Metrics for Rust f32::acosh

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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)

sample432.0ms (6%)

Memory

8.6MiB live, 641.4MiB allocated

Samples

278.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 162.0ms

ival-acosh: 128.0ms (79% of total)

ival->=: 24.0ms (14.8% of total)

exact: 7.0ms (4.3% of total)

ival-assert: 4.0ms (2.5% of total)

Bogosity

explain174.0ms (2.4%)

Memory

-35.5MiB live, 166.7MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
138	-	-	`(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))`
4	-	-	`(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	138	0
↳	`(*.f32 x x)`	overflow	138
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	138
`log.f32`	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`	oflow-rescue	4	0
↳	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`	overflow	4
↳	`(*.f32 x x)`	overflow	138
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	138

Confusion

	Predicted +	Predicted -
+	138	0
-	0	118

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	138	0	0
-	0	0	118

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	118
1	134
2	4

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

30.0ms

512×

valid

Compiler

Compiled 79 to 25 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-log: 5.0ms (26.8% of total)

ival-mult: 4.0ms (21.5% of total)

ival-sqrt: 4.0ms (21.5% of total)

ival-sub: 3.0ms (16.1% of total)

ival-add: 2.0ms (10.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess341.0ms (4.7%)

Memory

40.9MiB live, 266.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.5%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify326.0ms (4.5%)

Memory

8.1MiB live, 287.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

-26.8MiB live, 46.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0234375	(-.f32 (*.f32 x x) #s(literal 1 binary32))
accuracy	0.0390625	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
accuracy	0.4793138253739408	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
accuracy	14.817367249301142	(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))

Samples

14.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

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

ival-log: 3.0ms (33.4% of total)

ival-mult: 2.0ms (22.3% of total)

ival-sqrt: 2.0ms (22.3% of total)

ival-sub: 1.0ms (11.1% of total)

ival-add: 1.0ms (11.1% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify199.0ms (2.7%)

Memory

11.6MiB live, 238.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

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

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

rewrite277.0ms (3.8%)

Memory

-33.3MiB live, 282.9MiB allocated

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 320

Calls

Call 1

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

Outputs
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eval41.0ms (0.6%)

Memory: 26.3MiB live, 98.4MiB allocated
Compiler: Compiled 8 015 to 1 574 computations (80.4% saved)

prune11.0ms (0.1%)

Memory

-4.4MiB live, 33.0MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	359	8	367
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	359	9	368

Accuracy

100.0%

Counts

368 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.9%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
▶	98.5%	(log.f32 (+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))))
✓	49.5%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
▶	17.3%	(log.f32 (+.f32 x (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x))))))))
▶	96.8%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
	0.6%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (fma.f32 #s(literal 2 binary32) x (/.f32 #s(literal -1/2 binary32) x))))
▶	95.6%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
	97.3%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))))
▶	96.2%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))

Compiler

Compiled 175 to 141 computations (19.4% saved)

simplify440.0ms (6.1%)

Memory

5.5MiB live, 247.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(log.f32 (+.f32 x (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x))))))))
cost-diff	96	(.f32 #s(literal -1 binary32) (.f32 x x))
cost-diff	128	(-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x)))
cost-diff	160	(.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x)))))
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 (+ x (sqrt (- (* x x) 1)))) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))
cost-diff	0	(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
cost-diff	0	#s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))
cost-diff	0	(+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))
cost-diff	0	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
cost-diff	0	(*.f32 #s(literal 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	0	(sqrt.f32 (-.f32 x #s(literal 1 binary32)))
cost-diff	0	(*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))
cost-diff	0	(log.f32 (+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))))
cost-diff	64	(+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x))))

Rules

21 616×	`lower-fma.f64`
21 616×	`lower-fma.f32`
2 920×	`lower-*.f64`
2 910×	`lower-*.f32`
2 664×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	292
0	71	285
1	104	271
2	157	271
3	255	271
4	461	271
5	1071	271
6	1787	271
7	2954	271
8	4260	271
9	5223	271
10	5769	271
11	5972	271
12	6118	271
13	6232	271
14	6784	271
15	6976	271
16	7419	271
17	7731	271
0	8067	257

Stop Event

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

Calls

Call 1

Inputs
(log.f32 (+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))))
(+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x))))
x
(*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))
(sqrt.f32 (-.f32 x #s(literal 1 binary32)))
(-.f32 x #s(literal 1 binary32))
#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)
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.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 (+.f32 x (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x))))))))
(+.f32 x (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x)))))))
x
(sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x))))))
(.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x)))))
(-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32))
(pow.f32 x #s(literal 6 binary32))
#s(literal 6 binary32)
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x))))
(-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x)))
(+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32))
(pow.f32 x #s(literal 4 binary32))
#s(literal 4 binary32)
(.f32 #s(literal -1 binary32) (.f32 x x))
#s(literal -1 binary32)
(*.f32 x x)

Outputs
(log.f32 (+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))))
(log.f32 (fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x))
(+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x))))
(fma.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))) x)
x
(*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))
(*.f32 (sqrt.f32 (-.f32 x #s(literal -1 binary32))) (sqrt.f32 (-.f32 x #s(literal 1 binary32))))
(sqrt.f32 (-.f32 x #s(literal 1 binary32)))
(-.f32 x #s(literal 1 binary32))
#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)))
#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)))))
(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)
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.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 (+.f32 x (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x))))))))
(log.f32 (+.f32 (sqrt.f32 (/.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (fma.f32 x x (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal -1 binary32))))) x))
(+.f32 x (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x)))))))
(+.f32 (sqrt.f32 (/.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (fma.f32 x x (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal -1 binary32))))) x)
x
(sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x))))))
(sqrt.f32 (/.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (fma.f32 x x (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal -1 binary32)))))
(.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x)))))
(/.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (fma.f32 x x (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal -1 binary32))))
(-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32))
(pow.f32 x #s(literal 6 binary32))
#s(literal 6 binary32)
#s(literal 1 binary32)
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x))))
(/.f32 #s(literal 1 binary32) (fma.f32 x x (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal -1 binary32))))
(-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x)))
(fma.f32 x x (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal -1 binary32)))
(+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32))
(-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal -1 binary32))
(pow.f32 x #s(literal 4 binary32))
#s(literal 4 binary32)
(.f32 #s(literal -1 binary32) (.f32 x x))
(*.f32 (neg.f32 x) x)
#s(literal -1 binary32)
(*.f32 x x)

localize128.0ms (1.8%)

Memory

-26.7MiB live, 105.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.3865832343989418	(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x))))
accuracy	0.4793138253739408	(log.f32 (+.f32 x (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x))))))))
accuracy	14.817367249301142	(sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x))))))
accuracy	20.154693420387424	(.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x)))))
accuracy	0	(log.f32 x)
accuracy	0	(log.f32 #s(literal 2 binary32))
accuracy	0.3125	(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
accuracy	0.9272632038718875	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))
accuracy	0.00390625	(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
accuracy	0.0390625	(+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))
accuracy	0.4793138253739408	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
accuracy	0.6260524628210833	#s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))
accuracy	0	(*.f32 #s(literal 2 binary32) x)
accuracy	0.4793138253739408	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
accuracy	1.0553918235816915	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
accuracy	0.00390625	(sqrt.f32 (+.f32 #s(literal 1 binary32) x))
accuracy	0.0390625	(+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x))))
accuracy	0.45703125	(*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))
accuracy	0.4793138253739408	(log.f32 (+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))))

