Metrics for Rust f32::acosh

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB 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)

sample577.0ms (8%)

Memory

6.1MiB live, 595.6MiB allocated

Samples

415.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 160.0ms

ival-acosh: 103.0ms (64.4% of total)

ival->=: 47.0ms (29.4% of total)

exact: 6.0ms (3.8% of total)

ival-assert: 3.0ms (1.9% of total)

Bogosity

explain104.0ms (1.4%)

Memory

-21.6MiB live, 174.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
122	-	-	`(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))`
3	-	-	`(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	122	0
↳	`(*.f32 x x)`	overflow	122
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	122
`log.f32`	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`	oflow-rescue	3	0
↳	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`	overflow	3
↳	`(*.f32 x x)`	overflow	122
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	122

Confusion

	Predicted +	Predicted -
+	122	0
-	0	134

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	122	0	0
-	0	0	134

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	134
1	119
2	3

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

37.0ms

512×

valid

Compiler

Compiled 80 to 25 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-sub: 8.0ms (33.8% of total)

ival-log: 5.0ms (21.1% of total)

ival-mult: 4.0ms (16.9% of total)

ival-sqrt: 3.0ms (12.7% of total)

ival-add: 2.0ms (8.4% of total)

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

exact: 0.0ms (0% of total)

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

preprocess380.0ms (5.2%)

Memory

35.9MiB live, 297.9MiB allocated

Algorithm

1×	egg-herbie

Rules

14 947×	`lower-fma.f64`
14 947×	`lower-fma.f32`
2 105×	`lower-*.f64`
2 104×	`lower-*.f32`
1 442×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 10 to 7 computations (30% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.4%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify357.0ms (4.9%)

Memory

-16.4MiB live, 346.7MiB 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

14 947×	`lower-fma.f64`
14 947×	`lower-fma.f32`
2 105×	`lower-*.f64`
2 104×	`lower-*.f32`
1 442×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

localize24.0ms (0.3%)

Memory

6.7MiB live, 43.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.01953125	(-.f32 (*.f32 x x) #s(literal 1 binary32))
accuracy	0.03125	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
accuracy	0.3546026397871381	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
accuracy	13.24518548426158	(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))

Samples

16.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 4.0ms (37.5% of total)

ival-log: 3.0ms (28.2% of total)

ival-sqrt: 2.0ms (18.8% of total)

ival-sub: 1.0ms (9.4% of total)

ival-add: 1.0ms (9.4% of total)

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

exact: 0.0ms (0% of total)

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

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)

simplify212.0ms (2.9%)

Memory

14.7MiB live, 240.6MiB allocated

Algorithm

1×	egg-herbie

Rules

5 102×	`lower-fma.f64`
5 102×	`lower-fma.f32`
1 825×	`lower-*.f64`
1 825×	`lower-*.f32`
1 427×	`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 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (fma.f32 (*.f32 x x) #s(literal 1/6 binary32) #s(literal 1 binary32)) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f32 (.f32 (.f32 x x) x) (.f32 (.f32 #s(literal 3/40 binary32) x) (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) (fma.f32 (fma.f32 (*.f32 x x) #s(literal 1/6 binary32) #s(literal 1 binary32)) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32)))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+.f32 (-.f32 (log.f32 x) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (log.f32 #s(literal 2 binary32)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(+.f32 (+.f32 (/.f32 (-.f32 (/.f32 #s(literal -3/32 binary32) (.f32 x x)) #s(literal 1/4 binary32)) (.f32 x x)) (log.f32 x)) (log.f32 #s(literal 2 binary32)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (-.f32 (log.f32 #s(literal 2 binary32)) (/.f32 #s(literal 1/4 binary32) (.f32 x x))) (-.f32 (/.f32 (+.f32 (/.f32 #s(literal 5/96 binary32) (.f32 x x)) #s(literal 3/32 binary32)) (.f32 (.f32 (*.f32 x x) x) x)) (log.f32 x)))
(+ (log -1/2) (log (/ -1 x)))
(+.f32 (neg.f32 (log.f32 (neg.f32 x))) (log.f32 #s(literal -1/2 binary32)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f32 (+.f32 (log.f32 #s(literal -1/2 binary32)) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (neg.f32 (log.f32 (neg.f32 x))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+.f32 (+.f32 (log.f32 #s(literal -1/2 binary32)) (/.f32 #s(literal 1/4 binary32) (.f32 x x))) (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 (.f32 (.f32 x x) x) x)) (neg.f32 (log.f32 (neg.f32 x)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 (.f32 (.f32 x x) x) x)) (log.f32 #s(literal -1/2 binary32))) (+.f32 (+.f32 (/.f32 #s(literal 5/96 binary32) (pow.f32 x #s(literal 6 binary32))) (/.f32 #s(literal 1/4 binary32) (.f32 x x))) (neg.f32 (log.f32 (neg.f32 x)))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ x (sqrt -1))
(+.f32 (sqrt.f32 #s(literal -1 binary32)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f32 (fma.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f32 (fma.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 (*.f32 x x) #s(literal 1/8 binary32) #s(literal 1/2 binary32)) #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(* 2 x)
(*.f32 #s(literal 2 binary32) x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 #s(literal 2 binary32) x (/.f32 #s(literal -1/2 binary32) x))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 #s(literal 2 binary32) x (/.f32 (-.f32 (/.f32 #s(literal -1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 (-.f32 #s(literal 2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (.f32 x x) x) x))) x (/.f32 #s(literal -1/2 binary32) x))
(/ 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 (/.f32 (-.f32 #s(literal 1/8 binary32) (/.f32 #s(literal -1/16 binary32) (.f32 x x))) (.f32 x x)) #s(literal -1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f32 (-.f32 (-.f32 (/.f32 (-.f32 #s(literal 1/16 binary32) (/.f32 #s(literal -5/128 binary32) (.f32 x x))) (.f32 (.f32 (.f32 x x) x) x)) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) #s(literal -1/2 binary32)) x)
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 (*.f32 #s(literal 1/2 binary32) (/.f32 x (sqrt.f32 #s(literal -1 binary32)))) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) x) (fma.f32 (.f32 x x) #s(literal 1/8 binary32) #s(literal 1/2 binary32)) (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (fma.f32 (.f32 (.f32 #s(literal 1/16 binary32) (.f32 x x)) (.f32 (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) x)) x (.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 (.f32 x x) #s(literal 1/8 binary32) #s(literal 1/2 binary32)))) x (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 (fma.f32 (/.f32 (-.f32 (/.f32 #s(literal -1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (.f32 x x) x) x)) x x) (/.f32 #s(literal 1/2 binary32) 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))))))
(-.f32 (/.f32 #s(literal 1/2 binary32) x) (fma.f32 (/.f32 (-.f32 (/.f32 #s(literal -1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (.f32 x x) x) x)) x x))

rewrite285.0ms (3.9%)

Memory

-18.4MiB live, 308.0MiB allocated

Rules

2 497×	`lower-fma.f64`
2 497×	`lower-fma.f32`
1 615×	`lower-*.f64`
1 614×	`lower-*.f32`
1 306×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 320

Calls

Call 1

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

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

eval43.0ms (0.6%)

Memory: 5.0MiB live, 90.5MiB allocated
Compiler: Compiled 10 641 to 1 522 computations (85.7% saved)

prune66.0ms (0.9%)

