Metrics for A quarter-circle in the lower-left quadrant

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample895.0ms (28.2%)

Memory

61.2MiB live, 984.4MiB allocated; 314ms collecting garbage

Samples

589.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 370.0ms

ival-pow2: 191.0ms (51.7% of total)

ival-fmax: 77.0ms (20.8% of total)

ival-sub: 44.0ms (11.9% of total)

ival-add: 43.0ms (11.6% of total)

ival-true: 5.0ms (1.4% of total)

exact: 5.0ms (1.4% of total)

ival-assert: 3.0ms (0.8% of total)

adjust: 2.0ms (0.5% of total)

Bogosity

explain126.0ms (4%)

Memory

-24.6MiB live, 166.6MiB allocated; 32ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))`
-	-	`(pow.f64 x #s(literal 2 binary64))`
-	-	`(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))`
-	-	`y`
-	-	`#s(literal 2 binary64)`
-	-	`(+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
-	-	`(pow.f64 y #s(literal 2 binary64))`
-	-	`(fmax.f64 x y)`
-	-	`#s(literal 1/2 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

42.0ms

512×

valid

Compiler

Compiled 101 to 34 computations (66.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-pow2: 10.0ms (47.2% of total)

ival-fmax: 5.0ms (23.6% of total)

ival-sub: 2.0ms (9.4% of total)

ival-add: 2.0ms (9.4% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess269.0ms (8.5%)

Memory

27.0MiB live, 153.9MiB allocated; 27ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	75
1	39	71
2	84	71
3	159	71
4	218	71
5	356	71
6	879	71
7	5949	71
0	10	13
0	16	13
1	23	13
2	45	13
3	101	13
4	201	13
5	336	13
6	833	13
7	5603	13
0	8964	11

Stop Event

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

Calls

Call 1

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

Outputs

(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))

(fmax.f64 (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))

Compiler

Compiled 13 to 10 computations (23.1% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify180.0ms (5.7%)

Memory

13.4MiB live, 114.5MiB allocated; 20ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 y #s(literal 2 binary64))
cost-diff	0	(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))
cost-diff	1	(+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
cost-diff	1	(-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	42
0	16	42
1	23	42
2	45	42
3	101	42
4	201	42
5	336	42
6	833	42
7	5603	42
0	8964	37

Stop Event

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

Calls

Call 1

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

Outputs
(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))
(fmax.f64 (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
(-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
(+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(fma.f64 x x (*.f64 y y))
(pow.f64 y #s(literal 2 binary64))
(*.f64 y y)
y
#s(literal 2 binary64)
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 1/2 binary64)
(fmax.f64 x y)

localize29.0ms (0.9%)

Memory

-8.1MiB live, 35.4MiB allocated; 7ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(fmax.f64 x y)
accuracy	0.0	(-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
accuracy	0.00390625	(pow.f64 y #s(literal 2 binary64))
accuracy	0.0078125	(+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))

Samples

22.0ms

256×

valid

Compiler

Compiled 44 to 12 computations (72.7% saved)

Precisions

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

ival-pow2: 9.0ms (64.1% of total)

ival-fmax: 2.0ms (14.2% of total)

ival-sub: 1.0ms (7.1% of total)

ival-add: 1.0ms (7.1% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

6.2MiB live, 6.2MiB allocated; 0ms collecting garbage

Counts

5 → 12

Calls

Call 1

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

Outputs
(- (pow y 2) 1/2)
(- (+ (pow x 2) (pow y 2)) 1/2)
(pow y 2)
(+ (pow x 2) (pow y 2))
(fmax (- (+ (pow x 2) (pow y 2)) 1/2) (fmax x y))
(fmax x y)
(pow x 2)
(* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(- (pow x 2) 1/2)
(* (pow y 2) (- (+ 1 (/ (pow x 2) (pow y 2))) (* 1/2 (/ 1 (pow y 2)))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	inf	((- (+ (pow y 2) (pow x 2)) 1/2) (+ (pow y 2) (pow x 2)) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (pow y 2) (fmax x y))
1.0ms	x	@	inf	((- (+ (pow y 2) (pow x 2)) 1/2) (+ (pow y 2) (pow x 2)) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (pow y 2) (fmax x y))
1.0ms	x	@	0	((- (+ (pow y 2) (pow x 2)) 1/2) (+ (pow y 2) (pow x 2)) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (pow y 2) (fmax x y))
1.0ms	y	@	-inf	((- (+ (pow y 2) (pow x 2)) 1/2) (+ (pow y 2) (pow x 2)) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (pow y 2) (fmax x y))
0.0ms	y	@	0	((- (+ (pow y 2) (pow x 2)) 1/2) (+ (pow y 2) (pow x 2)) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (pow y 2) (fmax x y))

simplify139.0ms (4.4%)

Memory

2.6MiB live, 144.0MiB allocated; 31ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	80
1	67	80
2	241	80
3	1515	80
0	8810	67