Samples

106.0ms

256×

valid

Compiler

Compiled 262 to 38 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 92.0ms

ival-mult: 46.0ms (50.2% of total)

ival-log: 11.0ms (12% of total)

ival-sub: 9.0ms (9.8% of total)

ival-add: 7.0ms (7.6% of total)

ival-sqrt: 7.0ms (7.6% of total)

ival-pow: 7.0ms (7.6% of total)

ival-div: 3.0ms (3.3% of total)

exact: 1.0ms (1.1% of total)

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

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

series160.0ms (2.2%)

Memory

1.4MiB live, 109.6MiB allocated

Counts

22 → 252

Calls

Call 1

Inputs
#s(alt (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))) (patch (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))) #<representation binary32>) () ())
#s(alt (log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x))))) (patch (log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x))))) #<representation binary32>) () ())
#s(alt (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x))) (patch (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) 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 (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 (.f32 #s(literal 2 binary32) x) (patch (.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 #s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))) (patch #s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.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 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x))))) (patch (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x))))) #<representation binary32>) () ())
#s(alt (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x))) (patch (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x))) #<representation binary32>) () ())
#s(alt (.f32 #s(literal -1 binary32) (.f32 x x)) (patch (.f32 #s(literal -1 binary32) (.f32 x x)) #<representation binary32>) () ())
#s(alt (log.f32 (+.f32 x (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x)))))))) (patch (log.f32 (+.f32 x (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x)))))))) #<representation binary32>) () ())
#s(alt (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) (patch (sqrt.f32 (+.f32 #s(literal 1 binary32) x)) #<representation binary32>) () ())
#s(alt (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x)))))) (patch (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x)))))) #<representation binary32>) () ())
#s(alt (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x)))) (patch (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x)))) #<representation binary32>) () ())

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

Calls

3 calls:

Time

Variable

Point

Expression

93.0ms

((+ x (* (sqrt (- x 1)) (sqrt (+ 1 x)))) (log (+ x (* (sqrt (- x 1)) (sqrt (+ 1 x))))) (* (sqrt (- x 1)) (sqrt (+ 1 x))) (sqrt (- x 1)) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)) (log (+ x (sqrt (- (* x x) 1)))) (+ (log x) (log 2)) (log x) (log 2) (* (- (pow x 6) 1) (/ 1 (- (+ (pow x 4) 1) (* -1 (* x x))))) (- (+ (pow x 4) 1) (* -1 (* x x))) (* -1 (* x x)) (log (+ x (sqrt (* (- (pow x 6) 1) (/ 1 (- (+ (pow x 4) 1) (* -1 (* x x)))))))) (sqrt (+ 1 x)) (sqrt (* (- (pow x 6) 1) (/ 1 (- (+ (pow x 4) 1) (* -1 (* x x)))))) (/ 1 (- (+ (pow x 4) 1) (* -1 (* x x)))))

38.0ms

-inf

((+ x (* (sqrt (- x 1)) (sqrt (+ 1 x)))) (log (+ x (* (sqrt (- x 1)) (sqrt (+ 1 x))))) (* (sqrt (- x 1)) (sqrt (+ 1 x))) (sqrt (- x 1)) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)) (log (+ x (sqrt (- (* x x) 1)))) (+ (log x) (log 2)) (log x) (log 2) (* (- (pow x 6) 1) (/ 1 (- (+ (pow x 4) 1) (* -1 (* x x))))) (- (+ (pow x 4) 1) (* -1 (* x x))) (* -1 (* x x)) (log (+ x (sqrt (* (- (pow x 6) 1) (/ 1 (- (+ (pow x 4) 1) (* -1 (* x x)))))))) (sqrt (+ 1 x)) (sqrt (* (- (pow x 6) 1) (/ 1 (- (+ (pow x 4) 1) (* -1 (* x x)))))) (/ 1 (- (+ (pow x 4) 1) (* -1 (* x x)))))

20.0ms

inf

((+ x (* (sqrt (- x 1)) (sqrt (+ 1 x)))) (log (+ x (* (sqrt (- x 1)) (sqrt (+ 1 x))))) (* (sqrt (- x 1)) (sqrt (+ 1 x))) (sqrt (- x 1)) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)) (log (+ x (sqrt (- (* x x) 1)))) (+ (log x) (log 2)) (log x) (log 2) (* (- (pow x 6) 1) (/ 1 (- (+ (pow x 4) 1) (* -1 (* x x))))) (- (+ (pow x 4) 1) (* -1 (* x x))) (* -1 (* x x)) (log (+ x (sqrt (* (- (pow x 6) 1) (/ 1 (- (+ (pow x 4) 1) (* -1 (* x x)))))))) (sqrt (+ 1 x)) (sqrt (* (- (pow x 6) 1) (/ 1 (- (+ (pow x 4) 1) (* -1 (* x x)))))) (/ 1 (- (+ (pow x 4) 1) (* -1 (* x x)))))

simplify212.0ms (2.9%)

Memory

23.4MiB live, 141.0MiB allocated

Algorithm

1×	egg-herbie

Rules

14 602×	`lower-fma.f64`
14 602×	`lower-fma.f32`
4 734×	`lower-+.f64`
4 734×	`lower-+.f32`
3 780×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	363	3128
1	1031	2805
2	3233	2720
0	8465	2582

