Metrics for Rust f32::acosh

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB 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)

sample482.0ms (7.7%)

Memory

7.4MiB live, 557.7MiB allocated

Samples

288.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 154.0ms

ival-acosh: 97.0ms (62.9% of total)

ival->=: 47.0ms (30.5% of total)

exact: 6.0ms (3.9% of total)

ival-assert: 4.0ms (2.6% of total)

Bogosity

explain260.0ms (4.1%)

Memory

-32.3MiB live, 187.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
129	-	-	`(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))`
1	-	-	`(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	129	0
↳	`(*.f32 x x)`	overflow	129
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	129
`log.f32`	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`	oflow-rescue	1	0
↳	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`	overflow	1
↳	`(*.f32 x x)`	overflow	129
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	129

Confusion

	Predicted +	Predicted -
+	129	0
-	0	127

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	129	0	0
-	0	0	127

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	127
1	128
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

190.0ms

512×

valid

Compiler

Compiled 80 to 25 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 179.0ms

ival-log: 166.0ms (92.9% of total)

ival-mult: 4.0ms (2.2% of total)

ival-sub: 3.0ms (1.7% of total)

ival-sqrt: 3.0ms (1.7% of total)

ival-add: 2.0ms (1.1% of total)

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

exact: 0.0ms (0% of total)

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

preprocess462.0ms (7.4%)

Memory

19.0MiB live, 545.7MiB 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 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))

Compiler

Compiled 10 to 7 computations (30% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB 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
▶	52.8%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify579.0ms (9.2%)

Memory

-0.2MiB live, 459.5MiB 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 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
(+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
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)

localize50.0ms (0.8%)

Memory

7.6MiB live, 44.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(-.f32 (*.f32 x x) #s(literal 1 binary32))
accuracy	0.015625	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
accuracy	0.12861739147530546	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
accuracy	13.932351690314892	(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))

Samples

43.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 31.0ms (82.4% of total)

ival-log: 3.0ms (8% of total)

ival-sqrt: 2.0ms (5.3% of total)

ival-sub: 1.0ms (2.7% of total)

ival-add: 1.0ms (2.7% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

10.8MiB live, 10.8MiB 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 (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 (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 (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 (+ (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 (+ (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 (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 (* 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 (/ 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 (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 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 (* -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

12 calls:

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

simplify418.0ms (6.7%)

Memory

-5.8MiB live, 320.3MiB 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	1143	526
3	3327	488
4	7966	488
0	8526	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)
(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))))
(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 (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)))))
(+ (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))))
(+ (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)))))))
(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))))))))
(* 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)))))
(/ 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))
(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))))))
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)))))
(* -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))
(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))
(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 (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (*.f32 x #s(literal 1/6 binary32)) #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 x (fma.f32 (/.f32 #s(literal -1 binary32) (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (.f32 x #s(literal -1/6 binary32)) #s(literal -1 binary32)) (.f32 (.f32 x (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) (.f32 (*.f32 x x) #s(literal 3/40 binary32)))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f32 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (/.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 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (/.f32 (+.f32 #s(literal -1/4 binary32) (/.f32 #s(literal -3/32 binary32) (.f32 x x))) (.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 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (+.f32 (/.f32 (+.f32 #s(literal -3/32 binary32) (/.f32 #s(literal -5/96 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) (/.f32 #s(literal -1/4 binary32) (*.f32 x x)))))
(+ (log -1/2) (log (/ -1 x)))
(+.f32 (log.f32 #s(literal -1/2 binary32)) (neg.f32 (log.f32 (neg.f32 x))))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f32 (/.f32 #s(literal 1/4 binary32) (*.f32 x x)) (+.f32 (log.f32 #s(literal -1/2 binary32)) (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 (neg.f32 (log.f32 (neg.f32 x))) (/.f32 #s(literal 3/32 binary32) (.f32 x (.f32 x (.f32 x x))))) (+.f32 (/.f32 #s(literal 1/4 binary32) (.f32 x x)) (log.f32 #s(literal -1/2 binary32))))
(+ (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 (log.f32 #s(literal -1/2 binary32)) (neg.f32 (log.f32 (neg.f32 x)))) (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 x (.f32 x (.f32 x x)))) (+.f32 (/.f32 #s(literal 1/4 binary32) (.f32 x x)) (/.f32 #s(literal 5/96 binary32) (pow.f32 x #s(literal 6 binary32))))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ x (sqrt -1))
(+.f32 x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f32 x (fma.f32 x (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) #s(literal 1 binary32)) (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 x (fma.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (*.f32 x #s(literal 1/8 binary32)) #s(literal 1/2 binary32)) #s(literal 1 binary32)) (sqrt.f32 #s(literal -1 binary32)))
(* 2 x)
(*.f32 x #s(literal 2 binary32))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) x))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 x #s(literal 2 binary32) (/.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 x (+.f32 #s(literal 2 binary32) (/.f32 (+.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x))))) (/.f32 #s(literal -1/2 binary32) x))
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f32 (-.f32 #s(literal 1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 (+.f32 #s(literal 1/8 binary32) (/.f32 #s(literal 1/16 binary32) (.f32 x x))) (.f32 x x))) 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 #s(literal 1/2 binary32) (+.f32 (/.f32 #s(literal 1/8 binary32) (.f32 x x)) (/.f32 (+.f32 #s(literal 1/16 binary32) (/.f32 #s(literal 5/128 binary32) (.f32 x x))) (.f32 x (.f32 x (*.f32 x x)))))) x)
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 x (*.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) #s(literal 1/2 binary32)) (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 x (.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (.f32 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 x (fma.f32 x (/.f32 (.f32 (.f32 (.f32 x x) #s(literal 1/16 binary32)) (.f32 x x)) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) (.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 x (.f32 x #s(literal 1/8 binary32)) #s(literal 1/2 binary32)))) (sqrt.f32 #s(literal -1 binary32)))
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 #s(literal 1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) x))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+.f32 (/.f32 #s(literal -1/2 binary32) x) (fma.f32 x (/.f32 (+.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.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 #s(literal 1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) 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 x (/.f32 (+.f32 #s(literal 1/8 binary32) (/.f32 #s(literal 1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) (-.f32 (/.f32 #s(literal 1/2 binary32) x) x))

rewrite685.0ms (10.9%)

