Metrics for sqrt times

analyze2.0ms (0%)

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%	50%	0%	0%	50%	0%	2
50%	25%	25%	0%	0%	50%	0%	3
66.7%	25%	12.5%	0%	0%	62.5%	0%	4
80%	25%	6.2%	0%	0%	68.7%	0%	5
88.9%	25%	3.1%	0%	0%	71.8%	0%	6
94.1%	25%	1.6%	0%	0%	73.4%	0%	7
97%	25%	0.8%	0%	0%	74.2%	0%	8
98.5%	25%	0.4%	0%	0%	74.6%	0%	9
99.2%	25%	0.2%	0%	0%	74.8%	0%	10
99.6%	25%	0.1%	0%	0%	74.9%	0%	11
99.8%	25%	0%	0%	0%	74.9%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

const: 0.0ms (0% of total)

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

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

sample626.0ms (13.8%)

Results

426.0ms	8251×	0	valid
1.0ms	5×	1	valid
1.0ms	12×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 271.0ms

ival-sqrt: 139.0ms (51.4% of total)

ival-mult: 61.0ms (22.5% of total)

ival-sub: 57.0ms (21.1% of total)

const: 11.0ms (4.1% of total)

backward-pass: 3.0ms (1.1% of total)

Bogosity

preprocess25.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

132×	`sum3-define`
84×	`fma-define`
38×	`sub-neg`
36×	`fmsub-define`
22×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	28	26
2	47	24
3	71	24
4	104	24
5	150	24
6	175	24
7	215	24
8	284	24
0	6	7
1	12	7
2	13	7
0	13	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(* (sqrt (- x 1)) (sqrt x))

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

Call 2

Inputs
(* (sqrt (- x 1)) (sqrt x))
(* (sqrt (- (neg x) 1)) (sqrt (neg x)))
(neg (* (sqrt (- (neg x) 1)) (sqrt (neg x))))

Outputs
(* (sqrt (- x 1)) (sqrt x))
(* (sqrt (+ x -1)) (sqrt x))
(* (sqrt (- (neg x) 1)) (sqrt (neg x)))
(* (sqrt (- -1 x)) (sqrt (neg x)))
(neg (* (sqrt (- (neg x) 1)) (sqrt (neg x))))
(fnmsub (sqrt (- -1 x)) (sqrt (neg x)) 0)

explain85.0ms (1.9%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`#s(literal 1 binary64)`
-	-	`(-.f64 x #s(literal 1 binary64))`
-	-	`(sqrt.f64 (-.f64 x #s(literal 1 binary64)))`
-	-	`(sqrt.f64 x)`
-	-	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Results

65.0ms

512×

valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-sqrt: 41.0ms (83.6% of total)

ival-mult: 4.0ms (8.2% of total)

ival-sub: 3.0ms (6.1% of total)

const: 1.0ms (2% of total)

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

eval0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

4×	`sqrt-lowering-sqrt.f64`
4×	`+-lowering-+.f64`
4×	`-lowering-.f32`
4×	`-lowering-.f64`
4×	`+-lowering-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	12	18
2	13	18
0	13	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (sqrt (- x 1)) (sqrt x))
(sqrt (- x 1))
(- x 1)
x
1
(sqrt x)

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

localize25.0ms (0.5%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.3%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

16.0ms

256×

valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-sqrt: 4.0ms (51.5% of total)

ival-sub: 2.0ms (25.8% of total)

ival-mult: 2.0ms (25.8% of total)

const: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite419.0ms (9.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3242×	`/-lowering-/.f32`
3242×	`/-lowering-/.f64`
2606×	`-lowering-.f32`
2606×	`-lowering-.f64`
1554×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	30	15
2	161	14
3	1434	14
0	8150	14

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 383

Calls

Call 1

Inputs
(* (sqrt (- x 1)) (sqrt x))
(sqrt (- x 1))
(- x 1)
(sqrt x)