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 247

Calls

Call 1

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

Outputs
(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) (sqrt.f32 #s(literal -1 binary32))) (*.f32 x x) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (/.f32 (pow.f32 x #s(literal 3 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) #s(literal -1/6 binary32) (+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (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 (pow.f32 x #s(literal 3 binary32)) (fma.f32 (*.f32 x (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) #s(literal 3/40 binary32) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 binary32)))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 (*.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (fma.f32 (/.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)))
(+ (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 (pow.f32 x #s(literal 4 binary32)) (fma.f32 (.f32 (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32)) x (/.f32 #s(literal 1/8 binary32) (sqrt.f32 #s(literal -1 binary32)))) (fma.f32 (.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x) x (sqrt.f32 #s(literal -1 binary32))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(fma.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (fma.f32 #s(literal 1/8 binary32) (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (fma.f32 (fma.f32 (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32) (/.f32 #s(literal 1/8 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) x (sqrt.f32 #s(literal -1 binary32)))
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (/.f32 (pow.f32 x #s(literal 3 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) #s(literal -1/6 binary32) (+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (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 (pow.f32 x #s(literal 3 binary32)) (fma.f32 (*.f32 x (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) #s(literal 3/40 binary32) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 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) (sqrt.f32 #s(literal -1 binary32))) (*.f32 x x) (/.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 #s(literal 2 binary32) x)
(* 2 x)
(*.f32 #s(literal 2 binary32) x)
(* 2 x)
(*.f32 #s(literal 2 binary32) x)
(* 2 x)
(*.f32 #s(literal 2 binary32) x)
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f32 (/.f32 (pow.f32 x #s(literal 3 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) #s(literal -1/6 binary32) (+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (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 (pow.f32 x #s(literal 3 binary32)) (fma.f32 (*.f32 x (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) #s(literal 3/40 binary32) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 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) (sqrt.f32 #s(literal -1 binary32))) (*.f32 x x) (/.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)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 (*.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (fma.f32 (/.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)))
(+ (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 (pow.f32 x #s(literal 4 binary32)) (fma.f32 (.f32 (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32))) #s(literal 1/16 binary32)) x (/.f32 #s(literal 1/8 binary32) (sqrt.f32 #s(literal -1 binary32)))) (fma.f32 (.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x) x (sqrt.f32 #s(literal -1 binary32))))
(/ -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))
(log (sqrt -1))
(log.f32 (sqrt.f32 #s(literal -1 binary32)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f32 (log.f32 (sqrt.f32 #s(literal -1 binary32))) (/.f32 x (sqrt.f32 #s(literal -1 binary32))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
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(/ (- (+ 1 (/ 1 (pow x 6))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 8)))) (pow x 4))
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(*.f32 #s(literal 2 binary32) x)
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(fma.f32 (/.f32 #s(literal 1 binary32) x) #s(literal -1/2 binary32) (*.f32 #s(literal 2 binary32) x))
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))
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(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))))
(fma.f32 (/.f32 #s(literal -1 binary32) x) #s(literal 1/2 binary32) x)
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(-.f32 (fma.f32 (/.f32 #s(literal -1 binary32) x) #s(literal 1/2 binary32) x) (*.f32 (/.f32 #s(literal 1/8 binary32) (pow.f32 x #s(literal 4 binary32))) x))
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(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
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(/ 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)
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(/.f32 (+.f32 (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (*.f32 x x)) #s(literal 1/8 binary32)) x) x) #s(literal 1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f32 (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 5/128 binary32) (.f32 x x)) #s(literal 1/16 binary32)) (pow.f32 x #s(literal 4 binary32))) (+.f32 (/.f32 #s(literal 1/8 binary32) (.f32 x x)) #s(literal 1/2 binary32))) x)
(* 2 x)
(*.f32 #s(literal 2 binary32) x)
(* 2 x)
(*.f32 #s(literal 2 binary32) x)
(* 2 x)
(*.f32 #s(literal 2 binary32) x)
(* 2 x)
(*.f32 #s(literal 2 binary32) 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)))))
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(+ (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) (pow.f32 x #s(literal 4 binary32))) (/.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 (/.f32 #s(literal 5/96 binary32) (pow.f32 x #s(literal 6 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (/.f32 #s(literal 3/32 binary32) (pow.f32 x #s(literal 4 binary32)))) (log.f32 (/.f32 #s(literal -1 binary32) x))) (log.f32 #s(literal -1/2 binary32)))
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f32 (+.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f32 (+.f32 (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (*.f32 x x)) #s(literal 1/8 binary32)) x) x) #s(literal 1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f32 (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 5/128 binary32) (.f32 x x)) #s(literal 1/16 binary32)) (pow.f32 x #s(literal 4 binary32))) (+.f32 (/.f32 #s(literal 1/8 binary32) (.f32 x x)) #s(literal 1/2 binary32))) x)
(* -1 x)
(neg.f32 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f32 (*.f32 (/.f32 #s(literal 1/2 binary32) x) #s(literal 1 binary32)) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(-.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x) x)
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(neg.f32 (fma.f32 (/.f32 (+.f32 (/.f32 #s(literal -1/16 binary32) (*.f32 x x)) #s(literal -1/8 binary32)) (pow.f32 x #s(literal 4 binary32))) x (fma.f32 (/.f32 #s(literal -1 binary32) x) #s(literal 1/2 binary32) x)))
x
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f32 (/.f32 #s(literal -1 binary32) x) #s(literal 1/2 binary32) x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f32 (/.f32 #s(literal -1 binary32) x) #s(literal 1/2 binary32) x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f32 (/.f32 #s(literal -1 binary32) x) #s(literal 1/2 binary32) 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))))))
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(+ (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 5/96 binary32) (pow.f32 x #s(literal 6 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (/.f32 #s(literal 3/32 binary32) (pow.f32 x #s(literal 4 binary32)))) (log.f32 (/.f32 #s(literal -1 binary32) x))) (log.f32 #s(literal -1/2 binary32)))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+.f32 (-.f32 (log.f32 #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))) (log.f32 #s(literal -1 binary32)))
(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
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(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
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(+ (log -1) (+ (log 2) (* -1 (log (/ -1 x)))))
(+.f32 (-.f32 (log.f32 #s(literal 2 binary32)) (log.f32 (/.f32 #s(literal -1 binary32) x))) (log.f32 #s(literal -1 binary32)))
(+ (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)))
(pow x 2)
(*.f32 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(*.f32 x (fma.f32 (/.f32 (/.f32 #s(literal -1 binary32) x) x) x x))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(*.f32 x (fma.f32 (/.f32 (/.f32 #s(literal -1 binary32) x) x) x x))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(*.f32 x (fma.f32 (/.f32 (/.f32 #s(literal -1 binary32) x) x) x x))
(pow x 4)
(pow.f32 x #s(literal 4 binary32))
(* (pow x 4) (+ 1 (/ 1 (pow x 2))))
(fma.f32 x x (pow.f32 x #s(literal 4 binary32)))
(* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(fma.f32 x (+.f32 (pow.f32 x #s(literal 3 binary32)) x) #s(literal 1 binary32))
(* (pow x 4) (+ 1 (+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))))
(fma.f32 x (+.f32 (pow.f32 x #s(literal 3 binary32)) x) #s(literal 1 binary32))
(* -1 (pow x 2))
(*.f32 (neg.f32 x) x)
(* -1 (pow x 2))
(*.f32 (neg.f32 x) x)
(* -1 (pow x 2))
(*.f32 (neg.f32 x) x)
(* -1 (pow x 2))
(*.f32 (neg.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) (pow.f32 x #s(literal 4 binary32))) (/.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 (/.f32 #s(literal 5/96 binary32) (pow.f32 x #s(literal 6 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (/.f32 #s(literal 3/32 binary32) (pow.f32 x #s(literal 4 binary32)))) (log.f32 (/.f32 #s(literal -1 binary32) x))) (log.f32 #s(literal -1/2 binary32)))
(* -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) (pow.f32 x #s(literal 3 binary32)))) #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) (pow.f32 x #s(literal 3 binary32)))) #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 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 7 binary32)))) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 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) (pow.f32 x #s(literal 3 binary32)))) #s(literal 1/2 binary32) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) x)))))) (neg.f32 x))
(* -1 x)
(neg.f32 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f32 (*.f32 (/.f32 #s(literal 1/2 binary32) x) #s(literal 1 binary32)) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(-.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x) x)
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(neg.f32 (fma.f32 (/.f32 (+.f32 (/.f32 #s(literal -1/16 binary32) (*.f32 x x)) #s(literal -1/8 binary32)) (pow.f32 x #s(literal 4 binary32))) x (fma.f32 (/.f32 #s(literal -1 binary32) x) #s(literal 1/2 binary32) x)))
(/ 1 (pow x 4))
(/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 4 binary32)))
(/ (- 1 (/ 1 (pow x 2))) (pow x 4))
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) (*.f32 x x))) (pow.f32 x #s(literal 4 binary32)))
(/ (- (+ 1 (/ 1 (pow x 6))) (/ 1 (pow x 2))) (pow x 4))
(/.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 6 binary32))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (*.f32 x x))) (pow.f32 x #s(literal 4 binary32)))
(/ (- (+ 1 (/ 1 (pow x 6))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 8)))) (pow x 4))
(/.f32 (-.f32 (-.f32 (+.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 6 binary32))) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (*.f32 x x))) (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 8 binary32)))) (pow.f32 x #s(literal 4 binary32)))

rewrite351.0ms (4.8%)

