Metrics for sqrtexp (problem 3.4.4)

analyze214.0ms (2.7%)

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: 97.0ms

ival-exp: 31.0ms (32.1% of total)

ival-mult: 23.0ms (23.8% of total)

ival-sub: 21.0ms (21.7% of total)

ival-sqrt: 12.0ms (12.4% of total)

ival-div: 6.0ms (6.2% of total)

const: 3.0ms (3.1% of total)

backward-pass: 1.0ms (1% of total)

sample2.5s (31.5%)

Results

1.6s	5239×	1	valid
256.0ms	3017×	0	valid
202.0ms	2661×	0	unsamplable

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-exp: 898.0ms (54.7% of total)

ival-sub: 228.0ms (13.9% of total)

ival-mult: 141.0ms (8.6% of total)

backward-pass: 126.0ms (7.7% of total)

ival-sqrt: 120.0ms (7.3% of total)

ival-div: 99.0ms (6% of total)

const: 30.0ms (1.8% of total)

Bogosity

preprocess232.0ms (2.9%)

Algorithm

2×	egg-herbie

Rules

2108×	`-lowering-.f32`
2108×	`-lowering-.f64`
1708×	`--lowering--.f32`
1708×	`--lowering--.f64`
1500×	`fnmsub-define`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	19	29
1	52	27
2	85	27
3	137	27
4	252	20
5	456	18
6	978	18
7	3794	18
0	10	8
1	26	8
2	35	8
3	50	8
4	83	7
5	148	5
6	308	5
7	862	5
8	5004	5
0	8250	5

Stop Event

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

Calls

Call 1

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

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

Call 2

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

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

explain251.0ms (3.1%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
172	0	-	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
172	0	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
0	0	-	-	`x`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
0	0	-	-	`(*.f64 #s(literal 2 binary64) x)`
0	0	-	-	`#s(literal 1 binary64)`
0	1	(177.2369617688835)	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`

Results

174.0ms	340×	1	valid
21.0ms	172×	0	valid

Compiler

Compiled 107 to 32 computations (70.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 133.0ms

ival-exp: 55.0ms (41.4% of total)

ival-sub: 44.0ms (33.2% of total)

backward-pass: 10.0ms (7.5% of total)

ival-sqrt: 8.0ms (6% of total)

ival-mult: 7.0ms (5.3% of total)

ival-div: 5.0ms (3.8% of total)

const: 2.0ms (1.5% of total)

eval0.0ms (0%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`sqrt-lowering-sqrt.f64`
2×	`exp-lowering-exp.f32`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	9	13
0	9	13

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
1
(exp x)
x

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

localize30.0ms (0.4%)

Localize:

Found 3 expressions of interest:

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

Results

18.0ms

256×

valid

Compiler

Compiled 15 to 6 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-exp: 2.0ms (30.2% of total)

ival-add: 2.0ms (30.2% of total)

ival-sqrt: 2.0ms (30.2% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (sqrt (+ 1 (exp x)))>
#<alt (+ 1 (exp x))>
#<alt (exp x)>

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

Calls

9 calls:

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

rewrite337.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3504×	`/-lowering-/.f32`
3504×	`/-lowering-/.f64`
2980×	`-lowering-.f32`
2980×	`-lowering-.f64`
1782×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	24	11
2	155	11
3	1188	11
0	8378	11

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 241

Calls

Call 1

Inputs
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)

Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64)) (.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/4 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (expm1.f64 x) (expm1.f64 (*.f64 x #s(literal 2 binary64))))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64))))) (sqrt.f64 (.f64 (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64))))) (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (exp.f64 (.f64 x #s(literal 4 binary64))))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 4 binary64))))) (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (.f64 x #s(literal 3 binary64)))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64)))
(/.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 (.f64 x #s(literal 3 binary64)) #s(literal 3/2 binary64)))) (sqrt.f64 (.f64 (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x)) (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64)))) (exp.f64 (.f64 x #s(literal 3 binary64)))))))
(/.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) (sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 9 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64)))) (exp.f64 (.f64 x #s(literal 3 binary64)))) (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (exp.f64 (*.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (.f64 x #s(literal 3 binary64))))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -3 binary64)) (/.f64 (exp.f64 (.f64 x #s(literal 6 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)) (pow.f64 (/.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 9 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x))))) (sqrt.f64 (-.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64)))) (exp.f64 (*.f64 x #s(literal 3 binary64))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (exp.f64 (.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))) (hypot.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (.f64 x #s(literal 3 binary64))))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (neg.f64 (pow.f64 (expm1.f64 x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64)))))) (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))))) (neg.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (exp.f64 x)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
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(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (/.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 (.f64 x #s(literal 3 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (exp.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64)))) (expm1.f64 (.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(exp.f64 x)
(exp.f64 (*.f64 x #s(literal 1 binary64)))
(pow.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (exp.f64 x) #s(literal 1 binary64))

simplify235.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

3346×	`-lowering-.f32`
3346×	`-lowering-.f64`
1870×	`+-lowering-+.f64`
1870×	`+-lowering-+.f32`
1432×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	52	221
1	167	175
2	545	174
3	1199	171
4	2861	170
5	6815	170
0	8156	170

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)

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 (+ (* 1/2 (/ (* 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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (+.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 3/16 binary64))) (.f64 x (.f64 x #s(literal 7/192 binary64))))))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.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 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.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)))))))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)

eval30.0ms (0.4%)

Compiler: Compiled 6110 to 920 computations (84.9% saved)

prune45.0ms (0.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	269	8	277
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	269	9	278

Accuracy

100.0%

Counts

278 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
▶	99.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
	67.5%	(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
▶	67.3%	(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))))))))
▶	69.1%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x)))))
	67.1%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
	69.1%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
▶	73.3%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 158 to 119 computations (24.7% saved)

simplify26.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

500×	`fma-define`
400×	`fma-lowering-fma.f32`
400×	`fma-lowering-fma.f64`
146×	`sum3-define`
134×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	154
1	61	136
2	135	134
3	275	134
4	464	134
5	582	134
6	605	134
0	605	134

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(pow (/ 1 (+ 1 (exp x))) -1/2)
(/ 1 (+ 1 (exp x)))
1
(+ 1 (exp x))
(exp x)
x
-1/2
(sqrt 2)
2
(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
(/ 1 (sqrt (/ 1 (+ 1 (exp x)))))
1
(sqrt (/ 1 (+ 1 (exp x))))
(/ 1 (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
x

