x)
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal 0 binary64) (expm1.f64 x))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(+.f64 #s(literal -1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) (exp.f64 x)) #s(literal -1 binary64)))
(+.f64 (*.f64 (-.f64 #s(literal 0 binary64) (exp.f64 x)) #s(literal -1 binary64)) #s(literal -1 binary64))
(exp.f64 (log.f64 (expm1.f64 x)))
(fabs.f64 (expm1.f64 x))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(-.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 #s(literal -1 binary64) (/.f64 (exp.f64 x) #s(literal -1 binary64)))
(sqrt.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (exp.f64 x)) #s(literal -1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) (exp.f64 x)) #s(literal -1 binary64) #s(literal -1 binary64))
(expm1.f64 x)
(neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(/.f64 (expm1.f64 x) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (expm1.f64 x)))
(pow.f64 (expm1.f64 x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (expm1.f64 x))
(*.f64 (expm1.f64 x) #s(literal 1 binary64))
(*.f64 (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64)) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x)))

simplify218.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

2950×	`-lowering-.f32`
2950×	`-lowering-.f64`
2624×	`+-lowering-+.f64`
2624×	`+-lowering-+.f32`
1432×	`sum3-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	77	381
1	260	328
2	804	324
3	1875	321
4	3207	320
0	8073	320

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

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 (/ (- (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)))
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)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
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
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/2 binary64) x) (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))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 3/16 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))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 3/8 binary64))) (.f64 x (*.f64 x #s(literal 7/96 binary64)))))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 2 x)))
(.f64 #s(literal 2 binary64) (.f64 x (+.f64 x #s(literal 1 binary64))))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64))))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))))))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 x #s(literal 1/24 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)

eval70.0ms (0.9%)

Compiler: Compiled 10879 to 1319 computations (87.9% saved)

prune71.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	525	6	531
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	525	7	532

Accuracy

100.0%

Counts

532 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	69.1%	(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 3/8 binary64))) (.f64 x (*.f64 x #s(literal 7/96 binary64)))))))
✓	99.2%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
▶	71.1%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
▶	68.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
▶	70.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
▶	68.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
▶	74.5%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 137 to 107 computations (21.9% saved)

simplify162.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	(expm1.f64 (*.f64 #s(literal 2 binary64) x))
✓	cost-diff	(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)
✓	cost-diff	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	cost-diff	(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
✓	cost-diff	(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
✓	cost-diff	(+.f64 #s(literal 2 binary64) x)
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	cost-diff	(sqrt.f64 #s(literal 2 binary64))

Rules

2480×	`sum4-define`
2270×	`sum3-define`
2184×	`fma-lowering-fma.f32`
2184×	`fma-lowering-fma.f64`
1838×	`fnmsub-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	139
1	63	121
2	142	119
3	316	119
4	536	119
5	681	119
6	760	119
7	876	119
8	1126	119
9	1955	119
10	6096	119
0	8260	119

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(sqrt (+ 2 x))
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x
(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))))
2
#s(literal 2 binary64)
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))))
x
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))
(sqrt.f64 (-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal -1/6 binary64))))))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(-.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))))
2
#s(literal 2 binary64)
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
x
(+ 1 (* x (+ 1/2 (* x 1/6))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
1
#s(literal 1 binary64)
(* x (+ 1/2 (* x 1/6)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(+ 1/2 (* x 1/6))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(sqrt (/ (- (exp (* 2 x)) 1) x))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
(/ (- (exp (* 2 x)) 1) x)
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x

localize252.0ms (3.3%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(expm1.f64 (*.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)
✓	accuracy	100.0%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	accuracy	99.6%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 2 binary64))

Results

166.0ms	175×	1	valid
27.0ms	77×	0	invalid
1.0ms	4×	0	valid

Compiler

Compiled 141 to 25 computations (82.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

compiled-spec: 20.0ms (16.7% of total)

backward-pass: 19.0ms (15.9% of total)

ival-add: 17.0ms (14.2% of total)

ival-mult: 17.0ms (14.2% of total)

ival-sqrt: 16.0ms (13.4% of total)

ival-exp: 14.0ms (11.7% of total)

...c/correct-round.rkt:119:19: 10.0ms (8.4% of total)

ival-div: 4.0ms (3.3% of total)

ival-sub: 3.0ms (2.5% of total)

const: 1.0ms (0.8% of total)

series19.0ms (0.2%)

Counts

18 → 204

Calls

Call 1

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

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

Calls

51 calls:

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

rewrite243.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1612×	`fma-lowering-fma.f32`
1612×	`fma-lowering-fma.f64`
1538×	`-lowering-.f32`
1538×	`-lowering-.f64`
1522×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	120
1	77	103
2	238	101
3	848	101
4	3671	101
0	10324	101

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 877

Calls

Call 1

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

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

simplify315.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

5030×	`-lowering-.f32`
5030×	`-lowering-.f64`
3956×	`+-lowering-+.f64`
3956×	`+-lowering-+.f32`
1906×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	315	1880
1	1078	1515
2	3912	1468
0	8738	1468

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

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

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.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))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (.f64 #s(literal -1/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #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))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 (/.f64 (*.f64 x #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))))))))
(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 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))
(* 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 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ (sqrt (/ 1 (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 x (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.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))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 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))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 (.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 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))))))
(+.f64 (*.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))))))
(+.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 3/4 binary64) (.f64 x (*.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 (.f64 x (+.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 x x))) (/.f64 #s(literal 3/4 binary64) (.f64 x (*.f64 x (sqrt.f64 #s(literal 1/2 binary64))))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(* -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 (/.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 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(.f64 (+.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.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)) (-.f64 #s(literal 0 binary64) 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)))))
(.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.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) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) x)) (-.f64 #s(literal 0 binary64) x))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 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 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x x))))))
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 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 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 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 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.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))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 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))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 7/192 binary64) x) (sqrt.f64 #s(literal 2 binary64))))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(.f64 (.f64 x x) (+.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(.f64 x (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 1/16 (/ x (pow (sqrt 1/6) 2)))) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (*.f64 x #s(literal -1/16 binary64)) #s(literal 1/6 binary64))) (sqrt.f64 #s(literal 1/6 binary64))))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (.f64 x (.f64 x x)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(.f64 (.f64 x x) (+.f64 (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64))) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64)) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(+.f64 (.f64 (.f64 x x) (+.f64 (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64))) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1/6 binary64))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (.f64 x #s(literal -1/16 binary64)) #s(literal 1/6 binary64))) (sqrt.f64 #s(literal -1/6 binary64)))))) x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)) (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x (.f64 x x))) #s(literal 1/6 binary64)))))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 (.f64 x x) (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 2 binary64) (.f64 x x)))) x)))))
x
(* x (+ 1 (* 1/2 x)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(* 1/6 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(.f64 (-.f64 #s(literal -1/6 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (/ x (sqrt 2)))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 4/3 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))) (/ 1 (sqrt 2)))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 5/12 binary64) x) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (+ 2/3 (/ 1 (pow (sqrt 2) 4))) (* 4/3 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 4/3 (/ 1 (pow (sqrt 2) 2))) (sqrt 2))))) (/ 1 (sqrt 2)))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 (/.f64 (.f64 (.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 5/12 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(sqrt (/ (- (exp (* 2 x)) 1) x))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
(sqrt (/ (- (exp (* 2 x)) 1) x))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
(sqrt (/ (- (exp (* 2 x)) 1) x))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
(sqrt (/ (- (exp (* 2 x)) 1) x))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
(* (sqrt (/ (- (exp (* 2 x)) 1) x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)))
(* (sqrt (/ (- (exp (* 2 x)) 1) x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)))
(* (sqrt (/ (- (exp (* 2 x)) 1) x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)))
(* (sqrt (/ (- (exp (* 2 x)) 1) x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)))
2
#s(literal 2 binary64)
(+ 2 (* 2 x))
(+.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x))
(+ 2 (* x (+ 2 (* 4/3 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64)))))
(+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))))))
(/ (- (exp (* 2 x)) 1) x)
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)
(/ (- (exp (* 2 x)) 1) x)
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)
(/ (- (exp (* 2 x)) 1) x)
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)
(/ (- (exp (* 2 x)) 1) x)
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)
(/ (- (exp (* 2 x)) 1) x)
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)
(/ (- (exp (* 2 x)) 1) x)
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)
(/ (- (exp (* 2 x)) 1) x)
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)
(/ (- (exp (* 2 x)) 1) x)
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 2 x)))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64))))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))))))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* x (+ 1/2 (* 1/6 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))

eval129.0ms (1.7%)

Compiler: Compiled 15812 to 2630 computations (83.4% saved)

prune170.0ms (2.2%)