Memory

-12.2MiB live, 267.1MiB allocated

Rules

6 868×	`lower-fma.f64`
6 868×	`lower-fma.f32`
4 140×	`lower-/.f64`
4 136×	`lower-/.f32`
3 524×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	229
0	71	194
1	263	171
2	1999	171
0	8384	157

Stop Event

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

Counts

22 → 741

Calls

Call 1

Inputs
(+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x))))
(log.f32 (+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))))
(*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))
(sqrt.f32 (-.f32 x #s(literal 1 binary32)))
(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)
(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))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.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))
(.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x)))))
(-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x)))
(.f32 #s(literal -1 binary32) (.f32 x x))
(log.f32 (+.f32 x (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x))))))))
(sqrt.f32 (+.f32 #s(literal 1 binary32) x))
(sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x))))))
(/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x))))

Outputs
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eval375.0ms (5.2%)

Memory: -10.5MiB live, 149.3MiB allocated
Compiler: Compiled 22 125 to 3 912 computations (82.3% saved)

prune101.0ms (1.4%)

Memory

26.3MiB live, 63.2MiB allocated

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	984	4	988
Fresh	3	0	3
Picked	3	2	5
Done	0	1	1
Total	990	7	997

Accuracy

100.0%

Counts

997 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	26.3%	(log.f32 (+.f32 x (/.f32 (sqrt.f32 (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32))) (sqrt.f32 (-.f32 (*.f32 x x) #s(literal -1 binary32))))))
▶	49.5%	(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) x) (-.f32 #s(literal 1 binary32) (.f32 x x))))))))
✓	98.5%	(log.f32 (+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))))
✓	49.5%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
▶	95.6%	(log.f32 (+.f32 x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)))
✓	96.8%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
▶	97.1%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) x))))

Compiler

Compiled 77 to 59 computations (23.4% saved)

simplify322.0ms (4.4%)

Memory

-31.2MiB live, 96.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f32 (sqrt.f32 (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32))) (sqrt.f32 (-.f32 (*.f32 x x) #s(literal -1 binary32))))
cost-diff	0	(+.f32 x (/.f32 (sqrt.f32 (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32))) (sqrt.f32 (-.f32 (*.f32 x x) #s(literal -1 binary32)))))
cost-diff	0	(log.f32 (+.f32 x (/.f32 (sqrt.f32 (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32))) (sqrt.f32 (-.f32 (*.f32 x x) #s(literal -1 binary32))))))
cost-diff	64	(-.f32 (*.f32 x x) #s(literal -1 binary32))
cost-diff	0	(+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) x) (-.f32 #s(literal 1 binary32) (.f32 x x)))))))
cost-diff	0	(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) x) (-.f32 #s(literal 1 binary32) (.f32 x x))))))))
cost-diff	160	(.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) x) (-.f32 #s(literal 1 binary32) (.f32 x x))))))
cost-diff	256	(/.f32 (-.f32 #s(literal 1 binary32) x) (-.f32 #s(literal 1 binary32) (*.f32 x x)))
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)
cost-diff	0	(+.f32 x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x))
cost-diff	0	(log.f32 (+.f32 x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)))
cost-diff	0	(/.f32 #s(literal 1/2 binary32) x)
cost-diff	0	(log.f32 (/.f32 #s(literal 1/2 binary32) x))
cost-diff	0	(neg.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) x)))
cost-diff	0	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) x))))

Rules

8 926×	`lower-fma.f64`
8 926×	`lower-fma.f32`
2 320×	`lower--.f64`
2 310×	`lower--.f32`
2 252×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	251
0	65	251
1	95	245
2	120	245
3	172	245
4	251	245
5	576	245
6	1526	221
7	3876	221
8	6011	221
9	7770	221
0	8064	215

Stop Event

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

Calls

Call 1

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

localize190.0ms (2.6%)

Memory

2.1MiB live, 155.0MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.4793138253739408	(log.f32 (+.f32 x (/.f32 (sqrt.f32 (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32))) (sqrt.f32 (-.f32 (*.f32 x x) #s(literal -1 binary32))))))
accuracy	5.8583918377998545	(sqrt.f32 (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)))
accuracy	14.817367249301142	(sqrt.f32 (-.f32 (*.f32 x x) #s(literal -1 binary32)))
accuracy	14.840804749301142	(/.f32 (sqrt.f32 (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32))) (sqrt.f32 (-.f32 (*.f32 x x) #s(literal -1 binary32))))
accuracy	0.26171875	(/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) x) (-.f32 #s(literal 1 binary32) (*.f32 x x)))))
accuracy	0.45703125	(.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) x) (-.f32 #s(literal 1 binary32) (.f32 x x))))))
accuracy	0.4793138253739408	(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) x) (-.f32 #s(literal 1 binary32) (.f32 x x))))))))
accuracy	14.865919997493336	(/.f32 (-.f32 #s(literal 1 binary32) x) (-.f32 #s(literal 1 binary32) (*.f32 x x)))
accuracy	0.0390625	(+.f32 x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x))
accuracy	0.4793138253739408	(log.f32 (+.f32 x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)))
accuracy	1.152058749550944	#s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)
accuracy	0	(/.f32 #s(literal 1/2 binary32) x)
accuracy	0	(neg.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) x)))
accuracy	0.0078125	(log.f32 (/.f32 #s(literal 1/2 binary32) x))
accuracy	0.9272632038718875	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) x))))

Samples

152.0ms

256×

valid

Compiler

Compiled 241 to 38 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 139.0ms

ival-log: 53.0ms (38.2% of total)

ival-add: 39.0ms (28.1% of total)

ival-pow: 16.0ms (11.5% of total)

ival-sqrt: 10.0ms (7.2% of total)

ival-div: 7.0ms (5% of total)

ival-sub: 7.0ms (5% of total)

ival-mult: 5.0ms (3.6% of total)

exact: 1.0ms (0.7% of total)

ival-neg: 1.0ms (0.7% of total)

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

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

series118.0ms (1.6%)

Memory

23.1MiB live, 99.1MiB allocated

Counts

18 → 216

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

58.0ms

((log (+ x (sqrt (- (* x x) 1)))) (neg (log (/ 1/2 x))) (log (/ 1/2 x)) (/ 1/2 x) (log (+ x (* (sqrt (- x 1)) (sqrt (+ 1 x))))) (+ x (* (sqrt (- x 1)) (sqrt (+ 1 x)))) (* (sqrt (- x 1)) (sqrt (+ 1 x))) (/ (- 1 x) (- 1 (* x x))) (* (sqrt (- x 1)) (/ 1 (sqrt (/ (- 1 x) (- 1 (* x x)))))) (log (+ x (* (sqrt (- x 1)) (/ 1 (sqrt (/ (- 1 x) (- 1 (* x x)))))))) (+ x (* (sqrt (- x 1)) (/ 1 (sqrt (/ (- 1 x) (- 1 (* x x))))))) (- (* x x) -1) (log (+ x (/ (sqrt (- (pow x 4) 1)) (sqrt (- (* x x) -1))))) (+ x (/ (sqrt (- (pow x 4) 1)) (sqrt (- (* x x) -1)))) (/ (sqrt (- (pow x 4) 1)) (sqrt (- (* x x) -1))) (/ 1 (sqrt (/ (- 1 x) (- 1 (* x x))))) (sqrt (- (* x x) -1)) (sqrt (- (pow x 4) 1)))