Memory

0.7MiB live, 158.3MiB 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
▶	98.9%	(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x))
▶	55.4%	(log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
▶	55.4%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
▶	97.6%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
▶	95.8%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
	96.1%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))

Compiler

Compiled 112 to 72 computations (35.7% saved)

simplify469.0ms (6.5%)

Memory

-32.0MiB live, 299.0MiB 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	(fma.f32 x x #s(literal -1 binary32))
cost-diff	0	(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
cost-diff	0	(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
cost-diff	0	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
cost-diff	0	(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
cost-diff	0	#s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))
cost-diff	0	(+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))
cost-diff	0	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
cost-diff	0	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
cost-diff	0	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
cost-diff	64	(*.f32 #s(literal 2 binary32) x)
cost-diff	0	(-.f32 x #s(literal 1 binary32))
cost-diff	0	(sqrt.f32 (-.f32 x #s(literal 1 binary32)))
cost-diff	0	(fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)
cost-diff	0	(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x))

Rules

13 450×	`lower-fma.f64`
13 447×	`lower-fma.f32`
1 637×	`lower-+.f64`
1 634×	`lower-+.f32`
1 312×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	178
0	51	167
1	69	167
2	99	167
3	159	167
4	285	167
5	800	167
6	2780	167
7	5156	167
0	8106	167

Stop Event

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

Calls

Call 1

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

localize108.0ms (1.5%)

Memory

39.1MiB live, 116.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f32 x)
accuracy	0.109375	(fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
accuracy	0.3546026397871381	(log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
accuracy	13.245185484261587	(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
accuracy	0	(fma.f32 x x #s(literal -1 binary32))
accuracy	0.03125	(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
accuracy	0.3546026397871381	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
accuracy	13.245185484261587	(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
accuracy	0	(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
accuracy	0.03125	(+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))
accuracy	0.3546026397871381	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
accuracy	0.5256262208294116	#s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))
accuracy	0	(*.f32 #s(literal 2 binary32) x)
accuracy	0.3546026397871381	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
accuracy	1.2196245706296336	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
accuracy	0	(sqrt.f32 (+.f32 #s(literal 1 binary32) x))
accuracy	0.00390625	(sqrt.f32 (-.f32 x #s(literal 1 binary32)))
accuracy	0.08203125	(fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)
accuracy	0.3546026397871381	(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x))

Samples

63.0ms

256×

valid

Compiler

Compiled 166 to 30 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-sqrt: 24.0ms (47% of total)

ival-log: 9.0ms (17.6% of total)

ival-add: 7.0ms (13.7% of total)

ival-mult: 6.0ms (11.7% of total)

ival-sub: 4.0ms (7.8% of total)

ival-div: 2.0ms (3.9% of total)

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

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

exact: 0.0ms (0% of total)

series44.0ms (0.6%)

Memory

-25.7MiB live, 16.0MiB allocated

Counts

19 → 228

Calls

Call 1

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

Outputs
#s(alt (log (sqrt -1)) (taylor 0 x) (#s(alt (log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)) (patch (log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt (log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)) (patch (log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) 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 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)) (patch (log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) 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 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)) (patch (log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt (log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)) (patch (log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)) #<representation binary32>) () ())) ())
#s(alt (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)) (patch (log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) 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 (log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)) (patch (log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x)) #<representation binary32>) () ())) ())
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#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 (taylor 0 x) (#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* 1/2 x)) (taylor 0 x) (#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* -1/8 x)))) (taylor 0 x) (#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (taylor inf x) (#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (taylor inf x) (#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))) (taylor inf x) (#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (taylor -inf x) (#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))) (taylor -inf x) (#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))) (taylor -inf x) (#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())) ())

Calls

57 calls:

Time	Variable		Point	Expression
28.0ms	x	@	-inf	(+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)
2.0ms	x	@	-inf	(sqrt (- x 1))
2.0ms	x	@	-inf	(log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x))
1.0ms	x	@	-inf	(log (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))))
1.0ms	x	@	-inf	(sqrt (+ 1 x))

simplify196.0ms (2.7%)

Memory

17.8MiB live, 206.2MiB allocated

Algorithm

1×	egg-herbie

Rules

6 098×	`lower-fma.f64`
6 098×	`lower-fma.f32`
2 159×	`lower-+.f64`
2 159×	`lower-+.f32`
1 596×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	372	3061
1	1057	2617
2	3492	2540
0	8323	2419

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 222

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 (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 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 (- (pow (sqrt -1) 2) 1)))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))
(* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
-1
(- x 1)
(- x 1)
(- x 1)
x
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
x
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* 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))))))
(/ -1/2 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)))
(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 (* 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)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))

Outputs
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
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(- (+ (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)) (/.f32 #s(literal -1/2 binary32) #s(literal 0 binary32))) (neg.f32 (log.f32 (neg.f32 x))))
(- (+ (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 (-.f32 (/.f32 (.f32 (/.f32 #s(literal 3 binary32) #s(literal 0 binary32)) #s(literal -1/12 binary32)) (.f32 (.f32 x x) (.f32 x x))) (neg.f32 (log.f32 (neg.f32 x)))) (-.f32 (/.f32 #s(literal -1/2 binary32) #s(literal 0 binary32)) (log.f32 #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 (fma.f32 (fma.f32 (/.f32 #s(literal -1/2 binary32) #s(literal 0 binary32)) #s(literal 75 binary32) (/.f32 #s(literal 45 binary32) #s(literal 0 binary32))) (/.f32 #s(literal -1/720 binary32) (pow.f32 x #s(literal 6 binary32))) (/.f32 (.f32 (/.f32 #s(literal 3 binary32) #s(literal 0 binary32)) #s(literal -1/12 binary32)) (.f32 (.f32 x x) (.f32 x x)))) (neg.f32 (log.f32 (neg.f32 x)))) (-.f32 (/.f32 #s(literal -1/2 binary32) #s(literal 0 binary32)) (log.f32 #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)
1
#s(literal 1 binary32)
(+ 1 (* 1/2 x))
(fma.f32 #s(literal 1/2 binary32) x #s(literal 1 binary32))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(fma.f32 (fma.f32 #s(literal -1/8 binary32) x #s(literal 1/2 binary32)) x #s(literal 1 binary32))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(fma.f32 (fma.f32 (fma.f32 #s(literal 1/16 binary32) x #s(literal -1/8 binary32)) x #s(literal 1/2 binary32)) x #s(literal 1 binary32))
(sqrt x)
(sqrt.f32 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (*.f32 x x) x))) #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 5 binary32)))) #s(literal -1/8 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (*.f32 x x) x))) #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) x)))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 7 binary32)))) #s(literal 1/16 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 5 binary32)))) #s(literal -1/8 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (*.f32 x x) x))) #s(literal 1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) x))))) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f32 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (*.f32 x x) x))) #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) x))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 5 binary32)))) #s(literal -1/8 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (*.f32 x x) x))) #s(literal -1/2 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) x)))) x)
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f32 (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 5 binary32)))) #s(literal 1/8 binary32) (fma.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (.f32 (*.f32 x x) x))) #s(literal 1/2 binary32) (fma.f32 (/.f32 #s(literal 1/16 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 7 binary32)))) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) x)))))) (neg.f32 x))

rewrite336.0ms (4.6%)

Memory

-10.3MiB live, 431.8MiB allocated

Rules

3 203×	`lower-fma.f64`
3 200×	`lower-fma.f32`
2 169×	`lower-/.f64`
2 168×	`lower-/.f32`
1 776×	`lower-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	153
0	51	154
1	186	136
2	1289	136
0	8338	136