Memory

-23.3MiB live, 326.1MiB 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
(neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 x x)))
(exp.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32))))
(exp.f32 (*.f32 (neg.f32 (log.f32 (fma.f32 x x #s(literal -1 binary32)))) #s(literal -1 binary32)))
(+.f32 (*.f32 x x) #s(literal -1 binary32))
(+.f32 #s(literal -1 binary32) (*.f32 x x))
(+.f32 (+.f32 x #s(literal -1 binary32)) (*.f32 x (+.f32 x #s(literal -1 binary32))))
(+.f32 (/.f32 (.f32 x (.f32 x (.f32 x (.f32 x (.f32 x x))))) (fma.f32 x x (fma.f32 (.f32 x x) (.f32 x x) #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x (fma.f32 (.f32 x x) (*.f32 x x) #s(literal 1 binary32))))))
(+.f32 (/.f32 (.f32 x (.f32 x (*.f32 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 x #s(literal 1 binary32)) x) (.f32 (+.f32 x #s(literal 1 binary32)) #s(literal -1 binary32)))
(+.f32 (.f32 (+.f32 x #s(literal -1 binary32)) x) (.f32 (+.f32 x #s(literal -1 binary32)) #s(literal 1 binary32)))
(+.f32 (.f32 (+.f32 x #s(literal -1 binary32)) #s(literal 1 binary32)) (.f32 (+.f32 x #s(literal -1 binary32)) x))
(+.f32 (.f32 x (+.f32 x #s(literal 1 binary32))) (.f32 #s(literal -1 binary32) (+.f32 x #s(literal 1 binary32))))
(+.f32 (*.f32 x (+.f32 x #s(literal -1 binary32))) (+.f32 x #s(literal -1 binary32)))
(fabs.f32 (fma.f32 x x #s(literal -1 binary32)))
(pow.f32 (fma.f32 x x #s(literal -1 binary32)) #s(literal 1 binary32))
(pow.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) #s(literal 2 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 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32))) #s(literal -1 binary32))
(pow.f32 (sqrt.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) #s(literal 4 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 1/4 binary32))
(pow.f32 (/.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x #s(literal -1 binary32))) #s(literal 1 binary32)) #s(literal -1 binary32))
(pow.f32 (/.f32 (fma.f32 x (.f32 x (.f32 x x)) (-.f32 #s(literal 1 binary32) (.f32 (.f32 x x) #s(literal -1 binary32)))) (fma.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x))) #s(literal -1 binary32))) #s(literal -1 binary32))
(pow.f32 (exp.f32 #s(literal 1/2 binary32)) (*.f32 #s(literal 2 binary32) (log.f32 (fma.f32 x x #s(literal -1 binary32)))))
(pow.f32 (exp.f32 #s(literal 2 binary32)) (*.f32 #s(literal 1/2 binary32) (log.f32 (fma.f32 x x #s(literal -1 binary32)))))
(pow.f32 (exp.f32 #s(literal 1 binary32)) (log.f32 (fma.f32 x x #s(literal -1 binary32))))
(fma.f32 x x #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 x #s(literal -1 binary32)) (+.f32 x #s(literal -1 binary32)))
(fma.f32 x (/.f32 (.f32 x (.f32 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)))))
(fma.f32 (*.f32 x x) #s(literal 1 binary32) #s(literal -1 binary32))
(fma.f32 (.f32 x x) (/.f32 (.f32 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)))))
(fma.f32 (.f32 x x) (/.f32 (.f32 x (.f32 x (.f32 x x))) (fma.f32 x x (fma.f32 (.f32 x x) (.f32 x x) #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x (fma.f32 (.f32 x x) (.f32 x x) #s(literal 1 binary32))))))
(fma.f32 #s(literal 1 binary32) (*.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 (fma.f32 x x #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (+.f32 x #s(literal 1 binary32))) (*.f32 x (+.f32 x #s(literal -1 binary32))))
(fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (/.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (+.f32 x #s(literal 1 binary32))) (*.f32 x (+.f32 x #s(literal -1 binary32))))
(fma.f32 (.f32 x (.f32 x x)) (/.f32 x (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 x (.f32 x x)) (/.f32 (.f32 x (.f32 x x)) (fma.f32 x x (fma.f32 (.f32 x x) (.f32 x x) #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x (fma.f32 (.f32 x x) (.f32 x x) #s(literal 1 binary32))))))
(fma.f32 (.f32 x (.f32 x (.f32 x (.f32 x (.f32 x x))))) (/.f32 #s(literal 1 binary32) (fma.f32 x x (fma.f32 (.f32 x x) (.f32 x x) #s(literal 1 binary32)))) (neg.f32 (/.f32 #s(literal 1 binary32) (fma.f32 x x (fma.f32 (.f32 x x) (*.f32 x x) #s(literal 1 binary32))))))
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(/.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
(/.f32 (sqrt.f32 (fma.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x))) #s(literal -1 binary32))) (sqrt.f32 (fma.f32 x x (fma.f32 (.f32 x x) (.f32 x x) #s(literal 1 binary32)))))
(/.f32 (sqrt.f32 (fma.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x))) #s(literal -1 binary32))) (sqrt.f32 (fma.f32 x (.f32 x (.f32 x x)) (-.f32 #s(literal 1 binary32) (.f32 (.f32 x x) #s(literal -1 binary32))))))
(/.f32 (sqrt.f32 (fma.f32 (.f32 x x) (.f32 x x) #s(literal -1 binary32))) (sqrt.f32 (fma.f32 x x #s(literal 1 binary32))))
(/.f32 (sqrt.f32 (neg.f32 (fma.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x))) #s(literal -1 binary32)))) (sqrt.f32 (neg.f32 (fma.f32 x x (fma.f32 (.f32 x x) (.f32 x x) #s(literal 1 binary32))))))
(/.f32 (sqrt.f32 (neg.f32 (fma.f32 (.f32 x x) (.f32 x x) #s(literal -1 binary32)))) (sqrt.f32 (neg.f32 (fma.f32 x x #s(literal 1 binary32)))))
(/.f32 (neg.f32 (sqrt.f32 (fma.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x))) #s(literal -1 binary32)))) (neg.f32 (sqrt.f32 (fma.f32 x x (fma.f32 (.f32 x x) (.f32 x x) #s(literal 1 binary32))))))
(/.f32 (neg.f32 (sqrt.f32 (fma.f32 (.f32 x x) (.f32 x x) #s(literal -1 binary32)))) (neg.f32 (sqrt.f32 (fma.f32 x x #s(literal 1 binary32)))))
(/.f32 (exp.f32 (.f32 #s(literal 1/2 binary32) (log.f32 (fma.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x))) #s(literal -1 binary32))))) (exp.f32 (.f32 #s(literal 1/2 binary32) (log1p.f32 (fma.f32 x x (.f32 x (.f32 x (*.f32 x x))))))))
(/.f32 (exp.f32 (.f32 #s(literal 1/2 binary32) (log.f32 (fma.f32 (.f32 x x) (.f32 x x) #s(literal -1 binary32))))) (exp.f32 (.f32 #s(literal 1/2 binary32) (log1p.f32 (*.f32 x x)))))
(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
(*.f32 (sqrt.f32 (+.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 x #s(literal -1 binary32))))
(*.f32 (sqrt.f32 (+.f32 x #s(literal -1 binary32))) (sqrt.f32 (+.f32 x #s(literal 1 binary32))))
(.f32 (sqrt.f32 (fma.f32 (.f32 x x) (.f32 x (.f32 x (.f32 x x))) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (fma.f32 x x (fma.f32 (.f32 x x) (*.f32 x x) #s(literal 1 binary32))))))
(.f32 (sqrt.f32 (fma.f32 (.f32 x x) (*.f32 x x) #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))

eval46.0ms (0.7%)

Memory: 3.4MiB live, 86.8MiB allocated
Compiler: Compiled 10 641 to 1 536 computations (85.6% saved)

prune142.0ms (2.3%)

Memory

-1.3MiB live, 164.4MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	361	6	367
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	362	6	368

Accuracy

100.0%

Counts

368 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.8%	(log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
▶	52.8%	(log.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
▶	52.8%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
▶	98.8%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))))
▶	97.5%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 x #s(literal 2 binary32))))
	97.0%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)))

Compiler

Compiled 114 to 74 computations (35.1% saved)

simplify231.0ms (3.7%)

Memory

5.9MiB live, 319.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
cost-diff	0	(sqrt.f32 x)
cost-diff	0	(log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
cost-diff	736	(fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
cost-diff	0	(+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
cost-diff	0	(/.f32 #s(literal 1 binary32) (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
cost-diff	0	(log.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
cost-diff	704	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))
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	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 x #s(literal 2 binary32)))
cost-diff	0	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 x #s(literal 2 binary32))))
cost-diff	64	(*.f32 x #s(literal 2 binary32))
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)))))

Rules

15 462×	`lower-fma.f64`
15 458×	`lower-fma.f32`
3 214×	`lower-+.f64`
3 206×	`lower-+.f32`
2 254×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	192
0	46	173
1	66	173
2	97	173
3	135	173
4	253	173
5	664	173
6	1991	173
7	5219	173
0	8587	173

Stop Event

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

Calls

Call 1

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

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

localize121.0ms (1.9%)

Memory

25.6MiB live, 145.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f32 x)
accuracy	0.0703125	(fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
accuracy	0.12861739147530546	(log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
accuracy	13.932351690314897	(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
accuracy	0.10603682499126074	(/.f32 #s(literal 1 binary32) (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
accuracy	0.12861739147530546	(log.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
accuracy	0.1875	(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))
accuracy	13.932351690314897	(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
accuracy	0	(fma.f32 x x #s(literal -1 binary32))
accuracy	0.015625	(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
accuracy	0.12861739147530546	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
accuracy	13.932351690314897	(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
accuracy	0	(*.f32 x #s(literal 2 binary32))
accuracy	0.12861739147530546	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 x #s(literal 2 binary32))))
accuracy	0.8366478517439814	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 x #s(literal 2 binary32)))
accuracy	0	(+.f32 x (/.f32 #s(literal -1/2 binary32) x))
accuracy	0.015625	(+.f32 x #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x))))
accuracy	0.12861739147530546	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))))
accuracy	0.35837428560533074	#s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))