Pruning

15 alts after pruning (9 fresh and 6 done)

	Pruned	Kept	Total
New	1073	8	1081
Fresh	0	1	1
Picked	0	5	5
Done	0	1	1
Total	1073	15	1088

Accuracy

100.0%

Counts

1088 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	69.1%	(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 3/8 binary64))) (.f64 x (*.f64 x #s(literal 7/96 binary64)))))))
	3.0%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	99.2%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
✓	71.1%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
▶	68.3%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))))
▶	69.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))))
✓	68.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	70.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
✓	68.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
	2.4%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
	3.6%	(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
▶	2.2%	(sqrt.f64 (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
▶	2.4%	(sqrt.f64 x)
✓	74.5%	(sqrt.f64 #s(literal 2 binary64))
▶	73.5%	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))

Compiler

Compiled 241 to 183 computations (24.1% saved)

simplify20.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64)))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))))))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64)))))
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))))
✓	cost-diff	0	(*.f64 x #s(literal 1/6 binary64))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal 1/6 binary64)))
✓	cost-diff	0	(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
✓	cost-diff	0	(sqrt.f64 (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(log.f64 #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
✓	cost-diff	6528	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))

Rules

328×	`fma-define`
276×	`fma-lowering-fma.f32`
276×	`fma-lowering-fma.f64`
146×	`sum3-define`
132×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	144
1	60	121
2	148	118
3	249	118
4	362	118
5	453	118
6	474	118
0	474	118

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(exp (* 1/2 (log 2)))
(* 1/2 (log 2))
1/2
(log 2)
2
(sqrt x)
x
(sqrt (* x (* x (* x 1/6))))
(* x (* x (* x 1/6)))
x
(* x (* x 1/6))
(* x 1/6)
1/6
(sqrt (+ 2 (* x (+ 2 (* x 4/3)))))
(+ 2 (* x (+ 2 (* x 4/3))))
2
(* x (+ 2 (* x 4/3)))
x
(+ 2 (* x 4/3))
(* x 4/3)
4/3
(sqrt (+ 2 (* x (+ 2 (* x (+ 4/3 (* x 2/3)))))))
(+ 2 (* x (+ 2 (* x (+ 4/3 (* x 2/3))))))
2
(* x (+ 2 (* x (+ 4/3 (* x 2/3)))))
x
(+ 2 (* x (+ 4/3 (* x 2/3))))
(* x (+ 4/3 (* x 2/3)))
(+ 4/3 (* x 2/3))
4/3
(* x 2/3)
2/3

Outputs
(exp (* 1/2 (log 2)))
(sqrt.f64 #s(literal 2 binary64))
(* 1/2 (log 2))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(log 2)
(log.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(sqrt x)
(sqrt.f64 x)
x
(sqrt (* x (* x (* x 1/6))))
(sqrt.f64 (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(* x (* x (* x 1/6)))
(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
x
(* x (* x 1/6))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
(sqrt (+ 2 (* x (+ 2 (* x 4/3)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))))
(+ 2 (* x (+ 2 (* x 4/3))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64)))))
2
#s(literal 2 binary64)
(* x (+ 2 (* x 4/3)))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
x
(+ 2 (* x 4/3))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
(* x 4/3)
(*.f64 x #s(literal 4/3 binary64))
4/3
#s(literal 4/3 binary64)
(sqrt (+ 2 (* x (+ 2 (* x (+ 4/3 (* x 2/3)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))))
(+ 2 (* x (+ 2 (* x (+ 4/3 (* x 2/3))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))))))
2
#s(literal 2 binary64)
(* x (+ 2 (* x (+ 4/3 (* x 2/3)))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))
x
(+ 2 (* x (+ 4/3 (* x 2/3))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64)))))
(* x (+ 4/3 (* x 2/3)))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
(+ 4/3 (* x 2/3))
(+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))
4/3
#s(literal 4/3 binary64)
(* x 2/3)
(*.f64 x #s(literal 2/3 binary64))
2/3
#s(literal 2/3 binary64)

localize175.0ms (2.3%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))))
✓	accuracy	100.0%	(+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))
✓	accuracy	99.8%	(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
✓	accuracy	99.8%	(*.f64 x #s(literal 2/3 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))))
✓	accuracy	99.8%	(*.f64 x #s(literal 4/3 binary64))
✓	accuracy	100.0%	(.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64))))
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal 1/6 binary64)))
✓	accuracy	99.8%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	91.3%	(sqrt.f64 (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
✓	accuracy	100.0%	(log.f64 #s(literal 2 binary64))
✓	accuracy	99.5%	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))

Results

83.0ms	168×	0	invalid
39.0ms	88×	0	valid

Compiler

Compiled 146 to 27 computations (81.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

...c/correct-round.rkt:119:19: 23.0ms (36.4% of total)

ival-mult: 18.0ms (28.5% of total)

ival-sqrt: 9.0ms (14.3% of total)

ival-add: 6.0ms (9.5% of total)

ival-log: 4.0ms (6.3% of total)

ival-exp: 3.0ms (4.8% of total)

const: 1.0ms (1.6% of total)

backward-pass: 0.0ms (0% of total)

series15.0ms (0.2%)

Counts

20 → 204

Calls

Call 1

Inputs
#<alt (exp (* 1/2 (log 2)))>
#<alt (* 1/2 (log 2))>
#<alt (log 2)>
#<alt (sqrt x)>
#<alt (sqrt (* x (* x (* x 1/6))))>
#<alt (* x (* x (* x 1/6)))>
#<alt (* x (* x 1/6))>
#<alt (* x 1/6)>
#<alt (sqrt (+ 2 (* x (+ 2 (* x 4/3)))))>
#<alt (+ 2 (* x (+ 2 (* x 4/3))))>
#<alt (* x (+ 2 (* x 4/3)))>
#<alt (+ 2 (* x 4/3))>
#<alt (sqrt (+ 2 (* x (+ 2 (* x (+ 4/3 (* x 2/3)))))))>
#<alt (+ 2 (* x (+ 2 (* x (+ 4/3 (* x 2/3))))))>
#<alt (* x (+ 2 (* x (+ 4/3 (* x 2/3)))))>
#<alt (+ 2 (* x (+ 4/3 (* x 2/3))))>
#<alt (* x 4/3)>
#<alt (* x 2/3)>
#<alt (* x (+ 4/3 (* x 2/3)))>
#<alt (+ 4/3 (* x 2/3))>