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 12

Calls

Call 1

Inputs
(- (pow y 2) 1/2)
(- (+ (pow x 2) (pow y 2)) 1/2)
(pow y 2)
(+ (pow x 2) (pow y 2))
(fmax (- (+ (pow x 2) (pow y 2)) 1/2) (fmax x y))
(fmax x y)
(pow x 2)
(* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(- (pow x 2) 1/2)
(* (pow y 2) (- (+ 1 (/ (pow x 2) (pow y 2))) (* 1/2 (/ 1 (pow y 2)))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))

Outputs
(- (pow y 2) 1/2)
(fma.f64 y y #s(literal -1/2 binary64))
(- (+ (pow x 2) (pow y 2)) 1/2)
(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
(pow y 2)
(*.f64 y y)
(+ (pow x 2) (pow y 2))
(fma.f64 x x (*.f64 y y))
(fmax (- (+ (pow x 2) (pow y 2)) 1/2) (fmax x y))
(fmax.f64 (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
(fmax x y)
(fmax.f64 x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 x x (*.f64 y y))
(- (pow x 2) 1/2)
(fma.f64 x x #s(literal -1/2 binary64))
(* (pow y 2) (- (+ 1 (/ (pow x 2) (pow y 2))) (* 1/2 (/ 1 (pow y 2)))))
(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 x x (*.f64 y y))

rewrite45.0ms (1.4%)

Memory

5.7MiB live, 49.2MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
0	16	35
1	61	35
0	442	32

Stop Event

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

Counts

5 → 51

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (-.f64 (.f64 x x) #s(literal 1/2 binary64)) (-.f64 (.f64 x x) #s(literal 1/2 binary64)))) (-.f64 (.f64 y y) (-.f64 (*.f64 x x) #s(literal 1/2 binary64))))
(/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (.f64 (-.f64 (.f64 x x) #s(literal 1/2 binary64)) (-.f64 (.f64 x x) #s(literal 1/2 binary64))) (.f64 (.f64 y y) (-.f64 (*.f64 x x) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (neg.f64 (fma.f64 x x (fma.f64 y y #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x x (fma.f64 y y #s(literal 1/2 binary64))) (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (fma.f64 x x (fma.f64 y y #s(literal 1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 #s(literal 1/2 binary64) (fma.f64 x x (fma.f64 y y #s(literal 1/2 binary64))) (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 2 binary64))))
(fma.f64 (neg.f64 y) (neg.f64 y) (-.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (neg.f64 x) (neg.f64 x) (-.f64 (*.f64 y y) #s(literal 1/2 binary64)))
(fma.f64 (fabs.f64 y) (fabs.f64 y) (-.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (-.f64 (*.f64 y y) #s(literal 1/2 binary64)))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (-.f64 (*.f64 y y) #s(literal 1/2 binary64)))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) (-.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 x x (-.f64 (*.f64 y y) #s(literal 1/2 binary64)))
(fma.f64 y y (-.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 2 binary64)) (fma.f64 x x (fma.f64 y y #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x x (fma.f64 y y #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 3 binary64)) (fma.f64 #s(literal 1/2 binary64) (fma.f64 x x (fma.f64 y y #s(literal 1/2 binary64))) (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 2 binary64)))) (/.f64 #s(literal 1/8 binary64) (fma.f64 #s(literal 1/2 binary64) (fma.f64 x x (fma.f64 y y #s(literal 1/2 binary64))) (pow.f64 (fma.f64 x x (*.f64 y y)) #s(literal 2 binary64)))))
(-.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/2 binary64))
(+.f64 (-.f64 (.f64 x x) #s(literal 1/2 binary64)) (.f64 y y))
(+.f64 (.f64 x x) (-.f64 (.f64 y y) #s(literal 1/2 binary64)))
(+.f64 (.f64 y y) (-.f64 (.f64 x x) #s(literal 1/2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (.f64 x x) (.f64 y y)))
(/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (*.f64 (+.f64 y x) (-.f64 y x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (neg.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (*.f64 (+.f64 y x) (-.f64 y x)))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64))))
(fma.f64 (neg.f64 y) (neg.f64 y) (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 y y))
(fma.f64 (fabs.f64 y) (fabs.f64 y) (*.f64 x x))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 y y))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 y y))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) (*.f64 x x))
(fma.f64 x x (*.f64 y y))
(fma.f64 y y (*.f64 x x))
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (+.f64 y x) (-.f64 y x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (+.f64 y x) (-.f64 y x))))
(-.f64 (.f64 x x) (.f64 (neg.f64 y) y))
(-.f64 (.f64 y y) (.f64 (neg.f64 x) x))
(+.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 y #s(literal 4 binary64)))))
(+.f64 (.f64 x x) (.f64 y y))
(+.f64 (.f64 y y) (.f64 x x))
(fmax.f64 (-.f64 (fma.f64 x x (*.f64 y y)) #s(literal 1/2 binary64)) (fmax.f64 x y))
(*.f64 (neg.f64 y) (neg.f64 y))
(*.f64 (fabs.f64 y) (fabs.f64 y))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))))
(fmax.f64 x y)

eval15.0ms (0.5%)

