Metrics for Rust f32::acosh

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.3MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample466.0ms (10.8%)

Memory

-26.0MiB live, 653.8MiB allocated

Samples

305.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 195.0ms

ival-acosh: 160.0ms (82.2% of total)

ival->=: 26.0ms (13.4% of total)

exact: 6.0ms (3.1% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

explain137.0ms (3.2%)

Memory

2.6MiB live, 163.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
125	-	-	`(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))`
0	-	-	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
0	-	-	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`
0	-	-	`(*.f32 x x)`
0	-	-	`#s(literal 1 binary32)`
0	-	-	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f32`	`(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))`	oflow-rescue	125	0
↳	`(*.f32 x x)`	overflow	125
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	125

Confusion

	Predicted +	Predicted -
+	125	0
-	0	131

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	125	0	0
-	0	0	131

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	131
1	125

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

64.0ms

512×

valid

Compiler

Compiled 80 to 25 computations (68.8% saved)

Precisions

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

ival-log: 9.0ms (42.5% of total)

ival-sqrt: 4.0ms (18.9% of total)

ival-mult: 3.0ms (14.2% 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)

exact: 0.0ms (0% of total)

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

preprocess298.0ms (6.9%)

Memory

5.7MiB live, 244.5MiB allocated

Algorithm

1×	egg-herbie

Rules

29 894×	`lower-fma.f64`
29 894×	`lower-fma.f32`
4 210×	`lower-*.f64`
4 208×	`lower-*.f32`
2 884×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	10	7
2	14	7
3	17	7
4	21	7
5	28	7
6	35	7
0	7	9
0	12	9
1	21	9
2	25	9
3	40	9
4	71	9
5	132	9
6	292	9
7	572	9
8	2045	9
9	3155	9
10	4433	9
11	5106	9
12	5408	9
13	5593	9
14	5695	9
15	6014	9
16	6560	9
17	7671	9
0	8091	8

Stop Event

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

Calls

Call 1

Inputs
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Outputs
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))

Compiler

Compiled 10 to 7 computations (30% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.3%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify271.0ms (6.3%)

Memory

22.7MiB live, 252.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))
cost-diff	0	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
cost-diff	0	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
cost-diff	64	(-.f32 (*.f32 x x) #s(literal 1 binary32))

Rules

29 894×	`lower-fma.f64`
29 894×	`lower-fma.f32`
4 210×	`lower-*.f64`
4 208×	`lower-*.f32`
2 884×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	12	33
1	21	33
2	25	33
3	40	33
4	71	33
5	132	33
6	292	33
7	572	33
8	2045	33
9	3155	33
10	4433	33
11	5106	33
12	5408	33
13	5593	33
14	5695	33
15	6014	33
16	6560	33
17	7671	33
0	8091	29

Stop Event

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

Calls

Call 1

Inputs
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
x
(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))
(-.f32 (*.f32 x x) #s(literal 1 binary32))
(*.f32 x x)
#s(literal 1 binary32)

Outputs
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
x
(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))
(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
(-.f32 (*.f32 x x) #s(literal 1 binary32))
(fma.f32 x x #s(literal -1 binary32))
(*.f32 x x)
#s(literal 1 binary32)

localize51.0ms (1.2%)

Memory

-15.8MiB live, 32.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
accuracy	0.0078125	(-.f32 (*.f32 x x) #s(literal 1 binary32))
accuracy	0.01171875	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
accuracy	13.514778789975328	(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))

Samples

45.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

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

ival-log: 2.0ms (23.6% of total)

ival-mult: 2.0ms (23.6% of total)

ival-sqrt: 2.0ms (23.6% of total)

ival-sub: 1.0ms (11.8% of total)

ival-add: 1.0ms (11.8% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())
#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())
#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())
#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())

Outputs
#s(alt -1 (taylor 0 x) (#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (log (sqrt -1)) (taylor 0 x) (#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())) ())
#s(alt (+ x (sqrt -1)) (taylor 0 x) (#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1)))))) (taylor 0 x) (#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) (taylor 0 x) (#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1)))) (taylor 0 x) (#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2))))) (taylor inf x) (#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())) ())
#s(alt (* x (- 2 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())) ())
#s(alt (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))) (taylor inf x) (#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())) ())
#s(alt (* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (-.f32 (.f32 x x) #s(literal 1 binary32)) (patch (-.f32 (.f32 x x) #s(literal 1 binary32)) #<representation binary32>) () ())) ())
#s(alt (+ (log -1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))))) (taylor -inf x) (#s(alt (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) (patch (log.f32 (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())) ())
#s(alt (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x)) (taylor -inf x) (#s(alt (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) (patch (+.f32 x (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32)))) #<representation binary32>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) (patch (sqrt.f32 (-.f32 (.f32 x x) #s(literal 1 binary32))) #<representation binary32>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))
1.0ms	x	@	inf	((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))
1.0ms	x	@	-inf	((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))

Time

Variable

Point

Expression

2.0ms

((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))

1.0ms

inf

((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))

1.0ms

-inf

((- (* x x) 1) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)))

simplify219.0ms (5.1%)

Memory

-5.5MiB live, 192.0MiB allocated

Algorithm

1×	egg-herbie

Rules

10 204×	`lower-fma.f64`
10 204×	`lower-fma.f32`
3 650×	`lower-*.f64`
3 650×	`lower-*.f32`
2 854×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	559
1	411	533
2	1146	526
3	3331	488
4	7979	488
0	8531	459

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

Inputs
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))