Stop Event

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

Counts

19 → 936

Calls

Call 1

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

Outputs
(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
(/.f32 (-.f32 (pow.f32 (log.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x))) #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 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x))) (log.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x))) (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 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x))) (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))))
(/.f32 (-.f32 (pow.f32 (log.f32 (-.f32 (.f32 x x) (fma.f32 x 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 (-.f32 (.f32 x x) (fma.f32 x x #s(literal -1 binary32)))) (log.f32 (-.f32 (.f32 x x) (fma.f32 x 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 (-.f32 (*.f32 x x) (fma.f32 x 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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x 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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x 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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (*.f32 x 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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) #s(literal 3 binary32)) (pow.f32 (log.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))) #s(literal 3 binary32))) (fma.f32 (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (fma.f32 (log.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))) (log.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))) (.f32 (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (log.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (*.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))))))
(-.f32 (log.f32 (neg.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x)))) (log.f32 (neg.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(-.f32 (log.f32 (neg.f32 (-.f32 (*.f32 x x) (fma.f32 x x #s(literal -1 binary32))))) (log.f32 (neg.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(-.f32 (log.f32 (neg.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x)))) (log.f32 (neg.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 (neg.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x)))) (log.f32 (neg.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (*.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))))
(-.f32 (log.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x))) (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))
(-.f32 (log.f32 (-.f32 (*.f32 x x) (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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x 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 (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (log.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (*.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(-.f32 #s(literal 0 binary32) (log.f32 (/.f32 #s(literal 1 binary32) (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(+.f32 (log.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x))) (neg.f32 (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(+.f32 (log.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x))) (log.f32 (/.f32 #s(literal 1 binary32) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(+.f32 (log.f32 (-.f32 (*.f32 x x) (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 (log.f32 (-.f32 (*.f32 x x) (fma.f32 x x #s(literal -1 binary32)))) (log.f32 (/.f32 #s(literal 1 binary32) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(+.f32 (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (neg.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))))))
(+.f32 (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (neg.f32 (log.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (*.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))))
(+.f32 (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (log.f32 (/.f32 #s(literal 1 binary32) (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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (log.f32 (/.f32 #s(literal 1 binary32) (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (*.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))))
(neg.f32 (log.f32 (/.f32 #s(literal 1 binary32) (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(.f32 (neg.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x))) (/.f32 #s(literal 1 binary32) (neg.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(.f32 (neg.f32 (-.f32 (.f32 x x) (fma.f32 x x #s(literal -1 binary32)))) (/.f32 #s(literal 1 binary32) (neg.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(.f32 (neg.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (*.f32 x x) x))) (/.f32 #s(literal 1 binary32) (neg.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 (neg.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (/.f32 #s(literal 1 binary32) (neg.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))))
(.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x)) (/.f32 #s(literal 1 binary32) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))
(.f32 (-.f32 (.f32 x x) (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 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (*.f32 x x) x)) (/.f32 #s(literal 1 binary32) (fma.f32 x (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))) (fma.f32 x x #s(literal -1 binary32)))))
(.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x)) (/.f32 #s(literal 1 binary32) (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(*.f32 #s(literal 1 binary32) (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
(/.f32 (-.f32 (pow.f32 (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) #s(literal 3 binary32)) (pow.f32 (/.f32 (.f32 x x) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) #s(literal 3 binary32))) (fma.f32 (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (fma.f32 (/.f32 (.f32 x x) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (/.f32 (.f32 x x) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (.f32 (/.f32 (fma.f32 x x #s(literal -1 binary32)) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)) (/.f32 (*.f32 x x) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))))
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(+.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))))
(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
(/.f32 (-.f32 (pow.f32 (log.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x))) #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 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x))) (log.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (.f32 x x))) (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 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x))) (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))))
(/.f32 (-.f32 (pow.f32 (log.f32 (-.f32 (.f32 x x) (fma.f32 x 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 (-.f32 (.f32 x x) (fma.f32 x x #s(literal -1 binary32)))) (log.f32 (-.f32 (.f32 x x) (fma.f32 x 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 (-.f32 (*.f32 x x) (fma.f32 x 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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x 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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x 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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (*.f32 x 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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) #s(literal 3 binary32)) (pow.f32 (log.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))) #s(literal 3 binary32))) (fma.f32 (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (fma.f32 (log.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))) (log.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))) (.f32 (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (log.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (*.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))))))
(-.f32 (log.f32 (neg.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x)))) (log.f32 (neg.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(-.f32 (log.f32 (neg.f32 (-.f32 (*.f32 x x) (fma.f32 x x #s(literal -1 binary32))))) (log.f32 (neg.f32 (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(-.f32 (log.f32 (neg.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x)))) (log.f32 (neg.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 (neg.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x)))) (log.f32 (neg.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (*.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))))
(-.f32 (log.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x))) (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))
(-.f32 (log.f32 (-.f32 (*.f32 x x) (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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x 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 (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (log.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (*.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(-.f32 #s(literal 0 binary32) (log.f32 (/.f32 #s(literal 1 binary32) (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(+.f32 (log.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x))) (neg.f32 (log.f32 (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(+.f32 (log.f32 (-.f32 (fma.f32 x x #s(literal -1 binary32)) (*.f32 x x))) (log.f32 (/.f32 #s(literal 1 binary32) (-.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(+.f32 (log.f32 (-.f32 (*.f32 x x) (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 (log.f32 (-.f32 (*.f32 x x) (fma.f32 x x #s(literal -1 binary32)))) (log.f32 (/.f32 #s(literal 1 binary32) (-.f32 x (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))))
(+.f32 (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (neg.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))))))
(+.f32 (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (neg.f32 (log.f32 (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (*.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))))
(+.f32 (log.f32 (fma.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (log.f32 (/.f32 #s(literal 1 binary32) (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 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (fma.f32 x x #s(literal -1 binary32)) (.f32 (.f32 x x) x))) (log.f32 (/.f32 #s(literal 1 binary32) (-.f32 (fma.f32 x x (fma.f32 x x #s(literal -1 binary32))) (*.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)))))
(neg.f32 (log.f32 (/.f32 #s(literal 1 binary32) (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))))
(*.f32 (pow.f32 (sqrt.f32 (sqrt.f32 x)) #s(literal 1 binary32)) (pow.f32 (sqrt.f32 (sqrt.f32 x)) #s(literal 1 binary32)))
(.f32 (pow.f32 (.f32 (sqrt.f32 x) x) #s(literal 1/4 binary32)) (pow.f32 (sqrt.f32 x) #s(literal 1/4 binary32)))
(.f32 (pow.f32 (sqrt.f32 x) #s(literal 1/4 binary32)) (pow.f32 (.f32 (sqrt.f32 x) x) #s(literal 1/4 binary32)))
(*.f32 (pow.f32 #s(literal 1 binary32) #s(literal 1/4 binary32)) (sqrt.f32 x))
(*.f32 (pow.f32 #s(literal 1 binary32) #s(literal 1/2 binary32)) (sqrt.f32 x))
(*.f32 (sqrt.f32 (sqrt.f32 x)) (sqrt.f32 (sqrt.f32 x)))
(*.f32 (sqrt.f32 x) (pow.f32 #s(literal 1 binary32) #s(literal 1/4 binary32)))
(*.f32 (sqrt.f32 x) (pow.f32 #s(literal 1 binary32) #s(literal 1/2 binary32)))
(*.f32 (sqrt.f32 x) #s(literal 1 binary32))
(*.f32 #s(literal 1 binary32) (sqrt.f32 x))
(sqrt.f32 x)
(pow.f32 (sqrt.f32 (sqrt.f32 x)) #s(literal 2 binary32))
(pow.f32 (.f32 (.f32 (*.f32 x x) x) x) #s(literal 1/8 binary32))
(pow.f32 (sqrt.f32 x) #s(literal 1 binary32))
(pow.f32 (*.f32 x x) #s(literal 1/4 binary32))
(pow.f32 x #s(literal 1/2 binary32))
(fabs.f32 (neg.f32 (sqrt.f32 x)))
(fabs.f32 (sqrt.f32 x))
(exp.f32 (.f32 (.f32 (log.f32 x) #s(literal 1/2 binary32)) #s(literal 1 binary32)))
(exp.f32 (.f32 (.f32 (log.f32 x) #s(literal 2 binary32)) #s(literal 1/4 binary32)))
(exp.f32 (*.f32 (log.f32 x) #s(literal 1/2 binary32)))
(*.f32 (pow.f32 (-.f32 x #s(literal -1 binary32)) #s(literal 1/4 binary32)) (pow.f32 (-.f32 x #s(literal -1 binary32)) #s(literal 1/4 binary32)))
(.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 #s(literal 1 binary32) x))))
(.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 x x))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) x))))
(.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (.f32 x x))) (pow.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) x)) #s(literal 1/2 binary32)))
(.f32 (sqrt.f32 (fma.f32 (.f32 x x) x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (fma.f32 x x #s(literal 1 binary32)) x))))
(.f32 (sqrt.f32 (fma.f32 (.f32 x x) x #s(literal 1 binary32))) (sqrt.f32 (/.f32 #s(literal 1 binary32) (-.f32 (fma.f32 x x #s(literal 1 binary32)) x))))
(.f32 (sqrt.f32 (fma.f32 (.f32 x x) x #s(literal 1 binary32))) (pow.f32 (/.f32 #s(literal 1 binary32) (-.f32 (fma.f32 x x #s(literal 1 binary32)) x)) #s(literal 1/2 binary32)))
(*.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (pow.f32 #s(literal 1 binary32) #s(literal 1/2 binary32)))
(*.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) #s(literal 1 binary32))
(sqrt.f32 (-.f32 x #s(literal -1 binary32)))
(/.f32 (neg.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 x x)))) (neg.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) x))))
(/.f32 (neg.f32 (sqrt.f32 (fma.f32 (*.f32 x x) x #s(literal 1 binary32)))) (neg.f32 (sqrt.f32 (-.f32 (fma.f32 x x #s(literal 1 binary32)) x))))
(/.f32 (sqrt.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (*.f32 x x)))) (sqrt.f32 (neg.f32 (-.f32 #s(literal 1 binary32) x))))
(/.f32 (sqrt.f32 (neg.f32 (fma.f32 (*.f32 x x) x #s(literal 1 binary32)))) (sqrt.f32 (neg.f32 (-.f32 (fma.f32 x x #s(literal 1 binary32)) x))))
(/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 x x))) (sqrt.f32 (-.f32 #s(literal 1 binary32) x)))
(/.f32 (sqrt.f32 (fma.f32 (*.f32 x x) x #s(literal 1 binary32))) (sqrt.f32 (fma.f32 x x (-.f32 #s(literal 1 binary32) x))))
(/.f32 (sqrt.f32 (fma.f32 (*.f32 x x) x #s(literal 1 binary32))) (sqrt.f32 (-.f32 (fma.f32 x x #s(literal 1 binary32)) x)))
(/.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 #s(literal 1 binary32) x)) (sqrt.f32 (-.f32 #s(literal 1 binary32) (*.f32 x x)))))
(/.f32 #s(literal 1 binary32) (/.f32 (sqrt.f32 (-.f32 (fma.f32 x x #s(literal 1 binary32)) x)) (sqrt.f32 (fma.f32 (*.f32 x x) x #s(literal 1 binary32)))))
(/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 #s(literal 1 binary32) (-.f32 x #s(literal -1 binary32)))))
(pow.f32 (exp.f32 (log1p.f32 x)) #s(literal 1/2 binary32))
(pow.f32 (pow.f32 (-.f32 x #s(literal -1 binary32)) #s(literal 1/4 binary32)) #s(literal 2 binary32))
(pow.f32 (*.f32 (-.f32 x #s(literal -1 binary32)) (-.f32 x #s(literal -1 binary32))) #s(literal 1/4 binary32))
(pow.f32 (-.f32 x #s(literal -1 binary32)) #s(literal 1/2 binary32))
(exp.f32 (*.f32 (log1p.f32 x) #s(literal 1/2 binary32)))