Samples

47.0ms

256×

valid

Compiler

Compiled 184 to 27 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-log: 9.0ms (25.3% of total)

ival-div: 8.0ms (22.5% of total)

ival-add: 7.0ms (19.7% of total)

ival-mult: 5.0ms (14.1% of total)

ival-sqrt: 5.0ms (14.1% of total)

ival-sub: 1.0ms (2.8% of total)

exact: 1.0ms (2.8% of total)

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

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

series16.0ms (0.3%)

Memory

-9.5MiB live, 27.0MiB allocated

Counts

18 → 216

Calls

Call 1

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

Outputs
#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 (+ (log 2) (* -1 (log (/ 1 x)))) (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 (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2)))) (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>) () ())) ())
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#s(alt (- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (patch (log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (patch (log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) #<representation binary32>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f32 x) (patch (sqrt.f32 x) #<representation binary32>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f32 x) (patch (sqrt.f32 x) #<representation binary32>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f32 x) (patch (sqrt.f32 x) #<representation binary32>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f32 x) (patch (sqrt.f32 x) #<representation binary32>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f32 x) (patch (sqrt.f32 x) #<representation binary32>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f32 x) (patch (sqrt.f32 x) #<representation binary32>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f32 x) (patch (sqrt.f32 x) #<representation binary32>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f32 x) (patch (sqrt.f32 x) #<representation binary32>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f32 x) (patch (sqrt.f32 x) #<representation binary32>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f32 x) (patch (sqrt.f32 x) #<representation binary32>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f32 x) (patch (sqrt.f32 x) #<representation binary32>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f32 x) (patch (sqrt.f32 x) #<representation binary32>) () ())) ())

Calls

54 calls:

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

simplify276.0ms (4.4%)

Memory

-7.7MiB live, 389.1MiB allocated

Algorithm

1×	egg-herbie

Rules

7 406×	`lower-fma.f64`
7 406×	`lower-fma.f32`
3 070×	`lower-/.f32`
3 070×	`lower-/.f64`
3 012×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	250	2698
1	691	2468
2	2116	2367
3	7100	2364
0	8265	2275

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 212

Calls

Call 1

Inputs
(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)))))
(+ (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))))
(+ (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)))))))
(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))))))))
(* 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)))))
(/ 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))
(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))))))
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)))))
(* -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))))))
(/ -1/2 x)
(/ (- (pow x 2) 1/2) x)
(/ (- (pow x 2) 1/2) x)
(/ (- (pow x 2) 1/2) x)
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)))))
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)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 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)))))
(+ (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))))
(+ (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)))))))
(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))))))))
(* 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)))))
(/ 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 (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)))))
(+ (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))))
(+ (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)))))))
(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))))))))
(* 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)))))
(/ 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))
(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))))))
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)))))
(* -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))))))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 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))))
(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))))
(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))))))))
(* 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)))))
(/ 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 (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)))))
(+ (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))))
(+ (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 (sqrt -1))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (/ 1 (sqrt -1)))
(+ (* x (- (* 1/2 (/ x (pow (sqrt -1) 3))) (/ 1 (pow (sqrt -1) 2)))) (/ 1 (sqrt -1)))
(+ (* x (- (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/2 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (pow (sqrt -1) 2)))) (/ 1 (sqrt -1)))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (* 1/8 (/ 1 (pow x 2))))) x)
(/ (+ 1/2 (+ (/ 1/16 (pow x 4)) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (* 1/2 (/ 1 (pow x 2)))) 2)))
(* -1 (* x (- (+ (/ 1/8 (pow x 4)) (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) 2)))
(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))))))))
(* 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)))))
(/ 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))
(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))))))))
(* 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)))))
(* -1 (* x (+ 1 (pow (sqrt -1) 2))))
(* -1 (* x (- (+ 1 (pow (sqrt -1) 2)) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) (pow (sqrt -1) 2)))))
(* -1 (* x (- (+ 1 (+ (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4))) (pow (sqrt -1) 2))) (* 1/2 (/ 1 (pow x 2))))))
(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)))))
(+ (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))))
(+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x)))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (pow (sqrt -1) 2))))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

Outputs
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 x (fma.f32 #s(literal 1/6 binary32) (*.f32 x (/.f32 x (sqrt.f32 #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (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 x (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (/.f32 #s(literal 3/40 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32)))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)) (/.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 #s(literal 2 binary32)) (log.f32 x)) (/.f32 (+.f32 #s(literal -1/4 binary32) (/.f32 #s(literal -3/32 binary32) (.f32 x x))) (.f32 x x)))
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(+.f32 (-.f32 (log.f32 #s(literal 0 binary32)) (neg.f32 (log.f32 (neg.f32 x)))) (+.f32 (/.f32 (.f32 (/.f32 #s(literal 3 binary32) #s(literal 0 binary32)) #s(literal -1/12 binary32)) (.f32 (.f32 x x) (.f32 x x))) (/.f32 #s(literal -1/2 binary32) #s(literal 0 binary32))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(+.f32 (-.f32 (log.f32 #s(literal 0 binary32)) (neg.f32 (log.f32 (neg.f32 x)))) (+.f32 (/.f32 (.f32 (/.f32 #s(literal 3 binary32) #s(literal 0 binary32)) #s(literal -1/12 binary32)) (.f32 (.f32 x x) (.f32 x x))) (fma.f32 #s(literal -1/720 binary32) (/.f32 (fma.f32 #s(literal 2 binary32) (/.f32 #s(literal 45 binary32) #s(literal 0 binary32)) (/.f32 #s(literal 30 binary32) #s(literal 0 binary32))) (pow.f32 x #s(literal 6 binary32))) (/.f32 #s(literal -1/2 binary32) #s(literal 0 binary32)))))
(sqrt x)
(sqrt.f32 x)
(sqrt x)
(sqrt.f32 x)
(sqrt x)
(sqrt.f32 x)
(sqrt x)
(sqrt.f32 x)
(sqrt x)
(sqrt.f32 x)
(sqrt x)
(sqrt.f32 x)
(sqrt x)
(sqrt.f32 x)
(sqrt x)
(sqrt.f32 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f32 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f32 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f32 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f32 x)

rewrite411.0ms (6.6%)

Memory

9.6MiB live, 694.6MiB allocated

Rules

14 088×	`lower-fma.f64`
14 084×	`lower-fma.f32`
4 492×	`lower-*.f64`
4 490×	`lower-*.f32`
2 988×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	160
0	46	141
1	167	141
2	1039	141
0	8757	141