Outputs
-1
#s(literal -1 binary32)
(- (pow x 2) 1)
(fma.f32 x x #s(literal -1 binary32))
(- (pow x 2) 1)
(fma.f32 x x #s(literal -1 binary32))
(- (pow x 2) 1)
(fma.f32 x x #s(literal -1 binary32))
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (fma.f32 (*.f32 x x) #s(literal 1/6 binary32) #s(literal 1 binary32)) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f32 (.f32 (.f32 x x) x) (.f32 (.f32 #s(literal 3/40 binary32) x) (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) (fma.f32 (fma.f32 (*.f32 x x) #s(literal 1/6 binary32) #s(literal 1 binary32)) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32)))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ x (sqrt -1))
(+.f32 (sqrt.f32 #s(literal -1 binary32)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f32 (fma.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f32 (fma.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 (*.f32 x x) #s(literal 1/8 binary32) #s(literal 1/2 binary32)) #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 (*.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) x) (fma.f32 (.f32 x x) #s(literal 1/8 binary32) #s(literal 1/2 binary32)) (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (fma.f32 (.f32 #s(literal 1/16 binary32) (.f32 x x)) (.f32 (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) x) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32))) (fma.f32 #s(literal 1/8 binary32) (.f32 x x) #s(literal 1/2 binary32)))) (.f32 x x) (sqrt.f32 #s(literal -1 binary32)))
(pow x 2)
(*.f32 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 x x)) #s(literal 1/4 binary32)) (.f32 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (-.f32 (log.f32 #s(literal 2 binary32)) (/.f32 #s(literal 1/4 binary32) (.f32 x x))) (-.f32 (/.f32 (+.f32 (/.f32 #s(literal 5/96 binary32) (.f32 x x)) #s(literal 3/32 binary32)) (.f32 (.f32 (*.f32 x x) x) x)) (log.f32 x)))
(* 2 x)
(*.f32 #s(literal 2 binary32) x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 #s(literal 2 binary32) x (/.f32 #s(literal -1/2 binary32) x))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 #s(literal 2 binary32) x (/.f32 (-.f32 #s(literal -1/2 binary32) (/.f32 #s(literal 1/8 binary32) (*.f32 x x))) x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 (-.f32 #s(literal 2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (.f32 x x) x) x))) x (/.f32 #s(literal -1/2 binary32) x))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 x (/.f32 (+.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 (/.f32 (-.f32 #s(literal -1/8 binary32) (/.f32 #s(literal 1/16 binary32) (.f32 x x))) (.f32 (.f32 (.f32 x x) x) x)) x (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))
(pow x 2)
(*.f32 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(+ (log -1/2) (log (/ -1 x)))
(+.f32 (neg.f32 (log.f32 (neg.f32 x))) (log.f32 #s(literal -1/2 binary32)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f32 (+.f32 (log.f32 #s(literal -1/2 binary32)) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (neg.f32 (log.f32 (neg.f32 x))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 (.f32 (.f32 x x) x) x)) (log.f32 #s(literal -1/2 binary32))) (+.f32 (neg.f32 (log.f32 (neg.f32 x))) (/.f32 #s(literal 1/4 binary32) (.f32 x x))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f32 (+.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 (.f32 (.f32 x x) x) x)) (log.f32 #s(literal -1/2 binary32))) (/.f32 #s(literal 5/96 binary32) (pow.f32 x #s(literal 6 binary32)))) (+.f32 (neg.f32 (log.f32 (neg.f32 x))) (/.f32 #s(literal 1/4 binary32) (.f32 x x))))
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f32 (+.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f32 (-.f32 (/.f32 (-.f32 #s(literal 1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x x)) #s(literal -1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f32 (-.f32 (/.f32 (-.f32 #s(literal 1/16 binary32) (/.f32 #s(literal -5/128 binary32) (.f32 x x))) (.f32 (.f32 (.f32 x x) x) x)) (-.f32 #s(literal -1/2 binary32) (/.f32 #s(literal 1/8 binary32) (*.f32 x x)))) x)
(* -1 x)
(neg.f32 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f32 (/.f32 #s(literal 1/2 binary32) x) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(-.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x) x)
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (.f32 x x) x) x)) x (-.f32 (/.f32 #s(literal 1/2 binary32) x) x))

rewrite286.0ms (6.6%)

Memory

10.3MiB live, 194.3MiB allocated

Rules

4 994×	`lower-fma.f64`
4 994×	`lower-fma.f32`
3 230×	`lower-*.f64`
3 228×	`lower-*.f32`
2 612×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
0	12	28
1	49	28
2	322	28
3	3626	28
0	8646	24

Stop Event

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

Counts

4 → 320

Calls

Call 1

Inputs
(-.f32 (*.f32 x x) #s(literal 1 binary32))
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))