44.0ms

-inf

((log (+ x (sqrt (- (* x x) 1)))) (neg (log (/ 1/2 x))) (log (/ 1/2 x)) (/ 1/2 x) (log (+ x (* (sqrt (- x 1)) (sqrt (+ 1 x))))) (+ x (* (sqrt (- x 1)) (sqrt (+ 1 x)))) (* (sqrt (- x 1)) (sqrt (+ 1 x))) (/ (- 1 x) (- 1 (* x x))) (* (sqrt (- x 1)) (/ 1 (sqrt (/ (- 1 x) (- 1 (* x x)))))) (log (+ x (* (sqrt (- x 1)) (/ 1 (sqrt (/ (- 1 x) (- 1 (* x x)))))))) (+ x (* (sqrt (- x 1)) (/ 1 (sqrt (/ (- 1 x) (- 1 (* x x))))))) (- (* x x) -1) (log (+ x (/ (sqrt (- (pow x 4) 1)) (sqrt (- (* x x) -1))))) (+ x (/ (sqrt (- (pow x 4) 1)) (sqrt (- (* x x) -1)))) (/ (sqrt (- (pow x 4) 1)) (sqrt (- (* x x) -1))) (/ 1 (sqrt (/ (- 1 x) (- 1 (* x x))))) (sqrt (- (* x x) -1)) (sqrt (- (pow x 4) 1)))

8.0ms

inf

((log (+ x (sqrt (- (* x x) 1)))) (neg (log (/ 1/2 x))) (log (/ 1/2 x)) (/ 1/2 x) (log (+ x (* (sqrt (- x 1)) (sqrt (+ 1 x))))) (+ x (* (sqrt (- x 1)) (sqrt (+ 1 x)))) (* (sqrt (- x 1)) (sqrt (+ 1 x))) (/ (- 1 x) (- 1 (* x x))) (* (sqrt (- x 1)) (/ 1 (sqrt (/ (- 1 x) (- 1 (* x x)))))) (log (+ x (* (sqrt (- x 1)) (/ 1 (sqrt (/ (- 1 x) (- 1 (* x x)))))))) (+ x (* (sqrt (- x 1)) (/ 1 (sqrt (/ (- 1 x) (- 1 (* x x))))))) (- (* x x) -1) (log (+ x (/ (sqrt (- (pow x 4) 1)) (sqrt (- (* x x) -1))))) (+ x (/ (sqrt (- (pow x 4) 1)) (sqrt (- (* x x) -1)))) (/ (sqrt (- (pow x 4) 1)) (sqrt (- (* x x) -1))) (/ 1 (sqrt (/ (- 1 x) (- 1 (* x x))))) (sqrt (- (* x x) -1)) (sqrt (- (pow x 4) 1)))

simplify197.0ms (2.7%)

Memory

-8.9MiB live, 235.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 242×	`lower-fma.f64`
11 242×	`lower-fma.f32`
4 596×	`lower-+.f64`
4 596×	`lower-+.f32`
3 946×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	373	2958
1	1060	2477
2	3175	2446
0	8542	2335