eval353.0ms (4.9%)

Memory: 8.4MiB live, 361.3MiB allocated
Compiler: Compiled 38 331 to 4 294 computations (88.8% saved)

prune227.0ms (3.1%)

Memory

15.7MiB live, 528.5MiB allocated

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	1 541	4	1 545
Fresh	1	0	1
Picked	1	4	5
Done	0	0	0
Total	1 543	8	1 551

Accuracy

100.0%

Counts

1 551 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.9%	(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x))
✓	55.4%	(log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
✓	55.4%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
✓	97.6%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
▶	43.7%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))
▶	95.8%	(log.f32 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f32 x x)))
▶	1.3%	(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))
▶	96.1%	#s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))

Compiler

Compiled 69 to 43 computations (37.7% saved)

simplify327.0ms (4.5%)

Memory

-15.6MiB live, 281.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 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	(+.f32 x x)
cost-diff	0	#s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f32 x x))
cost-diff	0	(log.f32 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f32 x 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 #s(literal 2 binary32))
cost-diff	0	(log.f32 x)
cost-diff	0	(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
cost-diff	0	#s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))

Rules

13 963×	`lower-fma.f64`
13 963×	`lower-fma.f32`
1 639×	`lower-+.f64`
1 636×	`lower-+.f32`
1 446×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	161
0	47	153
1	64	153
2	96	153
3	154	153
4	280	153
5	792	153
6	2754	153
7	5112	153
0	8207	145

Stop Event

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

Calls

Call 1

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

localize76.0ms (1%)

Memory

10.7MiB live, 85.7MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.03125	(+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) (/.f32 #s(literal -1/2 binary32) x))))
accuracy	0.3546026397871381	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))))
accuracy	0.5256262208294116	#s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) (/.f32 #s(literal -1/2 binary32) x)))
accuracy	30.98243896586418	#s(approx (- x (/ 1/2 x)) (/.f32 #s(literal -1/2 binary32) x))
accuracy	0	(+.f32 x x)
accuracy	0.3546026397871381	(log.f32 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f32 x x)))
accuracy	1.2196245706296336	#s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f32 x x))
accuracy	0.3546026397871381	(log.f32 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary32)))
accuracy	30.526635476366685	#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	0.2578125	(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
accuracy	1.0046531247817392	#s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))

Samples

52.0ms

256×

valid

Compiler

Compiled 111 to 34 computations (69.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-sqrt: 12.0ms (28.3% of total)

ival-log: 11.0ms (26% of total)

ival-add: 8.0ms (18.9% of total)

ival-mult: 4.0ms (9.4% of total)

ival-sub: 4.0ms (9.4% of total)

ival-div: 3.0ms (7.1% of total)

exact: 1.0ms (2.4% of total)