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

simplify244.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

3384×	`-lowering-.f32`
3384×	`-lowering-.f64`
1818×	`fma-lowering-fma.f32`
1818×	`fma-lowering-fma.f64`
1688×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	443
1	473	389
2	1770	363
3	5464	355
0	8154	355

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval51.0ms (1.1%)

Compiler: Compiled 13678 to 1670 computations (87.8% saved)

prune75.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	426	5	431
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	427	5	432

Accuracy

100.0%

Counts

432 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
▶	99.7%	(+.f64 x (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64)))
▶	99.5%	(+.f64 x #s(literal -1/2 binary64))
▶	48.8%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
▶	98.5%	x

Compiler

Compiled 70 to 52 computations (25.7% saved)

simplify152.0ms (3.4%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x #s(literal -1 binary64))
✓	cost-diff	0	(*.f64 x (+.f64 x #s(literal -1 binary64)))
✓	cost-diff	0	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	cost-diff	0	(/.f64 #s(literal -1/8 binary64) x)
✓	cost-diff	0	(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
✓	cost-diff	128	(*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64))
✓	cost-diff	128	(+.f64 x (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64)))
✓	cost-diff	0	(+.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
✓	cost-diff	0	(-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
✓	cost-diff	0	(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))

Rules

2322×	`sum3-define`
1872×	`fmsub-define`
1756×	`sum4-define`
1738×	`fnmsub-define`
1668×	`fmm-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	85
1	39	84
2	77	84
3	122	81
4	200	81
5	349	81
6	1044	81
7	2914	81
8	6300	81
0	8009	81

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ x (- -1/2 (/ (+ 1/8 (/ 1/16 x)) x)))
x
(- -1/2 (/ (+ 1/8 (/ 1/16 x)) x))
-1/2
(/ (+ 1/8 (/ 1/16 x)) x)
(+ 1/8 (/ 1/16 x))
1/8
(/ 1/16 x)
1/16
x
(+ x -1/2)
x
-1/2
(+ x (* (+ -1/2 (/ -1/8 x)) 1))
x
(* (+ -1/2 (/ -1/8 x)) 1)
(+ -1/2 (/ -1/8 x))
-1/2
(/ -1/8 x)
-1/8
1
(sqrt (* x (+ x -1)))
(* x (+ x -1))
x
(+ x -1)
-1

Outputs
(+ x (- -1/2 (/ (+ 1/8 (/ 1/16 x)) x)))
(+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
x
(- -1/2 (/ (+ 1/8 (/ 1/16 x)) x))
(+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
-1/2
#s(literal -1/2 binary64)
(/ (+ 1/8 (/ 1/16 x)) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(+ 1/8 (/ 1/16 x))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
1/8
#s(literal 1/8 binary64)
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
1/16
#s(literal 1/16 binary64)
x
(+ x -1/2)
(+.f64 x #s(literal -1/2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(+ x (* (+ -1/2 (/ -1/8 x)) 1))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
x
(* (+ -1/2 (/ -1/8 x)) 1)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(+ -1/2 (/ -1/8 x))
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
-1/2
#s(literal -1/2 binary64)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
-1/8
#s(literal -1/8 binary64)
1
#s(literal 1 binary64)
(sqrt (* x (+ x -1)))
(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
(* x (+ x -1))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
x
(+ x -1)
(+.f64 x #s(literal -1 binary64))
-1
#s(literal -1 binary64)

localize78.0ms (1.7%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal -1 binary64))
✓	accuracy	100.0%	(*.f64 x (+.f64 x #s(literal -1 binary64)))
✓	accuracy	48.8%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	accuracy	100.0%	(/.f64 #s(literal -1/8 binary64) x)
✓	accuracy	100.0%	(+.f64 x (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
✓	accuracy	100.0%	(*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
✓	accuracy	100.0%	(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
✓	accuracy	100.0%	(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)