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 212

Calls

Call 1

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

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 (/.f32 (pow.f32 x #s(literal 3 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) #s(literal -1/6 binary32) (+.f32 (/.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 (pow.f32 x #s(literal 3 binary32)) (fma.f32 (*.f32 x (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) #s(literal 3/40 binary32) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32)))))
(* -1 (+ (log 1/2) (* -1 (log x))))
(-.f32 (log.f32 x) (log.f32 #s(literal 1/2 binary32)))
(* -1 (+ (log 1/2) (* -1 (log x))))
(-.f32 (log.f32 x) (log.f32 #s(literal 1/2 binary32)))
(* -1 (+ (log 1/2) (* -1 (log x))))
(-.f32 (log.f32 x) (log.f32 #s(literal 1/2 binary32)))
(* -1 (+ (log 1/2) (* -1 (log x))))
(-.f32 (log.f32 x) (log.f32 #s(literal 1/2 binary32)))
(+ (log 1/2) (* -1 (log x)))
(-.f32 (log.f32 #s(literal 1/2 binary32)) (log.f32 x))
(+ (log 1/2) (* -1 (log x)))
(-.f32 (log.f32 #s(literal 1/2 binary32)) (log.f32 x))
(+ (log 1/2) (* -1 (log x)))
(-.f32 (log.f32 #s(literal 1/2 binary32)) (log.f32 x))
(+ (log 1/2) (* -1 (log x)))
(-.f32 (log.f32 #s(literal 1/2 binary32)) (log.f32 x))
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ 1/2 x)
(/.f32 #s(literal 1/2 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 (/.f32 (pow.f32 x #s(literal 3 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) #s(literal -1/6 binary32) (+.f32 (/.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 (pow.f32 x #s(literal 3 binary32)) (fma.f32 (*.f32 x (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) #s(literal 3/40 binary32) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32)))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ x (sqrt -1))
(+.f32 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) (sqrt.f32 #s(literal -1 binary32))) (*.f32 x x) (/.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)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 (*.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (/.f32 #s(literal 1/8 binary32) (sqrt.f32 #s(literal -1 binary32))) (pow.f32 x #s(literal 4 binary32)) (fma.f32 (*.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x) x (sqrt.f32 #s(literal -1 binary32))))
(+ (sqrt -1) (* (pow x 2) (+ (* (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 (pow.f32 x #s(literal 4 binary32)) (fma.f32 #s(literal 1/16 binary32) (.f32 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)))) (fma.f32 (.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x) x (sqrt.f32 #s(literal -1 binary32))))
1
#s(literal 1 binary32)
(+ 1 (* -1 x))
(-.f32 #s(literal 1 binary32) x)
(+ 1 (* x (- x 1)))
(fma.f32 (-.f32 x #s(literal 1 binary32)) x #s(literal 1 binary32))
(+ 1 (* x (- (* x (+ 1 (* -1 x))) 1)))
(fma.f32 (fma.f32 (-.f32 #s(literal 1 binary32) x) x #s(literal -1 binary32)) x #s(literal 1 binary32))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f32 (*.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x) x (sqrt.f32 #s(literal -1 binary32)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f32 (/.f32 #s(literal 1/8 binary32) (sqrt.f32 #s(literal -1 binary32))) (pow.f32 x #s(literal 4 binary32)) (fma.f32 (*.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x) x (sqrt.f32 #s(literal -1 binary32))))
(+ (sqrt -1) (* (pow x 2) (+ (* (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 (pow.f32 x #s(literal 4 binary32)) (fma.f32 #s(literal 1/16 binary32) (.f32 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)))) (fma.f32 (.f32 (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32))) x) x (sqrt.f32 #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 (/.f32 (pow.f32 x #s(literal 3 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) #s(literal -1/6 binary32) (+.f32 (/.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 (pow.f32 x #s(literal 3 binary32)) (fma.f32 (*.f32 x (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) #s(literal 3/40 binary32) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32)))))
(sqrt -1)
(sqrt.f32 #s(literal -1 binary32))
(+ x (sqrt -1))
(+.f32 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) (sqrt.f32 #s(literal -1 binary32))) (*.f32 x x) (/.f32 #s(literal 1/2 binary32) (sqrt.f32 #s(literal -1 binary32)))) x #s(literal 1 binary32)) x (sqrt.f32 #s(literal -1 binary32)))
1
#s(literal 1 binary32)
(+ 1 (pow x 2))
(fma.f32 x x #s(literal 1 binary32))
(+ 1 (pow x 2))
(fma.f32 x x #s(literal 1 binary32))
(+ 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 (/.f32 (pow.f32 x #s(literal 3 binary32)) (neg.f32 (sqrt.f32 #s(literal -1 binary32)))) #s(literal -1/6 binary32) (+.f32 (/.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 (pow.f32 x #s(literal 3 binary32)) (fma.f32 (*.f32 x (/.f32 x (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 5 binary32)))) #s(literal 3/40 binary32) (/.f32 #s(literal 1/6 binary32) (sqrt.f32 #s(literal -1 binary32)))) (+.f32 (/.f32 x (sqrt.f32 #s(literal -1 binary32))) (log.f32 (sqrt.f32 #s(literal -1 binary32)))))
(sqrt -1)
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(+ x (sqrt -1))
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(/.f32 #s(literal 1/2 binary32) 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)) (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))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+.f32 (-.f32 (-.f32 (/.f32 #s(literal -3/32 binary32) (pow.f32 x #s(literal 4 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (log.f32 (/.f32 #s(literal -1 binary32) x))) (log.f32 #s(literal -2 binary32)))
(+ (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 (+.f32 #s(literal -15 binary32) (/.f32 #s(literal -45/2 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 binary32)))) (pow.f32 x #s(literal 6 binary32))) #s(literal 1/720 binary32) (+.f32 (-.f32 (/.f32 #s(literal -3/32 binary32) (pow.f32 x #s(literal 4 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (log.f32 #s(literal -2 binary32)))) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(*.f32 #s(literal 2 binary32) x)
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(*.f32 (-.f32 #s(literal 2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) 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 (/.f32 #s(literal 1/2 binary32) x) x)) (/.f32 #s(literal -1/8 binary32) (pow.f32 x #s(literal 4 binary32)))) 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 1/16 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 binary32))) (pow.f32 x #s(literal 6 binary32))) (-.f32 (+.f32 #s(literal -2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) x) x)) (/.f32 #s(literal -1/8 binary32) (pow.f32 x #s(literal 4 binary32))))) (neg.f32 x))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))))
(fma.f32 (/.f32 x (*.f32 x x)) #s(literal -1/2 binary32) x)
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2))))))
(fma.f32 (/.f32 x (*.f32 x x)) #s(literal -1/2 binary32) (fma.f32 (/.f32 #s(literal -1/8 binary32) (pow.f32 x #s(literal 4 binary32))) x x))
(* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2)))))))
(*.f32 (-.f32 (+.f32 (/.f32 (/.f32 #s(literal 1/16 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 binary32))) (pow.f32 x #s(literal 6 binary32))) (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) x) x) #s(literal 1 binary32))) (/.f32 #s(literal -1/8 binary32) (pow.f32 x #s(literal 4 binary32)))) (neg.f32 x))
(/ 1 x)
(/.f32 #s(literal 1 binary32) x)
(* -1 (/ (- (/ 1 x) 1) x))
(/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) x)) x)
(* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 #s(literal 1 binary32) x) #s(literal 1 binary32)) x) #s(literal 1 binary32)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1) x)) 1) x)) 1) x))
(/.f32 (+.f32 (/.f32 (-.f32 (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) x)) x) #s(literal 1 binary32)) x) #s(literal 1 binary32)) x)
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))))
(fma.f32 (/.f32 x (*.f32 x x)) #s(literal -1/2 binary32) x)
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2))))))
(fma.f32 (/.f32 x (*.f32 x x)) #s(literal -1/2 binary32) (fma.f32 (/.f32 #s(literal -1/8 binary32) (pow.f32 x #s(literal 4 binary32))) x x))
(* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2)))))))
(*.f32 (-.f32 (+.f32 (/.f32 (/.f32 #s(literal 1/16 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 binary32))) (pow.f32 x #s(literal 6 binary32))) (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) x) x) #s(literal 1 binary32))) (/.f32 #s(literal -1/8 binary32) (pow.f32 x #s(literal 4 binary32)))) (neg.f32 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)) (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))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))
(+.f32 (-.f32 (-.f32 (/.f32 #s(literal -3/32 binary32) (pow.f32 x #s(literal 4 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (log.f32 (/.f32 #s(literal -1 binary32) x))) (log.f32 #s(literal -2 binary32)))
(+ (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 (+.f32 #s(literal -15 binary32) (/.f32 #s(literal -45/2 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 binary32)))) (pow.f32 x #s(literal 6 binary32))) #s(literal 1/720 binary32) (+.f32 (-.f32 (/.f32 #s(literal -3/32 binary32) (pow.f32 x #s(literal 4 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (log.f32 #s(literal -2 binary32)))) (log.f32 (/.f32 #s(literal -1 binary32) x)))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(*.f32 #s(literal 2 binary32) x)
(* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))
(*.f32 (-.f32 #s(literal 2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) 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 (/.f32 #s(literal 1/2 binary32) x) x)) (/.f32 #s(literal -1/8 binary32) (pow.f32 x #s(literal 4 binary32)))) 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 1/16 binary32) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 binary32))) (pow.f32 x #s(literal 6 binary32))) (-.f32 (+.f32 #s(literal -2 binary32) (/.f32 (/.f32 #s(literal 1/2 binary32) x) x)) (/.f32 #s(literal -1/8 binary32) (pow.f32 x #s(literal 4 binary32))))) (neg.f32 x))
(pow x 2)
(*.f32 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal 1 binary32))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal 1 binary32))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f32 x x #s(literal 1 binary32))
(+ (log -1/2) (log (/ -1 x)))
(+.f32 (log.f32 (/.f32 #s(literal -1 binary32) x)) (log.f32 #s(literal -1/2 binary32)))
(+ (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) (pow.f32 x #s(literal 4 binary32))) (/.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 (/.f32 #s(literal 5/96 binary32) (pow.f32 x #s(literal 6 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))) (/.f32 #s(literal 3/32 binary32) (pow.f32 x #s(literal 4 binary32)))) (log.f32 (/.f32 #s(literal -1 binary32) x))) (log.f32 #s(literal -1/2 binary32)))
(/ 1/2 x)
(/.f32 #s(literal 1/2 binary32) x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f32 (+.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f32 (+.f32 (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (*.f32 x x)) #s(literal 1/8 binary32)) x) x) #s(literal 1/2 binary32)) x)
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f32 (+.f32 (/.f32 (+.f32 (/.f32 #s(literal 5/128 binary32) (.f32 x x)) #s(literal 1/16 binary32)) (pow.f32 x #s(literal 4 binary32))) (+.f32 (/.f32 #s(literal 1/8 binary32) (.f32 x x)) #s(literal 1/2 binary32))) x)
(* -1 x)
(neg.f32 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(*.f32 (-.f32 (/.f32 (/.f32 #s(literal 1/2 binary32) x) x) #s(literal 1 binary32)) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(fma.f32 (/.f32 (/.f32 (+.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 x x)) #s(literal 1/2 binary32)) x) x) x (neg.f32 x))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(neg.f32 (fma.f32 (-.f32 (/.f32 (+.f32 (/.f32 #s(literal -1/16 binary32) (*.f32 x x)) #s(literal -1/8 binary32)) (pow.f32 x #s(literal 4 binary32))) (/.f32 (/.f32 #s(literal 1/2 binary32) x) x)) 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) (pow.f32 x #s(literal 3 binary32)))) #s(literal 1/2 binary32) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) x)))) (neg.f32 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) (pow.f32 x #s(literal 3 binary32)))) #s(literal 1/2 binary32) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) x))))) (neg.f32 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 (/.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) (pow.f32 x #s(literal 7 binary32)))) (pow.f32 (sqrt.f32 #s(literal -1 binary32)) #s(literal 4 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) (pow.f32 x #s(literal 3 binary32)))) #s(literal 1/2 binary32) (neg.f32 (sqrt.f32 (/.f32 #s(literal 1 binary32) x)))))) (neg.f32 x))
(* -1 x)
(neg.f32 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(.f32 (+.f32 (/.f32 #s(literal -1/2 binary32) (.f32 x x)) #s(literal -1 binary32)) x)
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(.f32 (+.f32 (+.f32 (/.f32 #s(literal -1/2 binary32) (.f32 x x)) #s(literal -1 binary32)) (/.f32 #s(literal 1/8 binary32) (pow.f32 x #s(literal 4 binary32)))) x)
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(neg.f32 (fma.f32 (-.f32 (+.f32 (/.f32 #s(literal 1/16 binary32) (pow.f32 x #s(literal 6 binary32))) (/.f32 (/.f32 #s(literal 1/2 binary32) x) x)) (/.f32 #s(literal 1/8 binary32) (pow.f32 x #s(literal 4 binary32)))) x x))
(pow x 2)
(*.f32 x x)
(* (pow x 2) (- 1 (* 1/2 (/ 1 (pow x 4)))))
(*.f32 x (fma.f32 (/.f32 #s(literal -1/2 binary32) (pow.f32 x #s(literal 4 binary32))) x x))
(* (pow x 2) (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 4)))) (pow x 4)))))
(*.f32 x (fma.f32 (/.f32 (-.f32 #s(literal -1/2 binary32) (/.f32 #s(literal 1/8 binary32) (pow.f32 x #s(literal 4 binary32)))) (pow.f32 x #s(literal 4 binary32))) x x))
(* (pow x 2) (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 4)))) (pow x 8)))) (* 1/2 (/ 1 (pow x 4)))))
(*.f32 x (fma.f32 (-.f32 (/.f32 (+.f32 (/.f32 #s(literal -1/16 binary32) (pow.f32 x #s(literal 4 binary32))) #s(literal -1/8 binary32)) (pow.f32 x #s(literal 8 binary32))) (/.f32 #s(literal 1/2 binary32) (pow.f32 x #s(literal 4 binary32)))) x x))