Stop Event

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

Counts

18 → 1 116

Calls

Call 1

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

Outputs
(neg.f32 (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 #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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 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)))))
(+.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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 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 (.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)))))) (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 (.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)))))) (neg.f32 (log.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))))))
(-.f32 #s(literal 0 binary32) (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 #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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 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 #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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 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 (.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)))))) (log.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 #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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 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 x #s(approx (sqrt (- ( x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (neg.f32 (-.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 (.f32 (+.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))) (log.f32 (-.f32 #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x))) x)))
(/.f32 (-.f32 (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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 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 #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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 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 #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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 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 (-.f32 (pow.f32 (log.f32 (.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(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 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)))))) (log.f32 (.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)))))) (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 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)))))) (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 #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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 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 #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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 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 (-.f32 (.f32 (log.f32 (.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)))))) (log.f32 (.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))))))) (.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 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)))))) (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)))))
(neg.f32 (/.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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x))) (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)))))
(neg.f32 (/.f32 (.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))))) (neg.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))))))
(neg.f32 (/.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))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x)))) (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 (/.f32 (.f32 (+.f32 x #s(approx (sqrt (- ( x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))) (neg.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))))))
(+.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)
(+.f32 (/.f32 (.f32 x x) (-.f32 x #s(approx (sqrt (- ( x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x))))) (neg.f32 (/.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)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))))))
(pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 x #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x))))) #s(literal -1 binary32))
(fma.f32 x #s(literal 1 binary32) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x))))
(fma.f32 x (pow.f32 #s(literal 1 binary32) #s(literal 1/2 binary32)) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x))))
(fma.f32 (.f32 x x) (/.f32 #s(literal 1 binary32) (-.f32 x #s(approx (sqrt (- ( x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x))))) (neg.f32 (/.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)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))))))
(fma.f32 #s(literal 1 binary32) x #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x))))
(fma.f32 #s(literal -1 binary32) (neg.f32 x) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x))))
(fma.f32 (sqrt.f32 x) (sqrt.f32 x) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x))))
(fma.f32 (sqrt.f32 x) (.f32 (sqrt.f32 x) #s(literal 1 binary32)) #s(approx (sqrt (- ( x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x))))
(fma.f32 (sqrt.f32 x) (neg.f32 (neg.f32 (sqrt.f32 x))) #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x))))
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(/.f32 (-.f32 (pow.f32 (log.f32 (fma.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (.f32 x (.f32 x x)))) #s(literal 3 binary32)) (pow.f32 (log.f32 (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32)))) #s(literal 3 binary32))) (fma.f32 (log.f32 (fma.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (.f32 x (.f32 x x)))) (log.f32 (fma.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (.f32 x (.f32 x x)))) (fma.f32 (log.f32 (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32)))) (log.f32 (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32)))) (.f32 (log.f32 (fma.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (.f32 x (*.f32 x x)))) (log.f32 (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32))))))))
(/.f32 (-.f32 (pow.f32 (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal 1 binary32)))) #s(literal 3 binary32)) (pow.f32 (log.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) #s(literal 3 binary32))) (fma.f32 (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal 1 binary32)))) (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal 1 binary32)))) (fma.f32 (log.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (log.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (*.f32 (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal 1 binary32)))) (log.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))))
(/.f32 (-.f32 (pow.f32 (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal -1 binary32)))) #s(literal 3 binary32)) (pow.f32 (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) #s(literal 3 binary32))) (fma.f32 (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal -1 binary32)))) (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal -1 binary32)))) (fma.f32 (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (*.f32 (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal -1 binary32)))) (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))))
(/.f32 (-.f32 (.f32 (log.f32 #s(literal -1 binary32)) (log.f32 #s(literal -1 binary32))) (.f32 (neg.f32 (log.f32 (-.f32 (neg.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) (neg.f32 (log.f32 (-.f32 (neg.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))) (neg.f32 (log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(/.f32 (-.f32 (.f32 (log.f32 (fma.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (.f32 x (.f32 x x)))) (log.f32 (fma.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (.f32 x (.f32 x x))))) (.f32 (log.f32 (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32)))) (log.f32 (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32)))))) (+.f32 (log.f32 (fma.f32 (fma.f32 x x #s(literal -1 binary32)) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (.f32 x (.f32 x x)))) (log.f32 (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32))))))
(/.f32 (-.f32 (.f32 (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal 1 binary32)))) (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal 1 binary32))))) (.f32 (log.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) (log.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))) (+.f32 (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal 1 binary32)))) (log.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(/.f32 (-.f32 (.f32 (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal -1 binary32)))) (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal -1 binary32))))) (.f32 (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))) (+.f32 (log.f32 (fma.f32 x x (fma.f32 x (neg.f32 x) #s(literal -1 binary32)))) (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(*.f32 #s(literal 1 binary32) (log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))
(*.f32 #s(literal -1 binary32) (neg.f32 (log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(*.f32 (neg.f32 (log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) #s(literal -1 binary32))
(*.f32 (neg.f32 (neg.f32 (pow.f32 (log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))) #s(literal 3 binary32)))) (/.f32 #s(literal 1 binary32) (pow.f32 (neg.f32 (log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) #s(literal 2 binary32))))
(*.f32 (neg.f32 (pow.f32 (neg.f32 (log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))) #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (neg.f32 (log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))))))
(log.f32 (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
(exp.f32 (*.f32 #s(literal 1/2 binary32) (log.f32 x)))
(exp.f32 (.f32 (.f32 #s(literal 2 binary32) (log.f32 x)) #s(literal 1/4 binary32)))
(exp.f32 (.f32 (.f32 #s(literal 1/2 binary32) (log.f32 x)) #s(literal 1 binary32)))
(fabs.f32 (sqrt.f32 x))
(fabs.f32 (neg.f32 (sqrt.f32 x)))
(pow.f32 x #s(literal 1/2 binary32))
(pow.f32 (*.f32 x x) #s(literal 1/4 binary32))
(pow.f32 (sqrt.f32 x) #s(literal 1 binary32))
(pow.f32 (.f32 x (.f32 x (*.f32 x x))) #s(literal 1/8 binary32))
(pow.f32 (sqrt.f32 (sqrt.f32 x)) #s(literal 2 binary32))
(sqrt.f32 x)
(*.f32 (sqrt.f32 x) (pow.f32 #s(literal 1 binary32) #s(literal 1/4 binary32)))
(*.f32 (sqrt.f32 (sqrt.f32 x)) (sqrt.f32 (sqrt.f32 x)))
(*.f32 (pow.f32 #s(literal 1 binary32) #s(literal 1/4 binary32)) (sqrt.f32 x))
(.f32 (pow.f32 (sqrt.f32 x) #s(literal 1/4 binary32)) (pow.f32 (.f32 x (sqrt.f32 x)) #s(literal 1/4 binary32)))
(.f32 (pow.f32 (.f32 x (sqrt.f32 x)) #s(literal 1/4 binary32)) (pow.f32 (sqrt.f32 x) #s(literal 1/4 binary32)))
(*.f32 (pow.f32 (sqrt.f32 (sqrt.f32 x)) #s(literal 1 binary32)) (pow.f32 (sqrt.f32 (sqrt.f32 x)) #s(literal 1 binary32)))

eval182.0ms (2.9%)

Memory: -8.0MiB live, 312.6MiB allocated
Compiler: Compiled 36 834 to 3 675 computations (90% saved)

prune221.0ms (3.5%)

Memory

22.2MiB live, 453.0MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	1 682	3	1 685
Fresh	1	0	1
Picked	0	5	5
Done	0	0	0
Total	1 683	8	1 691

Accuracy

100.0%

Counts

1 691 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.8%	(log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
✓	52.8%	(log.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
✓	52.8%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
✓	98.8%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))))
▶	44.3%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))
▶	1.3%	(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))
✓	97.5%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 x #s(literal 2 binary32))))
▶	97.0%	#s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)))

Compiler

Compiled 70 to 45 computations (35.7% saved)

simplify212.0ms (3.4%)

Memory

-13.8MiB live, 195.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Rules

15 444×	`lower-fma.f64`
15 444×	`lower-fma.f32`
3 218×	`lower-+.f64`
3 214×	`lower-+.f32`
2 254×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	127
0	38	115
1	56	115
2	83	115
3	120	115
4	232	115
5	641	115
6	1964	115
7	5180	115
0	8544	109

Stop Event

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

Calls

Call 1

Inputs
#s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(log.f32 #s(literal 2 binary32))
#s(literal 2 binary32)
(log.f32 x)
x
(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))
#s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32))
#s(literal 0 binary32)
(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))
(+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))
x
#s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))
#s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))
(/.f32 #s(literal -1/2 binary32) x)
#s(literal -1/2 binary32)

Outputs
#s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(log.f32 #s(literal 2 binary32))
#s(literal 2 binary32)
(log.f32 x)
x
(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))
#s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32))
#s(literal 0 binary32)
(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))
(+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))
x
#s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))
#s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))
(/.f32 #s(literal -1/2 binary32) x)
#s(literal -1/2 binary32)

localize70.0ms (1.1%)

Memory

-24.1MiB live, 132.6MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.015625	(+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))
accuracy	0.12861739147530546	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))
accuracy	0.35837428560533074	#s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))
accuracy	30.98239722078972	#s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))
accuracy	0.12861739147530546	(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))
accuracy	30.5651631191705	#s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32))
accuracy	0	(log.f32 x)
accuracy	0	(log.f32 #s(literal 2 binary32))
accuracy	0.26953125	(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
accuracy	0.6825803691367809	#s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)))