Results

52.0ms

256×

valid

Compiler

Compiled 91 to 21 computations (76.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-add: 10.0ms (37% of total)

ival-div: 6.0ms (22.2% of total)

ival-sub: 4.0ms (14.8% of total)

ival-mult: 4.0ms (14.8% of total)

ival-sqrt: 2.0ms (7.4% of total)

const: 1.0ms (3.7% of total)

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

series6.0ms (0.1%)

Counts

12 → 144

Calls

Call 1

Inputs
#<alt (+ x (- -1/2 (/ (+ 1/8 (/ 1/16 x)) x)))>
#<alt (- -1/2 (/ (+ 1/8 (/ 1/16 x)) x))>
#<alt (/ (+ 1/8 (/ 1/16 x)) x)>
#<alt (+ 1/8 (/ 1/16 x))>
#<alt (+ x -1/2)>
#<alt (+ x (* (+ -1/2 (/ -1/8 x)) 1))>
#<alt (* (+ -1/2 (/ -1/8 x)) 1)>
#<alt (+ -1/2 (/ -1/8 x))>
#<alt (/ -1/8 x)>
#<alt (sqrt (* x (+ x -1)))>
#<alt (* x (+ x -1))>
#<alt (+ x -1)>

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

Calls

36 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(* x (+ x -1))
0.0ms	x	@	0	(/ (+ 1/8 (/ 1/16 x)) x)
0.0ms	x	@	0	(+ x (- -1/2 (/ (+ 1/8 (/ 1/16 x)) x)))
0.0ms	x	@	-inf	(/ (+ 1/8 (/ 1/16 x)) x)
0.0ms	x	@	0	(/ -1/8 x)

rewrite467.0ms (10.3%)

Algorithm

1×	batch-egg-rewrite

Rules

4296×	`/-lowering-/.f32`
4296×	`/-lowering-/.f64`
3926×	`-lowering-.f32`
3926×	`-lowering-.f64`
2436×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	69
1	138	68
2	1343	67
0	8687	67

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 629

Calls

Call 1

Inputs
(+ x (- -1/2 (/ (+ 1/8 (/ 1/16 x)) x)))
(- -1/2 (/ (+ 1/8 (/ 1/16 x)) x))
(/ (+ 1/8 (/ 1/16 x)) x)
(+ 1/8 (/ 1/16 x))
(+ x -1/2)
(+ x (* (+ -1/2 (/ -1/8 x)) 1))
(* (+ -1/2 (/ -1/8 x)) 1)
(+ -1/2 (/ -1/8 x))
(/ -1/8 x)
(sqrt (* x (+ x -1)))
(* x (+ x -1))
(+ x -1)

Outputs
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (-.f64 #s(literal 0 binary64) x)) x))
(+.f64 #s(literal -1/2 binary64) (-.f64 x (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(+.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)
(+.f64 (+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(+.f64 (+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))) (fma.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (/.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(+.f64 (fma.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))))) (neg.f64 (.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal 1 binary64)))) (fma.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (-.f64 #s(literal 0 binary64) x)) #s(literal 1 binary64) (.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal 1 binary64))))
(+.f64 (fma.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (-.f64 #s(literal 1/4 binary64) (.f64 x #s(literal -1/2 binary64))))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))))
(+.f64 (fma.f64 (+.f64 (.f64 x x) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/2 binary64))) (neg.f64 (.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal 1 binary64)))) (fma.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (-.f64 #s(literal 0 binary64) x)) #s(literal 1 binary64) (*.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal 1 binary64))))
(+.f64 (fma.f64 (+.f64 (.f64 x x) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/2 binary64))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (*.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))))
(-.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) x))
(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
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(fma.f64 x #s(literal -1 binary64) (*.f64 x x))
(fma.f64 #s(literal -1 binary64) x (*.f64 x x))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (neg.f64 (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 x x) (neg.f64 (.f64 x (*.f64 x x))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (-.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))) (+.f64 x #s(literal 1 binary64)))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) x) (+.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x) (+.f64 x #s(literal 1 binary64)))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (neg.f64 (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 x x) (neg.f64 (.f64 x (*.f64 x x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x))) (neg.f64 (-.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))))
(/.f64 (neg.f64 (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))) (neg.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) x)) (neg.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x)) (neg.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (+.f64 (neg.f64 (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (neg.f64 (.f64 x (*.f64 x x))))))
(*.f64 x (+.f64 x #s(literal -1 binary64)))
(*.f64 (+.f64 x #s(literal -1 binary64)) x)
(+.f64 x #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) x)
(-.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal -1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))) (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))) (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64)))))
(/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (neg.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))))
(/.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) x)))))
(/.f64 (neg.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64))) (neg.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))) (neg.f64 (neg.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (+.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal -1 binary64) x)))
(pow.f64 (/.f64 (+.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))) (+.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))))
(.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))