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

localize143.0ms (1.8%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (exp.f64 x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
✓	accuracy	99.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	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	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%	(.f64 x (+.f64 #s(literal 1 binary64) (.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%	(sqrt.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (exp.f64 x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))

Results

71.0ms	175×	0	valid
34.0ms	81×	0	invalid

Compiler

Compiled 163 to 26 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-mult: 9.0ms (20.5% of total)

ival-sqrt: 9.0ms (20.5% of total)

ival-add: 8.0ms (18.3% of total)

ival-div: 5.0ms (11.4% of total)

ival-pow: 5.0ms (11.4% of total)

...c/correct-round.rkt:119:19: 4.0ms (9.1% of total)

ival-exp: 3.0ms (6.8% of total)

const: 1.0ms (2.3% of total)

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

series16.0ms (0.2%)

Counts

18 → 204

Calls

Call 1

Inputs
#<alt (pow (/ 1 (+ 1 (exp x))) -1/2)>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (+ 1 (exp x))>
#<alt (exp x)>
#<alt (sqrt 2)>
#<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 (/ 1 (sqrt (/ 1 (+ 1 (exp x)))))>
#<alt (sqrt (/ 1 (+ 1 (exp 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 (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt (/ 1 (+ 1 (exp x)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))>
#<alt (* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (sqrt 1/2)))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt (* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))>
#<alt 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) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt (+ 1 (exp x)))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp x))))>
#<alt (sqrt (/ 1 (+ 1 (exp 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
2.0ms	x	@	0	(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))
1.0ms	x	@	inf	(sqrt (+ 2 (* x (+ 1 (* 1/2 x)))))
1.0ms	x	@	0	(* 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	@	inf	(sqrt (+ 2 (* x (+ 1 (* x (+ 1/2 (* x 1/6)))))))

rewrite347.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3914×	`-lowering-.f32`
3914×	`-lowering-.f64`
3622×	`/-lowering-/.f32`
3622×	`/-lowering-/.f64`
1692×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	124
1	160	102
2	1340	100
0	8243	100

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 617

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x)))))
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64))) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1/4 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1/4 binary64))))
(exp.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 (exp.f64 x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(neg.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) (expm1.f64 x)))) (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))
(/.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x)))) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) (expm1.f64 x)))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 (exp.f64 (.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))) (sqrt.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) (expm1.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (sqrt.f64 (expm1.f64 (+.f64 x x))) (sqrt.f64 (expm1.f64 x)))
(/.f64 (neg.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) (expm1.f64 x))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 2 binary64)))))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)) #s(literal -1/4 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)))
(.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x)))) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x))))))
(.f64 (hypot.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x))))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(exp.f64 (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))))
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(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 2 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 (exp.f64 x))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x)))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x))))))
(exp.f64 (neg.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))))
(fabs.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
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(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x))))))
(pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal -2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64)))
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(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/2 binary64))) #s(literal -1 binary64))
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(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (exp.f64 x))))))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1/4 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (exp.f64 x) (expm1.f64 x)))) #s(literal -1/2 binary64)))
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(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 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 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64))))) (/.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 x #s(literal 1/6 binary64))))
(fma.f64 #s(literal 1/2 binary64) x (.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)))
(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 (.f64 x x) #s(literal 1/6 binary64) (.f64 x #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64)))))) (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) x)) (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))) (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/216 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) x)) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x)))
(/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x)))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
(/.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) x)))
(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) x)))
(/.f64 (neg.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))))) (neg.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) x))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x)) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
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(/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (pow.f64 (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))))
(/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (pow.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x))) (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x #s(literal 1/2 binary64))))))
(.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 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 (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))))))
(.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 x (.f64 x #s(literal 1/6 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x))))
(.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x #s(literal 1/6 binary64)) (-.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))))
(.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x))))

simplify331.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

4672×	`-lowering-.f32`
4672×	`-lowering-.f64`
3142×	`/-lowering-/.f32`
3142×	`/-lowering-/.f64`
2658×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	266	1842
1	889	1461
2	3084	1421
0	8389	1421

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 (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
(/ 1 (+ 1 (exp x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* -1/4 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (pow (sqrt 2) 3))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2))))))
(* x (+ (sqrt 1/2) (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 3) (pow (sqrt 1/2) 3)))) (+ (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* (pow x 2) (sqrt 1/2)))) (/ 1/2 (* x (sqrt 1/2)))))))
(* -1 (* x (sqrt 1/2)))
(* -1 (* x (+ (sqrt 1/2) (* 1/2 (/ 1 (* x (sqrt 1/2)))))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (sqrt 1/2)))) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* 1/2 x))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
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) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt (+ 1 (exp x)))
(sqrt 1/2)
(+ (sqrt 1/2) (* -1/8 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (- (* -1/128 (/ x (pow (sqrt 1/2) 3))) (* 1/8 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (- (* x (- (* 1/2 (/ (* x (- 1/48 (* 1/512 (/ 1 (pow (sqrt 1/2) 4))))) (sqrt 1/2))) (* 1/128 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/8 (/ 1 (sqrt 1/2))))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp x))))
(sqrt (/ 1 (+ 1 (exp 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 (+ (* 1/2 (/ (* 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 (*.f64 #s(literal 7/192 binary64) x) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64))))))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/48 binary64) (.f64 x (*.f64 x #s(literal -1/480 binary64))))))))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/ 1 (+ 1 (exp x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+.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 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+.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)))))))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.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 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)))))
(* 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 (sqrt.f64 #s(literal 1/2 binary64)) (+.f64 (/.f64 (/.f64 #s(literal 3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 x x)) (/.f64 (/.f64 #s(literal -3/4 binary64) (.f64 x (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x)))) (/.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 #s(literal 0 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64)))) (.f64 #s(literal 1 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))))) #s(literal 1 binary64))))
(* -1 (* x (+ (sqrt 1/2) (* -1 (/ (- (* -1 (/ (+ (* -1/4 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (* x (pow (sqrt 1/2) 3)))) (* 1/2 (/ (- 2 (* 1/4 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2)))) x)) (* 1/2 (/ 1 (sqrt 1/2)))) x)))))
(.f64 (-.f64 (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -3/4 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 3/4 binary64) (.f64 x (sqrt.f64 #s(literal 1/2 binary64))))) x) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64)))) 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)))
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(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* (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))))

eval119.0ms (1.5%)

Compiler: Compiled 21342 to 2730 computations (87.2% saved)

prune116.0ms (1.5%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	967	8	975
Fresh	2	1	3
Picked	2	3	5
Done	0	1	1
Total	971	13	984