Memory: -27.0MiB live, 15.4MiB allocated; 8ms collecting garbage
Compiler: Compiled 1 126 to 240 computations (78.7% saved)

prune2.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	55	4	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	4	60

Accuracy

100.0%

Counts

60 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	67.8%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
▶	100.0%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
▶	65.7%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))
▶	57.8%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))

Compiler

Compiled 74 to 52 computations (29.7% saved)

simplify184.0ms (5.8%)

Memory

17.3MiB live, 123.3MiB allocated; 31ms collecting garbage

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fmax.f64 x y)
cost-diff	0	(fma.f64 y y #s(literal -1/2 binary64))
cost-diff	0	#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64)))
cost-diff	0	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
cost-diff	0	(fma.f64 y y #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
cost-diff	0	#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64))))
cost-diff	0	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
cost-diff	0	(fmax.f64 x y)
cost-diff	0	(fma.f64 x x #s(literal -1/2 binary64))
cost-diff	0	#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64)))
cost-diff	0	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))
cost-diff	0	(fmax.f64 x y)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x))
cost-diff	0	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	22	177
0	32	177
1	54	177
2	117	177
3	234	177
4	324	177
5	403	177
6	900	161
7	5757	161
0	9120	161

Stop Event

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

Calls

Call 1

Inputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x))
(*.f64 x x)
x
(fmax.f64 x y)
y
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64)))
(fma.f64 x x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(fmax.f64 x y)
y
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64))))
(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
x
(fma.f64 y y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
(fmax.f64 x y)
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64)))
(fma.f64 y y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
(fmax.f64 x y)
x

Outputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x))
(*.f64 x x)
x
(fmax.f64 x y)
y
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64)))
(fma.f64 x x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(fmax.f64 x y)
y
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64))))
(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
x
(fma.f64 y y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
(fmax.f64 x y)
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64)))
(fma.f64 y y #s(literal -1/2 binary64))
y
#s(literal -1/2 binary64)
(fmax.f64 x y)
x

localize44.0ms (1.4%)

Memory

13.0MiB live, 56.5MiB allocated; 7ms collecting garbage

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 y y #s(literal -1/2 binary64))
accuracy	0.0	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
accuracy	0.0	(fmax.f64 x y)
accuracy	21.37764394700248	#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64)))
accuracy	0.0	(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
accuracy	0.0	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
accuracy	0.0	(fmax.f64 x y)
accuracy	0.0	#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64))))
accuracy	0.0	(fma.f64 x x #s(literal -1/2 binary64))
accuracy	0.0	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))
accuracy	0.0	(fmax.f64 x y)
accuracy	22.6683822919091	#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64)))
accuracy	0.0	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))
accuracy	0.0	(fmax.f64 x y)
accuracy	0.0	(*.f64 x x)
accuracy	36.69832297793043	#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x))

Samples

33.0ms

256×

valid

Compiler

Compiled 140 to 17 computations (87.9% saved)

Precisions

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

ival-pow2: 5.0ms (30% of total)

ival-add: 4.0ms (24% of total)

ival-mult: 3.0ms (18% of total)

ival-fmax: 2.0ms (12% of total)

ival-sub: 1.0ms (6% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.3%)

Memory

-36.6MiB live, 6.9MiB allocated; 8ms collecting garbage

Counts

13 → 12

Calls

Call 1

Inputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x))
(*.f64 x x)
(fmax.f64 x y)
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64)))
(fma.f64 x x #s(literal -1/2 binary64))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64))))
(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
(fma.f64 y y #s(literal -1/2 binary64))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64)))

Outputs
(fmax (- (+ (pow x 2) (pow y 2)) 1/2) (fmax x y))
(- (pow y 2) 1/2)
(- (+ (pow x 2) (pow y 2)) 1/2)
(pow x 2)
(fmax x y)
-1/2
(- (pow x 2) 1/2)
(* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/2 (/ 1 (pow x 2)))))
(pow y 2)
(* (pow y 2) (- (+ 1 (/ (pow x 2) (pow y 2))) (* 1/2 (/ 1 (pow y 2)))))
(* (pow y 2) (- 1 (* 1/2 (/ 1 (pow y 2)))))

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	((fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (* x x) (fmax x y) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) -1/2) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) (+ (* y y) -1/2)) (+ (* y y) -1/2) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2))
1.0ms	x	@	-inf	((fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (* x x) (fmax x y) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) -1/2) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) (+ (* y y) -1/2)) (+ (* y y) -1/2) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2))
1.0ms	y	@	inf	((fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (* x x) (fmax x y) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) -1/2) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) (+ (* y y) -1/2)) (+ (* y y) -1/2) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2))
1.0ms	y	@	-inf	((fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (* x x) (fmax x y) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) -1/2) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) (+ (* y y) -1/2)) (+ (* y y) -1/2) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2))
1.0ms	x	@	0	((fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (* x x) (fmax x y) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) -1/2) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) (+ (* y y) -1/2)) (+ (* y y) -1/2) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2))

simplify117.0ms (3.7%)