Outputs
(expm1.f32 (.f32 (log.f32 (.f32 x x)) #s(literal 1 binary32)))
(expm1.f32 (log.f32 (*.f32 x x)))
(.f32 (exp.f32 (log.f32 (fma.f32 (.f32 (.f32 x x) x) x #s(literal -1 binary32)))) (exp.f32 (neg.f32 (log1p.f32 (.f32 x x)))))
(.f32 (exp.f32 (log.f32 (fma.f32 (.f32 (.f32 x x) x) (.f32 (.f32 x x) x) #s(literal -1 binary32)))) (exp.f32 (neg.f32 (log1p.f32 (fma.f32 x x (.f32 (.f32 (.f32 x x) x) x))))))
(*.f32 (exp.f32 (log1p.f32 x)) (exp.f32 (log.f32 (-.f32 x #s(literal 1 binary32)))))
(*.f32 (exp.f32 (log.f32 (-.f32 x #s(literal 1 binary32)))) (exp.f32 (log1p.f32 x)))
(.f32 (/.f32 (fma.f32 (.f32 (.f32 x x) x) x #s(literal -1 binary32)) (-.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 x x) x) x))) (-.f32 #s(literal 1 binary32) (*.f32 x x)))
(.f32 (/.f32 (fma.f32 (.f32 (.f32 x x) x) x #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 (.f32 x x) x) x) (.f32 x x) #s(literal 1 binary32))) (fma.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x) #s(literal 1 binary32)))
(.f32 (/.f32 (fma.f32 (.f32 (.f32 x x) x) (.f32 (.f32 x x) x) #s(literal -1 binary32)) (.f32 (fma.f32 (.f32 (.f32 x x) x) x (fma.f32 x x #s(literal 1 binary32))) (-.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x)) #s(literal 1 binary32)))) (-.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x)) #s(literal 1 binary32)))
(.f32 (/.f32 (fma.f32 (.f32 (.f32 x x) x) (.f32 (.f32 x x) x) #s(literal -1 binary32)) (fma.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x)) (.f32 x x) (.f32 (.f32 (fma.f32 x x #s(literal 1 binary32)) (fma.f32 x x #s(literal 1 binary32))) (fma.f32 x x #s(literal 1 binary32))))) (fma.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) (.f32 (.f32 x x) x) (.f32 (fma.f32 x x #s(literal 1 binary32)) (-.f32 (fma.f32 x x #s(literal 1 binary32)) (.f32 (.f32 (*.f32 x x) x) x)))))
(.f32 (/.f32 (fma.f32 (.f32 (.f32 x x) x) x #s(literal -1 binary32)) (fma.f32 (.f32 (*.f32 x x) x) x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)))
(.f32 (.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))))
(*.f32 (/.f32 (fma.f32 x x #s(literal 1 binary32)) (fma.f32 x x #s(literal 1 binary32))) (fma.f32 x x #s(literal -1 binary32)))
(.f32 (.f32 (sqrt.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (sqrt.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
(.f32 (sqrt.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (.f32 (sqrt.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32))) (fma.f32 (.f32 (*.f32 x x) x) x #s(literal -1 binary32)))
(.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (.f32 x x) x) x (fma.f32 x x #s(literal 1 binary32)))) (fma.f32 (.f32 (.f32 x x) x) (.f32 (*.f32 x x) x) #s(literal -1 binary32)))
(.f32 (neg.f32 (fma.f32 (.f32 (*.f32 x x) x) x #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 x x #s(literal 1 binary32)))))
(.f32 (neg.f32 (fma.f32 (.f32 (.f32 x x) x) (.f32 (.f32 x x) x) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (.f32 (*.f32 x x) x) x (fma.f32 x x #s(literal 1 binary32))))))
(.f32 (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
(*.f32 (-.f32 x #s(literal 1 binary32)) (+.f32 #s(literal 1 binary32) x))
(*.f32 (+.f32 #s(literal 1 binary32) x) (-.f32 x #s(literal 1 binary32)))
(*.f32 (fma.f32 x x #s(literal 1 binary32)) (/.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal 1 binary32))))
(.f32 (fma.f32 x x #s(literal 1 binary32)) (.f32 (fma.f32 x x #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(.f32 (fma.f32 (.f32 (*.f32 x x) x) x #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32))))
(.f32 (fma.f32 (.f32 (.f32 x x) x) (.f32 (.f32 x x) x) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (.f32 x x) x) x (-.f32 #s(literal 1 binary32) (.f32 #s(literal -1 binary32) (*.f32 x x))))))
(.f32 (fma.f32 (.f32 (.f32 x x) x) (.f32 (.f32 x x) x) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 (*.f32 x x) x) x (fma.f32 x x #s(literal 1 binary32)))))
(*.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
(*.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32)))
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(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 x x #s(literal 1 binary32))) (sqrt.f32 (fma.f32 (.f32 (.f32 x x) x) x #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (fma.f32 (.f32 (.f32 x x) x) x (fma.f32 x x #s(literal 1 binary32)))) (sqrt.f32 (fma.f32 (.f32 (.f32 x x) x) (.f32 (.f32 x x) x) #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32)))))
(pow.f32 (exp.f32 #s(literal 1/2 binary32)) (log.f32 (fma.f32 x x #s(literal -1 binary32))))
(pow.f32 (/.f32 (sqrt.f32 (fma.f32 x x #s(literal 1 binary32))) (sqrt.f32 (fma.f32 (.f32 (.f32 x x) x) x #s(literal -1 binary32)))) #s(literal -1 binary32))
(pow.f32 (/.f32 (sqrt.f32 (fma.f32 (.f32 (.f32 x x) x) x (fma.f32 x x #s(literal 1 binary32)))) (sqrt.f32 (fma.f32 (.f32 (.f32 x x) x) (.f32 (.f32 x x) x) #s(literal -1 binary32)))) #s(literal -1 binary32))
(pow.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32)))) #s(literal -1 binary32))
(pow.f32 (.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))) (*.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32)))) #s(literal 1/8 binary32))
(pow.f32 (sqrt.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) #s(literal 2 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32))) #s(literal -1/2 binary32))
(pow.f32 (*.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))) #s(literal 1/4 binary32))
(pow.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 1 binary32))
(pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1/2 binary32))
(fabs.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
(exp.f32 (-.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))) (*.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 1/2 binary32))))
(exp.f32 (.f32 (.f32 #s(literal 1/4 binary32) (log.f32 (fma.f32 x x #s(literal -1 binary32)))) #s(literal 2 binary32)))
(exp.f32 (.f32 (.f32 #s(literal 2 binary32) (log.f32 (fma.f32 x x #s(literal -1 binary32)))) #s(literal 1/4 binary32)))
(exp.f32 (.f32 (.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 1/2 binary32)) #s(literal 1 binary32)))
(exp.f32 (*.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 1/2 binary32)))

eval156.0ms (3.6%)

Memory: -15.0MiB live, 73.0MiB allocated
Compiler: Compiled 10 641 to 1 519 computations (85.7% saved)

prune120.0ms (2.8%)

Memory

28.1MiB live, 141.1MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	364	3	367
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	365	3	368

Accuracy

100.0%

Counts

368 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.3%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
▶	99.2%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
▶	98.2%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))

Status

Accuracy

Program

▶

54.3%

(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))

▶

99.2%

(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))

▶

98.2%

(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))

Compiler

Compiled 25 to 16 computations (36% saved)

simplify296.0ms (6.9%)

Memory

-0.7MiB live, 159.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f32 x x #s(literal -1 binary32))
cost-diff	0	(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
cost-diff	0	(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
cost-diff	0	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
cost-diff	0	(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
cost-diff	0	#s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))
cost-diff	0	(+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))
cost-diff	0	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
cost-diff	0	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
cost-diff	0	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
cost-diff	64	(*.f32 #s(literal 2 binary32) x)