rewrite181.0ms (2.5%)

Memory

1.7MiB live, 226.9MiB allocated

Rules

4 948×	`lower-/.f64`
4 940×	`lower-/.f32`
4 146×	`lower-fma.f64`
4 146×	`lower-fma.f32`
3 910×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	203
0	65	168
1	250	153
2	1664	126
0	9047	114

Stop Event

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

Counts

18 → 757

Calls

Call 1

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

Outputs
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eval132.0ms (1.8%)

Memory: 21.2MiB live, 180.5MiB allocated
Compiler: Compiled 20 192 to 3 549 computations (82.4% saved)

prune20.0ms (0.3%)

Memory

-23.4MiB live, 60.9MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	966	3	969
Fresh	0	0	0
Picked	1	3	4
Done	0	3	3
Total	967	9	976

Accuracy

100.0%

Counts

976 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.7%	(log.f32 (fma.f32 #s(literal 1 binary32) x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)))
✓	49.5%	(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) x) (-.f32 #s(literal 1 binary32) (.f32 x x))))))))
▶	49.5%	(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 x (-.f32 #s(literal 1 binary32) (*.f32 x x)))))))))
▶	46.1%	(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 x x)) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 x x))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) x)))))))))
✓	98.5%	(log.f32 (+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))))
✓	49.5%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
✓	95.6%	(log.f32 (+.f32 x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)))
✓	96.8%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
✓	97.1%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) x))))

Compiler

Compiled 129 to 82 computations (36.4% saved)

simplify159.0ms (2.2%)

Memory

30.6MiB live, 229.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)
cost-diff	0	(log.f32 (fma.f32 #s(literal 1 binary32) x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)))
cost-diff	96	(fma.f32 #s(literal 1 binary32) x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x))
cost-diff	0	(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 x (-.f32 #s(literal 1 binary32) (*.f32 x x)))))))))
cost-diff	64	(/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 x x)))
cost-diff	160	(.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 x (-.f32 #s(literal 1 binary32) (*.f32 x x)))))))
cost-diff	608	(-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 x (-.f32 #s(literal 1 binary32) (.f32 x x))))
cost-diff	160	(.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 x x)) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) x))))
cost-diff	160	(.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 x x)) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 x x))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) x)))))))
cost-diff	704	(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 x x))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) x)))
cost-diff	864	(/.f32 (-.f32 #s(literal 1 binary32) (.f32 x x)) (-.f32 #s(literal 1 binary32) (.f32 x x)))

Rules

13 500×	`lower-fma.f64`
13 498×	`lower-fma.f32`
3 146×	`lower-*.f64`
3 140×	`lower-*.f32`
2 178×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	435
0	57	365
1	95	301
2	164	275
3	321	275
4	1020	275
5	6212	275
0	8142	260

Stop Event

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

Calls

Call 1

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

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

localize83.0ms (1.1%)

Memory

-30.4MiB live, 172.1MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.4793138253739408	(log.f32 (fma.f32 #s(literal 1 binary32) x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)))
accuracy	1.152058749550944	#s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)
accuracy	29.884421912069076	(fma.f32 #s(literal 1 binary32) x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x))
accuracy	0.45703125	(.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 x (-.f32 #s(literal 1 binary32) (*.f32 x x)))))))
accuracy	0.4793138253739408	(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 x (-.f32 #s(literal 1 binary32) (*.f32 x x)))))))))
accuracy	0.8105471219401673	(/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 x x)))
accuracy	14.842482497493336	(/.f32 x (-.f32 #s(literal 1 binary32) (*.f32 x x)))
accuracy	0.4793138253739408	(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 x x)) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 x x))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) x)))))))))
accuracy	0.8105471219401673	(/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 x x)))
accuracy	13.761671930647701	(/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 x x))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) x)))
accuracy	16.174906984271242	(/.f32 (-.f32 #s(literal 1 binary32) (.f32 x x)) (-.f32 #s(literal 1 binary32) (.f32 x x)))