Memory

16.8MiB live, 116.7MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	90
1	59	90
2	189	82
3	928	82
4	6733	82
0	8219	70

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 12

Calls

Call 1

Inputs
(fmax (- (+ (pow x 2) (pow y 2)) 1/2) (fmax x y))
(- (pow y 2) 1/2)
(- (+ (pow x 2) (pow y 2)) 1/2)
(pow x 2)
(fmax x y)
-1/2
(- (pow x 2) 1/2)
(* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/2 (/ 1 (pow x 2)))))
(pow y 2)
(* (pow y 2) (- (+ 1 (/ (pow x 2) (pow y 2))) (* 1/2 (/ 1 (pow y 2)))))
(* (pow y 2) (- 1 (* 1/2 (/ 1 (pow y 2)))))

Outputs
(fmax (- (+ (pow x 2) (pow y 2)) 1/2) (fmax x y))
(fmax.f64 (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
(- (pow y 2) 1/2)
(fma.f64 y y #s(literal -1/2 binary64))
(- (+ (pow x 2) (pow y 2)) 1/2)
(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
(pow x 2)
(*.f64 x x)
(fmax x y)
(fmax.f64 x y)
-1/2
#s(literal -1/2 binary64)
(- (pow x 2) 1/2)
(fma.f64 x x #s(literal -1/2 binary64))
(* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) y #s(literal 1 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/2 binary64))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (- (+ 1 (/ (pow x 2) (pow y 2))) (* 1/2 (/ 1 (pow y 2)))))
(fma.f64 (fma.f64 (/.f64 (/.f64 x y) y) x #s(literal 1 binary64)) (*.f64 y y) #s(literal -1/2 binary64))
(* (pow y 2) (- 1 (* 1/2 (/ 1 (pow y 2)))))
(fma.f64 y y #s(literal -1/2 binary64))

rewrite49.0ms (1.5%)

Memory

7.8MiB live, 50.6MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	153
0	32	153
1	120	153
0	946	145

Stop Event

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

Counts

13 → 102

Calls

Call 1

Inputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x))
(*.f64 x x)
(fmax.f64 x y)
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64)))
(fma.f64 x x #s(literal -1/2 binary64))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64))))
(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
(fma.f64 y y #s(literal -1/2 binary64))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64)))

Outputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(fmax.f64 x y)
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64)))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (*.f64 x x) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64))) (neg.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1/2 binary64) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 x x)))))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1/2 binary64) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) #s(literal -1/2 binary64))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) #s(literal -1/2 binary64))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) #s(literal -1/2 binary64))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) #s(literal -1/2 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) #s(literal -1/2 binary64))
(fma.f64 (fabs.f64 x) (fabs.f64 x) #s(literal -1/2 binary64))
(fma.f64 x x #s(literal -1/2 binary64))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 x x) #s(literal -1/2 binary64))))
(-.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)))
(-.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x)))
(-.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 x) x))
(-.f64 #s(literal -1/2 binary64) (*.f64 x (neg.f64 x)))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 #s(literal -1/2 binary64) (*.f64 x x))
(+.f64 (*.f64 x x) #s(literal -1/2 binary64))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (fma.f64 y y #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (fma.f64 y y #s(literal -1/2 binary64)) (*.f64 x x)))
(/.f64 (+.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (+.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 2 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 x x (.f64 y y)) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 y y #s(literal -1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (*.f64 x x) (fma.f64 y y #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 y y #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (fma.f64 (fma.f64 y y #s(literal -1/2 binary64)) (-.f64 (fma.f64 y y #s(literal -1/2 binary64)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (fma.f64 x x (.f64 y y)) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 y y #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 (*.f64 x x) (fma.f64 y y #s(literal -1/2 binary64))))
(/.f64 (+.f64 (pow.f64 (fma.f64 y y #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (fma.f64 y y #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 y y #s(literal -1/2 binary64)) (.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (fma.f64 y y #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (fma.f64 y y #s(literal -1/2 binary64)) (-.f64 (fma.f64 y y #s(literal -1/2 binary64)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(fma.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 y)) (fma.f64 x x #s(literal -1/2 binary64)))
(fma.f64 (neg.f64 (fabs.f64 y)) (neg.f64 (fabs.f64 y)) (fma.f64 x x #s(literal -1/2 binary64)))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (fma.f64 y y #s(literal -1/2 binary64)))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (fma.f64 y y #s(literal -1/2 binary64)))
(fma.f64 (fabs.f64 (fabs.f64 y)) (fabs.f64 (fabs.f64 y)) (fma.f64 x x #s(literal -1/2 binary64)))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (fma.f64 y y #s(literal -1/2 binary64)))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) (fma.f64 x x #s(literal -1/2 binary64)))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (fma.f64 y y #s(literal -1/2 binary64)))
(fma.f64 (neg.f64 y) (neg.f64 y) (fma.f64 x x #s(literal -1/2 binary64)))
(fma.f64 (neg.f64 x) (neg.f64 x) (fma.f64 y y #s(literal -1/2 binary64)))
(fma.f64 (fabs.f64 y) (fabs.f64 y) (fma.f64 x x #s(literal -1/2 binary64)))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (fma.f64 y y #s(literal -1/2 binary64)))
(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
(fma.f64 y y (fma.f64 x x #s(literal -1/2 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) (fma.f64 y y #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (fma.f64 y y #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 x x) (fma.f64 y y #s(literal -1/2 binary64)))))
(-.f64 (fma.f64 y y #s(literal -1/2 binary64)) (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)))
(-.f64 (fma.f64 y y #s(literal -1/2 binary64)) (*.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x)))
(-.f64 (fma.f64 y y #s(literal -1/2 binary64)) (*.f64 (neg.f64 x) x))
(-.f64 (fma.f64 y y #s(literal -1/2 binary64)) (*.f64 x (neg.f64 x)))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y #s(literal -1/2 binary64)) (-.f64 (fma.f64 y y #s(literal -1/2 binary64)) (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 (fma.f64 y y #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (fma.f64 y y #s(literal -1/2 binary64)) (-.f64 (fma.f64 y y #s(literal -1/2 binary64)) (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (*.f64 y y) (fma.f64 x x #s(literal -1/2 binary64)))
(+.f64 (fma.f64 y y #s(literal -1/2 binary64)) (*.f64 x x))
(+.f64 (fma.f64 x x #s(literal -1/2 binary64)) (*.f64 y y))
(+.f64 #s(literal -1/2 binary64) (fma.f64 x x (*.f64 y y)))
(+.f64 (*.f64 x x) (fma.f64 y y #s(literal -1/2 binary64)))
(+.f64 (fma.f64 x x (*.f64 y y)) #s(literal -1/2 binary64))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal -1/2 binary64) (*.f64 y y)))
(/.f64 (neg.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1/4 binary64))) (neg.f64 (-.f64 (*.f64 y y) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 6 binary64)))) (neg.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1/2 binary64) (*.f64 y y)) (pow.f64 y #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 y y) #s(literal -1/2 binary64)))
(/.f64 (+.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 6 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (.f64 y y) #s(literal -1/2 binary64)))))
(/.f64 (+.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 6 binary64))) (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1/2 binary64) (*.f64 y y)) (pow.f64 y #s(literal 4 binary64))))
(fma.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 y)) #s(literal -1/2 binary64))
(fma.f64 (neg.f64 (fabs.f64 y)) (neg.f64 (fabs.f64 y)) #s(literal -1/2 binary64))
(fma.f64 (fabs.f64 (fabs.f64 y)) (fabs.f64 (fabs.f64 y)) #s(literal -1/2 binary64))
(fma.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)) #s(literal -1/2 binary64))
(fma.f64 (neg.f64 y) (neg.f64 y) #s(literal -1/2 binary64))
(fma.f64 (fabs.f64 y) (fabs.f64 y) #s(literal -1/2 binary64))
(fma.f64 y y #s(literal -1/2 binary64))
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (.f64 y y) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 y y) #s(literal -1/2 binary64))))
(-.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 (neg.f64 y)) (neg.f64 y)))
(-.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 (fabs.f64 y)) (fabs.f64 y)))
(-.f64 #s(literal -1/2 binary64) (*.f64 (neg.f64 y) y))
(-.f64 #s(literal -1/2 binary64) (*.f64 y (neg.f64 y)))
(+.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 y y)) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 y y)) (pow.f64 y #s(literal 4 binary64)))))
(+.f64 (*.f64 y y) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (*.f64 y y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64)))

eval22.0ms (0.7%)

Memory: -13.4MiB live, 29.7MiB allocated; 6ms collecting garbage
Compiler: Compiled 3 416 to 491 computations (85.6% saved)

prune5.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	137	6	143

Accuracy

100.0%

Counts

143 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	67.8%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
✓	100.0%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
✓	65.7%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))
▶	59.0%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))
✓	57.8%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))
▶	26.3%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))

Compiler

Compiled 112 to 80 computations (28.6% saved)

simplify174.0ms (5.5%)

Memory

8.9MiB live, 110.4MiB allocated; 18ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fmax.f64 x y)
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y))
cost-diff	0	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))
cost-diff	0	(fmax.f64 x y)
cost-diff	0	#s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))
cost-diff	0	#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64)))
cost-diff	0	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	89
0	22	89
1	38	89
2	90	89
3	176	89
4	250	89
5	329	89
6	826	89
7	5613	89
0	8976	78

