Metrics for sqrt times

analyze1.0ms (0%)

Memory

2.6MiB live, 2.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
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 8 computations (11.1% saved)

sample566.0ms (17.4%)

Memory

21.7MiB live, 708.8MiB allocated

Samples

383.0ms	8 248×	0	valid
2.0ms	8×	1	valid
1.0ms	13×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 234.0ms

ival-sqrt: 108.0ms (46.2% of total)

ival-mult: 66.0ms (28.2% of total)

ival-sub: 48.0ms (20.5% of total)

ival-true: 5.0ms (2.1% of total)

exact: 4.0ms (1.7% of total)

ival-assert: 3.0ms (1.3% of total)

adjust: 0.0ms (0% of total)

Bogosity

preprocess13.0ms (0.4%)

Memory

22.5MiB live, 22.4MiB allocated

Algorithm

2×	egg-herbie

Rules

38×	`sub-neg`
22×	`+-commutative`
12×	`*-commutative`
12×	`associate-+l-`
10×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	28	26
2	45	24
3	66	24
4	84	24
5	104	24
6	125	24
7	141	24
8	142	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))))
(* (sqrt (neg x)) (neg (sqrt (- -1 x))))

explain101.0ms (3.1%)

Memory

-3.7MiB live, 109.3MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

25.0ms

512×

valid

Compiler

Compiled 56 to 28 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-sqrt: 7.0ms (50.3% of total)

ival-sub: 3.0ms (21.6% of total)

ival-mult: 3.0ms (21.6% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

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)

simplify3.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated

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)

localize23.0ms (0.7%)

Memory

-6.6MiB live, 41.2MiB allocated

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))

Samples

15.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sub: 4.0ms (42.7% of total)

ival-sqrt: 3.0ms (32% of total)

ival-mult: 2.0ms (21.3% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.2%)

Memory

10.3MiB live, 10.3MiB allocated

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))
1.0ms	x	@	-inf	(sqrt x)
1.0ms	x	@	inf	(sqrt (- x 1))
0.0ms	x	@	-inf	(* (sqrt (- x 1)) (sqrt x))

rewrite417.0ms (12.8%)

Memory

-17.7MiB live, 509.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 558×	`/-lowering-/.f32`
4 558×	`/-lowering-/.f64`
3 416×	`accelerator-lowering-fma.f32`
3 416×	`accelerator-lowering-fma.f64`
3 070×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	30	15
2	157	15
3	1386	15
0	8365	15

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 368

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

simplify467.0ms (14.4%)

Memory

-1.0MiB live, 597.8MiB allocated

Algorithm

1×	egg-herbie

Rules

10 896×	`accelerator-lowering-fma.f32`
10 896×	`accelerator-lowering-fma.f64`
4 646×	`-lowering-.f32`
4 646×	`-lowering-.f64`
1 844×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	492
1	442	431
2	1553	410
3	4080	392
0	8296	368

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

eval47.0ms (1.5%)

Memory: -2.2MiB live, 111.8MiB allocated
Compiler: Compiled 11 351 to 1 520 computations (86.6% saved)

prune48.0ms (1.5%)

Memory

4.8MiB live, 121.5MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	412	4	416
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	413	4	417

Accuracy

100.0%

Counts

417 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
▶	99.4%	(+.f64 x #s(literal -1/2 binary64))
▶	50.7%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
▶	98.7%	x

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify24.0ms (0.8%)

Memory

10.8MiB live, 47.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	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	0	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
✓	cost-diff	0	(+.f64 x #s(literal -1/2 binary64))
✓	cost-diff	-64	(*.f64 x (+.f64 x #s(literal -1 binary64)))
✓	cost-diff	0	(+.f64 x #s(literal -1 binary64))
✓	cost-diff	0	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))

Rules

368×	`accelerator-lowering-fma.f32`
368×	`accelerator-lowering-fma.f64`
168×	`-lowering-.f32`
168×	`-lowering-.f64`
136×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	25	40
2	39	40
3	69	40
4	121	40
5	219	40
6	358	40
7	502	40
8	565	40
9	571	40
0	571	40

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize41.0ms (1.3%)

Memory

-14.2MiB live, 67.4MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 1/8 binary64) x)
✓	accuracy	100.0%	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
✓	accuracy	100.0%	(+.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 x #s(literal -1 binary64))
✓	accuracy	100.0%	(*.f64 x (+.f64 x #s(literal -1 binary64)))
✓	accuracy	50.7%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))

Samples

28.0ms

256×

valid

Compiler

Compiled 42 to 14 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-add: 9.0ms (53.1% of total)

ival-sqrt: 3.0ms (17.7% of total)

ival-div: 2.0ms (11.8% of total)

ival-mult: 2.0ms (11.8% of total)

ival-sub: 1.0ms (5.9% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB allocated

Counts

7 → 84

Calls

Call 1

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

Calls

21 calls:

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

rewrite674.0ms (20.7%)