Accuracy

100.0%

Counts

984 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
▶	67.9%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 binary64))
▶	69.5%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
▶	72.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
	3.1%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
	67.3%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))))))
✓	67.3%	(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))))))))
▶	67.1%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
▶	3.5%	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
	2.5%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
	2.3%	(sqrt.f64 (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
✓	73.3%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 219 to 173 computations (21% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x #s(literal 1/48 binary64))))
✓	cost-diff	(.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64))))))
✓	cost-diff	(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 binary64))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
✓	cost-diff	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
✓	cost-diff	(*.f64 x #s(literal -1/4 binary64))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
✓	cost-diff	(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
✓	cost-diff	(+.f64 #s(literal 2 binary64) x)
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	cost-diff	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))

Rules

104×	`fma-define`
96×	`fma-lowering-fma.f32`
96×	`fma-lowering-fma.f64`
86×	`-lowering-.f32`
86×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	112
1	59	101
2	114	101
3	179	101
4	191	101
0	191	101

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ 1 (sqrt 1/2))
1
(sqrt 1/2)
1/2
(sqrt (+ 2 x))
(+ 2 x)
2
x
(pow (+ 1/2 (* x -1/4)) -1/2)
(+ 1/2 (* x -1/4))
1/2
(* x -1/4)
x
-1/4
-1/2
(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
(* (* x x) (+ 1/2 (* x 1/6)))
(* x x)
x
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
1/6
(pow (+ 1/2 (* x (+ -1/4 (* x (* x 1/48))))) -1/2)
(+ 1/2 (* x (+ -1/4 (* x (* x 1/48)))))
1/2
(* x (+ -1/4 (* x (* x 1/48))))
x
(+ -1/4 (* x (* x 1/48)))
-1/4
(* x (* x 1/48))
(* x 1/48)
1/48
-1/2

Outputs
(/ 1 (sqrt 1/2))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
1
#s(literal 1 binary64)
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 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
(pow (+ 1/2 (* x -1/4)) -1/2)
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
(+ 1/2 (* x -1/4))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
1/2
#s(literal 1/2 binary64)
(* x -1/4)
(*.f64 x #s(literal -1/4 binary64))
x
-1/4
#s(literal -1/4 binary64)
-1/2
#s(literal -1/2 binary64)
(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
(* (* x x) (+ 1/2 (* x 1/6)))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
(* x x)
(*.f64 x x)
x
(+ 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)
(pow (+ 1/2 (* x (+ -1/4 (* x (* x 1/48))))) -1/2)
(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 binary64))
(+ 1/2 (* x (+ -1/4 (* x (* x 1/48)))))
(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64))))))
1/2
#s(literal 1/2 binary64)
(* x (+ -1/4 (* x (* x 1/48))))
(.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))
x
(+ -1/4 (* x (* x 1/48)))
(+.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x #s(literal 1/48 binary64))))
-1/4
#s(literal -1/4 binary64)
(* x (* x 1/48))
(.f64 x (.f64 x #s(literal 1/48 binary64)))
(* x 1/48)
(*.f64 x #s(literal 1/48 binary64))
1/48
#s(literal 1/48 binary64)
-1/2
#s(literal -1/2 binary64)

localize182.0ms (2.3%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))
✓	accuracy	100.0%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 x #s(literal 1/48 binary64)))
✓	accuracy	99.7%	(*.f64 x #s(literal 1/48 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (.f64 x 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	71.1%	(sqrt.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/4 binary64))
✓	accuracy	100.0%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	99.0%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))

Results

98.0ms	172×	0	valid
34.0ms	84×	0	invalid

Compiler

Compiled 124 to 27 computations (78.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 81.0ms

ival-sqrt: 39.0ms (48.2% of total)

ival-mult: 12.0ms (14.8% of total)

...c/correct-round.rkt:119:19: 10.0ms (12.4% of total)

ival-pow: 9.0ms (11.1% of total)

ival-add: 7.0ms (8.7% of total)

ival-div: 2.0ms (2.5% of total)

const: 1.0ms (1.2% of total)

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

series15.0ms (0.2%)

Counts

18 → 192

Calls

Call 1

Inputs
#<alt (/ 1 (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (sqrt (+ 2 x))>
#<alt (+ 2 x)>
#<alt (pow (+ 1/2 (* x -1/4)) -1/2)>
#<alt (+ 1/2 (* x -1/4))>
#<alt (* x -1/4)>
#<alt (sqrt (* (* x x) (+ 1/2 (* x 1/6))))>
#<alt (* (* x x) (+ 1/2 (* x 1/6)))>
#<alt (* x x)>
#<alt (+ 1/2 (* x 1/6))>
#<alt (pow (+ 1/2 (* x (+ -1/4 (* x (* x 1/48))))) -1/2)>
#<alt (+ 1/2 (* x (+ -1/4 (* x (* x 1/48)))))>
#<alt (* x (+ -1/4 (* x (* x 1/48))))>
#<alt (+ -1/4 (* x (* x 1/48)))>
#<alt (* x 1/6)>
#<alt (* x 1/48)>
#<alt (* x (* x 1/48))>

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 (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (/ 1 x)) (sqrt -4))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))>
#<alt (+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))>
#<alt (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))>
#<alt (+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/4))>
#<alt (* -1/4 x)>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* -1/4 x)>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* (pow x 2) (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (sqrt 2)>
#<alt (+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))>
#<alt (+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))>
#<alt (* (sqrt (/ 1 (pow x 3))) (sqrt 48))>
#<alt (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))) x)>
#<alt (/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48)))) x)>
#<alt (/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (+ (* 3456 (* (sqrt (/ 1 (pow x 9))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))))) x)>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -48) (sqrt -1))))>
#<alt (* -1 (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -48)))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 576 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* -1 (/ (+ (* -576 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 3456 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) x))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (* 1/48 (pow x 3))>
#<alt (* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 1/48 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))>
#<alt (* -1/4 x)>
#<alt (* x (- (* 1/48 (pow x 2)) 1/4))>
#<alt (* x (- (* 1/48 (pow x 2)) 1/4))>
#<alt (* x (- (* 1/48 (pow x 2)) 1/4))>
#<alt (* 1/48 (pow x 3))>
#<alt (* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 1/48 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))>
#<alt (* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))>
#<alt -1/4>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (- (* 1/48 (pow x 2)) 1/4)>
#<alt (* 1/48 (pow x 2))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* 1/48 (pow x 2))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/48 (* 1/4 (/ 1 (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 (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 x)>
#<alt (* 1/48 (pow x 2))>
#<alt (* 1/48 (pow x 2))>
#<alt (* 1/48 (pow x 2))>
#<alt (* 1/48 (pow x 2))>
#<alt (* 1/48 (pow x 2))>
#<alt (* 1/48 (pow x 2))>
#<alt (* 1/48 (pow x 2))>
#<alt (* 1/48 (pow x 2))>
#<alt (* 1/48 (pow x 2))>
#<alt (* 1/48 (pow x 2))>
#<alt (* 1/48 (pow x 2))>
#<alt (* 1/48 (pow x 2))>