Stop Event

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

Calls

Call 1

Inputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64)))
#s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(fmax.f64 x y)
x
y
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y))
(*.f64 y y)
y
(fmax.f64 x y)
x

Outputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64)))
#s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(fmax.f64 x y)
x
y
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y))
(*.f64 y y)
y
(fmax.f64 x y)
x

localize35.0ms (1.1%)

Memory

-0.0MiB live, 43.3MiB allocated; 7ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))
accuracy	0.0	(fmax.f64 x y)
accuracy	0.0	(*.f64 y y)
accuracy	35.28945792963472	#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y))
accuracy	0.0	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))
accuracy	0.0	(fmax.f64 x y)
accuracy	22.6683822919091	#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64)))
accuracy	31.94625632950662	#s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))

Samples

27.0ms

256×

valid

Compiler

Compiled 65 to 15 computations (76.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-add: 6.0ms (32.8% of total)

ival-pow2: 5.0ms (27.3% of total)

ival-mult: 3.0ms (16.4% of total)

ival-fmax: 2.0ms (10.9% of total)

ival-sub: 1.0ms (5.5% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Counts

7 → 11

Calls

Call 1

Inputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64)))
#s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))
(fmax.f64 x y)
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y))
(*.f64 y y)

Outputs
(fmax (- (+ (pow x 2) (pow y 2)) 1/2) (fmax x y))
(- (pow y 2) 1/2)
(- (+ (pow x 2) (pow y 2)) 1/2)
-1/2
(- (pow x 2) 1/2)
(fmax x y)
(pow x 2)
(* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/2 (/ 1 (pow x 2)))))
(pow y 2)
(* (pow y 2) (- (+ 1 (/ (pow x 2) (pow y 2))) (* 1/2 (/ 1 (pow y 2)))))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	((fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) -1/2) (fmax x y) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (* y y))
0.0ms	y	@	inf	((fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) -1/2) (fmax x y) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (* y y))
0.0ms	x	@	-inf	((fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) -1/2) (fmax x y) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (* y y))
0.0ms	x	@	inf	((fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) -1/2) (fmax x y) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (* y y))
0.0ms	x	@	0	((fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (+ (* x x) -1/2) (fmax x y) (fmax (- (+ (pow y 2) (pow x 2)) 1/2) (fmax x y)) (- (+ (pow y 2) (pow x 2)) 1/2) (* y y))

simplify127.0ms (4%)

Memory

-25.8MiB live, 115.8MiB allocated; 28ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	85
1	55	85
2	180	77
3	898	77
4	6580	77
0	8066	66

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 11

Calls

Call 1

Inputs
(fmax (- (+ (pow x 2) (pow y 2)) 1/2) (fmax x y))
(- (pow y 2) 1/2)
(- (+ (pow x 2) (pow y 2)) 1/2)
-1/2
(- (pow x 2) 1/2)
(fmax x y)
(pow x 2)
(* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 1/2 (/ 1 (pow x 2)))))
(pow y 2)
(* (pow y 2) (- (+ 1 (/ (pow x 2) (pow y 2))) (* 1/2 (/ 1 (pow y 2)))))

Outputs
(fmax (- (+ (pow x 2) (pow y 2)) 1/2) (fmax x y))
(fmax.f64 (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
(- (pow y 2) 1/2)
(fma.f64 y y #s(literal -1/2 binary64))
(- (+ (pow x 2) (pow y 2)) 1/2)
(fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))
-1/2
#s(literal -1/2 binary64)
(- (pow x 2) 1/2)
(fma.f64 x x #s(literal -1/2 binary64))
(fmax x y)
(fmax.f64 x y)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- (+ 1 (/ (pow y 2) (pow x 2))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 (/.f64 (/.f64 y x) x) y #s(literal 1 binary64)) (*.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -1/2 binary64))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (- (+ 1 (/ (pow x 2) (pow y 2))) (* 1/2 (/ 1 (pow y 2)))))
(fma.f64 (fma.f64 (/.f64 (/.f64 x y) y) x #s(literal 1 binary64)) (*.f64 y y) #s(literal -1/2 binary64))

rewrite53.0ms (1.7%)

Memory

9.3MiB live, 51.7MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	81
0	22	81
1	87	81
0	683	74

Stop Event

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

Counts

7 → 23

Calls

Call 1

Inputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64)))
#s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))
(fmax.f64 x y)
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y))
(*.f64 y y)

Outputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64)))
#s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))
(fmax.f64 x y)
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))
#s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y))
(*.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 y)))
(*.f64 (neg.f64 (fabs.f64 y)) (neg.f64 (fabs.f64 y)))
(*.f64 (fabs.f64 (fabs.f64 y)) (fabs.f64 (fabs.f64 y)))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 (neg.f64 y) (neg.f64 y))
(*.f64 (fabs.f64 y) (fabs.f64 y))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (neg.f64 y) #s(literal 2 binary64))
(pow.f64 (fabs.f64 y) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 y) y))
(neg.f64 (*.f64 y (neg.f64 y)))
(fabs.f64 (*.f64 y y))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))))

eval4.0ms (0.1%)