Samples

60.0ms

256×

valid

Compiler

Compiled 433 to 32 computations (92.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-div: 12.0ms (26.7% of total)

ival-mult: 8.0ms (17.8% of total)

ival-log: 7.0ms (15.6% of total)

ival-sqrt: 7.0ms (15.6% of total)

ival-add: 5.0ms (11.1% of total)

ival-sub: 5.0ms (11.1% of total)

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

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

exact: 0.0ms (0% of total)

series11.0ms (0.1%)

Memory

19.9MiB live, 19.9MiB allocated

Counts

13 → 156

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify191.0ms (2.6%)

Memory

11.1MiB live, 164.9MiB allocated

Algorithm

1×	egg-herbie

Rules

11 214×	`lower-fma.f64`
11 214×	`lower-fma.f32`
5 678×	`lower-*.f64`
5 678×	`lower-*.f32`
2 364×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	250	2343
1	714	1782
2	2147	1744
0	8243	1684

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 152

Calls

Call 1

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

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

rewrite315.0ms (4.3%)

Memory

7.1MiB live, 247.2MiB allocated

Rules

5 636×	`lower-/.f64`
5 626×	`lower-/.f32`
4 382×	`lower-*.f64`
4 376×	`lower-*.f32`
3 806×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	236
0	57	163
1	241	105
2	1833	89
0	9398	82

Stop Event

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

Counts

13 → 1 316

Calls

Call 1

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

Outputs
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eval841.0ms (11.6%)

Memory: 8.3MiB live, 385.2MiB allocated
Compiler: Compiled 67 583 to 8 364 computations (87.6% saved)

prune79.0ms (1.1%)

Memory

-5.0MiB live, 120.5MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	1 665	1	1 666
Fresh	0	0	0
Picked	1	2	3
Done	0	6	6
Total	1 666	9	1 675

Accuracy

100.0%

Counts

1 675 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	6.7%	(log.f32 (fma.f32 #s(literal 1 binary32) x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)))
	49.5%	(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) x))))))))
✓	49.5%	(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) x) (-.f32 #s(literal 1 binary32) (.f32 x x))))))))
✓	49.5%	(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 x (-.f32 #s(literal 1 binary32) (*.f32 x x)))))))))
✓	98.5%	(log.f32 (+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))))
✓	49.5%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
✓	95.6%	(log.f32 (+.f32 x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)))
✓	96.8%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
✓	97.1%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) x))))

Compiler

Compiled 348 to 180 computations (48.3% saved)

regimes17.0ms (0.2%)

Memory

10.8MiB live, 50.0MiB allocated

Counts

17 → 1

Calls

Call 1

Inputs
(log.f32 (+.f32 x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)))
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
(log.f32 (fma.f32 #s(literal 1 binary32) x #s(approx (* (sqrt (- x 1)) (sqrt (+ 1 x))) x)))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) x))))
(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (fma.f32 #s(literal 2 binary32) x (/.f32 #s(literal -1/2 binary32) x))))
(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
(log.f32 (+.f32 x (*.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (sqrt.f32 (+.f32 #s(literal 1 binary32) x)))))
(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (-.f32 #s(literal 1 binary32) x) (-.f32 #s(literal 1 binary32) (.f32 x x))))))))
(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (-.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 x (-.f32 #s(literal 1 binary32) (*.f32 x x)))))))))
(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) x))))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))
(log.f32 (+.f32 x (.f32 (sqrt.f32 (-.f32 x #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (sqrt.f32 (.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 x x)) (-.f32 #s(literal 1 binary32) (.f32 x x))) (/.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (*.f32 x x))) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) x)))))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (-.f32 (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))) (/.f32 #s(literal 1/4 binary32) (*.f32 x x))))
(log.f32 (+.f32 x (/.f32 (sqrt.f32 (-.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32))) (sqrt.f32 (-.f32 (*.f32 x x) #s(literal -1 binary32))))))
(log.f32 (+.f32 x (sqrt.f32 (.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (*.f32 x x))))))))

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

Calls

3 calls:

6.0ms	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
5.0ms	x
5.0ms	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
98.5%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes14.0ms (0.2%)

Memory

-37.9MiB live, 23.1MiB allocated

Counts

8 → 1

Calls

Call 1

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

Calls

3 calls:

7.0ms	(+.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)))))
3.0ms	x

Results

Accuracy	Segments	Branch
97.1%	1	`x`
97.1%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
97.1%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes6.0ms (0.1%)

Memory

11.1MiB live, 11.1MiB allocated

Accuracy

Total -27.9b remaining (-2000.6%)

Threshold costs -27.9b (-2000.6%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
95.6%	1	`x`
95.6%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
95.6%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify39.0ms (0.5%)

Memory

9.4MiB live, 49.0MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative-binary32-+.f32`
10×	`neg-mul-1-binary32-*.f32-neg.f32`
8×	`unsub-neg-binary32--.f32-neg.f32-+.f32`
8×	`-commutative-binary32-.f32`
6×	`sub-neg-binary32-neg.f32-+.f32--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	41
1	39	41
2	44	41
3	50	41
4	57	41
5	66	41

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

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

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

soundness713.0ms (9.8%)

Memory

-25.3MiB live, 452.4MiB allocated

Rules

14 602×	`lower-fma.f64`
14 602×	`lower-fma.f32`
10 204×	`lower-fma.f64`
10 204×	`lower-fma.f32`
6 868×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	363	3128
1	1031	2805
2	3233	2720
0	8465	2582
0	7	28
0	12	28
1	49	28
2	322	28
3	3626	28
0	8646	24
0	43	229
0	71	194
1	263	171
2	1999	171
0	8384	157
0	150	559
1	411	533
2	1146	526
3	3331	488
4	7979	488
0	8531	459

Stop Event

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

Compiler

Compiled 80 to 59 computations (26.3% saved)

preprocess33.0ms (0.5%)

Memory: 20.8MiB live, 99.2MiB allocated
Compiler: Compiled 88 to 66 computations (25% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample432.0ms (6%)

explain174.0ms (2.4%)

preprocess341.0ms (4.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify326.0ms (4.5%)

localize24.0ms (0.3%)

series6.0ms (0.1%)

simplify199.0ms (2.7%)

rewrite277.0ms (3.8%)

eval41.0ms (0.6%)

prune11.0ms (0.1%)

simplify440.0ms (6.1%)

localize128.0ms (1.8%)

series160.0ms (2.2%)

simplify212.0ms (2.9%)

rewrite351.0ms (4.8%)

eval375.0ms (5.2%)

prune101.0ms (1.4%)

simplify322.0ms (4.4%)

localize190.0ms (2.6%)

series118.0ms (1.6%)

simplify197.0ms (2.7%)

rewrite181.0ms (2.5%)

eval132.0ms (1.8%)

prune20.0ms (0.3%)

simplify159.0ms (2.2%)

localize83.0ms (1.1%)

series11.0ms (0.1%)

simplify191.0ms (2.6%)

rewrite315.0ms (4.3%)

eval841.0ms (11.6%)

prune79.0ms (1.1%)

regimes17.0ms (0.2%)

regimes14.0ms (0.2%)

regimes6.0ms (0.1%)

simplify39.0ms (0.5%)

soundness713.0ms (9.8%)

preprocess33.0ms (0.5%)

end0.0ms (0%)

Profiling