Calls

48 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
1.0ms	x	@	-inf	(sqrt (+ 2 x))
1.0ms	x	@	-inf	(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
1.0ms	x	@	inf	(pow (+ 1/2 (* x -1/4)) -1/2)
1.0ms	x	@	-inf	(pow (+ 1/2 (* x (+ -1/4 (* x (* x 1/48))))) -1/2)

rewrite345.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3926×	`-lowering-.f32`
3926×	`-lowering-.f64`
3108×	`/-lowering-/.f32`
3108×	`/-lowering-/.f64`
2086×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	96
1	147	85
2	1042	84
0	8238	84

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 435

Calls

Call 1

Inputs
(/ 1 (sqrt 1/2))
(sqrt 1/2)
(sqrt (+ 2 x))
(+ 2 x)
(pow (+ 1/2 (* x -1/4)) -1/2)
(+ 1/2 (* x -1/4))
(* x -1/4)
(sqrt (* (* x x) (+ 1/2 (* x 1/6))))
(* (* x x) (+ 1/2 (* x 1/6)))
(* x x)
(+ 1/2 (* x 1/6))
(pow (+ 1/2 (* x (+ -1/4 (* x (* x 1/48))))) -1/2)
(+ 1/2 (* x (+ -1/4 (* x (* x 1/48)))))
(* x (+ -1/4 (* x (* x 1/48))))
(+ -1/4 (* x (* x 1/48)))
(* x 1/6)
(* x 1/48)
(* x (* x 1/48))

Outputs
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 1/2 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(neg.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1/2 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))))
(exp.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(sqrt.f64 #s(literal 1/2 binary64))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 #s(literal 1/4 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 1/2 binary64))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/2 binary64))) #s(literal -1 binary64))
(*.f64 (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (.f64 x (+.f64 x #s(literal -2 binary64))))) (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (*.f64 x x))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64))))))
(/.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 4 binary64) (.f64 x #s(literal -2 binary64))))))
(/.f64 (pow.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (*.f64 x x)))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 2 binary64) x))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 x x) #s(literal -4 binary64))) (sqrt.f64 (+.f64 x #s(literal -2 binary64))))
(/.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64)))))))
(/.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (neg.f64 (pow.f64 (-.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 2 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 2 binary64) x))) #s(literal 1/2 binary64))
(.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 x (+.f64 x #s(literal -2 binary64))))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 x (+.f64 x #s(literal -2 binary64)))))))
(.f64 (pow.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 4 binary64) (.f64 x (+.f64 x #s(literal -2 binary64)))))))
(.f64 (pow.f64 (-.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x))))
(.f64 (pow.f64 (-.f64 #s(literal 4 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) x) #s(literal 1/4 binary64)))
(+.f64 #s(literal 2 binary64) x)
(+.f64 x #s(literal 2 binary64))
(+.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x))))
(-.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x)))
(-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal -2 binary64))) (/.f64 #s(literal 4 binary64) (+.f64 x #s(literal -2 binary64))))
(neg.f64 (/.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64)))))))
(neg.f64 (/.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 2 binary64) x))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (*.f64 x x))) (-.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 4 binary64) (.f64 x #s(literal -2 binary64)))) (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -2 binary64)) (+.f64 (*.f64 x x) #s(literal -4 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))))
(/.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64)))))
(/.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (+.f64 #s(literal 4 binary64) (.f64 x #s(literal -2 binary64)))))
(/.f64 (-.f64 #s(literal 4 binary64) (*.f64 x x)) (-.f64 #s(literal 2 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))) (neg.f64 (+.f64 (.f64 x x) (+.f64 #s(literal 4 binary64) (.f64 x #s(literal -2 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 2 binary64) x)))
(/.f64 (+.f64 (*.f64 x x) #s(literal -4 binary64)) (+.f64 x #s(literal -2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (.f64 (-.f64 #s(literal 2 binary64) x) (.f64 x x))) (.f64 (-.f64 #s(literal 2 binary64) x) (-.f64 #s(literal 2 binary64) x)))
(/.f64 (.f64 (+.f64 #s(literal 512 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 64 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 #s(literal -8 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 64 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 4 binary64) (.f64 x (+.f64 x #s(literal -2 binary64))))))
(/.f64 (.f64 (-.f64 #s(literal 64 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 16 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x x) #s(literal 4 binary64)))) (-.f64 #s(literal 2 binary64) x)))
(/.f64 (.f64 (-.f64 #s(literal 16 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 #s(literal 2 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (*.f64 x (+.f64 x #s(literal -2 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 2 binary64) x))))
(/.f64 (neg.f64 (+.f64 (*.f64 x x) #s(literal -4 binary64))) (neg.f64 (+.f64 x #s(literal -2 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (-.f64 #s(literal 2 binary64) x)) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x))) (+.f64 (.f64 (/.f64 (.f64 x x) (-.f64 #s(literal 2 binary64) x)) (/.f64 (.f64 x x) (-.f64 #s(literal 2 binary64) x))) (.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x))))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x))) (.f64 (/.f64 (.f64 x x) (-.f64 #s(literal 2 binary64) x)) (/.f64 (.f64 x x) (-.f64 #s(literal 2 binary64) x)))) (+.f64 (/.f64 #s(literal 4 binary64) (-.f64 #s(literal 2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 2 binary64) x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) x))
(.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 x (+.f64 x #s(literal -2 binary64))))))
(.f64 (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 4 binary64) (*.f64 x #s(literal -2 binary64))))))
(.f64 (-.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 2 binary64) x)))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 8 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 4 binary64) (.f64 x (+.f64 x #s(literal -2 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 4 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 2 binary64) x))))
(.f64 (+.f64 (.f64 x x) #s(literal -4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -2 binary64))))
(exp.f64 (.f64 #s(literal -1/2 binary64) (log.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))))))
(exp.f64 (.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))) #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64))))) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64)))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64)))) #s(literal -1/4 binary64)) (.f64 (log.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/4 binary64)))) #s(literal -1/4 binary64))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
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(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) #s(literal 1/48 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64))))
(.f64 (+.f64 #s(literal -1/64 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/110592 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/48 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 1/48 binary64)) #s(literal 1/4 binary64))))))
(.f64 (+.f64 #s(literal -1/64 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/110592 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2304 binary64))) (+.f64 #s(literal 1/16 binary64) (.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) #s(literal -1/48 binary64)))))))
(.f64 (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2304 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) #s(literal -1/48 binary64)))))
(.f64 (+.f64 #s(literal 1/64 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/110592 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) #s(literal 1/48 binary64)) (+.f64 (.f64 (.f64 x x) #s(literal 1/48 binary64)) #s(literal 1/4 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2304 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (neg.f64 (.f64 (*.f64 x x) #s(literal -1/48 binary64))))))
(.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/2304 binary64))) #s(literal -1/16 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (*.f64 x x) #s(literal 1/48 binary64)) #s(literal 1/4 binary64))))
(*.f64 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 x #s(literal 1/48 binary64))
(*.f64 #s(literal 1/48 binary64) x)
(.f64 x (.f64 x #s(literal 1/48 binary64)))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(.f64 #s(literal 1/48 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/48 binary64)) x)