Rules

19 528×	`lower-fma.f64`
19 526×	`lower-fma.f32`
3 070×	`lower-+.f64`
3 066×	`lower-+.f32`
2 916×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	107
0	31	102
1	46	102
2	57	102
3	81	102
4	122	102
5	246	102
6	521	102
7	1078	102
8	2687	102
9	4393	102
10	5439	102
11	5884	102
12	5992	102
13	6071	102
14	6147	102
15	6869	102
16	7525	102
17	7957	102
0	8005	102

Stop Event

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

Calls

Call 1

Inputs
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
(*.f32 #s(literal 2 binary32) x)
#s(literal 2 binary32)
x
(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
(+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))
x
#s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))
(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
(/.f32 #s(literal 1/2 binary32) x)
#s(literal 1/2 binary32)
(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
(fma.f32 x x #s(literal -1 binary32))
x
#s(literal -1 binary32)

Outputs
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f32 x x))
(*.f32 #s(literal 2 binary32) x)
(+.f32 x x)
#s(literal 2 binary32)
x
(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
(log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x))
(+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))
(+.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x)
x
#s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))
(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
(/.f32 #s(literal 1/2 binary32) x)
#s(literal 1/2 binary32)
(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
(fma.f32 x x #s(literal -1 binary32))
x
#s(literal -1 binary32)

localize222.0ms (5.1%)

Memory

-33.2MiB live, 63.8MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f32 x x #s(literal -1 binary32))
accuracy	0.00390625	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
accuracy	0.01171875	(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
accuracy	13.514778789975328	(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
accuracy	0	(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
accuracy	0.00390625	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
accuracy	0.01171875	(+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))
accuracy	0.32653508914678747	#s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))
accuracy	0	(*.f32 #s(literal 2 binary32) x)
accuracy	0.00390625	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
accuracy	0.6452821584179159	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))

Samples

155.0ms

256×

valid

Compiler

Compiled 87 to 19 computations (78.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 147.0ms

ival-sqrt: 112.0ms (76% of total)

ival-log: 25.0ms (17% of total)

ival-add: 3.0ms (2% of total)

ival-mult: 3.0ms (2% of total)

ival-div: 2.0ms (1.4% of total)

ival-sub: 2.0ms (1.4% of total)

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

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

exact: 0.0ms (0% of total)

series7.0ms (0.2%)

Memory

12.2MiB live, 12.2MiB allocated

Counts

11 → 132

Calls

Call 1

Inputs
#s(alt (.f32 #s(literal 2 binary32) x) (patch (.f32 #s(literal 2 binary32) x) #<representation binary32>) () ())
#s(alt (log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (.f32 #s(literal 2 binary32) x))) (patch (log.f32 #s(approx (+ x (sqrt (- ( x x) 1))) (*.f32 #s(literal 2 binary32) x))) #<representation binary32>) () ())
#s(alt #s(approx (+ x (sqrt (- (* x x) 1))) (.f32 #s(literal 2 binary32) x)) (patch #s(approx (+ x (sqrt (- ( x x) 1))) (*.f32 #s(literal 2 binary32) x)) #<representation binary32>) () ())
#s(alt (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) (patch (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) #<representation binary32>) () ())
#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #<representation binary32>) () ())
#s(alt #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #<representation binary32>) () ())
#s(alt (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) (patch (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) #<representation binary32>) () ())
#s(alt (log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) #<representation binary32>) () ())
#s(alt (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x) (patch (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x) #<representation binary32>) () ())
#s(alt (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (patch (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) #<representation binary32>) () ())
#s(alt (fma.f32 x x #s(literal -1 binary32)) (patch (fma.f32 x x #s(literal -1 binary32)) #<representation binary32>) () ())