Outputs
#<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 (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 3))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (/ x (sqrt 2)))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 4/3 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))) (/ 1 (sqrt 2)))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (/ 1 (pow (sqrt 2) 4)) (* 4/3 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 4/3 (/ 1 (pow (sqrt 2) 2))) (sqrt 2))))) (/ 1 (sqrt 2)))))>
#<alt (* x (sqrt 4/3))>
#<alt (* x (+ (sqrt 4/3) (/ 1 (* x (sqrt 4/3)))))>
#<alt (* x (+ (sqrt 4/3) (+ (* 1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (* (pow x 2) (sqrt 4/3)))) (/ 1 (* x (sqrt 4/3))))))>
#<alt (* x (+ (sqrt 4/3) (+ (* 1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (* (pow x 2) (sqrt 4/3)))) (+ (* 1/2 (/ (- (/ 1 (pow (sqrt 4/3) 4)) (* 2 (/ 1 (pow (sqrt 4/3) 2)))) (* (pow x 3) (sqrt 4/3)))) (/ 1 (* x (sqrt 4/3)))))))>
#<alt (* -1 (* x (sqrt 4/3)))>
#<alt (* -1 (* x (+ (sqrt 4/3) (/ 1 (* x (sqrt 4/3))))))>
#<alt (* -1 (* x (+ (sqrt 4/3) (* -1 (/ (- (* -1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (* x (sqrt 4/3)))) (/ 1 (sqrt 4/3))) x)))))>
#<alt (* -1 (* x (+ (sqrt 4/3) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (* x (pow (sqrt 4/3) 3)))) (* 1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (sqrt 4/3)))) x)) (/ 1 (sqrt 4/3))) x)))))>
#<alt 2>
#<alt (+ 2 (* 2 x))>
#<alt (+ 2 (* x (+ 2 (* 4/3 x))))>
#<alt (+ 2 (* x (+ 2 (* 4/3 x))))>
#<alt (* 4/3 (pow x 2))>
#<alt (* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))))>
#<alt (* 4/3 (pow x 2))>
#<alt (* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 4/3 x)))>
#<alt (* x (+ 2 (* 4/3 x)))>
#<alt (* x (+ 2 (* 4/3 x)))>
#<alt (* 4/3 (pow x 2))>
#<alt (* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))>
#<alt (* 4/3 (pow x 2))>
#<alt (* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))>
#<alt 2>
#<alt (+ 2 (* 4/3 x))>
#<alt (+ 2 (* 4/3 x))>
#<alt (+ 2 (* 4/3 x))>
#<alt (* 4/3 x)>
#<alt (* x (+ 4/3 (* 2 (/ 1 x))))>
#<alt (* x (+ 4/3 (* 2 (/ 1 x))))>
#<alt (* x (+ 4/3 (* 2 (/ 1 x))))>
#<alt (* 4/3 x)>
#<alt (* x (+ 4/3 (* 2 (/ 1 x))))>
#<alt (* x (+ 4/3 (* 2 (/ 1 x))))>
#<alt (* x (+ 4/3 (* 2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (/ x (sqrt 2)))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 4/3 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))) (/ 1 (sqrt 2)))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (+ 2/3 (/ 1 (pow (sqrt 2) 4))) (* 4/3 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 4/3 (/ 1 (pow (sqrt 2) 2))) (sqrt 2))))) (/ 1 (sqrt 2)))))>
#<alt (* (sqrt (pow x 3)) (sqrt 2/3))>
#<alt (* (pow x 2) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 2/3)))) (* (sqrt (/ 1 x)) (sqrt 2/3))))>
#<alt (* (pow x 2) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 2/3)))) (+ (* (sqrt (/ 1 x)) (sqrt 2/3)) (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 2/3))))))>
#<alt (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 4/9 (/ x (pow (sqrt 2/3) 2)))) (sqrt 2/3)))) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 2/3)))) (+ (* (sqrt (/ 1 x)) (sqrt 2/3)) (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 2/3)))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))>
#<alt (* (pow x 2) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -2/3)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -2/3)))))>
#<alt (* (pow x 2) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -2/3)))) (+ (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -2/3))) (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -2/3))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (sqrt x) (/ (sqrt -1) (sqrt -2/3)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -4/9 (/ x (pow (sqrt -2/3) 2))))) (sqrt -2/3))))) (pow x 3))) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -2/3)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -2/3))))))>
#<alt 2>
#<alt (+ 2 (* 2 x))>
#<alt (+ 2 (* x (+ 2 (* 4/3 x))))>
#<alt (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x))))))>
#<alt (* 2/3 (pow x 3))>
#<alt (* (pow x 3) (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* (pow x 3) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/3 (+ (* 4/3 (/ 1 x)) (+ (* 2 (/ 1 (pow x 3))) (/ 2 (pow x 2))))))>
#<alt (* 2/3 (pow x 3))>
#<alt (* (pow x 3) (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 4/3 (* 2 (/ 1 x))) x)) 2/3)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 2/3)))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 4/3 x)))>
#<alt (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))>
#<alt (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))>
#<alt (* 2/3 (pow x 3))>
#<alt (* (pow x 3) (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* (pow x 3) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))>
#<alt (* (pow x 3) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))>
#<alt (* 2/3 (pow x 3))>
#<alt (* (pow x 3) (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 4/3 (* 2 (/ 1 x))) x)) 2/3)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 4/3 (* 2 (/ 1 x))) x)) 2/3)))>
#<alt 2>
#<alt (+ 2 (* 4/3 x))>
#<alt (+ 2 (* x (+ 4/3 (* 2/3 x))))>
#<alt (+ 2 (* x (+ 4/3 (* 2/3 x))))>
#<alt (* 2/3 (pow x 2))>
#<alt (* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* (pow x 2) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))>
#<alt (* 2/3 (pow x 2))>
#<alt (* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* (pow x 2) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))>
#<alt (* 4/3 x)>
#<alt (* 4/3 x)>
#<alt (* 4/3 x)>
#<alt (* 4/3 x)>
#<alt (* 4/3 x)>
#<alt (* 4/3 x)>
#<alt (* 4/3 x)>
#<alt (* 4/3 x)>
#<alt (* 4/3 x)>
#<alt (* 4/3 x)>
#<alt (* 4/3 x)>
#<alt (* 4/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 2/3 x)>
#<alt (* 4/3 x)>
#<alt (* x (+ 4/3 (* 2/3 x)))>
#<alt (* x (+ 4/3 (* 2/3 x)))>
#<alt (* x (+ 4/3 (* 2/3 x)))>
#<alt (* 2/3 (pow x 2))>
#<alt (* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* 2/3 (pow x 2))>
#<alt (* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt 4/3>
#<alt (+ 4/3 (* 2/3 x))>
#<alt (+ 4/3 (* 2/3 x))>
#<alt (+ 4/3 (* 2/3 x))>
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* x (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* x (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* 2/3 x)>
#<alt (* x (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* x (+ 2/3 (* 4/3 (/ 1 x))))>
#<alt (* x (+ 2/3 (* 4/3 (/ 1 x))))>

Calls

51 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(sqrt (+ 2 (* x (+ 2 (* x 4/3)))))
1.0ms	x	@	-inf	(sqrt (+ 2 (* x (+ 2 (* x (+ 4/3 (* x 2/3)))))))
1.0ms	x	@	0	(sqrt (* x (* x (* x 1/6))))
1.0ms	x	@	inf	(sqrt (+ 2 (* x (+ 2 (* x (+ 4/3 (* x 2/3)))))))
1.0ms	x	@	inf	(sqrt (+ 2 (* x (+ 2 (* x 4/3)))))

rewrite175.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1982×	`-lowering-.f32`
1982×	`-lowering-.f64`
1800×	`fma-define`
1508×	`fma-lowering-fma.f32`
1508×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	132
1	66	109
2	183	106
3	343	106
4	583	106
5	1029	106
6	2362	106
0	8379	106

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 432

Calls

Call 1

Inputs
(exp (* 1/2 (log 2)))
(* 1/2 (log 2))
(log 2)
(sqrt x)
(sqrt (* x (* x (* x 1/6))))
(* x (* x (* x 1/6)))
(* x (* x 1/6))
(* x 1/6)
(sqrt (+ 2 (* x (+ 2 (* x 4/3)))))
(+ 2 (* x (+ 2 (* x 4/3))))
(* x (+ 2 (* x 4/3)))
(+ 2 (* x 4/3))
(sqrt (+ 2 (* x (+ 2 (* x (+ 4/3 (* x 2/3)))))))
(+ 2 (* x (+ 2 (* x (+ 4/3 (* x 2/3))))))
(* x (+ 2 (* x (+ 4/3 (* x 2/3)))))
(+ 2 (* x (+ 4/3 (* x 2/3))))
(* x 4/3)
(* x 2/3)
(* x (+ 4/3 (* x 2/3)))
(+ 4/3 (* x 2/3))

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

simplify246.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

4552×	`-lowering-.f32`
4552×	`-lowering-.f64`
1984×	`sum3-define`
1906×	`+-lowering-+.f64`
1906×	`+-lowering-+.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	1626
1	749	1408
2	2554	1301
3	6995	1301
0	8341	1301