simplify294.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

4328×	`-lowering-.f32`
4328×	`-lowering-.f64`
3110×	`+-lowering-+.f64`
3110×	`+-lowering-+.f32`
1712×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	342	1846
1	1065	1600
2	3518	1575
3	7175	1569
0	8102	1569

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

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 (+ (* 1/2 (/ (* x (- 1/4 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
(* 2 (* (sqrt (/ 1 x)) (sqrt -1)))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1))))
(+ (* -4 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
(+ (* -2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (+ (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (* (sqrt -1) (+ 32 (* -4 x))))) (* 4 (* (sqrt x) (sqrt -1)))) (pow x 3))) (* 2 (* (sqrt (/ 1 x)) (sqrt -1)))))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(+ 1/2 (* -1/4 x))
(* -1/4 x)
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* x (- (* 1/2 (/ 1 x)) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/2 (/ 1 x)))))
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* -1/4 x)
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(* (sqrt (/ 1 (pow x 3))) (sqrt 48))
(/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))) x)
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48)))) x)
(/ (+ (* -576 (* (sqrt (/ 1 (pow x 7))) (/ 1 (sqrt 48)))) (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 48)))) (+ (* 3456 (* (sqrt (/ 1 (pow x 9))) (/ 1 (sqrt 48)))) (* (sqrt (/ 1 x)) (sqrt 48))))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (* (sqrt -48) (sqrt -1))))
(* -1 (/ (+ (* 288 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -48)))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 576 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -288 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* -1 (/ (+ (* -576 (* (sqrt x) (/ (sqrt -1) (sqrt -48)))) (* 3456 (* (sqrt (/ 1 x)) (/ (sqrt -1) (sqrt -48))))) x))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -48) (sqrt -1)))) x))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(* 1/48 (pow x 3))
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))
(* 1/48 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))
(* -1/4 x)
(* x (- (* 1/48 (pow x 2)) 1/4))
(* x (- (* 1/48 (pow x 2)) 1/4))
(* x (- (* 1/48 (pow x 2)) 1/4))
(* 1/48 (pow x 3))
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* 1/48 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))
-1/4
(- (* 1/48 (pow x 2)) 1/4)
(- (* 1/48 (pow x 2)) 1/4)
(- (* 1/48 (pow x 2)) 1/4)
(* 1/48 (pow x 2))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* 1/48 (pow x 2))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (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)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 x)
(* 1/48 (pow x 2))
(* 1/48 (pow x 2))
(* 1/48 (pow x 2))
(* 1/48 (pow x 2))
(* 1/48 (pow x 2))
(* 1/48 (pow x 2))
(* 1/48 (pow x 2))
(* 1/48 (pow x 2))
(* 1/48 (pow x 2))
(* 1/48 (pow x 2))
(* 1/48 (pow x 2))
(* 1/48 (pow x 2))

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 x (sqrt.f64 #s(literal 2 binary64))) #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 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal -1/16 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 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.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 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 (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))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.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 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(* x (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal 2 binary64) x)
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #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 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/4 (* 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 5/64 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(* (sqrt (/ 1 x)) (sqrt -4))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64)))
(+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal -4 binary64) (sqrt.f64 #s(literal -4 binary64)))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4))))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -4 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -4 binary64))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -8 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -4 binary64)))))
(+ (* -8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt -4)))) (+ (* -4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -4)))) (+ (* -1/2 (* (sqrt (/ 1 (pow x 7))) (/ (+ 32 (* 16 (/ x (pow (sqrt -4) 2)))) (sqrt -4)))) (* (sqrt (/ 1 x)) (sqrt -4)))))
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(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x x)))))
(* (pow x 3) (- (+ 1/48 (/ 1/2 (pow x 3))) (* 1/4 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x x)))))
(* 1/48 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/48 binary64))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))
(.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x x)))))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) (+ 1/48 (/ 1/2 (pow x 3))))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x x)))))
(* -1/4 x)
(/.f64 x #s(literal -4 binary64))
(* x (- (* 1/48 (pow x 2)) 1/4))
(.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64))))
(* x (- (* 1/48 (pow x 2)) 1/4))
(.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64))))
(* x (- (* 1/48 (pow x 2)) 1/4))
(.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/48 binary64))))
(* 1/48 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/48 binary64))
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
(* (pow x 3) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
(* 1/48 (pow x 3))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/48 binary64))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))
(.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))
(.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
(* -1 (* (pow x 3) (- (* 1/4 (/ 1 (pow x 2))) 1/48)))
(.f64 (.f64 x (.f64 x x)) (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
-1/4
#s(literal -1/4 binary64)
(- (* 1/48 (pow x 2)) 1/4)
(+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) #s(literal 1/48 binary64)))
(- (* 1/48 (pow x 2)) 1/4)
(+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) #s(literal 1/48 binary64)))
(- (* 1/48 (pow x 2)) 1/4)
(+.f64 #s(literal -1/4 binary64) (.f64 (.f64 x x) #s(literal 1/48 binary64)))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
(* (pow x 2) (- 1/48 (* 1/4 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/4 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))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 x)
(*.f64 x #s(literal 1/48 binary64))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))
(* 1/48 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/48 binary64))

eval76.0ms (1%)