Outputs
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f32 #s(literal 2 binary32) x) (patch (.f32 #s(literal 2 binary32) x) #<representation binary32>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f32 #s(literal 2 binary32) x) (patch (.f32 #s(literal 2 binary32) x) #<representation binary32>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f32 #s(literal 2 binary32) x) (patch (.f32 #s(literal 2 binary32) x) #<representation binary32>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f32 #s(literal 2 binary32) x) (patch (.f32 #s(literal 2 binary32) x) #<representation binary32>) () ())) ())
#s(alt (log (sqrt -1)) (taylor 0 x) (#s(alt (log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (.f32 #s(literal 2 binary32) x))) (patch (log.f32 #s(approx (+ x (sqrt (- ( x x) 1))) (*.f32 #s(literal 2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt (log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (.f32 #s(literal 2 binary32) x))) (patch (log.f32 #s(approx (+ x (sqrt (- ( x x) 1))) (*.f32 #s(literal 2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (.f32 #s(literal 2 binary32) x))) (patch (log.f32 #s(approx (+ x (sqrt (- ( x x) 1))) (*.f32 #s(literal 2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (.f32 #s(literal 2 binary32) x))) (patch (log.f32 #s(approx (+ x (sqrt (- ( x x) 1))) (*.f32 #s(literal 2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt #s(approx (+ x (sqrt (- (* x x) 1))) (.f32 #s(literal 2 binary32) x)) (patch #s(approx (+ x (sqrt (- ( x x) 1))) (*.f32 #s(literal 2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (+ x (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (+ x (sqrt (- (* x x) 1))) (.f32 #s(literal 2 binary32) x)) (patch #s(approx (+ x (sqrt (- ( x x) 1))) (*.f32 #s(literal 2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1)))))) (taylor 0 x) (#s(alt #s(approx (+ x (sqrt (- (* x x) 1))) (.f32 #s(literal 2 binary32) x)) (patch #s(approx (+ x (sqrt (- ( x x) 1))) (*.f32 #s(literal 2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) (taylor 0 x) (#s(alt #s(approx (+ x (sqrt (- (* x x) 1))) (.f32 #s(literal 2 binary32) x)) (patch #s(approx (+ x (sqrt (- ( x x) 1))) (*.f32 #s(literal 2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (log (sqrt -1)) (taylor 0 x) (#s(alt (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) (patch (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) (patch (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) (patch (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) (patch (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) #<representation binary32>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #<representation binary32>) () ())) ())
#s(alt (+ x (sqrt -1)) (taylor 0 x) (#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1)))))) (taylor 0 x) (#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) (taylor 0 x) (#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #<representation binary32>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1)))) (taylor 0 x) (#s(alt #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1)))))) (taylor 0 x) (#s(alt #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (/ -1/2 x) (taylor 0 x) (#s(alt (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) (patch (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (- (pow x 2) 1/2) x) (taylor 0 x) (#s(alt (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) (patch (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (- (pow x 2) 1/2) x) (taylor 0 x) (#s(alt (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) (patch (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (- (pow x 2) 1/2) x) (taylor 0 x) (#s(alt (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) (patch (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (log (sqrt -1)) (taylor 0 x) (#s(alt (log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) #<representation binary32>) () ())) ())
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#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))))) (taylor -inf x) (#s(alt (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) (patch (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) #<representation binary32>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #<representation binary32>) () ())) ())
#s(alt (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #<representation binary32>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #<representation binary32>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x)) (taylor -inf x) (#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #<representation binary32>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) (patch (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) (patch (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) (patch (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) (patch (-.f32 x (/.f32 #s(literal 1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (+ (log -1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt (log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) #<representation binary32>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) #<representation binary32>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) #<representation binary32>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))))) (taylor -inf x) (#s(alt (log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) #<representation binary32>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x) (patch (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x) #<representation binary32>) () ())) ())
#s(alt (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x) (patch (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x) #<representation binary32>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x) (patch (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x) #<representation binary32>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x)) (taylor -inf x) (#s(alt (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x) (patch (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x) #<representation binary32>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (patch (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (patch (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (patch (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (patch (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f32 x x #s(literal -1 binary32)) (patch (fma.f32 x x #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f32 x x #s(literal -1 binary32)) (patch (fma.f32 x x #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f32 x x #s(literal -1 binary32)) (patch (fma.f32 x x #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f32 x x #s(literal -1 binary32)) (patch (fma.f32 x x #s(literal -1 binary32)) #<representation binary32>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

((* 2 x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1))

1.0ms

inf

((* 2 x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1))

1.0ms

((* 2 x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1))

simplify249.0ms (5.8%)

Memory

-17.0MiB live, 136.9MiB allocated

Algorithm

1×	egg-herbie

Rules

9 986×	`lower-fma.f64`
9 986×	`lower-fma.f32`
3 992×	`lower-*.f64`
3 992×	`lower-*.f32`
2 998×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	1505
1	425	1435
2	1185	1385
3	3452	1315
0	8302	1254

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 128

Calls

Call 1

Inputs
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(/ -1/2 x)
(/ (- (pow x 2) 1/2) x)
(/ (- (pow x 2) 1/2) x)
(/ (- (pow x 2) 1/2) x)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))

Outputs
(* 2 x)
(*.f32 x #s(literal 2 binary32))
(* 2 x)
(*.f32 x #s(literal 2 binary32))
(* 2 x)
(*.f32 x #s(literal 2 binary32))
(* 2 x)
(*.f32 x #s(literal 2 binary32))
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (fma.f32 (*.f32 x x) #s(literal 1/6 binary32) #s(literal 1 binary32)) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f32 (.f32 (.f32 #s(literal 3/40 binary32) (.f32 x x)) (.f32 (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) x)) x (fma.f32 (fma.f32 (*.f32 x x) #s(literal 1/6 binary32) #s(literal 1 binary32)) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32)))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ x (sqrt -1))
(+.f32 (sqrt.f32 #s(literal -1 binary32)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f32 (fma.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f32 (fma.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 (*.f32 x x) #s(literal 1/8 binary32) #s(literal 1/2 binary32)) #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
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(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f32 (+.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 x x)) #s(literal -1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f32 (-.f32 (/.f32 (+.f32 (/.f32 #s(literal 5/128 binary32) (.f32 x x)) #s(literal 1/16 binary32)) (.f32 (.f32 (.f32 x x) x) x)) (-.f32 #s(literal -1/2 binary32) (/.f32 #s(literal 1/8 binary32) (*.f32 x x)))) x)
(* -1 x)
(neg.f32 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f32 (/.f32 #s(literal 1/2 binary32) x) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(-.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x) x)
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(fma.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (.f32 x x) x) x)) x (-.f32 (/.f32 #s(literal 1/2 binary32) x) x))
(pow x 2)
(*.f32 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal -1 binary32))

rewrite339.0ms (7.8%)

Memory

8.8MiB live, 199.7MiB allocated

Rules

9 898×	`lower-fma.f64`
9 896×	`lower-fma.f32`
4 192×	`lower-*.f64`
4 190×	`lower-*.f32`
3 658×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	98
0	31	93
1	125	93
2	836	93
0	8500	93

Stop Event

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

Counts

11 → 419

Calls

Call 1

Inputs
(*.f32 #s(literal 2 binary32) x)
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
(+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))
#s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))
(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
(fma.f32 x x #s(literal -1 binary32))