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(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 (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 3))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(sqrt 2)
(+ (sqrt 2) (/ x (sqrt 2)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 4/3 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))) (/ 1 (sqrt 2)))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (/ 1 (pow (sqrt 2) 4)) (* 4/3 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 4/3 (/ 1 (pow (sqrt 2) 2))) (sqrt 2))))) (/ 1 (sqrt 2)))))
(* x (sqrt 4/3))
(* x (+ (sqrt 4/3) (/ 1 (* x (sqrt 4/3)))))
(* x (+ (sqrt 4/3) (+ (* 1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (* (pow x 2) (sqrt 4/3)))) (/ 1 (* x (sqrt 4/3))))))
(* x (+ (sqrt 4/3) (+ (* 1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (* (pow x 2) (sqrt 4/3)))) (+ (* 1/2 (/ (- (/ 1 (pow (sqrt 4/3) 4)) (* 2 (/ 1 (pow (sqrt 4/3) 2)))) (* (pow x 3) (sqrt 4/3)))) (/ 1 (* x (sqrt 4/3)))))))
(* -1 (* x (sqrt 4/3)))
(* -1 (* x (+ (sqrt 4/3) (/ 1 (* x (sqrt 4/3))))))
(* -1 (* x (+ (sqrt 4/3) (* -1 (/ (- (* -1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (* x (sqrt 4/3)))) (/ 1 (sqrt 4/3))) x)))))
(* -1 (* x (+ (sqrt 4/3) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (* x (pow (sqrt 4/3) 3)))) (* 1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (sqrt 4/3)))) x)) (/ 1 (sqrt 4/3))) x)))))
2
(+ 2 (* 2 x))
(+ 2 (* x (+ 2 (* 4/3 x))))
(+ 2 (* x (+ 2 (* 4/3 x))))
(* 4/3 (pow x 2))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(* (pow x 2) (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))))
(* 4/3 (pow x 2))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(* (pow x 2) (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))))
(* 2 x)
(* x (+ 2 (* 4/3 x)))
(* x (+ 2 (* 4/3 x)))
(* x (+ 2 (* 4/3 x)))
(* 4/3 (pow x 2))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(* 4/3 (pow x 2))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
2
(+ 2 (* 4/3 x))
(+ 2 (* 4/3 x))
(+ 2 (* 4/3 x))
(* 4/3 x)
(* x (+ 4/3 (* 2 (/ 1 x))))
(* x (+ 4/3 (* 2 (/ 1 x))))
(* x (+ 4/3 (* 2 (/ 1 x))))
(* 4/3 x)
(* x (+ 4/3 (* 2 (/ 1 x))))
(* x (+ 4/3 (* 2 (/ 1 x))))
(* x (+ 4/3 (* 2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (/ x (sqrt 2)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 4/3 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))) (/ 1 (sqrt 2)))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (+ 2/3 (/ 1 (pow (sqrt 2) 4))) (* 4/3 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 4/3 (/ 1 (pow (sqrt 2) 2))) (sqrt 2))))) (/ 1 (sqrt 2)))))
(* (sqrt (pow x 3)) (sqrt 2/3))
(* (pow x 2) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 2/3)))) (* (sqrt (/ 1 x)) (sqrt 2/3))))
(* (pow x 2) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 2/3)))) (+ (* (sqrt (/ 1 x)) (sqrt 2/3)) (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 2/3))))))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 4/9 (/ x (pow (sqrt 2/3) 2)))) (sqrt 2/3)))) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 2/3)))) (+ (* (sqrt (/ 1 x)) (sqrt 2/3)) (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 2/3)))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))
(* (pow x 2) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -2/3)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -2/3)))))
(* (pow x 2) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -2/3)))) (+ (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -2/3))) (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -2/3))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (sqrt x) (/ (sqrt -1) (sqrt -2/3)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -4/9 (/ x (pow (sqrt -2/3) 2))))) (sqrt -2/3))))) (pow x 3))) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -2/3)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -2/3))))))
2
(+ 2 (* 2 x))
(+ 2 (* x (+ 2 (* 4/3 x))))
(+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x))))))
(* 2/3 (pow x 3))
(* (pow x 3) (+ 2/3 (* 4/3 (/ 1 x))))
(* (pow x 3) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(* (pow x 3) (+ 2/3 (+ (* 4/3 (/ 1 x)) (+ (* 2 (/ 1 (pow x 3))) (/ 2 (pow x 2))))))
(* 2/3 (pow x 3))
(* (pow x 3) (+ 2/3 (* 4/3 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 4/3 (* 2 (/ 1 x))) x)) 2/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 2/3)))
(* 2 x)
(* x (+ 2 (* 4/3 x)))
(* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))
(* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))
(* 2/3 (pow x 3))
(* (pow x 3) (+ 2/3 (* 4/3 (/ 1 x))))
(* (pow x 3) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(* (pow x 3) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(* 2/3 (pow x 3))
(* (pow x 3) (+ 2/3 (* 4/3 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 4/3 (* 2 (/ 1 x))) x)) 2/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 4/3 (* 2 (/ 1 x))) x)) 2/3)))
2
(+ 2 (* 4/3 x))
(+ 2 (* x (+ 4/3 (* 2/3 x))))
(+ 2 (* x (+ 4/3 (* 2/3 x))))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(* (pow x 2) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(* (pow x 2) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 4/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 2/3 x)
(* 4/3 x)
(* x (+ 4/3 (* 2/3 x)))
(* x (+ 4/3 (* 2/3 x)))
(* x (+ 4/3 (* 2/3 x)))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(* 2/3 (pow x 2))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
4/3
(+ 4/3 (* 2/3 x))
(+ 4/3 (* 2/3 x))
(+ 4/3 (* 2/3 x))
(* 2/3 x)
(* x (+ 2/3 (* 4/3 (/ 1 x))))
(* x (+ 2/3 (* 4/3 (/ 1 x))))
(* x (+ 2/3 (* 4/3 (/ 1 x))))
(* 2/3 x)
(* x (+ 2/3 (* 4/3 (/ 1 x))))
(* x (+ 2/3 (* 4/3 (/ 1 x))))
(* x (+ 2/3 (* 4/3 (/ 1 x))))