Compiler: Compiled 13788 to 1907 computations (86.2% saved)

prune69.0ms (0.9%)

Pruning

13 alts after pruning (5 fresh and 8 done)

	Pruned	Kept	Total
New	625	2	627
Fresh	1	3	4
Picked	1	4	5
Done	0	4	4
Total	627	13	640

Accuracy

100.0%

Counts

640 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
✓	67.9%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 binary64))
✓	69.5%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
✓	72.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
▶	2.7%	(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
▶	3.1%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
▶	67.3%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))))))
✓	67.3%	(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))))))))
✓	67.1%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
▶	2.5%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
▶	2.5%	(sqrt.f64 x)
✓	73.3%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 171 to 136 computations (20.5% saved)

simplify173.0ms (2.2%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Program
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
✓	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	(sqrt.f64 (.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 x #s(literal 1/6 binary64))
✓	cost-diff	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
✓	cost-diff	(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
✓	cost-diff	(sqrt.f64 #s(literal 1/2 binary64))
✓	cost-diff	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(+.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) x))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))))
✓	cost-diff	(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x))))))
✓	cost-diff	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))))))

Rules

2738×	`fma-lowering-fma.f32`
2738×	`fma-lowering-fma.f64`
1800×	`fma-define`
1758×	`fmsub-define`
1512×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	211
1	72	188
2	181	178
3	456	178
4	949	178
5	1973	178
6	4436	178
7	7124	178
0	8543	178

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(sqrt (+ 2 (* x (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))))))
(+ 2 (* x (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x))))))
2
(* x (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))))
x
(+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x))))
1
(/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))
(* (- 1/4 (* (* x x) 1/36)) x)
(- 1/4 (* (* x x) 1/36))
1/4
(* (* x x) 1/36)
(* x x)
1/36
(+ 1/2 (* -1/6 x))
1/2
(* -1/6 x)
-1/6
(sqrt x)
x
(* x (sqrt 1/2))
x
(sqrt 1/2)
1/2
(* (sqrt (+ 1/2 (* x 1/6))) x)
(sqrt (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
1/2
(* x 1/6)
x
1/6
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(* 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

Outputs
(sqrt (+ 2 (* x (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64))))))))
(+ 2 (* x (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x))))))
(+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))))))
2
#s(literal 2 binary64)
(* x (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64))))))
x
(+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/6 binary64)))))
1
#s(literal 1 binary64)
(/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))
(/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/6 binary64))))
(* (- 1/4 (* (* x x) 1/36)) x)
(.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/36 binary64))))
(- 1/4 (* (* x x) 1/36))
(-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))
1/4
#s(literal 1/4 binary64)
(* (* x x) 1/36)
(.f64 (.f64 x x) #s(literal 1/36 binary64))
(* x x)
(*.f64 x x)
1/36
#s(literal 1/36 binary64)
(+ 1/2 (* -1/6 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/6 binary64)))
1/2
#s(literal 1/2 binary64)
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
-1/6
#s(literal -1/6 binary64)
(sqrt x)
(sqrt.f64 x)
x
(* x (sqrt 1/2))
(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
x
(sqrt 1/2)
(sqrt.f64 #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* (sqrt (+ 1/2 (* x 1/6))) x)
(.f64 x (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))
(sqrt (+ 1/2 (* x 1/6)))
(sqrt.f64 (+.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))
x
1/6
#s(literal 1/6 binary64)
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(sqrt.f64 (.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 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)

localize181.0ms (2.3%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (.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	99.8%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64))))
✓	accuracy	99.8%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	99.8%	(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/2 binary64))
✓	accuracy	99.8%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))))
✓	accuracy	100.0%	(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/6 binary64) x)))
✓	accuracy	99.9%	(.f64 (.f64 x x) #s(literal 1/36 binary64))
✓	accuracy	99.8%	(*.f64 #s(literal -1/6 binary64) x)

Results

76.0ms	165×	0	invalid
56.0ms	91×	0	valid

Compiler

Compiled 222 to 31 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-mult: 17.0ms (32.7% of total)

...c/correct-round.rkt:119:19: 16.0ms (30.8% of total)

ival-sqrt: 8.0ms (15.4% of total)

ival-add: 6.0ms (11.5% of total)

ival-div: 2.0ms (3.8% of total)

ival-sub: 1.0ms (1.9% of total)

const: 1.0ms (1.9% of total)

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

series11.0ms (0.1%)

Counts

18 → 204

Calls

Call 1

Inputs
#<alt (sqrt (+ 2 (* x (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))))))>
#<alt (+ 2 (* x (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x))))))>
#<alt (* x (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))))>
#<alt (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x))))>
#<alt (sqrt x)>
#<alt (* x (sqrt 1/2))>
#<alt (sqrt 1/2)>
#<alt (* (sqrt (+ 1/2 (* x 1/6))) x)>
#<alt (sqrt (+ 1/2 (* x 1/6)))>
#<alt (+ 1/2 (* x 1/6))>
#<alt (* x 1/6)>
#<alt (sqrt (* 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 (* x (+ 1/2 (* x 1/6)))>
#<alt (* -1/6 x)>
#<alt (* (* x x) 1/36)>
#<alt (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))>

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 (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 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 (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (sqrt 1/2))>
#<alt (* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))))))>
#<alt (* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3))))))))>
#<alt (sqrt 1/2)>
#<alt (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))>
#<alt (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))>
#<alt (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))>
#<alt (* (sqrt x) (sqrt 1/6))>
#<alt (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))>
#<alt (* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (+ 1/2 (* 1/6 x))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 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 x)>
#<alt (+ (sqrt x) (* 1/4 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))>
#<alt (* (sqrt (pow x 3)) (sqrt 1/6))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))>
#<alt (* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))>
#<alt (* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))>
#<alt (* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))>
#<alt (* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (+ 1 (* x (+ 1/2 (* 1/6 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* x (+ 1/2 (* 1/6 x)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))>
#<alt (* -1/6 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 (* 1/36 (pow x 2))>
#<alt (* 1/36 (pow x 2))>
#<alt (* 1/36 (pow x 2))>
#<alt (* 1/36 (pow x 2))>
#<alt (* 1/36 (pow x 2))>
#<alt (* 1/36 (pow x 2))>
#<alt (* 1/36 (pow x 2))>
#<alt (* 1/36 (pow x 2))>
#<alt (* 1/36 (pow x 2))>
#<alt (* 1/36 (pow x 2))>
#<alt (* 1/36 (pow x 2))>
#<alt (* 1/36 (pow x 2))>
#<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	@	inf	(* x (sqrt 1/2))
1.0ms	x	@	-inf	(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
1.0ms	x	@	-inf	(* (sqrt (+ 1/2 (* x 1/6))) x)
0.0ms	x	@	inf	(/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))
0.0ms	x	@	0	(* x (sqrt 1/2))

rewrite335.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3490×	`-lowering-.f32`
3490×	`-lowering-.f64`
2988×	`/-lowering-/.f32`
2988×	`/-lowering-/.f64`
1930×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	172
1	161	109
2	1548	106
0	8277	106