Outputs
(*.f32 #s(literal -2 binary32) (neg.f32 x))
(.f32 (.f32 x #s(literal 2 binary32)) #s(literal 1 binary32))
(*.f32 (neg.f32 x) #s(literal -2 binary32))
(.f32 #s(literal -1 binary32) (.f32 #s(literal -2 binary32) x))
(.f32 #s(literal 1 binary32) (.f32 x #s(literal 2 binary32)))
(*.f32 x #s(literal 2 binary32))
(*.f32 #s(literal 2 binary32) x)
(/.f32 #s(literal -2 binary32) (/.f32 #s(literal -1 binary32) x))
(/.f32 (*.f32 #s(literal -2 binary32) x) #s(literal -1 binary32))
(/.f32 (*.f32 x #s(literal 2 binary32)) #s(literal 1 binary32))
(/.f32 (neg.f32 x) #s(literal -1/2 binary32))
(/.f32 #s(literal -1 binary32) (/.f32 #s(literal -1/2 binary32) x))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) x) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1/2 binary32) x))
(/.f32 x #s(literal 1/2 binary32))
(/.f32 #s(literal 2 binary32) (/.f32 #s(literal 1 binary32) x))
(-.f32 #s(literal 0 binary32) (*.f32 #s(literal -2 binary32) x))
(pow.f32 (*.f32 x #s(literal 2 binary32)) #s(literal 1 binary32))
(pow.f32 (/.f32 #s(literal 1/2 binary32) x) #s(literal -1 binary32))
(neg.f32 (*.f32 #s(literal -2 binary32) x))
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 x #s(literal 2 binary32))))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 x #s(literal 2 binary32)))
(log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x))
(/.f32 (-.f32 (.f32 (log.f32 (.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))) (log.f32 (.f32 (+.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))))) (.f32 (log.f32 (-.f32 x #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) (log.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))))) (+.f32 (log.f32 (.f32 (+.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))) (log.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))))
(/.f32 (-.f32 (.f32 (log.f32 (fma.f32 (.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x))) (log.f32 (fma.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x)))) (.f32 (log.f32 (fma.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (.f32 x x))) (log.f32 (fma.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (.f32 x x))))) (+.f32 (log.f32 (fma.f32 (.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x))) (log.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (*.f32 x x)))))
(/.f32 (-.f32 (pow.f32 (log.f32 (.f32 (+.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))) #s(literal 3 binary32)) (pow.f32 (log.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) #s(literal 3 binary32))) (fma.f32 (log.f32 (.f32 (+.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))) (log.f32 (.f32 (+.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))) (fma.f32 (log.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) (log.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) (.f32 (log.f32 (.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))) (log.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))))))
(/.f32 (-.f32 (pow.f32 (log.f32 (fma.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x))) #s(literal 3 binary32)) (pow.f32 (log.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (.f32 x x))) #s(literal 3 binary32))) (fma.f32 (log.f32 (fma.f32 (.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x))) (log.f32 (fma.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x))) (fma.f32 (log.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (.f32 x x))) (log.f32 (fma.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (.f32 x x))) (.f32 (log.f32 (fma.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x))) (log.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (*.f32 x x)))))))
(-.f32 (log.f32 (.f32 (+.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x))) (log.f32 (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x)))
(-.f32 (log.f32 (.f32 (neg.f32 (+.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x)) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))) (log.f32 (neg.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))))
(-.f32 (log.f32 (neg.f32 (fma.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x)))) (log.f32 (neg.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (*.f32 x x)))))
(-.f32 (log.f32 (.f32 (+.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))) (log.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))))
(-.f32 (log.f32 (fma.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x))) (log.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 x (-.f32 x #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))))))
(-.f32 (log.f32 (fma.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x))) (log.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (*.f32 x x))))
(-.f32 #s(literal 0 binary32) (log.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x))))
(+.f32 (log.f32 (.f32 (+.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))) (neg.f32 (log.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))))
(+.f32 (log.f32 (.f32 (+.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))) (log.f32 (/.f32 #s(literal 1 binary32) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))))
(+.f32 (log.f32 (fma.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x))) (neg.f32 (log.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (*.f32 x x)))))
(+.f32 (log.f32 (fma.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x))) (log.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (*.f32 x x)))))
(neg.f32 (log.f32 (/.f32 #s(literal 1 binary32) (+.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x))))
(.f32 (/.f32 (.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))) (.f32 (fma.f32 x x (.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (+.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))) (fma.f32 x x (.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (+.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x))))
(.f32 (/.f32 (fma.f32 (.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))) #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (.f32 (.f32 x x) x)) (.f32 (fma.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x) (.f32 x x)) (-.f32 (.f32 x x) (.f32 #s(approx (sqrt (- ( x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x))))) (-.f32 (.f32 x x) (.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x))))
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(/.f32 (.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (sqrt.f32 (fma.f32 (.f32 (*.f32 x x) x) x #s(literal -1 binary32)))) (sqrt.f32 (fma.f32 x x #s(literal 1 binary32))))
(/.f32 (.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (sqrt.f32 (fma.f32 (.f32 (.f32 (.f32 x x) x) x) (.f32 x x) #s(literal -1 binary32)))) (sqrt.f32 (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))))
(/.f32 (*.f32 (+.f32 #s(literal 1 binary32) x) (fma.f32 x x #s(literal -1 binary32))) (+.f32 #s(literal 1 binary32) x))
(/.f32 (*.f32 (-.f32 x #s(literal 1 binary32)) (fma.f32 x x #s(literal -1 binary32))) (-.f32 x #s(literal 1 binary32)))
(/.f32 (*.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 x #s(literal 1 binary32))) (-.f32 x #s(literal 1 binary32)))
(/.f32 (*.f32 (fma.f32 x x #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) x)) (+.f32 #s(literal 1 binary32) x))
(/.f32 (-.f32 (.f32 (/.f32 (.f32 (.f32 (.f32 x x) x) x) (fma.f32 x x #s(literal 1 binary32))) (/.f32 (.f32 (.f32 (.f32 x x) x) x) (fma.f32 x x #s(literal 1 binary32)))) (.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32))))) (fma.f32 (/.f32 (.f32 (.f32 x x) x) (fma.f32 x x #s(literal 1 binary32))) x (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(/.f32 (-.f32 (.f32 (/.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32)))) (.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))))) (+.f32 (/.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32)))))
(/.f32 (-.f32 (pow.f32 (/.f32 (.f32 (.f32 (.f32 x x) x) x) (fma.f32 x x #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (.f32 (.f32 (.f32 x x) x) x) (fma.f32 x x #s(literal 1 binary32))) (/.f32 (.f32 (.f32 (.f32 x x) x) x) (fma.f32 x x #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32))) (.f32 (/.f32 (.f32 (.f32 (*.f32 x x) x) x) (fma.f32 x x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))))