Outputs
(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 (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (.f64 x (.f64 x x)))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (.f64 x (.f64 x x)))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (.f64 x (.f64 x x)))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(.f64 (sqrt.f64 #s(literal -1/6 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (.f64 x (.f64 x x)))))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* 1/6 (pow x 3))
(.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (/ x (sqrt 2)))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 4/3 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))) (/ 1 (sqrt 2)))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 x #s(literal 5/12 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (/ 1 (pow (sqrt 2) 4)) (* 4/3 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 4/3 (/ 1 (pow (sqrt 2) 2))) (sqrt 2))))) (/ 1 (sqrt 2)))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))) #s(literal -2/3 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 5/6 binary64) (sqrt.f64 #s(literal 2 binary64)))) (.f64 x #s(literal 1/2 binary64))))))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(* x (+ (sqrt 4/3) (/ 1 (* x (sqrt 4/3)))))
(+.f64 (*.f64 x (sqrt.f64 #s(literal 4/3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 4/3 binary64))))
(* x (+ (sqrt 4/3) (+ (* 1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (* (pow x 2) (sqrt 4/3)))) (/ 1 (* x (sqrt 4/3))))))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 4/3 binary64))) (.f64 x (+.f64 (sqrt.f64 #s(literal 4/3 binary64)) (/.f64 (/.f64 #s(literal 5/8 binary64) (sqrt.f64 #s(literal 4/3 binary64))) (.f64 x x)))))
(* x (+ (sqrt 4/3) (+ (* 1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (* (pow x 2) (sqrt 4/3)))) (+ (* 1/2 (/ (- (/ 1 (pow (sqrt 4/3) 4)) (* 2 (/ 1 (pow (sqrt 4/3) 2)))) (* (pow x 3) (sqrt 4/3)))) (/ 1 (* x (sqrt 4/3)))))))
(+.f64 (.f64 x (+.f64 (sqrt.f64 #s(literal 4/3 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 4/3 binary64))) (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 #s(literal 4/3 binary64)) #s(literal 4 binary64))) #s(literal -3/2 binary64)) (.f64 x (.f64 x x))) (/.f64 #s(literal 5/4 binary64) (*.f64 x x)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 4/3 binary64))))
(* -1 (* x (sqrt 4/3)))
(*.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 4/3 binary64))))
(* -1 (* x (+ (sqrt 4/3) (/ 1 (* x (sqrt 4/3))))))
(-.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 4/3 binary64))) (*.f64 x (sqrt.f64 #s(literal 4/3 binary64))))
(* -1 (* x (+ (sqrt 4/3) (* -1 (/ (- (* -1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (* x (sqrt 4/3)))) (/ 1 (sqrt 4/3))) x)))))
(-.f64 (.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 4/3 binary64)))) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 4/3 binary64))) (/.f64 #s(literal 5/8 binary64) (*.f64 x (sqrt.f64 #s(literal 4/3 binary64))))) #s(literal 1 binary64)))
(* -1 (* x (+ (sqrt 4/3) (* -1 (/ (- (* -1 (/ (+ (* -1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (* x (pow (sqrt 4/3) 3)))) (* 1/2 (/ (- 2 (/ 1 (pow (sqrt 4/3) 2))) (sqrt 4/3)))) x)) (/ 1 (sqrt 4/3))) x)))))
(-.f64 (.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 4/3 binary64)))) (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 4/3 binary64))) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal -15/32 binary64) (sqrt.f64 #s(literal 4/3 binary64))) x) (/.f64 #s(literal 5/8 binary64) (sqrt.f64 #s(literal 4/3 binary64)))) x)) #s(literal 1 binary64)))
2
#s(literal 2 binary64)
(+ 2 (* 2 x))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 2 binary64)))
(+ 2 (* x (+ 2 (* 4/3 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64)))))
(+ 2 (* x (+ 2 (* 4/3 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64)))))
(* 4/3 (pow x 2))
(.f64 x (.f64 x #s(literal 4/3 binary64)))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
(* (pow x 2) (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64)))))
(* (pow x 2) (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64)))))
(* 4/3 (pow x 2))
(.f64 x (.f64 x #s(literal 4/3 binary64)))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
(* (pow x 2) (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64)))))
(* (pow x 2) (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64)))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 4/3 x)))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
(* x (+ 2 (* 4/3 x)))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
(* x (+ 2 (* 4/3 x)))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
(* 4/3 (pow x 2))
(.f64 x (.f64 x #s(literal 4/3 binary64)))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
(* 4/3 (pow x 2))
(.f64 x (.f64 x #s(literal 4/3 binary64)))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
(* (pow x 2) (+ 4/3 (* 2 (/ 1 x))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
2
#s(literal 2 binary64)
(+ 2 (* 4/3 x))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
(+ 2 (* 4/3 x))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
(+ 2 (* 4/3 x))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* x (+ 4/3 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
(* x (+ 4/3 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
(* x (+ 4/3 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* x (+ 4/3 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
(* x (+ 4/3 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
(* x (+ 4/3 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (/ x (sqrt 2)))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 4/3 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))) (/ 1 (sqrt 2)))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 x #s(literal 5/12 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- (+ 2/3 (/ 1 (pow (sqrt 2) 4))) (* 4/3 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 4/3 (/ 1 (pow (sqrt 2) 2))) (sqrt 2))))) (/ 1 (sqrt 2)))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 (/.f64 #s(literal 5/12 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))))))))
(* (sqrt (pow x 3)) (sqrt 2/3))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2/3 binary64)))
(* (pow x 2) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 2/3)))) (* (sqrt (/ 1 x)) (sqrt 2/3))))
(.f64 (.f64 x x) (+.f64 (.f64 #s(literal 2/3 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal 2/3 binary64)))) (.f64 (sqrt.f64 #s(literal 2/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* (pow x 2) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 2/3)))) (+ (* (sqrt (/ 1 x)) (sqrt 2/3)) (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 2/3))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 #s(literal 2/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2/3 binary64))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 2/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (/ (- 2 (* 4/9 (/ x (pow (sqrt 2/3) 2)))) (sqrt 2/3)))) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 2/3)))) (+ (* (sqrt (/ 1 x)) (sqrt 2/3)) (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 2/3)))))))
(.f64 (.f64 x x) (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal 2/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2/3 binary64))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 2/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x #s(literal -2/3 binary64))) (sqrt.f64 #s(literal 2/3 binary64)))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))
(.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2/3 binary64))))
(* (pow x 2) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -2/3)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -2/3)))))
(.f64 (.f64 x x) (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 2/3 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -2/3 binary64))) (.f64 (sqrt.f64 #s(literal -2/3 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* (pow x 2) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -2/3)))) (+ (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -2/3))) (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -2/3))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 #s(literal -2/3 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2/3 binary64))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 #s(literal 2/3 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (sqrt x) (/ (sqrt -1) (sqrt -2/3)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -4/9 (/ x (pow (sqrt -2/3) 2))))) (sqrt -2/3))))) (pow x 3))) (+ (* 2/3 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -2/3)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -2/3))))))
(.f64 (.f64 x x) (-.f64 (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 2/3 binary64) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal -2/3 binary64))) (.f64 (sqrt.f64 #s(literal -2/3 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) (/.f64 (-.f64 (.f64 (/.f64 (+.f64 #s(literal 2 binary64) (.f64 x #s(literal -2/3 binary64))) (sqrt.f64 #s(literal -2/3 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2/3 binary64))))) (.f64 x (*.f64 x x)))))
2
#s(literal 2 binary64)
(+ 2 (* 2 x))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 2 binary64)))
(+ 2 (* x (+ 2 (* 4/3 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64)))))
(+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))))))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* (pow x 3) (+ 2/3 (* 4/3 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))))
(* (pow x 3) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))
(* (pow x 3) (+ 2/3 (+ (* 4/3 (/ 1 x)) (+ (* 2 (/ 1 (pow x 3))) (/ 2 (pow x 2))))))
(.f64 x (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (+.f64 (/.f64 #s(literal 4/3 binary64) x) (/.f64 #s(literal 2 binary64) (.f64 x (*.f64 x x)))))) #s(literal 2 binary64)))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* (pow x 3) (+ 2/3 (* 4/3 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 4/3 (* 2 (/ 1 x))) x)) 2/3)))
(.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -2/3 binary64) (/.f64 (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 2 binary64) x)) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 4/3 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 2/3)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal -2/3 binary64) (/.f64 (+.f64 (+.f64 #s(literal -4/3 binary64) (/.f64 #s(literal -2 binary64) x)) (/.f64 #s(literal -2 binary64) (.f64 x x))) x))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 4/3 x)))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))
(* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))
(* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* (pow x 3) (+ 2/3 (* 4/3 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))))
(* (pow x 3) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))
(* (pow x 3) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* (pow x 3) (+ 2/3 (* 4/3 (/ 1 x))))
(.f64 x (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 4/3 (* 2 (/ 1 x))) x)) 2/3)))
(.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -2/3 binary64) (/.f64 (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 2 binary64) x)) x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 4/3 (* 2 (/ 1 x))) x)) 2/3)))
(.f64 (.f64 x (*.f64 x x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal -2/3 binary64) (/.f64 (+.f64 #s(literal 4/3 binary64) (/.f64 #s(literal 2 binary64) x)) x))))
2
#s(literal 2 binary64)
(+ 2 (* 4/3 x))
(+.f64 #s(literal 2 binary64) (*.f64 x #s(literal 4/3 binary64)))
(+ 2 (* x (+ 4/3 (* 2/3 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64)))))
(+ 2 (* x (+ 4/3 (* 2/3 x))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64)))))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
(* (pow x 2) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64)))))
(* (pow x 2) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64)))))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
(* (pow x 2) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64)))))
(* (pow x 2) (+ 2/3 (+ (* 4/3 (/ 1 x)) (/ 2 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64)))))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* 4/3 x)
(*.f64 x #s(literal 4/3 binary64))
(* x (+ 4/3 (* 2/3 x)))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
(* x (+ 4/3 (* 2/3 x)))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
(* x (+ 4/3 (* 2/3 x)))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
(* (pow x 2) (+ 2/3 (* 4/3 (/ 1 x))))
(.f64 x (+.f64 #s(literal 4/3 binary64) (.f64 x #s(literal 2/3 binary64))))
4/3
#s(literal 4/3 binary64)
(+ 4/3 (* 2/3 x))
(+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))
(+ 4/3 (* 2/3 x))
(+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))
(+ 4/3 (* 2/3 x))
(+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 4/3 (/ 1 x))))
(+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))
(* x (+ 2/3 (* 4/3 (/ 1 x))))
(+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))
(* x (+ 2/3 (* 4/3 (/ 1 x))))
(+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))
(* 2/3 x)
(*.f64 x #s(literal 2/3 binary64))
(* x (+ 2/3 (* 4/3 (/ 1 x))))
(+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))
(* x (+ 2/3 (* 4/3 (/ 1 x))))
(+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))
(* x (+ 2/3 (* 4/3 (/ 1 x))))
(+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))

eval91.0ms (1.2%)

Compiler: Compiled 8552 to 1426 computations (83.3% saved)

prune77.0ms (1%)

Pruning

16 alts after pruning (7 fresh and 9 done)

	Pruned	Kept	Total
New	630	6	636
Fresh	3	1	4
Picked	2	3	5
Done	0	6	6
Total	635	16	651

Accuracy

100.0%

Counts

651 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.0%	(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
▶	69.1%	(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 3/8 binary64))) (.f64 x (*.f64 x #s(literal 7/96 binary64)))))))
▶	1.6%	(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
▶	3.0%	(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
✓	99.2%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
✓	71.1%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
✓	68.3%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))))
✓	68.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	70.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
✓	68.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
	2.4%	(sqrt.f64 (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))))))
▶	2.2%	(sqrt.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64))))
	3.6%	(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))
✓	2.4%	(sqrt.f64 x)
✓	74.5%	(sqrt.f64 #s(literal 2 binary64))
✓	73.5%	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))

Compiler

Compiled 221 to 166 computations (24.9% saved)

simplify148.0ms (1.9%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal 2/3 binary64))
✓	cost-diff	0	(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
✓	cost-diff	0	(sqrt.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64))))
✓	cost-diff	0	(*.f64 x #s(literal 1/6 binary64))
✓	cost-diff	0	(sqrt.f64 (*.f64 x #s(literal 1/6 binary64)))
✓	cost-diff	0	(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
✓	cost-diff	0	(sqrt.f64 #s(literal 4/3 binary64))
✓	cost-diff	0	(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
✓	cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 3/8 binary64))) (.f64 x (*.f64 x #s(literal 7/96 binary64)))))))
✓	cost-diff	128	(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 3/8 binary64))) (.f64 x (*.f64 x #s(literal 7/96 binary64))))
✓	cost-diff	128	(.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 3/8 binary64))) (.f64 x (.f64 x #s(literal 7/96 binary64)))))