simplify334.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

3082×	`-lowering-.f32`
3082×	`-lowering-.f64`
1976×	`sum5-define`
1598×	`+-lowering-+.f64`
1598×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	898
1	349	856
2	1072	732
3	3565	696
4	7635	696
0	8621	696

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

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

eval185.0ms (4.1%)

Compiler: Compiled 20408 to 2258 computations (88.9% saved)

prune106.0ms (2.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	771	2	773
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	773	5	778

Accuracy

100.0%

Counts

778 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
▶	99.7%	(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
✓	99.5%	(+.f64 x #s(literal -1/2 binary64))
✓	48.8%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	98.5%	x

Compiler

Compiled 33 to 24 computations (27.3% saved)

simplify171.0ms (3.8%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
✓	cost-diff	(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
✓	cost-diff	(+.f64 x #s(literal -1/2 binary64))
✓	cost-diff	(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
✓	cost-diff	(+.f64 x #s(literal -1/2 binary64))
✓	cost-diff	(/.f64 #s(literal -1/8 binary64) x)
✓	cost-diff	(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))

Rules

2600×	`fnmadd-define`
2302×	`sum3-define`
1762×	`fnmsub-define`
1668×	`fmm-def`
1472×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	49
1	21	48
2	48	48
3	79	47
4	141	47
5	303	47
6	658	47
7	1484	47
8	3984	47
9	7317	47
0	8344	47

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (/ -1/8 x) (+ x -1/2))
(/ -1/8 x)
-1/8
x
(+ x -1/2)
-1/2
(- (+ x -1/2) (/ (+ 1/8 (/ 1/16 x)) x))
(+ x -1/2)
x
-1/2
(/ (+ 1/8 (/ 1/16 x)) x)
(+ 1/8 (/ 1/16 x))
1/8
(/ 1/16 x)
1/16

Outputs
(+ (/ -1/8 x) (+ x -1/2))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
-1/8
#s(literal -1/8 binary64)
x
(+ x -1/2)
(+.f64 x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(- (+ x -1/2) (/ (+ 1/8 (/ 1/16 x)) x))
(-.f64 x (+.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal 1/2 binary64)))
(+ x -1/2)
(+.f64 x #s(literal -1/2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(/ (+ 1/8 (/ 1/16 x)) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(+ 1/8 (/ 1/16 x))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
1/8
#s(literal 1/8 binary64)
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
1/16
#s(literal 1/16 binary64)

localize46.0ms (1%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
✓	accuracy	100.0%	(+.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
✓	accuracy	100.0%	(/.f64 #s(literal -1/8 binary64) x)
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(+.f64 x #s(literal -1/2 binary64))

Results

28.0ms

256×

valid

Compiler

Compiled 51 to 13 computations (74.5% saved)

Precisions

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

ival-div: 6.0ms (50.6% of total)

ival-add: 4.0ms (33.7% of total)

ival-sub: 1.0ms (8.4% of total)

const: 1.0ms (8.4% of total)

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

series1.0ms (0%)

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (+ (/ -1/8 x) (+ x -1/2))>
#<alt (/ -1/8 x)>
#<alt (+ x -1/2)>
#<alt (- (+ x -1/2) (/ (+ 1/8 (/ 1/16 x)) x))>
#<alt (/ (+ 1/8 (/ 1/16 x)) x)>
#<alt (+ 1/8 (/ 1/16 x))>