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

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

series91.0ms (1.3%)

Memory

5.8MiB live, 119.2MiB allocated

Counts

13 → 144

Calls

Call 1

Inputs
#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) #<representation binary32>) () ())
#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())
#s(alt (log.f32 x) (patch (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 #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 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f32 x x))) (patch (log.f32 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f32 x x))) #<representation binary32>) () ())
#s(alt #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f32 x x)) (patch #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f32 x x)) #<representation binary32>) () ())
#s(alt (+.f32 x x) (patch (+.f32 x x) #<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 (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 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 #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 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 #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) #<representation binary32>) () ())) ())
#s(alt (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 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 #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 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 #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) #<representation binary32>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) #<representation binary32>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))) (taylor -inf x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) #<representation binary32>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))) (taylor -inf x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) #<representation binary32>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))) (taylor -inf x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (log x)) (taylor 0 x) (#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (log x)) (taylor 0 x) (#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (log x)) (taylor 0 x) (#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (log x)) (taylor 0 x) (#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (log -1) (+ (log 2) (* -1 (log (/ -1 x))))) (taylor -inf x) (#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (log -1) (+ (log 2) (* -1 (log (/ -1 x))))) (taylor -inf x) (#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (log -1) (+ (log 2) (* -1 (log (/ -1 x))))) (taylor -inf x) (#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (+ (log -1) (+ (log 2) (* -1 (log (/ -1 x))))) (taylor -inf x) (#s(alt (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (patch (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) #<representation binary32>) () ())) ())
#s(alt (log x) (taylor 0 x) (#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())) ())
#s(alt (log x) (taylor 0 x) (#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())) ())
#s(alt (log x) (taylor 0 x) (#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())) ())
#s(alt (log x) (taylor 0 x) (#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())) ())
#s(alt (* -1 (log (/ 1 x))) (taylor inf x) (#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())) ())
#s(alt (* -1 (log (/ 1 x))) (taylor inf x) (#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())) ())
#s(alt (* -1 (log (/ 1 x))) (taylor inf x) (#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())) ())
#s(alt (* -1 (log (/ 1 x))) (taylor inf x) (#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log.f32 x) (patch (log.f32 x) #<representation binary32>) () ())) ())
#s(alt (log (sqrt -1)) (taylor 0 x) (#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 (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#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 (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f32 #s(approx (+ (* (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 (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1))))) (taylor 0 x) (#s(alt (log.f32 #s(approx (+ (* (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 (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#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 (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#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 (+ (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 #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 (- (+ (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 #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 (+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x)))) (taylor -inf x) (#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 (- (+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x)))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))) (taylor -inf x) (#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 (- (+ (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 #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 (- (+ (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 #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 (sqrt -1) (taylor 0 x) (#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 (+ x (sqrt -1)) (taylor 0 x) (#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 (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1)))))) (taylor 0 x) (#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 (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1)))))))) (taylor 0 x) (#s(alt #s(approx (+ (* (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>) () ())) ())
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#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

36 calls:

Time	Variable		Point	Expression
63.0ms	x	@	0	(+ (log x) (log 2))
15.0ms	x	@	-inf	(+ (log x) (log 2))
6.0ms	x	@	inf	(+ (log x) (log 2))
0.0ms	x	@	inf	(+ x x)
0.0ms	x	@	-inf	(log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x))

simplify237.0ms (3.3%)

Memory

-18.0MiB live, 231.7MiB allocated

Algorithm

1×	egg-herbie

Rules

4 862×	`lower-fma.f64`
4 862×	`lower-fma.f32`
1 838×	`lower-*.f64`
1 838×	`lower-*.f32`
1 751×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	273	2076
1	755	1597
2	2407	1538
3	6945	1533
0	8075	1483