(/.f32 (-.f32 (pow.f32 (/.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) #s(literal 3 binary32))) (fma.f32 (/.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) (fma.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (/.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32)))))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 (.f32 x x) x) x #s(literal -1 binary32)))) (neg.f32 (-.f32 #s(literal -1 binary32) (*.f32 x x))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 (.f32 (.f32 (.f32 x x) x) x) (.f32 x x) #s(literal -1 binary32)))) (neg.f32 (neg.f32 (fma.f32 (*.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32)))))
(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 x x) x) x))) (neg.f32 (-.f32 #s(literal -1 binary32) (.f32 x x))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) (fma.f32 x x #s(literal 1 binary32))) (fma.f32 x x #s(literal 1 binary32))) (*.f32 (fma.f32 x x #s(literal 1 binary32)) (fma.f32 x x #s(literal 1 binary32))))
(/.f32 (-.f32 (.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32))) (.f32 (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32)) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))))
(/.f32 (-.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 x x) x) x)) (-.f32 #s(literal -1 binary32) (.f32 x x)))
(/.f32 (neg.f32 (fma.f32 (.f32 (.f32 x x) x) x #s(literal -1 binary32))) (-.f32 #s(literal -1 binary32) (*.f32 x x)))
(/.f32 (neg.f32 (fma.f32 (.f32 (.f32 (.f32 x x) x) x) (.f32 x x) #s(literal -1 binary32))) (neg.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32))))))
(/.f32 (neg.f32 (fma.f32 (.f32 (.f32 (.f32 x x) x) x) (.f32 x x) #s(literal -1 binary32))) (neg.f32 (fma.f32 (*.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))))
(/.f32 (fma.f32 (.f32 (.f32 x x) x) x #s(literal -1 binary32)) (fma.f32 x x #s(literal 1 binary32)))
(/.f32 (fma.f32 (.f32 (.f32 (.f32 x x) x) x) (.f32 x x) #s(literal -1 binary32)) (+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)))))
(/.f32 (fma.f32 (.f32 (.f32 (.f32 x x) x) x) (.f32 x x) #s(literal -1 binary32)) (fma.f32 (*.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32)))
(/.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1 binary32))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(literal -1 binary32) (.f32 x x)) (-.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 x x) x) x))))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)))) (fma.f32 (.f32 (.f32 (.f32 x x) x) x) (.f32 x x) #s(literal -1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32))))
(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal -1 binary32) (.f32 x x))) (/.f32 (.f32 (.f32 (.f32 x x) x) x) (-.f32 #s(literal -1 binary32) (*.f32 x x))))
(-.f32 (/.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (+.f32 #s(literal 1 binary32) (.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32))))) (/.f32 #s(literal 1 binary32) (+.f32 #s(literal 1 binary32) (.f32 (*.f32 x x) (fma.f32 x x #s(literal 1 binary32))))))
(-.f32 (/.f32 (.f32 (.f32 (*.f32 x x) x) x) (fma.f32 x x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32))))
(-.f32 (/.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))))
(-.f32 (*.f32 x x) #s(literal 1 binary32))
(fma.f32 (/.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (.f32 (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32)) (fma.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x) #s(literal -1 binary32)))) (fma.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x) #s(literal -1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32)))))
(fma.f32 (/.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (fma.f32 (.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (.f32 (.f32 (.f32 x x) x) x)) (.f32 x x) (.f32 (.f32 (fma.f32 x x #s(literal 1 binary32)) (fma.f32 x x #s(literal 1 binary32))) (fma.f32 x x #s(literal 1 binary32))))) (fma.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) (.f32 (.f32 x x) x)) x (.f32 (fma.f32 x x #s(literal 1 binary32)) (-.f32 (fma.f32 x x #s(literal 1 binary32)) (.f32 (.f32 (.f32 x x) x) x)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32)))))
(fma.f32 (/.f32 (.f32 (.f32 (.f32 x x) x) x) (-.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 x x) x) x))) (-.f32 #s(literal 1 binary32) (*.f32 x x)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (/.f32 (.f32 (.f32 (.f32 x x) x) x) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x))) (+.f32 #s(literal 1 binary32) (.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) x) x)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (/.f32 (.f32 (.f32 (.f32 x x) x) x) (fma.f32 (.f32 (.f32 (.f32 x x) x) x) (.f32 x x) #s(literal 1 binary32))) (-.f32 (fma.f32 (.f32 (.f32 x x) x) x #s(literal 1 binary32)) (.f32 x x)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (/.f32 (.f32 (.f32 (.f32 x x) x) x) (fma.f32 (.f32 (*.f32 x x) x) x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (*.f32 (neg.f32 x) #s(literal -1 binary32)) x #s(literal -1 binary32))
(fma.f32 (/.f32 (.f32 (.f32 x x) x) (fma.f32 x x #s(literal 1 binary32))) x (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (/.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32))) (/.f32 (.f32 x x) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (/.f32 x (fma.f32 x x #s(literal 1 binary32))) (/.f32 (.f32 (.f32 x x) x) #s(literal 1 binary32)) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (exp.f32 (log.f32 x)) (exp.f32 (log.f32 x)) #s(literal -1 binary32))
(fma.f32 (-.f32 x #s(literal 1 binary32)) #s(literal 1 binary32) (*.f32 (-.f32 x #s(literal 1 binary32)) x))
(fma.f32 (-.f32 x #s(literal 1 binary32)) x (*.f32 (-.f32 x #s(literal 1 binary32)) #s(literal 1 binary32)))
(fma.f32 (+.f32 #s(literal 1 binary32) x) x (*.f32 (+.f32 #s(literal 1 binary32) x) #s(literal -1 binary32)))
(fma.f32 (*.f32 (neg.f32 x) x) #s(literal -1 binary32) #s(literal -1 binary32))
(fma.f32 (.f32 (.f32 (*.f32 x x) x) x) (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(fma.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (/.f32 #s(literal 1 binary32) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32)))))
(fma.f32 (neg.f32 x) (*.f32 x #s(literal -1 binary32)) #s(literal -1 binary32))
(fma.f32 (neg.f32 x) (neg.f32 x) #s(literal -1 binary32))
(fma.f32 #s(literal -1 binary32) (*.f32 (neg.f32 x) x) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (-.f32 x #s(literal 1 binary32)) (*.f32 x (-.f32 x #s(literal 1 binary32))))
(fma.f32 #s(literal 1 binary32) (*.f32 x x) #s(literal -1 binary32))
(fma.f32 (*.f32 x x) #s(literal 1 binary32) #s(literal -1 binary32))
(fma.f32 x (neg.f32 (*.f32 x #s(literal -1 binary32))) #s(literal -1 binary32))
(fma.f32 x (-.f32 x #s(literal 1 binary32)) (*.f32 #s(literal 1 binary32) (-.f32 x #s(literal 1 binary32))))
(fma.f32 x (+.f32 #s(literal 1 binary32) x) (*.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) x)))
(fma.f32 x x #s(literal -1 binary32))
(pow.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32))) #s(literal -1 binary32))
(pow.f32 (*.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32))) #s(literal 1/2 binary32))
(pow.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 2 binary32))
(pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1 binary32))
(fabs.f32 (fma.f32 x x #s(literal -1 binary32)))
(+.f32 (.f32 #s(literal 1 binary32) (-.f32 x #s(literal 1 binary32))) (.f32 x (-.f32 x #s(literal 1 binary32))))
(+.f32 (.f32 x (-.f32 x #s(literal 1 binary32))) (.f32 #s(literal 1 binary32) (-.f32 x #s(literal 1 binary32))))
(+.f32 (.f32 x (+.f32 #s(literal 1 binary32) x)) (.f32 #s(literal -1 binary32) (+.f32 #s(literal 1 binary32) x)))
(+.f32 (.f32 (-.f32 x #s(literal 1 binary32)) #s(literal 1 binary32)) (.f32 (-.f32 x #s(literal 1 binary32)) x))
(+.f32 (.f32 (-.f32 x #s(literal 1 binary32)) x) (.f32 (-.f32 x #s(literal 1 binary32)) #s(literal 1 binary32)))
(+.f32 (.f32 (+.f32 #s(literal 1 binary32) x) x) (.f32 (+.f32 #s(literal 1 binary32) x) #s(literal -1 binary32)))
(+.f32 (/.f32 (.f32 (.f32 (*.f32 x x) x) x) (fma.f32 x x #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal 1 binary32)))))
(+.f32 (/.f32 (.f32 (.f32 (.f32 (.f32 (.f32 x x) x) x) x) x) (fma.f32 (.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (*.f32 x x) (fma.f32 x x #s(literal 1 binary32)) #s(literal 1 binary32)))))
(+.f32 #s(literal -1 binary32) (*.f32 x x))
(+.f32 (*.f32 x x) #s(literal -1 binary32))
(exp.f32 (.f32 (log.f32 (.f32 (fma.f32 x x #s(literal -1 binary32)) (fma.f32 x x #s(literal -1 binary32)))) #s(literal 1/2 binary32)))
(exp.f32 (.f32 (.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 1/2 binary32)) #s(literal 2 binary32)))
(exp.f32 (*.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 1 binary32)))
(exp.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))))
(neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 x x)))