Outputs
#<alt (/ -1/8 x)>
#<alt (/ (- (* -1/2 x) 1/8) x)>
#<alt (/ (- (* x (- x 1/2)) 1/8) x)>
#<alt (/ (- (* x (- x 1/2)) 1/8) x)>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))>
#<alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))>
#<alt (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt -1/2>
#<alt (- x 1/2)>
#<alt (- x 1/2)>
#<alt (- x 1/2)>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (/ -1/16 (pow x 2))>
#<alt (/ (- (* -1/8 x) 1/16) (pow x 2))>
#<alt (/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))>
#<alt (/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))>
#<alt x>
#<alt (* x (- 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))>
#<alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ 1 x)) 1)))>
#<alt (* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))>
#<alt (* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ (+ 1/16 (* 1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* 1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* 1/8 x)) (pow x 2))>
#<alt (/ 1/8 x)>
#<alt (/ (+ 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ (+ 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ (+ 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ 1/8 x)>
#<alt (/ (+ 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ (+ 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ (+ 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ 1/16 x)>
#<alt (/ (+ 1/16 (* 1/8 x)) x)>
#<alt (/ (+ 1/16 (* 1/8 x)) x)>
#<alt (/ (+ 1/16 (* 1/8 x)) x)>
#<alt 1/8>
#<alt (+ 1/8 (* 1/16 (/ 1 x)))>
#<alt (+ 1/8 (* 1/16 (/ 1 x)))>
#<alt (+ 1/8 (* 1/16 (/ 1 x)))>
#<alt 1/8>
#<alt (+ 1/8 (* 1/16 (/ 1 x)))>
#<alt (+ 1/8 (* 1/16 (/ 1 x)))>
#<alt (+ 1/8 (* 1/16 (/ 1 x)))>

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+ (/ -1/8 x) (+ x -1/2))
0.0ms	x	@	0	(- (+ x -1/2) (/ (+ 1/8 (/ 1/16 x)) x))
0.0ms	x	@	-inf	(- (+ x -1/2) (/ (+ 1/8 (/ 1/16 x)) x))
0.0ms	x	@	inf	(+ (/ -1/8 x) (+ x -1/2))
0.0ms	x	@	-inf	(+ (/ -1/8 x) (+ x -1/2))

rewrite311.0ms (6.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4038×	`/-lowering-/.f32`
4038×	`/-lowering-/.f64`
3290×	`-lowering-.f32`
3290×	`-lowering-.f64`
2402×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	90	35
2	1039	34
0	8580	34

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 337

Calls

Call 1

Inputs
(+ (/ -1/8 x) (+ x -1/2))
(/ -1/8 x)
(+ x -1/2)
(- (+ x -1/2) (/ (+ 1/8 (/ 1/16 x)) x))
(/ (+ 1/8 (/ 1/16 x)) x)
(+ 1/8 (/ 1/16 x))