Memory

25.2MiB live, 581.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 554×	`accelerator-lowering-fma.f32`
5 554×	`accelerator-lowering-fma.f64`
3 852×	`-lowering-.f32`
3 852×	`-lowering-.f64`
3 714×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	32
1	82	32
2	666	32
3	7797	32
0	8309	32

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 414

Calls

Call 1

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

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 x (+.f64 x #s(literal -1 binary64))))))
(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (fma.f64 x (.f64 x (-.f64 #s(literal 0 binary64) x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (-.f64 #s(literal 0 binary64) x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))))
(/.f64 (sqrt.f64 (.f64 (.f64 x (+.f64 x #s(literal -1 binary64))) (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
(/.f64 (sqrt.f64 (.f64 x (fma.f64 x (.f64 x x) #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 (sqrt.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64))) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 x)) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(pow.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.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))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (+.f64 x #s(literal -1 binary64))) (sqrt.f64 x))
(.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 x #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) x)
(+.f64 (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(-.f64 x #s(literal 1 binary64))
(-.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)))
(fma.f64 x #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64) #s(literal -1 binary64))
(fma.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 #s(literal 1 binary64) x #s(literal -1 binary64))
(fma.f64 (/.f64 (*.f64 x x) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(fma.f64 (/.f64 (.f64 x x) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(neg.f64 (-.f64 #s(literal 1 binary64) x))
(neg.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))))
(neg.f64 (/.f64 (fma.f64 x (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))))
(/.f64 (fma.f64 x (*.f64 x x) #s(literal -1 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (*.f64 x x) #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (fma.f64 x (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) x)))))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64)) (.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x (.f64 x x) #s(literal 1 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64)) (.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x (.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal -1 binary64) x))
(/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64)) (*.f64 (+.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (-.f64 (.f64 x (fma.f64 x x x)) (.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 (-.f64 #s(literal 0 binary64) (fma.f64 x (*.f64 x x) #s(literal -1 binary64)))) (neg.f64 (-.f64 #s(literal 0 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (fma.f64 x (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64))) (neg.f64 (+.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal -1 binary64) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (.f64 (/.f64 (*.f64 x x) (+.f64 x #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)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64))) (/.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) (fma.f64 x (/.f64 x (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(/.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (-.f64 #s(literal 0 binary64) x))))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) (fma.f64 x (.f64 x (*.f64 x x)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))) (fma.f64 x x #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))
(*.f64 (fma.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) (fma.f64 x (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))))
(*.f64 (fma.f64 x (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))) (fma.f64 x (.f64 x x) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64)))
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(.f64 (/.f64 (fma.f64 x (.f64 x x) #s(literal -1 binary64)) (*.f64 (fma.f64 x (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal -1 binary64)) x))) (-.f64 (fma.f64 x x #s(literal -1 binary64)) x))
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(/.f64 (.f64 (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal 1/134217728 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 1/16 binary64)) x)))) (fma.f64 (/.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))) (-.f64 (/.f64 #s(literal 1/512 binary64) (.f64 x (*.f64 x x))) #s(literal 1/8 binary64)) #s(literal 1/64 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/262144 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 1/16 binary64)) x)))) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/262144 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (fma.f64 (/.f64 #s(literal 1/64 binary64) (.f64 x x)) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 x x))) #s(literal 1/16 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 (/.f64 #s(literal 1/4096 binary64) (.f64 x (.f64 x x))) x)) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 x x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 1/16 binary64)) x))))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/64 binary64) (.f64 x x))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
(.f64 (+.f64 #s(literal -1/8 binary64) (neg.f64 (/.f64 #s(literal 1/512 binary64) (.f64 x (*.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/4 binary64) (neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 1/16 binary64)) x)))))
(.f64 (+.f64 #s(literal -1/4 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 1/16 binary64)) x))) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/64 binary64) (.f64 x x))))
(.f64 (+.f64 (/.f64 #s(literal 1/64 binary64) (.f64 x x)) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/64 binary64) (.f64 x x))) (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/64 binary64) (*.f64 x x)))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))) (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 1/16 binary64)) x) (.f64 (/.f64 #s(literal 1/64 binary64) (.f64 x x)) (.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))) #s(literal 1/64 binary64))) (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 1/16 binary64)) x) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 1/16 binary64)) x) #s(literal 1/4 binary64)) #s(literal 1/16 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x)))) (-.f64 #s(literal 1/16 binary64) (.f64 (/.f64 #s(literal 1/64 binary64) (.f64 x x)) (.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))))) (-.f64 #s(literal 1/4 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) x) #s(literal 1/16 binary64)) x)))
(.f64 (/.f64 (+.f64 #s(literal 1/4 binary64) (/.f64 #s(literal -1/64 binary64) (.f64 x x))) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1/512 binary64) (.f64 x (.f64 x x))))) (fma.f64 (/.f64 #s(literal 1/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 8 binary64))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1/8 binary64) x))
(neg.f64 (/.f64 #s(literal -1/8 binary64) x))
(neg.f64 (*.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -8 binary64)))
(/.f64 #s(literal 1/8 binary64) x)
(/.f64 #s(literal -1/8 binary64) (-.f64 #s(literal 0 binary64) x))
(/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 8 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 8 binary64))
(/.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal -1 binary64))
(pow.f64 (*.f64 x #s(literal 8 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/8 binary64) x))
(*.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1 binary64) x))
(.f64 #s(literal -1/8 binary64) (.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/8 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/8 binary64))
(.f64 (pow.f64 (.f64 x #s(literal 8 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x #s(literal 8 binary64)) #s(literal -1/2 binary64)))

simplify330.0ms (10.1%)