Samples

46.0ms

256×

valid

Compiler

Compiled 85 to 28 computations (67.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-log: 11.0ms (30.5% of total)

ival-add: 7.0ms (19.4% of total)

ival-sqrt: 7.0ms (19.4% of total)

ival-div: 5.0ms (13.9% of total)

ival-mult: 3.0ms (8.3% of total)

ival-sub: 1.0ms (2.8% of total)

exact: 1.0ms (2.8% of total)

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

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

series105.0ms (1.7%)

Memory

15.2MiB live, 121.2MiB allocated

Counts

10 → 108

Calls

Call 1

Inputs
#s(alt #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) (patch #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) #<representation binary32>) () ())
#s(alt (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)) (patch (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)) #<representation binary32>) () ())
#s(alt (log.f32 #s(literal 2 binary32)) (patch (log.f32 #s(literal 2 binary32)) #<representation binary32>) () ())
#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())
#s(alt (log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32))) (patch (log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32))) #<representation binary32>) () ())
#s(alt #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)) (patch #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)) #<representation binary32>) () ())
#s(alt (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) (patch (log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) #<representation binary32>) () ())
#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) #<representation binary32>) () ())
#s(alt #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #<representation binary32>) () ())
#s(alt #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) #<representation binary32>) () ())

Outputs
#s(alt (log (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) (patch #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) (patch #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 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 #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) (patch #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 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 #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) (patch #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) (patch #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) #<representation binary32>) () ())) ())
#s(alt (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) (patch #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) #<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 #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) (patch #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) #<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 #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) (patch #s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))) #<representation binary32>) () ())) ())
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#s(alt (+ x (sqrt -1)) (taylor 0 x) (#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) #<representation binary32>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) #<representation binary32>) () ())) ())
#s(alt (* x (- 2 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) #<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 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) #<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 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (patch (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (* 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #<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 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #<representation binary32>) () ())) ())
#s(alt (/ -1/2 x) (taylor 0 x) (#s(alt #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (- (pow x 2) 1/2) x) (taylor 0 x) (#s(alt #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (- (pow x 2) 1/2) x) (taylor 0 x) (#s(alt #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (/ (- (pow x 2) 1/2) x) (taylor 0 x) (#s(alt #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) #<representation binary32>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 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 #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 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 #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 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 #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) (patch #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)) #<representation binary32>) () ())) ())

Calls

27 calls:

Time	Variable		Point	Expression
42.0ms	x	@	0	(+ (log 2) (log x))
16.0ms	x	@	inf	(+ (log 2) (log x))
13.0ms	x	@	-inf	(+ (log 2) (log x))
0.0ms	x	@	0	(log x)
0.0ms	x	@	-inf	(log (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))))

simplify166.0ms (2.6%)

Memory

33.2MiB live, 270.4MiB allocated

Algorithm

1×	egg-herbie

Rules

6 008×	`lower-fma.f64`
6 008×	`lower-fma.f32`
2 950×	`lower-*.f64`
2 950×	`lower-*.f32`
1 966×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	211	1406
1	586	1219
2	1773	1163
0	5209	1123

Stop Event

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

Counts

108 → 105

Calls

Call 1

Inputs
(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)))))
(+ (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))))
(+ (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)))))))
(+ (log 2) (log x))
(+ (log 2) (log x))
(+ (log 2) (log x))
(+ (log 2) (log x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(log x)
(log x)
(log x)
(log x)
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (* -1 (log (/ -1 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)))))
(+ (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))))
(+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x)))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (pow (sqrt -1) 2))))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(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))))))))
(* 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)))))
(* -1 (* x (+ 1 (pow (sqrt -1) 2))))
(* -1 (* x (- (+ 1 (pow (sqrt -1) 2)) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) (pow (sqrt -1) 2)))))
(* -1 (* x (- (+ 1 (+ (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4))) (pow (sqrt -1) 2))) (* 1/2 (/ 1 (pow x 2))))))
(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)))))
(+ (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))))
(+ (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)))))))
(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))))))))
(* 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)))))
(/ 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))
(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))))))
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)))))
(* -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))))))
(/ -1/2 x)
(/ (- (pow x 2) 1/2) x)
(/ (- (pow x 2) 1/2) x)
(/ (- (pow x 2) 1/2) x)
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)))))
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)))