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 141

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 (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(+ (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 (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 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 (- (pow (sqrt -1) 2) 1)))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))
(* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))
(* 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))
(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 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (fma.f32 (*.f32 #s(literal 1/6 binary32) x) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (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 (fma.f32 (fma.f32 (.f32 #s(literal 3/40 binary32) x) (/.f32 x (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 x x) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 x x)) #s(literal 1/4 binary32)) (.f32 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 5/96 binary32) (.f32 x x)) #s(literal 3/32 binary32)) (.f32 (.f32 (.f32 x x) x) x))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(-.f32 (-.f32 (log.f32 #s(literal -2 binary32)) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(-.f32 (+.f32 (log.f32 #s(literal -2 binary32)) (/.f32 #s(literal -3/32 binary32) (.f32 (.f32 (.f32 x x) x) x))) (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (/.f32 #s(literal 1/4 binary32) (.f32 x x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(-.f32 (fma.f32 (+.f32 #s(literal -15 binary32) (/.f32 #s(literal -45/2 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 binary32)))) (/.f32 #s(literal 1/720 binary32) (pow.f32 x #s(literal 6 binary32))) (-.f32 (/.f32 #s(literal -3/32 binary32) (.f32 (.f32 (.f32 x x) x) x)) (/.f32 #s(literal 1/4 binary32) (.f32 x x)))) (-.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -2 binary32))))
(+ (log 2) (log x))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(+ (log 2) (log x))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(+ (log 2) (log x))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(+ (log 2) (log x))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(-.f32 (log.f32 #s(literal -1 binary32)) (-.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal 2 binary32))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(-.f32 (log.f32 #s(literal -1 binary32)) (-.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal 2 binary32))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(-.f32 (log.f32 #s(literal -1 binary32)) (-.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal 2 binary32))))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(-.f32 (log.f32 #s(literal -1 binary32)) (-.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal 2 binary32))))
(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 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (fma.f32 (*.f32 #s(literal 1/6 binary32) x) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (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 (fma.f32 (fma.f32 (.f32 #s(literal 3/40 binary32) x) (/.f32 x (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 x x) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 x x)) #s(literal 1/4 binary32)) (.f32 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 5/96 binary32) (.f32 x x)) #s(literal 3/32 binary32)) (.f32 (.f32 (.f32 x x) x) x))) (/.f32 #s(literal 1/4 binary32) (*.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)) (/.f32 #s(literal -1/2 binary32) #s(literal 0 binary32))) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(- (+ (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 (+.f32 (/.f32 (.f32 (/.f32 #s(literal 3 binary32) #s(literal 0 binary32)) #s(literal -1/12 binary32)) (.f32 (.f32 (.f32 x x) x) x)) (log.f32 #s(literal 0 binary32))) (-.f32 (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 (fma.f32 (fma.f32 (/.f32 #s(literal -1/2 binary32) #s(literal 0 binary32)) #s(literal 75 binary32) (/.f32 #s(literal 45 binary32) #s(literal 0 binary32))) (/.f32 #s(literal -1/720 binary32) (pow.f32 x #s(literal 6 binary32))) (+.f32 (/.f32 (.f32 (/.f32 #s(literal 3 binary32) #s(literal 0 binary32)) #s(literal -1/12 binary32)) (.f32 (.f32 (.f32 x x) x) x)) (log.f32 #s(literal 0 binary32)))) (-.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (/.f32 #s(literal -1/2 binary32) #s(literal 0 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 (fma.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f32 (fma.f32 (fma.f32 (*.f32 #s(literal 1/8 binary32) x) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(* 2 x)
(+.f32 x x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 (/.f32 (-.f32 (/.f32 #s(literal -1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x) #s(literal 1 binary32) (+.f32 x x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f32 (-.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (.f32 x x) x) 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 (.f32 #s(literal 1/2 binary32) x) (.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 (/.f32 (-.f32 (/.f32 #s(literal -1/8 binary32) (.f32 x x)) #s(literal 1/2 binary32)) x) #s(literal 1 binary32)))
(* -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))))))
(.f32 (-.f32 (/.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 (.f32 (.f32 x x) x) x))) x)
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (fma.f32 (*.f32 #s(literal 1/6 binary32) x) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (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 (fma.f32 (fma.f32 (.f32 #s(literal 3/40 binary32) x) (/.f32 x (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 x x) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 x x)) #s(literal 1/4 binary32)) (.f32 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 5/96 binary32) (.f32 x x)) #s(literal 3/32 binary32)) (.f32 (.f32 (.f32 x x) x) x))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(-.f32 (-.f32 (log.f32 #s(literal -2 binary32)) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(-.f32 (+.f32 (log.f32 #s(literal -2 binary32)) (/.f32 #s(literal -3/32 binary32) (.f32 (.f32 (.f32 x x) x) x))) (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (/.f32 #s(literal 1/4 binary32) (.f32 x x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(-.f32 (fma.f32 (+.f32 #s(literal -15 binary32) (/.f32 #s(literal -45/2 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 binary32)))) (/.f32 #s(literal 1/720 binary32) (pow.f32 x #s(literal 6 binary32))) (-.f32 (/.f32 #s(literal -3/32 binary32) (.f32 (.f32 (.f32 x x) x) x)) (/.f32 #s(literal 1/4 binary32) (.f32 x x)))) (-.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -2 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 (fma.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f32 (fma.f32 (fma.f32 (*.f32 #s(literal 1/8 binary32) x) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(* 2 x)
(+.f32 x x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 (/.f32 (-.f32 (/.f32 #s(literal -1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x) #s(literal 1 binary32) (+.f32 x x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f32 (-.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (.f32 x x) x) x))) x)
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(+.f32 x x)
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) x)
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))
(.f32 (-.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) (/.f32 #s(literal 1/8 binary32) (.f32 (.f32 (*.f32 x x) x) x))) x)
(* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))
(.f32 (-.f32 (-.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) (/.f32 #s(literal 1/8 binary32) (.f32 (.f32 (.f32 x x) x) x))) (/.f32 #s(literal 1/16 binary32) (.f32 (pow.f32 x #s(literal 6 binary32)) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 binary32))))) x)
(* 2 x)
(+.f32 x x)
(* 2 x)
(+.f32 x x)
(* 2 x)
(+.f32 x x)
(* 2 x)
(+.f32 x x)
(* 2 x)
(+.f32 x x)
(* 2 x)
(+.f32 x x)
(* 2 x)
(+.f32 x x)
(* 2 x)
(+.f32 x x)
(* 2 x)
(+.f32 x x)
(* 2 x)
(+.f32 x x)
(* 2 x)
(+.f32 x x)
(* 2 x)
(+.f32 x x)
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (fma.f32 (*.f32 #s(literal 1/6 binary32) x) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (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 (fma.f32 (fma.f32 (.f32 #s(literal 3/40 binary32) x) (/.f32 x (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 x x) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 x x)) #s(literal 1/4 binary32)) (.f32 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 5/96 binary32) (.f32 x x)) #s(literal 3/32 binary32)) (.f32 (.f32 (.f32 x x) 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)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f32 (+.f32 (log.f32 #s(literal -1/2 binary32)) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (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 (+.f32 (log.f32 #s(literal -1/2 binary32)) (/.f32 #s(literal 3/32 binary32) (.f32 (.f32 (.f32 x x) x) x))) (+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (/.f32 #s(literal 1/4 binary32) (.f32 x x))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(+.f32 (+.f32 (+.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 (.f32 (.f32 x x) x) x)) (log.f32 (/.f32 #s(literal -1 binary32) x))) (log.f32 #s(literal -1/2 binary32))) (/.f32 #s(literal 5/96 binary32) (pow.f32 x #s(literal 6 binary32)))) (/.f32 #s(literal 1/4 binary32) (.f32 x x)))
(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 (fma.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f32 (fma.f32 (fma.f32 (*.f32 #s(literal 1/8 binary32) x) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(* 2 x)
(+.f32 x x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 (/.f32 (-.f32 (/.f32 #s(literal -1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x) #s(literal 1 binary32) (+.f32 x x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f32 (-.f32 (-.f32 #s(literal 2 binary32) (/.f32 #s(literal 1/2 binary32) (.f32 x x))) (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (.f32 x x) x) x))) x)
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f32 (+.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f32 (-.f32 #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 (+.f32 (/.f32 #s(literal 5/128 binary32) (.f32 x x)) #s(literal 1/16 binary32)) (.f32 (.f32 (.f32 x x) x) x)) (+.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32))) x)
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 (*.f32 #s(literal 1/2 binary32) x) (/.f32 x (sqrt.f32 #s(literal -1 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 (fma.f32 (.f32 #s(literal 1/8 binary32) x) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) (.f32 x x) (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (fma.f32 (fma.f32 (.f32 #s(literal 1/16 binary32) x) (/.f32 x (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 x x) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) (*.f32 x x) (sqrt.f32 #s(literal -1 binary32)))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x x)
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 (/.f32 (-.f32 (/.f32 #s(literal -1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x) #s(literal 1 binary32) x)
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 (-.f32 (/.f32 #s(literal -1/2 binary32) (.f32 x x)) (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (*.f32 x x) x) x))) x x)
(* -1 x)
(neg.f32 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(fma.f32 (/.f32 #s(literal 1/2 binary32) (*.f32 x x)) x (neg.f32 x))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(neg.f32 (fma.f32 (/.f32 (-.f32 (/.f32 #s(literal -1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x) #s(literal 1 binary32) x))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(.f32 (-.f32 (/.f32 #s(literal 1/2 binary32) (.f32 x x)) (-.f32 #s(literal 1 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (.f32 x x) x) x)))) x)
(/ -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 (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x x)
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x x)
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x x)
x
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f32 (/.f32 #s(literal -1/2 binary32) (*.f32 x x)) x x)

rewrite219.0ms (3%)

Memory

3.4MiB live, 309.6MiB allocated

Rules

2 545×	`lower-fma.f64`
2 545×	`lower-fma.f32`
1 954×	`lower-/.f64`
1 954×	`lower-/.f32`
1 461×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	152
0	47	139
1	184	133
2	1431	105
0	8821	97

Stop Event

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

Counts

13 → 108

Calls

Call 1

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

eval20.0ms (0.3%)

Memory: 13.9MiB live, 49.5MiB allocated
Compiler: Compiled 3 800 to 534 computations (85.9% saved)

prune317.0ms (4.4%)

Memory

-124.4MiB live, 127.2MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	247	2	249
Fresh	0	0	0
Picked	2	2	4
Done	0	4	4
Total	249	8	257

Accuracy

100.0%

Counts

257 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.9%	(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x))
✓	55.4%	(log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
✓	55.4%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
▶	43.5%	(log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x))
✓	97.6%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
✓	95.8%	(log.f32 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f32 x x)))
✓	96.1%	#s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))
▶	6.1%	#s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32))