Memory

-12.8MiB live, 506.8MiB allocated

Algorithm

1×	egg-herbie

Rules

7 462×	`accelerator-lowering-fma.f32`
7 462×	`accelerator-lowering-fma.f64`
4 370×	`-lowering-.f32`
4 370×	`-lowering-.f64`
1 906×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	100	529
1	264	507
2	808	429
3	2506	405
4	6571	400
0	8214	391

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

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)
(* -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 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)))
(* -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)))
-1/2
(- 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)
(/ (+ 1/8 (* 1/2 x)) x)
(/ (+ 1/8 (* 1/2 x)) x)
(/ (+ 1/8 (* 1/2 x)) x)
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
1/2
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* 1/8 (/ 1 x)))
(+ 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)

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

eval59.0ms (1.8%)

Memory: -11.8MiB live, 143.2MiB allocated
Compiler: Compiled 10 521 to 1 341 computations (87.3% saved)

prune88.0ms (2.7%)

Memory

3.6MiB live, 119.6MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	498	0	498
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	498	4	502

Accuracy

100.0%

Counts

502 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(-.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)))
✓	99.4%	(+.f64 x #s(literal -1/2 binary64))
✓	50.7%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal -1 binary64))))
✓	98.7%	x

Compiler

Compiled 46 to 32 computations (30.4% saved)

regimes5.0ms (0.2%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

5 → 1

Calls

Call 1

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

Calls

2 calls:

2.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes4.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	x
2.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes3.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

2 calls:

1.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
1.0ms	x

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

simplify11.0ms (0.4%)

Memory

-24.3MiB live, 17.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	12	11
2	21	11
3	33	11
4	42	11
5	48	11
6	50	11

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness287.0ms (8.8%)

Memory

-36.0MiB live, 189.8MiB allocated

Rules

10 896×	`accelerator-lowering-fma.f32`
10 896×	`accelerator-lowering-fma.f64`
4 646×	`-lowering-.f32`
4 646×	`-lowering-.f64`
1 844×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	492
1	442	431
2	1553	410
3	4080	392
0	8296	368

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 15 to 10 computations (33.3% saved)

preprocess28.0ms (0.9%)

Memory: 14.6MiB live, 53.2MiB allocated
Compiler: Compiled 40 to 28 computations (30% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	12	26
1	28	26
2	45	24
3	66	24
4	84	24
5	104	24
6	125	24
7	141	24
8	142	24
0	6	7
1	12	7
2	13	7
0	13	7

Iter	Nodes	Cost
0	12	40
1	25	40
2	39	40
3	69	40
4	121	40
5	219	40
6	358	40
7	502	40
8	565	40
9	571	40
0	571	40

Iter	Nodes	Cost
0	12	26
1	28	26
2	45	24
3	66	24
4	84	24
5	104	24
6	125	24
7	141	24
8	142	24
0	6	7
1	12	7
2	13	7
0	13	7

Iter	Nodes	Cost
0	12	40
1	25	40
2	39	40
3	69	40
4	121	40
5	219	40
6	358	40
7	502	40
8	565	40
9	571	40
0	571	40

analyze1.0ms (0%)

sample566.0ms (17.4%)

preprocess13.0ms (0.4%)

explain101.0ms (3.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize23.0ms (0.7%)

series5.0ms (0.2%)

rewrite417.0ms (12.8%)

simplify467.0ms (14.4%)

eval47.0ms (1.5%)

prune48.0ms (1.5%)

simplify24.0ms (0.8%)

localize41.0ms (1.3%)

series3.0ms (0.1%)

rewrite674.0ms (20.7%)

simplify330.0ms (10.1%)

eval59.0ms (1.8%)

prune88.0ms (2.7%)

regimes5.0ms (0.2%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

simplify11.0ms (0.4%)

soundness287.0ms (8.8%)

preprocess28.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	26
1	28	26
2	45	24
3	66	24
4	84	24
5	104	24
6	125	24
7	141	24
8	142	24
0	6	7
1	12	7
2	13	7
0	13	7

Iter	Nodes	Cost
0	12	40
1	25	40
2	39	40
3	69	40
4	121	40
5	219	40
6	358	40
7	502	40
8	565	40
9	571	40
0	571	40