Outputs
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
(+.f64 #s(literal -1/2 binary64) (+.f64 x (/.f64 #s(literal -1/8 binary64) x)))
(+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1/8 binary64) x))
(+.f64 (+.f64 x (/.f64 #s(literal -1/8 binary64) x)) #s(literal -1/2 binary64))
(+.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) (.f64 x x)) (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)) (neg.f64 (/.f64 (.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64))) (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x))))
(+.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64)) x)
(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) (.f64 x x)) (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)) (/.f64 (.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64))) (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)))
(-.f64 (/.f64 (.f64 (+.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal -1/2 binary64))) (+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x))) (/.f64 (/.f64 #s(literal 1/64 binary64) (.f64 x x)) (+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/8 binary64) x))))
(-.f64 (/.f64 (*.f64 (+.f64 x (/.f64 #s(literal -1/8 binary64) x)) (+.f64 x (/.f64 #s(literal -1/8 binary64) x))) (+.f64 (+.f64 x (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (+.f64 (+.f64 x (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1/2 binary64))))
(fma.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
(fma.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 x #s(literal 1/2 binary64))))) (/.f64 #s(literal -1/8 binary64) x))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/8 binary64) (+.f64 x #s(literal -1/2 binary64)))
(fma.f64 (+.f64 (*.f64 x x) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1/2 binary64))) (/.f64 #s(literal -1/8 binary64) x))
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(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 x x)) #s(literal -1/64 binary64))) (neg.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/64 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1/256 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 #s(literal 1/64 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) (/.f64 #s(literal 1/64 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (+.f64 (.f64 (/.f64 (/.f64 #s(literal 1/256 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) (/.f64 (/.f64 #s(literal 1/256 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (.f64 (/.f64 #s(literal 1/64 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) (/.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/64 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) (/.f64 #s(literal 1/64 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (.f64 (/.f64 (/.f64 #s(literal 1/256 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) (/.f64 (/.f64 #s(literal 1/256 binary64) (.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))) (+.f64 (/.f64 #s(literal 1/64 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) (/.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 x x)) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) #s(literal -1 binary64))
(*.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) (/.f64 x #s(literal 1/16 binary64))))))
(.f64 (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal 1/4096 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/256 binary64) (.f64 x x)) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/128 binary64) x)))))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))
(.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 #s(literal -1/256 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
(*.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))
(.f64 (+.f64 #s(literal -1/512 binary64) (neg.f64 (/.f64 #s(literal 1/4096 binary64) (.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/64 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) (/.f64 x #s(literal 1/16 binary64)))))))
(.f64 (+.f64 #s(literal -1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(.f64 (+.f64 (/.f64 #s(literal 1/256 binary64) (.f64 x x)) #s(literal -1/64 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))))

simplify140.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1998×	`fnmsub-define`
1958×	`-lowering-.f32`
1958×	`-lowering-.f64`
1034×	`times-frac`
872×	`/-lowering-/.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	406
1	182	400
2	476	337
3	1547	319
4	4654	319
0	8146	319

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
-1/2
(- x 1/2)
(- x 1/2)
(- x 1/2)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (- 1 (* 1/2 (/ 1 x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/ 1/8 x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/ 1/8 x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/ 1/16 x)
(/ (+ 1/16 (* 1/8 x)) x)
(/ (+ 1/16 (* 1/8 x)) x)
(/ (+ 1/16 (* 1/8 x)) x)
1/8
(+ 1/8 (* 1/16 (/ 1 x)))
(+ 1/8 (* 1/16 (/ 1 x)))
(+ 1/8 (* 1/16 (/ 1 x)))
1/8
(+ 1/8 (* 1/16 (/ 1 x)))
(+ 1/8 (* 1/16 (/ 1 x)))
(+ 1/8 (* 1/16 (/ 1 x)))

Outputs
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ (- (* -1/2 x) 1/8) x)
(+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(/ (- (* x (- x 1/2)) 1/8) x)
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(/ (- (* x (- x 1/2)) 1/8) x)
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
-1/2
#s(literal -1/2 binary64)
(- x 1/2)
(+.f64 x #s(literal -1/2 binary64))
(- x 1/2)
(+.f64 x #s(literal -1/2 binary64))
(- x 1/2)
(+.f64 x #s(literal -1/2 binary64))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal -1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)))
x
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(+.f64 x #s(literal -1/2 binary64))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(+.f64 x (+.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal 1/8 binary64))) x) x)
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal 1/8 binary64))) x) x)
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/.f64 (/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal 1/8 binary64))) x) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
(/ (+ 1/16 (* 1/8 x)) x)
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal 1/8 binary64))) x)
(/ (+ 1/16 (* 1/8 x)) x)
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal 1/8 binary64))) x)
(/ (+ 1/16 (* 1/8 x)) x)
(/.f64 (+.f64 #s(literal 1/16 binary64) (*.f64 x #s(literal 1/8 binary64))) x)
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* 1/16 (/ 1 x)))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
(+ 1/8 (* 1/16 (/ 1 x)))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
(+ 1/8 (* 1/16 (/ 1 x)))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* 1/16 (/ 1 x)))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
(+ 1/8 (* 1/16 (/ 1 x)))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
(+ 1/8 (* 1/16 (/ 1 x)))
(+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))

eval66.0ms (1.5%)