eval203.0ms (4.7%)

Memory: -4.3MiB live, 79.6MiB allocated
Compiler: Compiled 14 902 to 1 917 computations (87.1% saved)

prune495.0ms (11.5%)

Memory

14.4MiB live, 231.9MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	547	0	547
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	547	3	550

Accuracy

100.0%

Counts

550 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

54.3%

(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))

✓

99.2%

(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))

✓

98.2%

(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))

Compiler

Compiled 57 to 36 computations (36.8% saved)

regimes102.0ms (2.4%)

Memory

-20.7MiB live, 18.0MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Outputs
(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))

Calls

3 calls:

98.0ms	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
2.0ms	x
2.0ms	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
99.2%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes4.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))

Outputs
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))

Calls

3 calls:

1.0ms	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
1.0ms	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
1.0ms	x

Results

Accuracy	Segments	Branch
98.2%	1	`x`
98.2%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
98.2%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

simplify6.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary32`
8×	`*-commutative_binary32`
8×	`sub-neg_binary32`
6×	`neg-sub0_binary32`
6×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	28
1	23	28
2	31	28
3	37	28
4	42	28
5	44	28

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))

Outputs

(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))

(log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))) x))

(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))

soundness294.0ms (6.8%)

Memory

-32.5MiB live, 166.3MiB allocated

Rules

10 204×	`lower-fma.f64`
10 204×	`lower-fma.f32`
3 650×	`lower-*.f64`
3 650×	`lower-*.f32`
2 854×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	559
1	411	533
2	1146	526
3	3331	488
4	7979	488
0	8531	459

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 21 to 14 computations (33.3% saved)

preprocess93.0ms (2.1%)

Memory: 16.1MiB live, 97.7MiB allocated
Compiler: Compiled 76 to 50 computations (34.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample466.0ms (10.8%)

explain137.0ms (3.2%)

preprocess298.0ms (6.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify271.0ms (6.3%)

localize51.0ms (1.2%)

series6.0ms (0.1%)

simplify219.0ms (5.1%)

rewrite286.0ms (6.6%)

eval156.0ms (3.6%)

prune120.0ms (2.8%)

simplify296.0ms (6.9%)

localize222.0ms (5.1%)

series7.0ms (0.2%)

simplify249.0ms (5.8%)

rewrite339.0ms (7.8%)

eval203.0ms (4.7%)

prune495.0ms (11.5%)

regimes102.0ms (2.4%)

regimes4.0ms (0.1%)

simplify6.0ms (0.1%)

soundness294.0ms (6.8%)

preprocess93.0ms (2.1%)

end0.0ms (0%)

Profiling