Rules

3632×	`fma-define`
2700×	`fma-lowering-fma.f32`
2700×	`fma-lowering-fma.f64`
1334×	`-lowering-.f32`
1334×	`-lowering-.f64`

Iterations

Useful iterations: 10 (0.0ms)

Iter	Nodes	Cost
0	30	137
1	64	129
2	187	129
3	607	125
4	1576	122
5	2546	122
6	2773	122
7	2964	122
8	3043	122
9	3232	122
10	3268	119
11	3952	119
12	3952	119
13	3952	119
14	4033	119
15	4305	119
0	4305	119

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (sqrt 2) (* x (* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96))))))
(sqrt 2)
2
(* x (* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96)))))
x
(* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96))))
(/ 1/2 (sqrt 2))
1/2
(+ (+ 1 (* x 3/8)) (* x (* x 7/96)))
(+ 1 (* x 3/8))
1
(* x 3/8)
3/8
(* x (* x 7/96))
(* x 7/96)
7/96
(* x (sqrt 4/3))
x
(sqrt 4/3)
4/3
(pow (* x x) 1/4)
(* x x)
x
1/4
(* (sqrt (* x 1/6)) x)
(sqrt (* x 1/6))
(* x 1/6)
x
1/6
(sqrt (* x (* (* x x) 2/3)))
(* x (* (* x x) 2/3))
x
(* (* x x) 2/3)
(* x x)
2/3

Outputs
(+ (sqrt 2) (* x (* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64))))) (sqrt.f64 #s(literal 2 binary64))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
2
#s(literal 2 binary64)
(* x (* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96)))))
(/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 (*.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64))))) (sqrt.f64 #s(literal 2 binary64)))
x
(* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96))))
(/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 (.f64 x #s(literal 7/192 binary64)) #s(literal 3/16 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ (+ 1 (* x 3/8)) (* x (* x 7/96)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64)))))
(+ 1 (* x 3/8))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 3/8 binary64)))
1
#s(literal 1 binary64)
(* x 3/8)
(*.f64 x #s(literal 3/8 binary64))
3/8
#s(literal 3/8 binary64)
(* x (* x 7/96))
(.f64 x (.f64 x #s(literal 7/96 binary64)))
(* x 7/96)
(*.f64 x #s(literal 7/96 binary64))
7/96
#s(literal 7/96 binary64)
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
x
(sqrt 4/3)
(sqrt.f64 #s(literal 4/3 binary64))
4/3
#s(literal 4/3 binary64)
(pow (* x x) 1/4)
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(* x x)
(*.f64 x x)
x
1/4
#s(literal 1/4 binary64)
(* (sqrt (* x 1/6)) x)
(.f64 x (sqrt.f64 (.f64 x #s(literal 1/6 binary64))))
(sqrt (* x 1/6))
(sqrt.f64 (*.f64 x #s(literal 1/6 binary64)))
(* x 1/6)
(*.f64 x #s(literal 1/6 binary64))
x
1/6
#s(literal 1/6 binary64)
(sqrt (* x (* (* x x) 2/3)))
(sqrt.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64))))
(* x (* (* x x) 2/3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
x
(* (* x x) 2/3)
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* x x)
(*.f64 x x)
2/3
#s(literal 2/3 binary64)

localize208.0ms (2.7%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
✓	accuracy	99.9%	(.f64 (.f64 x x) #s(literal 2/3 binary64))
✓	accuracy	92.4%	(sqrt.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64))))
✓	accuracy	99.9%	(sqrt.f64 (*.f64 x #s(literal 1/6 binary64)))
✓	accuracy	99.9%	(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
✓	accuracy	99.8%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	86.9%	(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 4/3 binary64))
✓	accuracy	99.8%	(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal 7/96 binary64)))
✓	accuracy	99.8%	(*.f64 x #s(literal 7/96 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 3/8 binary64))) (.f64 x (*.f64 x #s(literal 7/96 binary64))))))
✓	accuracy	99.5%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))

Results

75.0ms	168×	0	invalid
38.0ms	12×	5	exit
38.0ms	76×	0	valid

Compiler

Compiled 154 to 31 computations (79.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-mult: 23.0ms (33.1% of total)

...c/correct-round.rkt:119:19: 18.0ms (25.9% of total)

ival-sqrt: 11.0ms (15.8% of total)

ival-pow: 6.0ms (8.6% of total)

backward-pass: 4.0ms (5.8% of total)

ival-add: 4.0ms (5.8% of total)

ival-div: 2.0ms (2.9% of total)

const: 1.0ms (1.4% of total)

series69.0ms (0.9%)

Counts

18 → 180

Calls

Call 1

Inputs
#<alt (* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96))))>
#<alt (+ (+ 1 (* x 3/8)) (* x (* x 7/96)))>
#<alt (+ (sqrt 2) (* x (* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96))))))>
#<alt (sqrt 2)>
#<alt (* x (sqrt 4/3))>
#<alt (sqrt 4/3)>
#<alt (pow (* x x) 1/4)>
#<alt (* x x)>
#<alt (* (sqrt (* x 1/6)) x)>
#<alt (sqrt (* x 1/6))>
#<alt (* x 1/6)>
#<alt (sqrt (* x (* (* x x) 2/3)))>
#<alt (* x (* (* x x) 2/3))>
#<alt (* (* x x) 2/3)>
#<alt (/ 1/2 (sqrt 2))>
#<alt (* x (* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96)))))>
#<alt (* x 7/96)>
#<alt (* x (* x 7/96))>

Outputs
#<alt (/ 1/2 (sqrt 2))>
#<alt (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))>
#<alt (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 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) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 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) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt 1>
#<alt (+ 1 (* 3/8 x))>
#<alt (+ 1 (* x (+ 3/8 (* 7/96 x))))>
#<alt (+ 1 (* x (+ 3/8 (* 7/96 x))))>
#<alt (* 7/96 (pow x 2))>
#<alt (* (pow x 2) (+ 7/96 (* 3/8 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/96 (+ (* 3/8 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 7/96 (+ (* 3/8 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 7/96 (pow x 2))>
#<alt (* (pow x 2) (+ 7/96 (* 3/8 (/ 1 x))))>
#<alt (* (pow x 2) (+ 7/96 (+ (* 3/8 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 7/96 (+ (* 3/8 (/ 1 x)) (/ 1 (pow x 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 4/3))>
#<alt (* x (sqrt 4/3))>
#<alt (* x (sqrt 4/3))>
#<alt (* x (sqrt 4/3))>
#<alt (* x (sqrt 4/3))>
#<alt (* x (sqrt 4/3))>
#<alt (* x (sqrt 4/3))>
#<alt (* x (sqrt 4/3))>
#<alt (* x (sqrt 4/3))>
#<alt (* x (sqrt 4/3))>
#<alt (* x (sqrt 4/3))>
#<alt (* x (sqrt 4/3))>
#<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) (sqrt -1)))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<alt (* -1 (* (sqrt x) (sqrt -1)))>
#<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 (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* (sqrt (pow x 3)) (sqrt 2/3))>
#<alt (* (sqrt (pow x 3)) (sqrt 2/3))>
#<alt (* (sqrt (pow x 3)) (sqrt 2/3))>
#<alt (* (sqrt (pow x 3)) (sqrt 2/3))>
#<alt (* (sqrt (pow x 3)) (sqrt 2/3))>
#<alt (* (sqrt (pow x 3)) (sqrt 2/3))>
#<alt (* (sqrt (pow x 3)) (sqrt 2/3))>
#<alt (* (sqrt (pow x 3)) (sqrt 2/3))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))>
#<alt (* 2/3 (pow x 3))>
#<alt (* 2/3 (pow x 3))>
#<alt (* 2/3 (pow x 3))>
#<alt (* 2/3 (pow x 3))>
#<alt (* 2/3 (pow x 3))>
#<alt (* 2/3 (pow x 3))>
#<alt (* 2/3 (pow x 3))>
#<alt (* 2/3 (pow x 3))>
#<alt (* 2/3 (pow x 3))>
#<alt (* 2/3 (pow x 3))>
#<alt (* 2/3 (pow x 3))>
#<alt (* 2/3 (pow x 3))>
#<alt (* 2/3 (pow x 2))>
#<alt (* 2/3 (pow x 2))>
#<alt (* 2/3 (pow x 2))>
#<alt (* 2/3 (pow x 2))>
#<alt (* 2/3 (pow x 2))>
#<alt (* 2/3 (pow x 2))>
#<alt (* 2/3 (pow x 2))>
#<alt (* 2/3 (pow x 2))>
#<alt (* 2/3 (pow x 2))>
#<alt (* 2/3 (pow x 2))>
#<alt (* 2/3 (pow x 2))>
#<alt (* 2/3 (pow x 2))>
#<alt (* 1/2 (/ x (sqrt 2)))>
#<alt (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))>
#<alt (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))>
#<alt (* 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))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 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 (* -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 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))>
#<alt (* 7/96 x)>
#<alt (* 7/96 x)>
#<alt (* 7/96 x)>
#<alt (* 7/96 x)>
#<alt (* 7/96 x)>
#<alt (* 7/96 x)>
#<alt (* 7/96 x)>
#<alt (* 7/96 x)>
#<alt (* 7/96 x)>
#<alt (* 7/96 x)>
#<alt (* 7/96 x)>
#<alt (* 7/96 x)>
#<alt (* 7/96 (pow x 2))>
#<alt (* 7/96 (pow x 2))>
#<alt (* 7/96 (pow x 2))>
#<alt (* 7/96 (pow x 2))>
#<alt (* 7/96 (pow x 2))>
#<alt (* 7/96 (pow x 2))>
#<alt (* 7/96 (pow x 2))>
#<alt (* 7/96 (pow x 2))>
#<alt (* 7/96 (pow x 2))>
#<alt (* 7/96 (pow x 2))>
#<alt (* 7/96 (pow x 2))>
#<alt (* 7/96 (pow x 2))>