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 476

Calls

Call 1

Inputs
(sqrt (+ 2 (* x (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))))))
(+ 2 (* x (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x))))))
(* x (+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))))
(+ 1 (/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x))))
(sqrt x)
(* x (sqrt 1/2))
(sqrt 1/2)
(* (sqrt (+ 1/2 (* x 1/6))) x)
(sqrt (+ 1/2 (* x 1/6)))
(+ 1/2 (* x 1/6))
(* x 1/6)
(sqrt (* x (+ 1 (* x (+ 1/2 (* x 1/6))))))
(* x (+ 1 (* x (+ 1/2 (* x 1/6)))))
(+ 1 (* x (+ 1/2 (* x 1/6))))
(* x (+ 1/2 (* x 1/6)))
(* -1/6 x)
(* (* x x) 1/36)
(/ (* (- 1/4 (* (* x x) 1/36)) x) (+ 1/2 (* -1/6 x)))

Outputs
(exp.f64 (.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)))))))) #s(literal 1/2 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))))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 4 binary64) (.f64 (.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 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) #s(literal 2 binary64)))) (+.f64 #s(literal 8 binary64) (.f64 (.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 x) (.f64 (+.f64 #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 #s(literal 1 binary64) (sqrt.f64 (/.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 4 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #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 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.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 x) (.f64 (+.f64 #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)))))))))) (sqrt.f64 (+.f64 #s(literal 4 binary64) (.f64 (.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 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))))) #s(literal 2 binary64))))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 8 binary64) (.f64 (.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 x) (.f64 (+.f64 #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)))))))))) (sqrt.f64 (+.f64 (.f64 (.f64 x x) (.f64 (+.f64 #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 #s(literal 4 binary64) (.f64 (.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))))))))
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(.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) #s(literal -1 binary64)) (/.f64 (neg.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/6 binary64)))))
(.f64 (/.f64 (neg.f64 x) #s(literal -1 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64))))
(.f64 (/.f64 (neg.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64)))) #s(literal -1 binary64)) (/.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/6 binary64)))))

simplify280.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

5162×	`-lowering-.f32`
5162×	`-lowering-.f64`
3836×	`+-lowering-+.f64`
3836×	`+-lowering-+.f32`
1842×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	282	2191
1	985	1941
2	3685	1823
0	8290	1823

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 (+ (* 1/2 (/ (* 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 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)))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (sqrt 1/2))
(* x (+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2)))))
(* x (+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* x (+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2)))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* -1 (* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6))))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* -1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (* 1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3))))))))
(sqrt 1/2)
(+ (sqrt 1/2) (* 1/12 (/ x (sqrt 1/2))))
(+ (sqrt 1/2) (* x (+ (* -1/288 (/ x (pow (sqrt 1/2) 3))) (* 1/12 (/ 1 (sqrt 1/2))))))
(+ (sqrt 1/2) (* x (+ (* x (- (* 1/3456 (/ x (pow (sqrt 1/2) 5))) (* 1/288 (/ 1 (pow (sqrt 1/2) 3))))) (* 1/12 (/ 1 (sqrt 1/2))))))
(* (sqrt x) (sqrt 1/6))
(* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt 1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* -1 (* (sqrt x) (* (sqrt -1) (sqrt -1/6))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))))
(* -1 (* x (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (pow (sqrt -1/6) 3)))) (+ (* 1/128 (* (sqrt (/ 1 (pow x 7))) (/ (sqrt -1) (pow (sqrt -1/6) 5)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))))
1/2
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(+ 1/2 (* 1/6 x))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 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 x)
(+ (sqrt x) (* 1/4 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))
(* (sqrt (pow x 3)) (sqrt 1/6))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))
(* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* x (+ 1/2 (* 1/6 x)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1/6 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)
(* 1/36 (pow x 2))
(* 1/36 (pow x 2))
(* 1/36 (pow x 2))
(* 1/36 (pow x 2))
(* 1/36 (pow x 2))
(* 1/36 (pow x 2))
(* 1/36 (pow x 2))
(* 1/36 (pow x 2))
(* 1/36 (pow x 2))
(* 1/36 (pow x 2))
(* 1/36 (pow x 2))
(* 1/36 (pow x 2))
(* 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 #s(literal 1/2 binary64) (/.f64 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 x (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (.f64 x (/.f64 #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 x (+.f64 (*.f64 x (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 3/16 binary64) (sqrt.f64 #s(literal 2 binary64))))))))
(* (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 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64)))) (.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (pow x 2) (+ (* 1/4 (* (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 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 (.f64 (-.f64 #s(literal 2 binary64) (/.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 1/6 binary64)))))))
(* (sqrt (pow x 3)) (* (sqrt -1) (sqrt -1/6)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 #s(literal -1/6 binary64)) (sqrt.f64 (.f64 x (.f64 x x)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6)))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(.f64 x (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (.f64 (/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ (sqrt -1) (sqrt -1/6)))) (* -1/2 (* (sqrt (/ 1 x)) (/ (* (sqrt -1) (- 2 (* -1/16 (/ x (pow (sqrt -1/6) 2))))) (sqrt -1/6))))) (pow x 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ (sqrt -1) (sqrt -1/6)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (sqrt -1/6))))))
(+.f64 (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1/6 binary64)))))) (.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)) (sqrt.f64 #s(literal -1/6 binary64))) (/.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (-.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 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x 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)))))))
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(+.f64 (sqrt.f64 x) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (.f64 x (*.f64 x x)))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/12 (sqrt x)) (* 1/4 (sqrt (/ 1 x))))))
(+.f64 (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal 1 binary64)) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/4 binary64) (.f64 x x))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/4 (sqrt (/ 1 x))) (* x (+ (* -1/32 (sqrt (/ 1 x))) (* 1/12 (sqrt (/ 1 x))))))))
(+.f64 (sqrt.f64 x) (.f64 (.f64 x x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/4 binary64) (.f64 #s(literal 5/96 binary64) x)))))
(* (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 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64)))) (.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* (pow x 2) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6)))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (pow x 2) (+ (* -1/32 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt 1/6) 3)))) (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt 1/6)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 5))) (/ 1 (sqrt 1/6)))) (* (sqrt (/ 1 x)) (sqrt 1/6))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 1/6 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))))
(* (sqrt (pow x 3)) (* (pow (sqrt -1) 2) (sqrt 1/6)))
(.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (sqrt.f64 #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(* (pow x 2) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6)))))
(.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64)))) (neg.f64 (.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* (pow x 2) (+ (* -1/2 (* (sqrt (/ 1 (pow x 5))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))
(.f64 (.f64 x x) (+.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (pow x 2) (+ (* -1 (/ (+ (* 1/32 (* (sqrt x) (/ (pow (sqrt -1) 2) (pow (sqrt 1/6) 3)))) (* 1/2 (* (sqrt x) (/ (pow (sqrt -1) 2) (sqrt 1/6))))) (pow x 3))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (sqrt 1/6)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (sqrt 1/6))))))
(+.f64 (.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/4 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 #s(literal 1/6 binary64)))) (neg.f64 (.f64 (sqrt.f64 #s(literal 1/6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))) (.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (.f64 (sqrt.f64 x) (+.f64 (/.f64 #s(literal -3/16 binary64) (sqrt.f64 #s(literal 1/6 binary64))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/6 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 (* 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 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x 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 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(.f64 (.f64 x 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 #s(literal 1/6 binary64) (.f64 x x))
(* (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 #s(literal 1/6 binary64) (.f64 x x))
(* (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)))))
(* 1/2 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 #s(literal 1/6 binary64) (.f64 x x))
(* (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 #s(literal 1/6 binary64) (.f64 x x))
(* (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 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))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 binary64)))
(* 1/36 (pow x 2))
(.f64 x (.f64 x #s(literal 1/36 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 #s(literal 1/6 binary64) (.f64 x x))
(* (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 #s(literal 1/6 binary64) (.f64 x x))
(* (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))))