Compiler

Compiled 66 to 41 computations (37.9% saved)

simplify512.0ms (7.1%)

Memory

-10.9MiB live, 258.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

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

Rules

10 694×	`lower-fma.f64`
10 694×	`lower-fma.f32`
1 688×	`lower-+.f64`
1 687×	`lower-+.f32`
1 604×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	71
0	24	71
1	36	71
2	53	71
3	86	71
4	135	71
5	312	71
6	650	71
7	2079	71
8	3480	71
9	4775	71
10	5367	71
11	5583	71
12	5694	71
13	5790	71
14	6494	71
15	7110	71
16	7462	71
17	7766	71
18	7956	71
0	8074	67

Stop Event

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

Calls

Call 1

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

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

localize91.0ms (1.3%)

Memory

2.0MiB live, 82.7MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0.03125	(+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)
accuracy	0.3546026397871381	(log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x))
accuracy	0.5256262208294116	#s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)))
accuracy	31.284987589220417	#s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))
accuracy	30.043149059375367	#s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32))

Samples

61.0ms

256×

valid

Compiler

Compiled 45 to 21 computations (53.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

ival-sub: 36.0ms (65.8% of total)

ival-log: 5.0ms (9.1% of total)

ival-sqrt: 5.0ms (9.1% of total)

ival-add: 3.0ms (5.5% of total)

ival-mult: 3.0ms (5.5% of total)

ival-div: 2.0ms (3.7% of total)

exact: 1.0ms (1.8% of total)

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

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

series3.0ms (0%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

5 → 60

Calls

Call 1

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

Outputs
#s(alt (log (sqrt -1)) (taylor 0 x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 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 #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 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 #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) #<representation binary32>) () ())) ())
#s(alt (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 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 #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 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 #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) #<representation binary32>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) #<representation binary32>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))) (taylor -inf x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) #<representation binary32>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))) (taylor -inf x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) #<representation binary32>) () ())) ())
#s(alt (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))) (taylor -inf x) (#s(alt #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) (patch #s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32)) #<representation binary32>) () ())) ())
#s(alt (log (sqrt -1)) (taylor 0 x) (#s(alt (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) #<representation binary32>) () ())) ())
#s(alt (+ (log (sqrt -1)) (/ x (sqrt -1))) (taylor 0 x) (#s(alt (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 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 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 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 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) #<representation binary32>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 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 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) 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 (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) 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 (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) #<representation binary32>) () ())) ())
#s(alt (+ (log -1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) #<representation binary32>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) #<representation binary32>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) #<representation binary32>) () ())) ())
#s(alt (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6))))))) (taylor -inf x) (#s(alt (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) (patch (log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x)) #<representation binary32>) () ())) ())
#s(alt (sqrt -1) (taylor 0 x) (#s(alt (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) (patch (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) #<representation binary32>) () ())) ())
#s(alt (+ x (sqrt -1)) (taylor 0 x) (#s(alt (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) (patch (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) #<representation binary32>) () ())) ())
#s(alt (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1)))))) (taylor 0 x) (#s(alt (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) (patch (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 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 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) (patch (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) #<representation binary32>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) (patch (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) #<representation binary32>) () ())) ())
#s(alt (* x (- 2 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) (patch (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 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 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) (patch (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 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 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) (patch (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) #<representation binary32>) () ())) ())
#s(alt (/ 1/2 x) (taylor -inf x) (#s(alt (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) (patch (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) #<representation binary32>) () ())) ())
#s(alt (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) (patch (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) #<representation binary32>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x)) (taylor -inf x) (#s(alt (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) (patch (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) #<representation binary32>) () ())) ())
#s(alt (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x)) (taylor -inf x) (#s(alt (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x) (patch (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 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)) #s(literal -1 binary32))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) #<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)) #s(literal -1 binary32))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 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 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 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 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) #<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)) #s(literal -1 binary32))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 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 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 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 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) #<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)) #s(literal -1 binary32))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 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 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 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 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) (patch #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) #<representation binary32>) () ())) ())
#s(alt (/ -1/2 x) (taylor 0 x) (#s(alt #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) (patch #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (/ (- (pow x 2) 1/2) x) (taylor 0 x) (#s(alt #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) (patch #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (/ (- (pow x 2) 1/2) x) (taylor 0 x) (#s(alt #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) (patch #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (/ (- (pow x 2) 1/2) x) (taylor 0 x) (#s(alt #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) (patch #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) (patch #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) (patch #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) (patch #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* x (- 1 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) (patch #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) (patch #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) (patch #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) (patch #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) #<representation binary32>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1))) (taylor -inf x) (#s(alt #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) (patch #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32)) #<representation binary32>) () ())) ())

Calls

15 calls:

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

simplify319.0ms (4.4%)

Memory

6.9MiB live, 231.8MiB allocated

Algorithm

1×	egg-herbie

Rules

5 582×	`lower-fma.f64`
5 582×	`lower-fma.f32`
2 174×	`lower-*.f64`
2 174×	`lower-*.f32`
1 635×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	198	923
1	527	756
2	1536	742
3	4069	671
0	8284	646