Calls

45 calls:

Time	Variable		Point	Expression
52.0ms	x	@	0	(pow (* x x) 1/4)
6.0ms	x	@	inf	(* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96))))
1.0ms	x	@	inf	(+ (sqrt 2) (* x (* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96))))))
1.0ms	x	@	0	(* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96))))
0.0ms	x	@	0	(* x (sqrt 4/3))

rewrite294.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

4140×	`-lowering-.f32`
4140×	`-lowering-.f64`
2860×	`/-lowering-/.f32`
2860×	`/-lowering-/.f64`
1554×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	113
1	87	104
2	335	101
3	1904	96
0	8605	96

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 746

Calls

Call 1

Inputs
(* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96))))
(+ (+ 1 (* x 3/8)) (* x (* x 7/96)))
(+ (sqrt 2) (* x (* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96))))))
(sqrt 2)
(* x (sqrt 4/3))
(sqrt 4/3)
(pow (* x x) 1/4)
(* x x)
(* (sqrt (* x 1/6)) x)
(sqrt (* x 1/6))
(* x 1/6)
(sqrt (* x (* (* x x) 2/3)))
(* x (* (* x x) 2/3))
(* (* x x) 2/3)
(/ 1/2 (sqrt 2))
(* x (* (/ 1/2 (sqrt 2)) (+ (+ 1 (* x 3/8)) (* x (* x 7/96)))))
(* x 7/96)
(* x (* x 7/96))

Outputs
(+.f64 (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)) (/.f64 (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64)))) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))))
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 3/8 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))) (.f64 x (*.f64 #s(literal 7/96 binary64) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64))))))
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(.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 3/8 binary64))))) (.f64 (.f64 x (*.f64 x #s(literal 7/96 binary64))) (/.f64 x #s(literal 2 binary64)))))
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(.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64)))))) #s(literal -1 binary64)))
(.f64 (/.f64 x #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (*.f64 x #s(literal 7/96 binary64))))) (sqrt.f64 #s(literal 2 binary64))))
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(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64)))))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64)))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/2 binary64))
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(.f64 (/.f64 (/.f64 x #s(literal 2 binary64)) #s(literal -1 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (*.f64 x #s(literal 7/96 binary64))))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 2 binary64)))))
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(.f64 (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64)))))) #s(literal 1 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal -3/2 binary64)))
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(.f64 #s(literal 1 binary64) (.f64 x #s(literal 7/96 binary64)))
(*.f64 x #s(literal 7/96 binary64))
(*.f64 #s(literal 7/96 binary64) x)
(.f64 (.f64 x #s(literal 7/96 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 7/96 binary64)))))
(/.f64 (.f64 x (.f64 x #s(literal 7/96 binary64))) #s(literal 1 binary64))
(/.f64 (.f64 (.f64 x x) #s(literal -7/96 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 7/96 binary64))))
(.f64 x (.f64 x #s(literal 7/96 binary64)))
(.f64 #s(literal 7/96 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 7/96 binary64)) x)
(.f64 (.f64 x (*.f64 x #s(literal 7/96 binary64))) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal 7/96 binary64))

simplify194.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

2842×	`-lowering-.f32`
2842×	`-lowering-.f64`
1998×	`fma-lowering-fma.f32`
1998×	`fma-lowering-fma.f64`
1360×	`fmm-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	1293
1	359	1214
2	1088	1178
3	3160	1098
4	6745	1098
0	8263	1098

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 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) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 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) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
1
(+ 1 (* 3/8 x))
(+ 1 (* x (+ 3/8 (* 7/96 x))))
(+ 1 (* x (+ 3/8 (* 7/96 x))))
(* 7/96 (pow x 2))
(* (pow x 2) (+ 7/96 (* 3/8 (/ 1 x))))
(* (pow x 2) (+ 7/96 (+ (* 3/8 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/96 (+ (* 3/8 (/ 1 x)) (/ 1 (pow x 2)))))
(* 7/96 (pow x 2))
(* (pow x 2) (+ 7/96 (* 3/8 (/ 1 x))))
(* (pow x 2) (+ 7/96 (+ (* 3/8 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 7/96 (+ (* 3/8 (/ 1 x)) (/ 1 (pow x 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 4/3))
(* x (sqrt 4/3))
(* x (sqrt 4/3))
(* x (sqrt 4/3))
(* x (sqrt 4/3))
(* x (sqrt 4/3))
(* x (sqrt 4/3))
(* x (sqrt 4/3))
(* x (sqrt 4/3))
(* x (sqrt 4/3))
(* x (sqrt 4/3))
(* x (sqrt 4/3))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* (sqrt x) (sqrt -1)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* (sqrt x) (sqrt 1/6))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* (sqrt (pow x 3)) (sqrt 2/3))
(* (sqrt (pow x 3)) (sqrt 2/3))
(* (sqrt (pow x 3)) (sqrt 2/3))
(* (sqrt (pow x 3)) (sqrt 2/3))
(* (sqrt (pow x 3)) (sqrt 2/3))
(* (sqrt (pow x 3)) (sqrt 2/3))
(* (sqrt (pow x 3)) (sqrt 2/3))
(* (sqrt (pow x 3)) (sqrt 2/3))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))
(* 2/3 (pow x 3))
(* 2/3 (pow x 3))
(* 2/3 (pow x 3))
(* 2/3 (pow x 3))
(* 2/3 (pow x 3))
(* 2/3 (pow x 3))
(* 2/3 (pow x 3))
(* 2/3 (pow x 3))
(* 2/3 (pow x 3))
(* 2/3 (pow x 3))
(* 2/3 (pow x 3))
(* 2/3 (pow x 3))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 2/3 (pow x 2))
(* 1/2 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (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))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* 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 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/96 x)
(* 7/96 x)
(* 7/96 x)
(* 7/96 x)
(* 7/96 x)
(* 7/96 x)
(* 7/96 x)
(* 7/96 x)
(* 7/96 x)
(* 7/96 x)
(* 7/96 x)
(* 7/96 x)
(* 7/96 (pow x 2))
(* 7/96 (pow x 2))
(* 7/96 (pow x 2))
(* 7/96 (pow x 2))
(* 7/96 (pow x 2))
(* 7/96 (pow x 2))
(* 7/96 (pow x 2))
(* 7/96 (pow x 2))
(* 7/96 (pow x 2))
(* 7/96 (pow x 2))
(* 7/96 (pow x 2))
(* 7/96 (pow x 2))