Compiler: Compiled 11439 to 1073 computations (90.6% saved)

prune47.0ms (1%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	453	0	453
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	453	5	458

Accuracy

100.0%

Counts

458 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
✓	99.7%	(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
✓	99.5%	(+.f64 x #s(literal -1/2 binary64))
✓	48.8%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	98.5%	x

Compiler

Compiled 89 to 50 computations (43.8% saved)

regimes6.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

Inputs
x
(+.f64 x #s(literal -1/2 binary64))
(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
(+.f64 x (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64)))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Outputs
(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes2.0ms (0.1%)

Counts

5 → 1

Calls

Call 1

Inputs
x
(+.f64 x #s(literal -1/2 binary64))
(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
(+.f64 x (*.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64)))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))

Outputs
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(+.f64 x #s(literal -1/2 binary64))

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
99.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
98.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

24×	`+-commutative_binary64`
16×	`sub-neg_binary64`
12×	`*-commutative_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	21	33
2	31	33
3	41	33
4	55	33
5	63	33
6	67	33
7	68	33

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
(+.f64 x #s(literal -1/2 binary64))
x

Outputs
(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(+.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 x #s(literal -1/2 binary64)))
(+.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal -1/8 binary64) x))
(+.f64 x #s(literal -1/2 binary64))
x

soundness806.0ms (17.8%)

Rules

4296×	`/-lowering-/.f32`
4296×	`/-lowering-/.f64`
3926×	`-lowering-.f32`
3926×	`-lowering-.f64`
3384×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	443
1	473	389
2	1770	363
3	5464	355
0	8154	355
0	20	69
1	138	68
2	1343	67
0	8687	67

Stop Event

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

Compiler

Compiled 57 to 31 computations (45.6% saved)

preprocess29.0ms (0.6%)

Compiler: Compiled 84 to 40 computations (52.4% saved)

sqrt times

analyze2.0ms (0%)

sample626.0ms (13.8%)

preprocess25.0ms (0.6%)

explain85.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify12.0ms (0.3%)

localize25.0ms (0.5%)

series5.0ms (0.1%)

rewrite419.0ms (9.2%)

simplify244.0ms (5.4%)

eval51.0ms (1.1%)

prune75.0ms (1.6%)

simplify152.0ms (3.4%)

localize78.0ms (1.7%)

series6.0ms (0.1%)

rewrite467.0ms (10.3%)

simplify334.0ms (7.4%)

eval185.0ms (4.1%)

prune106.0ms (2.3%)

simplify171.0ms (3.8%)

localize46.0ms (1%)

series1.0ms (0%)

rewrite311.0ms (6.9%)

simplify140.0ms (3.1%)

eval66.0ms (1.5%)

prune47.0ms (1%)

regimes6.0ms (0.1%)

regimes2.0ms (0.1%)

regimes3.0ms (0.1%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify9.0ms (0.2%)

soundness806.0ms (17.8%)

preprocess29.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	26
1	28	26
2	47	24
3	71	24
4	104	24
5	150	24
6	175	24
7	215	24
8	284	24
0	6	7
1	12	7
2	13	7
0	13	7

Iter	Nodes	Cost
0	12	26
1	28	26
2	47	24
3	71	24
4	104	24
5	150	24
6	175	24
7	215	24
8	284	24
0	6	7
1	12	7
2	13	7
0	13	7

Iter	Nodes	Cost
0	12	26
1	28	26
2	47	24
3	71	24
4	104	24
5	150	24
6	175	24
7	215	24
8	284	24
0	6	7
1	12	7
2	13	7
0	13	7