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 57

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 (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(+ (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 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (fma.f32 (*.f32 x x) #s(literal 1/6 binary32) #s(literal 1 binary32)) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f32 (fma.f32 (fma.f32 (.f32 x x) #s(literal 1/6 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32))) (.f32 (.f32 #s(literal 3/40 binary32) (.f32 x x)) (/.f32 (*.f32 x x) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))))) x (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 x x)) #s(literal 1/4 binary32)) (.f32 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 5/96 binary32) (.f32 x x)) #s(literal 3/32 binary32)) (.f32 (.f32 (.f32 x x) x) x))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))
(-.f32 (log.f32 #s(literal -2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(-.f32 (-.f32 (log.f32 #s(literal -2 binary32)) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(-.f32 (+.f32 (+.f32 (/.f32 #s(literal -3/32 binary32) (.f32 (.f32 (.f32 x x) x) x)) (log.f32 #s(literal -2 binary32))) (/.f32 #s(literal -1/4 binary32) (.f32 x x))) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))
(-.f32 (fma.f32 (+.f32 #s(literal -15 binary32) (/.f32 #s(literal -45/2 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 binary32)))) (/.f32 #s(literal 1/720 binary32) (pow.f32 x #s(literal 6 binary32))) (+.f32 (+.f32 (/.f32 #s(literal -3/32 binary32) (.f32 (.f32 (.f32 x x) x) x)) (log.f32 #s(literal -2 binary32))) (/.f32 #s(literal -1/4 binary32) (.f32 x x)))) (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 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (fma.f32 (*.f32 x x) #s(literal 1/6 binary32) #s(literal 1 binary32)) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f32 (fma.f32 (fma.f32 (.f32 x x) #s(literal 1/6 binary32) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32))) (.f32 (.f32 #s(literal 3/40 binary32) (.f32 x x)) (/.f32 (*.f32 x x) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))))) x (log.f32 (sqrt.f32 #s(literal -1 binary32))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 x x)) #s(literal 1/4 binary32)) (.f32 x x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f32 (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 (+.f32 (/.f32 #s(literal 5/96 binary32) (.f32 x x)) #s(literal 3/32 binary32)) (.f32 (.f32 (.f32 x x) 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)) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+.f32 (-.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (/.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))))))
(+.f32 (+.f32 (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 (.f32 (.f32 x x) x) x)) (/.f32 #s(literal 1/4 binary32) (.f32 x x))) (log.f32 (/.f32 #s(literal -1 binary32) 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 (+.f32 (/.f32 #s(literal 5/96 binary32) (pow.f32 x #s(literal 6 binary32))) (/.f32 #s(literal 1/4 binary32) (.f32 x x))) (log.f32 #s(literal -1/2 binary32))) (+.f32 (/.f32 #s(literal 3/32 binary32) (.f32 (.f32 (.f32 x x) x) x)) (log.f32 (/.f32 #s(literal -1 binary32) x))))
(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 (fma.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f32 (fma.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (fma.f32 (*.f32 x x) #s(literal 1/8 binary32) #s(literal 1/2 binary32)) #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(* 2 x)
(*.f32 #s(literal 2 binary32) x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 #s(literal 2 binary32) x (/.f32 #s(literal -1/2 binary32) x))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f32 #s(literal 2 binary32) x (/.f32 (-.f32 (/.f32 #s(literal -1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f32 (-.f32 #s(literal 2 binary32) (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (.f32 x x) x) x))) x (/.f32 #s(literal -1/2 binary32) x))
(/ 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 (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 x x)) #s(literal -1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f32 (-.f32 (-.f32 (/.f32 (+.f32 (/.f32 #s(literal 5/128 binary32) (.f32 x x)) #s(literal 1/16 binary32)) (.f32 (.f32 (.f32 x x) x) x)) #s(literal -1/2 binary32)) (/.f32 #s(literal -1/8 binary32) (*.f32 x x))) x)
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 (*.f32 #s(literal 1/2 binary32) (/.f32 x (sqrt.f32 #s(literal -1 binary32)))) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) x) (fma.f32 (.f32 x x) #s(literal 1/8 binary32) #s(literal 1/2 binary32)) (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (fma.f32 (.f32 #s(literal 1/16 binary32) (.f32 x x)) (/.f32 (.f32 x x) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) (.f32 (/.f32 #s(literal 1 binary32) (sqrt.f32 #s(literal -1 binary32))) (fma.f32 #s(literal 1/8 binary32) (.f32 x x) #s(literal 1/2 binary32)))) (.f32 x x) (sqrt.f32 #s(literal -1 binary32)))
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)))))
(fma.f32 (+.f32 (/.f32 (-.f32 #s(literal -1/8 binary32) (/.f32 #s(literal 1/16 binary32) (.f32 x x))) (.f32 (.f32 (.f32 x x) x) x)) #s(literal 1 binary32)) x (/.f32 #s(literal -1/2 binary32) 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 (-.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (.f32 x x)) #s(literal 1/8 binary32)) (.f32 (.f32 (.f32 x x) x) x)) #s(literal 1 binary32)) x (/.f32 #s(literal 1/2 binary32) 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)))))
(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
x
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(-.f32 x (/.f32 #s(literal 1/2 binary32) x))

rewrite289.0ms (4%)

Memory

-4.1MiB live, 412.3MiB allocated

Rules

6 327×	`lower-fma.f64`
6 327×	`lower-fma.f32`
2 187×	`lower-*.f64`
2 187×	`lower-*.f32`
1 945×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	68
0	24	67
1	110	65
2	906	65
0	8800	61

Stop Event

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

Counts

5 → 60

Calls

Call 1

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

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

eval11.0ms (0.2%)

Memory: -6.7MiB live, 30.8MiB allocated
Compiler: Compiled 2 509 to 361 computations (85.6% saved)

prune20.0ms (0.3%)

Memory

17.8MiB live, 56.2MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	0	0
Picked	0	2	2
Done	0	6	6
Total	117	8	125

Accuracy

100.0%

Counts

125 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.9%	(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) x))
✓	55.4%	(log.f32 (fma.f32 (sqrt.f32 x) (sqrt.f32 x) (sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))))
✓	55.4%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
✓	43.5%	(log.f32 (+.f32 #s(approx (sqrt (- (* x x) 1)) #s(approx (- x (/ 1/2 x)) #s(literal -1 binary32))) x))
✓	97.6%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
✓	95.8%	(log.f32 #s(approx (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x) (+.f32 x x)))
✓	96.1%	#s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))
✓	6.1%	#s(approx (log (+ (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)) #s(literal 0 binary32))

Compiler

Compiled 156 to 83 computations (46.8% saved)

regimes33.0ms (0.5%)

Memory

-12.0MiB live, 33.0MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

3 calls:

24.0ms	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
4.0ms	x
4.0ms	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
98.9%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

24.8MiB live, 24.8MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
97.6%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes35.0ms (0.5%)

Memory

-11.5MiB live, 27.8MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

30.0ms	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
3.0ms	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
2.0ms	x

Results

Accuracy	Segments	Branch
95.8%	1	`x`
95.8%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
95.8%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory

-22.4MiB live, 15.7MiB allocated

Accuracy

Total -1.6b remaining (-5.2%)

Threshold costs -1.6b (-5.2%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	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
6.1%	1	`x`
6.1%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
6.1%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

simplify7.0ms (0.1%)

Memory

21.1MiB live, 21.1MiB allocated

Algorithm

1×	egg-herbie

Rules

9×	`neg-mul-1_binary32`
9×	`+-commutative_binary32`
8×	`unsub-neg_binary32`
7×	`*-commutative_binary32`
6×	`sub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	56
1	37	56
2	48	56
3	59	56
4	75	56
5	98	56
6	101	56

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness697.0ms (9.6%)

Memory

-15.9MiB live, 438.7MiB allocated

Rules

6 098×	`lower-fma.f64`
6 098×	`lower-fma.f32`
5 102×	`lower-fma.f64`
5 102×	`lower-fma.f32`
2 545×	`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	372	3061
1	1057	2617
2	3492	2540
0	8323	2419
0	38	152
0	47	139
1	184	133
2	1431	105
0	8821	97
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×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 103 to 64 computations (37.9% saved)

preprocess137.0ms (1.9%)

Memory: -4.9MiB live, 69.6MiB allocated
Compiler: Compiled 102 to 64 computations (37.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample577.0ms (8%)

explain104.0ms (1.4%)

preprocess380.0ms (5.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify357.0ms (4.9%)

localize24.0ms (0.3%)

series5.0ms (0.1%)

simplify212.0ms (2.9%)

rewrite285.0ms (3.9%)

eval43.0ms (0.6%)

prune66.0ms (0.9%)

simplify469.0ms (6.5%)

localize108.0ms (1.5%)

series44.0ms (0.6%)

simplify196.0ms (2.7%)

rewrite336.0ms (4.6%)

eval353.0ms (4.9%)

prune227.0ms (3.1%)

simplify327.0ms (4.5%)

localize76.0ms (1%)

series91.0ms (1.3%)

simplify237.0ms (3.3%)

rewrite219.0ms (3%)

eval20.0ms (0.3%)

prune317.0ms (4.4%)

simplify512.0ms (7.1%)

localize91.0ms (1.3%)

series3.0ms (0%)

simplify319.0ms (4.4%)

rewrite289.0ms (4%)

eval11.0ms (0.2%)

prune20.0ms (0.3%)

regimes33.0ms (0.5%)

regimes10.0ms (0.1%)

regimes35.0ms (0.5%)

regimes7.0ms (0.1%)

simplify7.0ms (0.1%)

soundness697.0ms (9.6%)

preprocess137.0ms (1.9%)

end0.0ms (0%)

Profiling