Memory: 6.7MiB live, 6.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 691 to 117 computations (83.1% saved)

prune5.0ms (0.2%)

Memory

8.0MiB live, 8.0MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	34	6	40

Accuracy

100.0%

Counts

40 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	67.8%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
✓	100.0%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
✓	65.7%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))
✓	59.0%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))
✓	57.8%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))
✓	26.3%	(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))

Compiler

Compiled 237 to 118 computations (50.2% saved)

regimes8.0ms (0.3%)

Memory

13.4MiB live, 13.4MiB allocated; 0ms collecting garbage

Counts

7 → 1

Calls

Call 1

Inputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))

Outputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))

Calls

3 calls:

3.0ms	x
3.0ms	y
2.0ms	(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))

Results

Accuracy	Segments	Branch
100.0%	1	`(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))`
100.0%	1	`x`
100.0%	1	`y`

Compiler

Compiled 15 to 14 computations (6.7% saved)

regimes10.0ms (0.3%)

Memory

-32.4MiB live, 11.7MiB allocated; 6ms collecting garbage

Counts

5 → 3

Calls

Call 1

Inputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))

Outputs

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y))

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))

Calls

3 calls:

5.0ms	(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))
2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
72.3%	3	`(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))`
93.7%	3	`x`
90.4%	3	`y`

Compiler

Compiled 15 to 14 computations (6.7% saved)

regimes4.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated; 0ms collecting garbage

Counts

4 → 3

Calls

Call 1

Inputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))

Outputs

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y))

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))

Calls

2 calls:

2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
90.4%	3	`y`
84.9%	3	`x`

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes3.0ms (0.1%)

Memory

7.1MiB live, 7.1MiB allocated; 0ms collecting garbage

Counts

3 → 3

Calls

Call 1

Inputs

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))

Outputs

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y))

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))

Calls

2 calls:

2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
84.9%	3	`x`
82.6%	3	`y`

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes4.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))

Outputs

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))

(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))

Calls

3 calls:

1.0ms	(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))
1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
65.4%	2	`(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))`
57.8%	1	`y`
65.3%	3	`x`

Compiler

Compiled 15 to 14 computations (6.7% saved)

regimes3.0ms (0.1%)

Memory

7.3MiB live, 7.3MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))

Outputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))

Calls

3 calls:

1.0ms	(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
26.3%	1	`y`
26.3%	1	`x`
26.3%	1	`(fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y))`

Compiler

Compiled 15 to 14 computations (6.7% saved)

bsearch51.0ms (1.6%)

Memory

-13.6MiB live, 48.4MiB allocated; 19ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
36.0ms	6.741673281989708e+96	4.303193434492935e+108
11.0ms	-2.55181343707014e+99	-2.7944491728565046e+97

Samples

28.0ms

272×

valid

Compiler

Compiled 611 to 473 computations (22.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-pow2: 16.0ms (74.6% of total)

ival-fmax: 2.0ms (9.3% of total)

ival-sub: 1.0ms (4.7% of total)

ival-add: 1.0ms (4.7% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

bsearch34.0ms (1.1%)

Memory

-5.1MiB live, 37.4MiB allocated; 10ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.652346512706702e+72	3.144177181656037e+76
18.0ms	-3.992410057943645e+56	-7.604282633656106e+52

Samples

21.0ms

256×

valid

Compiler

Compiled 576 to 446 computations (22.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-pow2: 5.0ms (49.1% of total)

ival-fmax: 2.0ms (19.7% of total)

ival-sub: 1.0ms (9.8% of total)

ival-add: 1.0ms (9.8% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

bsearch2.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated; 0ms collecting garbage

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	6.741673281989708e+96	4.303193434492935e+108
1.0ms	-2.55181343707014e+99	-2.7944491728565046e+97

Compiler

Compiled 594 to 456 computations (23.2% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.137045313387547e-125	5.30658996148629e-113

Compiler

Compiled 16 to 15 computations (6.3% saved)

simplify42.0ms (1.3%)

Memory

-10.7MiB live, 32.4MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	227
1	73	227
2	116	227
3	189	227
4	291	227
5	642	227
6	3760	227

Stop Event

1×	node limit

Calls

Call 1

Inputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
(if (<=.f64 x #s(literal -89999999999999995239003105908881210659462449075541017585360148541035824959381373504563820781109248 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 x x)) (fmax.f64 x y)) (if (<=.f64 x #s(literal 19000000000000001777369121119351456119351921765605704372162215764939342617718772661026034550833152 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 x x)) (fmax.f64 x y))))
(if (<=.f64 y #s(literal -5600000000000000302319679497363580131560174706654969856 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 y y)) (fmax.f64 x y)) (if (<=.f64 y #s(literal 1999999999999999887603621897589142048114448258041101063088247784112914432 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 y y)) (fmax.f64 x y))))
(if (<=.f64 x #s(literal -89999999999999995239003105908881210659462449075541017585360148541035824959381373504563820781109248 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 x x)) (fmax.f64 x y)) (if (<=.f64 x #s(literal 19000000000000001777369121119351456119351921765605704372162215764939342617718772661026034550833152 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 y y)) (fmax.f64 x y)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))))
(if (<=.f64 (fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y)) #s(literal 4763410263543689/47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y)))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))