Outputs
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 x (fma.f32 x (*.f32 x (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (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 x (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (/.f32 #s(literal 3/40 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32)))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)) (/.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 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (/.f32 (+.f32 #s(literal -1/4 binary32) (/.f32 #s(literal -3/32 binary32) (.f32 x x))) (.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 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)) (/.f32 #s(literal -1/4 binary32) (.f32 x x))) (/.f32 (+.f32 #s(literal -3/32 binary32) (/.f32 #s(literal -5/96 binary32) (.f32 x x))) (.f32 x (.f32 x (*.f32 x x)))))
(+ (log -1/2) (log (/ -1 x)))
(+.f32 (log.f32 #s(literal -1/2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f32 (/.f32 #s(literal 1/4 binary32) (*.f32 x x)) (+.f32 (log.f32 #s(literal -1/2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f32 (log.f32 #s(literal -1/2 binary32)) (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (+.f32 (/.f32 #s(literal 1/4 binary32) (.f32 x x)) (/.f32 #s(literal 3/32 binary32) (.f32 x (.f32 x (.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 #s(literal 1/4 binary32) (.f32 x x)) (+.f32 (log.f32 #s(literal -1/2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))) (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 x (.f32 x (.f32 x x)))) (/.f32 #s(literal 5/96 binary32) (pow.f32 x #s(literal 6 binary32)))))
(+ (log 2) (log x))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (log x))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (log x))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (log x))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+.f32 (log.f32 #s(literal 2 binary32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+.f32 (log.f32 #s(literal 2 binary32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+.f32 (log.f32 #s(literal 2 binary32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+.f32 (log.f32 #s(literal 2 binary32)) (-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))))
(log x)
(log.f32 x)
(log x)
(log.f32 x)
(log x)
(log.f32 x)
(log x)
(log.f32 x)
(* -1 (log (/ 1 x)))
(log.f32 x)
(* -1 (log (/ 1 x)))
(log.f32 x)
(* -1 (log (/ 1 x)))
(log.f32 x)
(* -1 (log (/ 1 x)))
(log.f32 x)
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -1 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 x (fma.f32 x (*.f32 x (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (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 x (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (/.f32 #s(literal 3/40 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32)))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)) (/.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 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (/.f32 (+.f32 #s(literal -1/4 binary32) (/.f32 #s(literal -3/32 binary32) (.f32 x x))) (.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 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)) (/.f32 #s(literal -1/4 binary32) (.f32 x x))) (/.f32 (+.f32 #s(literal -3/32 binary32) (/.f32 #s(literal -5/96 binary32) (.f32 x x))) (.f32 x (.f32 x (*.f32 x x)))))
(+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal 0 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x)))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (pow (sqrt -1) 2))))))
(+.f32 (-.f32 (log.f32 #s(literal 0 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))) (/.f32 #s(literal -1/2 binary32) #s(literal 0 binary32)))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(+.f32 (log.f32 #s(literal 0 binary32)) (+.f32 (-.f32 (/.f32 (.f32 #s(literal 2 binary32) (/.f32 #s(literal -1/8 binary32) #s(literal 0 binary32))) (.f32 x (.f32 x (.f32 x x)))) (log.f32 (/.f32 #s(literal -1 binary32) x))) (/.f32 #s(literal -1/2 binary32) #s(literal 0 binary32))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(+.f32 (-.f32 (log.f32 #s(literal 0 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))) (+.f32 (/.f32 (.f32 #s(literal 2 binary32) (/.f32 #s(literal -1/8 binary32) #s(literal 0 binary32))) (.f32 x (.f32 x (.f32 x x)))) (fma.f32 #s(literal -1/720 binary32) (/.f32 (fma.f32 #s(literal 2 binary32) (/.f32 #s(literal 45 binary32) #s(literal 0 binary32)) (/.f32 #s(literal 30 binary32) #s(literal 0 binary32))) (pow.f32 x #s(literal 6 binary32))) (/.f32 #s(literal -1/2 binary32) #s(literal 0 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 x (fma.f32 x (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) #s(literal 1 binary32)) (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 x (fma.f32 x (fma.f32 #s(literal 1/8 binary32) (*.f32 x (/.f32 x (sqrt.f32 #s(literal -1 binary32)))) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) #s(literal 1 binary32)) (sqrt.f32 #s(literal -1 binary32)))
(* 2 x)
(*.f32 x #s(literal 2 binary32))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f32 x (+.f32 #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) (.f32 x x))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1/2 binary32) (/.f32 #s(literal -1/8 binary32) (.f32 x x))) x) (.f32 x #s(literal 2 binary32)))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f32 x (+.f32 (+.f32 #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) (.f32 x x))) (/.f32 (+.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x))))))
(* -1 (* x (+ 1 (pow (sqrt -1) 2))))
#s(literal 0 binary32)
(* -1 (* x (- (+ 1 (pow (sqrt -1) 2)) (* 1/2 (/ 1 (pow x 2))))))
(.f32 x (/.f32 #s(literal 1/2 binary32) (.f32 x x)))
(* -1 (* x (+ 1 (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) (pow (sqrt -1) 2)))))
(neg.f32 (.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1/2 binary32) (/.f32 #s(literal -1/8 binary32) (.f32 x x))) x)))
(* -1 (* x (- (+ 1 (+ (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4))) (pow (sqrt -1) 2))) (* 1/2 (/ 1 (pow x 2))))))
(neg.f32 (.f32 x (+.f32 (/.f32 (+.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) (/.f32 #s(literal -1/2 binary32) (.f32 x x)))))
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 x (fma.f32 x (*.f32 x (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (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 x (fma.f32 (.f32 x x) (fma.f32 (.f32 x x) (/.f32 #s(literal 3/40 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32)))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)) (/.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 (log.f32 #s(literal 2 binary32)) (+.f32 (log.f32 x) (/.f32 (+.f32 #s(literal -1/4 binary32) (/.f32 #s(literal -3/32 binary32) (.f32 x x))) (.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 (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)) (/.f32 #s(literal -1/4 binary32) (.f32 x x))) (/.f32 (+.f32 #s(literal -3/32 binary32) (/.f32 #s(literal -5/96 binary32) (.f32 x x))) (.f32 x (.f32 x (*.f32 x x)))))
(+ (log -1/2) (log (/ -1 x)))
(+.f32 (log.f32 #s(literal -1/2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f32 (/.f32 #s(literal 1/4 binary32) (*.f32 x x)) (+.f32 (log.f32 #s(literal -1/2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f32 (log.f32 #s(literal -1/2 binary32)) (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (+.f32 (/.f32 #s(literal 1/4 binary32) (.f32 x x)) (/.f32 #s(literal 3/32 binary32) (.f32 x (.f32 x (.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 #s(literal 1/4 binary32) (.f32 x x)) (+.f32 (log.f32 #s(literal -1/2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))) (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 x (.f32 x (.f32 x x)))) (/.f32 #s(literal 5/96 binary32) (pow.f32 x #s(literal 6 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 x (fma.f32 x (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) #s(literal 1 binary32)) (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 x (fma.f32 x (fma.f32 #s(literal 1/8 binary32) (*.f32 x (/.f32 x (sqrt.f32 #s(literal -1 binary32)))) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) #s(literal 1 binary32)) (sqrt.f32 #s(literal -1 binary32)))
(* 2 x)
(*.f32 x #s(literal 2 binary32))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f32 x (+.f32 #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) (.f32 x x))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1/2 binary32) (/.f32 #s(literal -1/8 binary32) (.f32 x x))) x) (.f32 x #s(literal 2 binary32)))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f32 x (+.f32 (+.f32 #s(literal 2 binary32) (/.f32 #s(literal -1/2 binary32) (.f32 x x))) (/.f32 (+.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x))))))
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f32 (+.f32 #s(literal 1/2 binary32) (/.f32 #s(literal 1/8 binary32) (*.f32 x x))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(neg.f32 (/.f32 (+.f32 #s(literal -1/2 binary32) (/.f32 (+.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x x))) 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 #s(literal 1/2 binary32) (/.f32 #s(literal 1/8 binary32) (.f32 x x))) (/.f32 (+.f32 #s(literal 1/16 binary32) (/.f32 #s(literal 5/128 binary32) (.f32 x x))) (.f32 x (.f32 x (*.f32 x x))))) x)
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 x (*.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) #s(literal 1/2 binary32)) (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 x (.f32 x (fma.f32 #s(literal 1/8 binary32) (.f32 x (/.f32 x (sqrt.f32 #s(literal -1 binary32)))) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 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 x (.f32 x (fma.f32 (.f32 x x) (fma.f32 (*.f32 x x) (/.f32 #s(literal 1/16 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) (/.f32 #s(literal 1/8 binary32) (sqrt.f32 #s(literal -1 binary32)))) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))))) (sqrt.f32 #s(literal -1 binary32)))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x)
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) x) x)
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x (+.f32 (/.f32 (+.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) (/.f32 #s(literal -1/2 binary32) (*.f32 x x))) x)
(* -1 x)
(neg.f32 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(fma.f32 x (/.f32 #s(literal 1/2 binary32) (*.f32 x x)) (neg.f32 x))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(neg.f32 (fma.f32 #s(literal 1 binary32) (/.f32 (+.f32 #s(literal -1/2 binary32) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) x) x))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(neg.f32 (fma.f32 x (+.f32 (/.f32 (+.f32 #s(literal -1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x (.f32 x (.f32 x x)))) (/.f32 #s(literal -1/2 binary32) (*.f32 x x))) x))
(/ -1/2 x)
(/.f32 #s(literal -1/2 binary32) x)
(/ (- (pow x 2) 1/2) x)
(+.f32 x (/.f32 #s(literal -1/2 binary32) x))
(/ (- (pow x 2) 1/2) x)
(+.f32 x (/.f32 #s(literal -1/2 binary32) x))
(/ (- (pow x 2) 1/2) x)
(+.f32 x (/.f32 #s(literal -1/2 binary32) x))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x)
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x)
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 x (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x)
x
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f32 x (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f32 x (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f32 x (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x)

rewrite320.0ms (5.1%)

Memory

-21.8MiB live, 415.2MiB allocated

Rules

12 640×	`lower-fma.f64`
12 640×	`lower-fma.f32`
4 494×	`lower-*.f64`
4 494×	`lower-*.f32`
3 020×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	119
0	38	105
1	150	105
2	1027	105
0	8418	99

Stop Event

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

Counts

10 → 142

Calls

Call 1

Inputs
#s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(log.f32 #s(literal 2 binary32))
(log.f32 x)
(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))
#s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32))
(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))
(+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))
#s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))
#s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))