eval85.0ms (1.1%)

Compiler: Compiled 18284 to 2104 computations (88.5% saved)

prune87.0ms (1.1%)

Pruning

15 alts after pruning (2 fresh and 13 done)

	Pruned	Kept	Total
New	743	2	745
Fresh	0	0	0
Picked	0	5	5
Done	0	8	8
Total	743	15	758

Accuracy

100.0%

Counts

758 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
✓	67.9%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 binary64))
✓	69.5%	(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
✓	72.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
✓	2.7%	(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
	1.7%	(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
✓	3.1%	(*.f64 x (sqrt.f64 #s(literal 1/2 binary64)))
✓	67.3%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))))))
	67.3%	(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64))) (/.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/6 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/36 binary64))))))))
✓	67.3%	(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))))))))
✓	67.1%	(sqrt.f64 (+.f64 #s(literal 2 binary64) x))
✓	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
✓	2.5%	(sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/6 binary64)))))))
✓	2.5%	(sqrt.f64 x)
✓	73.3%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 376 to 218 computations (42% saved)

regimes33.0ms (0.4%)

Counts

22 → 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 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
(sqrt.f64 (.f64 (.f64 x 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 #s(literal 1/2 binary64) x)))))
(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 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 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 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64))) (/.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/6 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/36 binary64))))))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1/2 binary64))
(+.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 x (*.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.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 #s(literal 1 binary64) (exp.f64 x)))

Calls

3 calls:

14.0ms

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

7.0ms

6.0ms

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

Results

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

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes6.0ms (0.1%)

Accuracy

Total -45.9b remaining (-268.8%)

Threshold costs -45.9b (-268.8%)

Counts

17 → 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 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 x #s(literal 1/6 binary64))) x)
(pow.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) #s(literal -1/2 binary64))
(sqrt.f64 (.f64 x (.f64 #s(literal 1/6 binary64) (*.f64 x x))))
(.f64 (sqrt.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/6 binary64)))) x)
(sqrt.f64 (.f64 (.f64 x 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 #s(literal 1/2 binary64) x)))))
(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 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) x))))))
(pow.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (*.f64 x #s(literal 1/48 binary64)))))) #s(literal -1/2 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 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/36 binary64))) x) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/6 binary64) x)))))))
(sqrt.f64 (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/1296 binary64))) (/.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/6 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 (*.f64 x x) #s(literal 1/36 binary64))))))))

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
73.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	7
1	11	7

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness764.0ms (9.6%)

Rules

3346×	`-lowering-.f32`
3346×	`-lowering-.f64`
2108×	`-lowering-.f32`
2108×	`-lowering-.f64`
1870×	`+-lowering-+.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	52	221
1	167	175
2	545	174
3	1199	171
4	2861	170
5	6815	170
0	8156	170
0	10	8
1	26	8
2	35	8
3	50	8
4	83	7
5	148	5
6	308	5
7	862	5
8	5004	5
0	8250	5

Stop Event

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

Compiler

Compiled 23 to 20 computations (13% saved)

preprocess23.0ms (0.3%)

Compiler: Compiled 42 to 34 computations (19% saved)

analyze214.0ms (2.7%)

sample2.5s (31.5%)

preprocess232.0ms (2.9%)

explain251.0ms (3.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize30.0ms (0.4%)

series2.0ms (0%)

rewrite337.0ms (4.2%)

simplify235.0ms (2.9%)

eval30.0ms (0.4%)

prune45.0ms (0.6%)

simplify26.0ms (0.3%)

localize143.0ms (1.8%)

series16.0ms (0.2%)

rewrite347.0ms (4.4%)

simplify331.0ms (4.1%)

eval119.0ms (1.5%)

prune116.0ms (1.5%)

simplify13.0ms (0.2%)

localize182.0ms (2.3%)

series15.0ms (0.2%)

rewrite345.0ms (4.3%)

simplify294.0ms (3.7%)

eval76.0ms (1%)

prune69.0ms (0.9%)

simplify173.0ms (2.2%)

localize181.0ms (2.3%)

series11.0ms (0.1%)

rewrite335.0ms (4.2%)

simplify280.0ms (3.5%)

eval85.0ms (1.1%)

prune87.0ms (1.1%)

regimes33.0ms (0.4%)

regimes6.0ms (0.1%)

simplify7.0ms (0.1%)

soundness764.0ms (9.6%)

preprocess23.0ms (0.3%)

end0.0ms (0%)

Profiling