Outputs
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x (fma.f64 y y #s(literal -1/2 binary64)))) (fmax.f64 x y))
(if (<=.f64 x #s(literal -89999999999999995239003105908881210659462449075541017585360148541035824959381373504563820781109248 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 x x)) (fmax.f64 x y)) (if (<=.f64 x #s(literal 19000000000000001777369121119351456119351921765605704372162215764939342617718772661026034550833152 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 x x)) (fmax.f64 x y))))
(if (or (<=.f64 x #s(literal -89999999999999995239003105908881210659462449075541017585360148541035824959381373504563820781109248 binary64)) (not (<=.f64 x #s(literal 19000000000000001777369121119351456119351921765605704372162215764939342617718772661026034550833152 binary64)))) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 y y #s(literal -1/2 binary64))) (fmax.f64 x y)))
(if (<=.f64 y #s(literal -5600000000000000302319679497363580131560174706654969856 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 y y)) (fmax.f64 x y)) (if (<=.f64 y #s(literal 1999999999999999887603621897589142048114448258041101063088247784112914432 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 y y)) (fmax.f64 x y))))
(if (or (<=.f64 y #s(literal -5600000000000000302319679497363580131560174706654969856 binary64)) (not (<=.f64 y #s(literal 1999999999999999887603621897589142048114448258041101063088247784112914432 binary64)))) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 y y)) (fmax.f64 x y)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (fma.f64 x x #s(literal -1/2 binary64))) (fmax.f64 x y)))
(if (<=.f64 x #s(literal -89999999999999995239003105908881210659462449075541017585360148541035824959381373504563820781109248 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 x x)) (fmax.f64 x y)) (if (<=.f64 x #s(literal 19000000000000001777369121119351456119351921765605704372162215764939342617718772661026034550833152 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 y y)) (fmax.f64 x y)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y))))
(if (or (<=.f64 x #s(literal -89999999999999995239003105908881210659462449075541017585360148541035824959381373504563820781109248 binary64)) (not (<=.f64 x #s(literal 19000000000000001777369121119351456119351921765605704372162215764939342617718772661026034550833152 binary64)))) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 x x)) (fmax.f64 x y)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (.f64 y y)) (fmax.f64 x y)))
(if (<=.f64 (fmax.f64 (-.f64 (+.f64 (pow.f64 y #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fmax.f64 x y)) #s(literal 4763410263543689/47634102635436893179040485073748265163400240214004076398607741693502376385799646303105256699577209032590132615988260237052123652332890095616 binary64)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y)) (fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) (*.f64 x x)) (fmax.f64 x y)))
(fmax.f64 #s(approx (- (+ (pow y 2) (pow x 2)) 1/2) #s(approx (+ (* x x) -1/2) #s(literal -1/2 binary64))) (fmax.f64 x y))

derivations420.0ms (13.2%)

Memory

51.5MiB live, 278.6MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	80
1	67	80
2	241	80
3	1515	80
0	8810	67
0	30	90
1	59	90
2	189	82
3	928	82
4	6733	82
0	8219	70

Stop Event

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

Compiler

Compiled 227 to 56 computations (75.3% saved)

preprocess58.0ms (1.8%)

Memory: -36.8MiB live, 64.3MiB allocated; 23ms collecting garbage
Compiler: Compiled 480 to 132 computations (72.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample895.0ms (28.2%)

explain126.0ms (4%)

preprocess269.0ms (8.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify180.0ms (5.7%)

localize29.0ms (0.9%)

series4.0ms (0.1%)

simplify139.0ms (4.4%)

rewrite45.0ms (1.4%)

eval15.0ms (0.5%)

prune2.0ms (0.1%)

simplify184.0ms (5.8%)

localize44.0ms (1.4%)

series8.0ms (0.3%)

simplify117.0ms (3.7%)

rewrite49.0ms (1.5%)

eval22.0ms (0.7%)

prune5.0ms (0.1%)

simplify174.0ms (5.5%)

localize35.0ms (1.1%)

series3.0ms (0.1%)

simplify127.0ms (4%)

rewrite53.0ms (1.7%)

eval4.0ms (0.1%)

prune5.0ms (0.2%)

regimes8.0ms (0.3%)

regimes10.0ms (0.3%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

bsearch51.0ms (1.6%)

bsearch34.0ms (1.1%)

bsearch2.0ms (0.1%)

bsearch0.0ms (0%)

simplify42.0ms (1.3%)

derivations420.0ms (13.2%)

preprocess58.0ms (1.8%)

end0.0ms (0%)

Profiling