Outputs
#s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (log.f32 (*.f32 x #s(literal 2 binary32))))
(neg.f32 (/.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32))) (neg.f32 (fma.f32 (log.f32 x) (log.f32 (/.f32 x #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))))))
(neg.f32 (/.f32 (.f32 (log.f32 (.f32 x #s(literal 2 binary32))) (log.f32 (/.f32 #s(literal 2 binary32) x))) (neg.f32 (log.f32 (/.f32 #s(literal 2 binary32) x)))))
(neg.f32 (/.f32 (neg.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32)))) (fma.f32 (log.f32 x) (log.f32 (/.f32 x #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))))
(neg.f32 (/.f32 (neg.f32 (.f32 (log.f32 (.f32 x #s(literal 2 binary32))) (log.f32 (/.f32 #s(literal 2 binary32) x)))) (log.f32 (/.f32 #s(literal 2 binary32) x))))
(+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(+.f32 (*.f32 (log.f32 x) #s(literal 1/2 binary32)) (fma.f32 (log.f32 x) #s(literal 1/2 binary32) (log.f32 #s(literal 2 binary32))))
(+.f32 (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (neg.f32 (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x)))))
(+.f32 (log.f32 (.f32 #s(literal 2 binary32) (sqrt.f32 x))) (.f32 (log.f32 x) #s(literal 1/2 binary32)))
(+.f32 (+.f32 (log.f32 #s(literal 2 binary32)) (.f32 (log.f32 x) #s(literal 1/2 binary32))) (.f32 (log.f32 x) #s(literal 1/2 binary32)))
(pow.f32 (/.f32 #s(literal 1 binary32) (log.f32 (*.f32 x #s(literal 2 binary32)))) #s(literal -1 binary32))
(fma.f32 #s(literal 1 binary32) (log.f32 x) (log.f32 #s(literal 2 binary32)))
(fma.f32 #s(literal 1 binary32) (*.f32 (log.f32 x) #s(literal 1/2 binary32)) (fma.f32 (log.f32 x) #s(literal 1/2 binary32) (log.f32 #s(literal 2 binary32))))
(fma.f32 #s(literal 2 binary32) (*.f32 (log.f32 x) #s(literal 1/2 binary32)) (log.f32 #s(literal 2 binary32)))
(fma.f32 #s(literal 2 binary32) (.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) #s(literal 1/2 binary32)) (fma.f32 (log.f32 x) #s(literal 1/2 binary32) (log.f32 #s(literal 2 binary32))))
(fma.f32 (log.f32 x) #s(literal 1/2 binary32) (fma.f32 (log.f32 x) #s(literal 1/2 binary32) (log.f32 #s(literal 2 binary32))))
(fma.f32 #s(literal 1/2 binary32) (log.f32 x) (fma.f32 (log.f32 x) #s(literal 1/2 binary32) (log.f32 #s(literal 2 binary32))))
(fma.f32 #s(literal 1/2 binary32) (*.f32 #s(literal 2 binary32) (log.f32 x)) (log.f32 #s(literal 2 binary32)))
(fma.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (/.f32 #s(literal 1 binary32) (log.f32 (/.f32 #s(literal 2 binary32) x))) (neg.f32 (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x)))))
(fma.f32 (*.f32 (log.f32 x) #s(literal 1/2 binary32)) #s(literal 2 binary32) (log.f32 #s(literal 2 binary32)))
(fma.f32 #s(literal 1/4 binary32) (*.f32 #s(literal 2 binary32) (log.f32 x)) (fma.f32 (log.f32 x) #s(literal 1/2 binary32) (log.f32 #s(literal 2 binary32))))
(-.f32 (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))))
(-.f32 (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 x #s(literal 2 binary32)))) (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 x #s(literal 2 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (log.f32 (*.f32 x #s(literal 2 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (/.f32 #s(literal 1 binary32) (log.f32 (*.f32 x #s(literal 2 binary32)))) #s(literal 1 binary32)))
(/.f32 #s(literal 1 binary32) (/.f32 (+.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (*.f32 (log.f32 #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x)))) (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32)))))
(/.f32 #s(literal 1 binary32) (/.f32 (log.f32 (/.f32 x #s(literal 2 binary32))) (.f32 (log.f32 (.f32 x #s(literal 2 binary32))) (log.f32 (/.f32 x #s(literal 2 binary32))))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (log.f32 (*.f32 x #s(literal 2 binary32))))))
(/.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32))) (fma.f32 (log.f32 x) (log.f32 (/.f32 x #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))))
(/.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32))) (+.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (*.f32 (log.f32 #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x)))))
(/.f32 (.f32 (log.f32 (.f32 x #s(literal 2 binary32))) (log.f32 (/.f32 #s(literal 2 binary32) x))) (log.f32 (/.f32 #s(literal 2 binary32) x)))
(/.f32 (neg.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32)))) (neg.f32 (fma.f32 (log.f32 x) (log.f32 (/.f32 x #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))))
(/.f32 (neg.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32)))) (neg.f32 (+.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (*.f32 (log.f32 #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))))))
(/.f32 (neg.f32 (.f32 (log.f32 (.f32 x #s(literal 2 binary32))) (log.f32 (/.f32 #s(literal 2 binary32) x)))) (neg.f32 (log.f32 (/.f32 #s(literal 2 binary32) x))))
(/.f32 (.f32 (log.f32 (.f32 x #s(literal 2 binary32))) (log.f32 (/.f32 x #s(literal 2 binary32)))) (log.f32 (/.f32 x #s(literal 2 binary32))))
(/.f32 (-.f32 (.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (.f32 (log.f32 (/.f32 #s(literal 2 binary32) x)) (pow.f32 (log.f32 x) #s(literal 2 binary32)))) (*.f32 (log.f32 (/.f32 #s(literal 2 binary32) x)) (log.f32 (/.f32 #s(literal 2 binary32) x))))
(/.f32 (neg.f32 (neg.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32))))) (neg.f32 (neg.f32 (fma.f32 (log.f32 x) (log.f32 (/.f32 x #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))))))
(/.f32 (neg.f32 (neg.f32 (.f32 (log.f32 (.f32 x #s(literal 2 binary32))) (log.f32 (/.f32 #s(literal 2 binary32) x))))) (neg.f32 (neg.f32 (log.f32 (/.f32 #s(literal 2 binary32) x)))))
(/.f32 (neg.f32 (.f32 (log.f32 (.f32 x #s(literal 2 binary32))) (log.f32 (/.f32 x #s(literal 2 binary32))))) (neg.f32 (log.f32 (/.f32 x #s(literal 2 binary32)))))
(/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) #s(literal 3 binary32)) (pow.f32 (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) #s(literal 3 binary32))) (fma.f32 (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (fma.f32 (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (*.f32 (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x)))))))
(/.f32 (-.f32 (.f32 (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x)))) (.f32 (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))))) (+.f32 (/.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))) (/.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x)))))
(.f32 #s(literal 1 binary32) (log.f32 (.f32 x #s(literal 2 binary32))))
(.f32 (log.f32 (.f32 x #s(literal 2 binary32))) (*.f32 (log.f32 (/.f32 #s(literal 2 binary32) x)) (/.f32 #s(literal 1 binary32) (log.f32 (/.f32 #s(literal 2 binary32) x)))))
(*.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (log.f32 x) (log.f32 (/.f32 x #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32)))))
(.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (log.f32 x) #s(literal 2 binary32)) (.f32 (log.f32 #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal 2 binary32) x))))))
(.f32 (fma.f32 (log.f32 x) (log.f32 (/.f32 x #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))) (.f32 (log.f32 (*.f32 x #s(literal 2 binary32))) (/.f32 #s(literal 1 binary32) (fma.f32 (log.f32 x) (log.f32 (/.f32 x #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))))))
(.f32 (.f32 (log.f32 (*.f32 x #s(literal 2 binary32))) (log.f32 (/.f32 #s(literal 2 binary32) x))) (/.f32 #s(literal 1 binary32) (log.f32 (/.f32 #s(literal 2 binary32) x))))
(*.f32 (neg.f32 (+.f32 (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 3 binary32)) (pow.f32 (log.f32 x) #s(literal 3 binary32)))) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 (log.f32 x) (log.f32 (/.f32 x #s(literal 2 binary32))) (pow.f32 (log.f32 #s(literal 2 binary32)) #s(literal 2 binary32))))))
(.f32 (neg.f32 (.f32 (log.f32 (*.f32 x #s(literal 2 binary32))) (log.f32 (/.f32 #s(literal 2 binary32) x)))) (/.f32 #s(literal 1 binary32) (neg.f32 (log.f32 (/.f32 #s(literal 2 binary32) x)))))
(.f32 (.f32 (log.f32 (*.f32 x #s(literal 2 binary32))) (log.f32 (/.f32 x #s(literal 2 binary32)))) (/.f32 #s(literal 1 binary32) (log.f32 (/.f32 x #s(literal 2 binary32)))))
(log.f32 (*.f32 x #s(literal 2 binary32)))
(log.f32 #s(literal 2 binary32))
(+.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) (.f32 (log.f32 x) #s(literal 1/2 binary32)))
(fma.f32 #s(literal 1 binary32) (.f32 (log.f32 x) #s(literal 1/2 binary32)) (.f32 (log.f32 x) #s(literal 1/2 binary32)))
(fma.f32 #s(literal 2 binary32) (.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) #s(literal 1/2 binary32)) (*.f32 (log.f32 x) #s(literal 1/2 binary32)))
(fma.f32 (log.f32 x) #s(literal 1/2 binary32) (*.f32 (log.f32 x) #s(literal 1/2 binary32)))
(fma.f32 #s(literal 1/2 binary32) (log.f32 x) (*.f32 (log.f32 x) #s(literal 1/2 binary32)))
(fma.f32 #s(literal 1/4 binary32) (.f32 #s(literal 2 binary32) (log.f32 x)) (.f32 (log.f32 x) #s(literal 1/2 binary32)))
(/.f32 (+.f32 (pow.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) #s(literal 3 binary32)) (pow.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) #s(literal 3 binary32))) (fma.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) (.f32 (log.f32 x) #s(literal 1/2 binary32)) (-.f32 (.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) (.f32 (log.f32 x) #s(literal 1/2 binary32))) (.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) (.f32 (log.f32 x) #s(literal 1/2 binary32))))))
(/.f32 (-.f32 (.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) (.f32 (log.f32 x) #s(literal 1/2 binary32))) (.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) (.f32 (log.f32 x) #s(literal 1/2 binary32)))) (-.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) (.f32 (log.f32 x) #s(literal 1/2 binary32))))
(*.f32 #s(literal 1 binary32) (log.f32 x))
(.f32 #s(literal 2 binary32) (.f32 (log.f32 x) #s(literal 1/2 binary32)))
(.f32 #s(literal 1/2 binary32) (.f32 #s(literal 2 binary32) (log.f32 x)))
(.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) #s(literal 2 binary32))
(log.f32 x)
(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))
#s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32))
(neg.f32 (log.f32 (/.f32 #s(literal 1 binary32) (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))))
(+.f32 (log.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x)))) (log.f32 (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x) (*.f32 x x)))))
(+.f32 (log.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x)))) (neg.f32 (log.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x) (*.f32 x x)))))
(+.f32 (log.f32 (.f32 (+.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))) (log.f32 (/.f32 #s(literal 1 binary32) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))))
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(/.f32 #s(literal 1 binary32) (/.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 x (-.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))) (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x)))))
(/.f32 #s(literal 1 binary32) (/.f32 (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x) (.f32 (+.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x))))
(/.f32 #s(literal -1 binary32) (neg.f32 (/.f32 #s(literal 1 binary32) (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))))
(/.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x))) (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x) (*.f32 x x)))
(/.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x))) (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 x (-.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))))
(/.f32 (.f32 (+.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))
(/.f32 (neg.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x)))) (neg.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x) (*.f32 x x))))
(/.f32 (neg.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x)))) (neg.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 x (-.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))))))
(/.f32 (.f32 (+.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (neg.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))) (neg.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))))
(/.f32 (.f32 (+.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x)) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x))
(/.f32 (-.f32 (.f32 (.f32 x x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) (.f32 (-.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))) (.f32 (-.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))))
(/.f32 (neg.f32 (neg.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x))))) (neg.f32 (neg.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x) (*.f32 x x)))))
(/.f32 (neg.f32 (.f32 (+.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (neg.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))))) (neg.f32 (neg.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))))
(/.f32 (neg.f32 (.f32 (+.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x))) (neg.f32 (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x)))
(/.f32 (-.f32 (pow.f32 (/.f32 (.f32 x x) (-.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) #s(literal 3 binary32)) (pow.f32 (/.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) #s(literal 3 binary32))) (fma.f32 (/.f32 (.f32 x x) (-.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) (/.f32 (.f32 x x) (-.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) (fma.f32 (/.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) (/.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) (.f32 (/.f32 (.f32 x x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) (/.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))))))
(/.f32 (-.f32 (.f32 (/.f32 (.f32 x x) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) (/.f32 (.f32 x x) (-.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))) (.f32 (/.f32 (.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) (/.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))))) (+.f32 (/.f32 (.f32 x x) (-.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) (/.f32 (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))))
(.f32 #s(literal 1 binary32) (+.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))
(.f32 (+.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 (-.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (/.f32 #s(literal 1 binary32) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))))
(.f32 (fma.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x))) (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x) (*.f32 x x))))
(.f32 (fma.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x))) (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 x (-.f32 x #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))))))
(.f32 (fma.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x) (.f32 x x)) (.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (/.f32 #s(literal 1 binary32) (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x) (*.f32 x x)))))
(.f32 (.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))) (/.f32 #s(literal 1 binary32) (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))))
(.f32 (neg.f32 (fma.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (.f32 #s(approx (sqrt (- ( x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (.f32 x (.f32 x x)))) (/.f32 #s(literal 1 binary32) (neg.f32 (fma.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x) (*.f32 x x)))))
(.f32 (.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (neg.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))) (/.f32 #s(literal 1 binary32) (neg.f32 (-.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))))
(.f32 (.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x)) (/.f32 #s(literal 1 binary32) (-.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))) x)))
#s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))
#s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x))