Outputs
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/16 binary64) x))) (sqrt.f64 #s(literal 2 binary64)))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 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))) (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(/.f64 (.f64 x (.f64 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))) (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64))))))
1
#s(literal 1 binary64)
(+ 1 (* 3/8 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 3/8 binary64)))
(+ 1 (* x (+ 3/8 (* 7/96 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64)))))
(+ 1 (* x (+ 3/8 (* 7/96 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64)))))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* (pow x 2) (+ 7/96 (* 3/8 (/ 1 x))))
(.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64))))
(* (pow x 2) (+ 7/96 (+ (* 3/8 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64)))))
(* (pow x 2) (+ 7/96 (+ (* 3/8 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64)))))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* (pow x 2) (+ 7/96 (* 3/8 (/ 1 x))))
(.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64))))
(* (pow x 2) (+ 7/96 (+ (* 3/8 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64)))))
(* (pow x 2) (+ 7/96 (+ (* 3/8 (/ 1 x)) (/ 1 (pow x 2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64)))))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/16 binary64) x))) (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))))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64))))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (.f64 x (.f64 x (*.f64 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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 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 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64))))))) (.f64 (.f64 x x) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (.f64 x (.f64 x (*.f64 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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 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) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 #s(literal 2 binary64))) 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 (sqrt.f64 #s(literal 2 binary64)) x) x) (/.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 #s(literal 2 binary64)))) x)))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(* x (sqrt 4/3))
(*.f64 x (sqrt.f64 #s(literal 4/3 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) (sqrt -1)))
(*.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 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)
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt (pow x 3)) (sqrt 1/6))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 1/6 binary64)))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/6 binary64)))
(* (sqrt x) (sqrt 1/6))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 1/6 binary64)))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 x) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1/6 binary64)))))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* (sqrt (pow x 3)) (sqrt 2/3))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2/3 binary64)))
(* (sqrt (pow x 3)) (sqrt 2/3))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2/3 binary64)))
(* (sqrt (pow x 3)) (sqrt 2/3))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2/3 binary64)))
(* (sqrt (pow x 3)) (sqrt 2/3))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2/3 binary64)))
(* (sqrt (pow x 3)) (sqrt 2/3))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2/3 binary64)))
(* (sqrt (pow x 3)) (sqrt 2/3))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2/3 binary64)))
(* (sqrt (pow x 3)) (sqrt 2/3))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2/3 binary64)))
(* (sqrt (pow x 3)) (sqrt 2/3))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) (sqrt.f64 #s(literal 2/3 binary64)))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (sqrt.f64 #s(literal -2/3 binary64))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (sqrt.f64 #s(literal -2/3 binary64))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (sqrt.f64 #s(literal -2/3 binary64))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -2/3)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (sqrt.f64 #s(literal -2/3 binary64))))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* 2/3 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64)))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* 2/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 2/3 binary64))
(* 1/2 (/ x (sqrt 2)))
(*.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2)))))
(/.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 3/16 binary64) x))) (sqrt.f64 #s(literal 2 binary64)))
(* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))
(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64)))))))
(* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2)))))
(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64)))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (.f64 x (.f64 x (*.f64 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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64)))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64)))))))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(/.f64 (.f64 x (.f64 x (*.f64 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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 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) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 #s(literal 2 binary64))) x)))
(* -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) (+.f64 #s(literal 3/16 binary64) (/.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 #s(literal 2 binary64))) x)))
(* 7/96 x)
(*.f64 x #s(literal 7/96 binary64))
(* 7/96 x)
(*.f64 x #s(literal 7/96 binary64))
(* 7/96 x)
(*.f64 x #s(literal 7/96 binary64))
(* 7/96 x)
(*.f64 x #s(literal 7/96 binary64))
(* 7/96 x)
(*.f64 x #s(literal 7/96 binary64))
(* 7/96 x)
(*.f64 x #s(literal 7/96 binary64))
(* 7/96 x)
(*.f64 x #s(literal 7/96 binary64))
(* 7/96 x)
(*.f64 x #s(literal 7/96 binary64))
(* 7/96 x)
(*.f64 x #s(literal 7/96 binary64))
(* 7/96 x)
(*.f64 x #s(literal 7/96 binary64))
(* 7/96 x)
(*.f64 x #s(literal 7/96 binary64))
(* 7/96 x)
(*.f64 x #s(literal 7/96 binary64))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))
(* 7/96 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/96 binary64))

eval129.0ms (1.7%)

Compiler: Compiled 19210 to 2392 computations (87.5% saved)

prune115.0ms (1.5%)

Pruning

15 alts after pruning (5 fresh and 10 done)

	Pruned	Kept	Total
New	960	5	965
Fresh	2	0	2
Picked	3	2	5
Done	1	8	9
Total	966	15	981

Accuracy

100.0%

Counts

981 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	6.0%	(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
	2.6%	(/.f64 (.f64 x (.f64 x (*.f64 x #s(literal 7/192 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
	69.1%	(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64))))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) x)) (sqrt.f64 #s(literal 2 binary64)))
	3.3%	(.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
	1.6%	(.f64 (sqrt.f64 (.f64 x #s(literal 2/3 binary64))) x)
	2.9%	(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64)))))))
✓	3.0%	(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
✓	99.2%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
✓	71.1%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
✓	68.9%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
✓	70.4%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
✓	68.8%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	2.4%	(sqrt.f64 x)
✓	74.5%	(sqrt.f64 #s(literal 2 binary64))
✓	73.5%	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))

Compiler

Compiled 389 to 216 computations (44.5% saved)

regimes32.0ms (0.4%)

Counts

27 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
(.f64 (sqrt.f64 (.f64 x #s(literal 2/3 binary64))) x)
(sqrt.f64 (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(sqrt.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64))))
(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))))
(/.f64 (.f64 x (.f64 x (*.f64 x #s(literal 7/192 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))))))
(.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))))
(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64))))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) x)) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 3/8 binary64))) (.f64 x (*.f64 x #s(literal 7/96 binary64)))))))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) 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 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))

Calls

3 calls:

16.0ms

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

7.0ms

6.0ms

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

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	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))))`
99.2%	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)

regimes9.0ms (0.1%)

Accuracy

Total -46.9b remaining (-287.5%)

Threshold costs -46.9b (-287.5%)

Counts

25 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 x (sqrt.f64 #s(literal 4/3 binary64)))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
(.f64 (sqrt.f64 (.f64 x #s(literal 2/3 binary64))) x)
(sqrt.f64 (.f64 x (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(sqrt.f64 (.f64 x (.f64 (*.f64 x x) #s(literal 2/3 binary64))))
(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))
(sqrt.f64 (.f64 x (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x #s(literal 4/3 binary64))))))
(/.f64 (.f64 x (.f64 x (*.f64 x #s(literal 7/192 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
(sqrt.f64 (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64)))))))
(.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal 7/192 binary64)))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 4/3 binary64) (*.f64 x #s(literal 2/3 binary64))))))))
(.f64 x (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (.f64 x #s(literal 7/192 binary64)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) x))
(+.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (.f64 x #s(literal 7/96 binary64))))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) x)) (sqrt.f64 #s(literal 2 binary64)))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 x (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 3/8 binary64))) (.f64 x (*.f64 x #s(literal 7/96 binary64)))))))

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

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
74.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	9	10

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(sqrt.f64 #s(literal 2 binary64))

Outputs
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(sqrt.f64 #s(literal 2 binary64))

soundness306.0ms (4%)

Rules

2950×	`-lowering-.f32`
2950×	`-lowering-.f64`
2624×	`+-lowering-+.f64`
2624×	`+-lowering-+.f32`
1432×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	8
1	24	8
2	31	8
3	44	8
4	63	8
5	96	8
6	149	8
7	271	8
8	606	8
9	1557	8
10	2233	8
11	2410	8
12	2438	8
0	2438	8
0	77	381
1	260	328
2	804	324
3	1875	321
4	3207	320
0	8073	320

Stop Event

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

Compiler

Compiled 32 to 25 computations (21.9% saved)

preprocess23.0ms (0.3%)

Compiler: Compiled 48 to 36 computations (25% saved)

analyze224.0ms (2.9%)

sample2.7s (34.3%)

preprocess179.0ms (2.3%)

explain260.0ms (3.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify44.0ms (0.6%)

localize130.0ms (1.7%)

series5.0ms (0.1%)

rewrite263.0ms (3.4%)

simplify218.0ms (2.8%)

eval70.0ms (0.9%)

prune71.0ms (0.9%)

simplify162.0ms (2.1%)

localize252.0ms (3.3%)

series19.0ms (0.2%)

rewrite243.0ms (3.1%)

simplify315.0ms (4.1%)

eval129.0ms (1.7%)

prune170.0ms (2.2%)

simplify20.0ms (0.3%)

localize175.0ms (2.3%)

series15.0ms (0.2%)

rewrite175.0ms (2.3%)

simplify246.0ms (3.2%)

eval91.0ms (1.2%)

prune77.0ms (1%)

simplify148.0ms (1.9%)

localize208.0ms (2.7%)

series69.0ms (0.9%)

rewrite294.0ms (3.8%)

simplify194.0ms (2.5%)

eval129.0ms (1.7%)

prune115.0ms (1.5%)

regimes32.0ms (0.4%)

regimes9.0ms (0.1%)

simplify7.0ms (0.1%)

soundness306.0ms (4%)

preprocess23.0ms (0.3%)

end0.0ms (0%)

Profiling