eval21.0ms (0.3%)

Memory: 7.6MiB live, 43.7MiB allocated
Compiler: Compiled 5 024 to 565 computations (88.8% saved)

prune35.0ms (0.6%)

Memory

9.1MiB live, 86.6MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	0	0
Picked	0	3	3
Done	0	5	5
Total	247	8	255

Accuracy

100.0%

Counts

255 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.8%	(log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
✓	52.8%	(log.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
✓	52.8%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
✓	98.8%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (+.f32 x (/.f32 #s(literal -1/2 binary32) x)))))
✓	44.3%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))
✓	1.3%	(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))
✓	97.5%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 x #s(literal 2 binary32))))
✓	97.0%	#s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)))

Compiler

Compiled 148 to 78 computations (47.3% saved)

regimes11.0ms (0.2%)

Memory

20.5MiB live, 20.5MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 x #s(literal 2 binary32))))
(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (+ x (/ -1/2 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)))))
(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)))))
(log.f32 (/.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)))
#s(approx (log (/ 1 (/ 1 (+ x (sqrt (+ (* x x) -1)))))) (+.f32 (log.f32 #s(literal 2 binary32)) (log.f32 x)))

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

Calls

3 calls:

3.0ms	x
3.0ms	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
3.0ms	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
98.8%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

-31.7MiB live, 13.4MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))

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

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

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

Calls

3 calls:

4.0ms	(+.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
97.5%	1	`x`
97.5%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
97.5%	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

9.5MiB live, 9.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))

Outputs
(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))

Calls

3 calls:

1.0ms	x
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))))

Results

Accuracy	Segments	Branch
1.3%	1	`x`
1.3%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
1.3%	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

11.3MiB live, 11.3MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary32`
2×	`*-commutative_binary32`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	43
1	30	43

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 x #s(literal 2 binary32))))

(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))

Outputs

(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 x #s(literal 2 binary32))))

(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))

soundness648.0ms (10.3%)

Memory

-10.7MiB live, 354.2MiB allocated

Rules

10 204×	`lower-fma.f64`
10 204×	`lower-fma.f32`
7 406×	`lower-fma.f64`
7 406×	`lower-fma.f32`
4 994×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	559
1	411	533
2	1143	526
3	3327	488
4	7966	488
0	8526	459
0	250	2698
1	691	2468
2	2116	2367
3	7100	2364
0	8265	2275
0	7	28
0	12	28
1	49	28
2	322	28
3	3626	28
0	8646	24

Stop Event

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

Compiler

Compiled 68 to 39 computations (42.6% saved)

preprocess80.0ms (1.3%)

Memory: -16.0MiB live, 59.3MiB allocated
Compiler: Compiled 82 to 54 computations (34.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample482.0ms (7.7%)

explain260.0ms (4.1%)

preprocess462.0ms (7.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify579.0ms (9.2%)

localize50.0ms (0.8%)

series5.0ms (0.1%)

simplify418.0ms (6.7%)

rewrite685.0ms (10.9%)

eval46.0ms (0.7%)

prune142.0ms (2.3%)

simplify231.0ms (3.7%)

localize121.0ms (1.9%)

series16.0ms (0.3%)

simplify276.0ms (4.4%)

rewrite411.0ms (6.6%)

eval182.0ms (2.9%)

prune221.0ms (3.5%)

simplify212.0ms (3.4%)

localize70.0ms (1.1%)

series105.0ms (1.7%)

simplify166.0ms (2.6%)

rewrite320.0ms (5.1%)

eval21.0ms (0.3%)

prune35.0ms (0.6%)

regimes11.0ms (0.2%)

regimes8.0ms (0.1%)

regimes4.0ms (0.1%)

simplify6.0ms (0.1%)

soundness648.0ms (10.3%)

preprocess80.0ms (1.3%)

end0.0ms (0%)

Profiling