Metrics for Rust f32::acosh

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample772.0ms (15.8%)

Memory

-129.5MiB live, 552.0MiB allocated

Samples

563.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 412.0ms

ival-acosh: 372.0ms (90.4% of total)

ival->=: 28.0ms (6.8% of total)

exact: 7.0ms (1.7% of total)

ival-assert: 4.0ms (1% of total)

Bogosity

explain100.0ms (2%)

Memory

6.5MiB live, 205.1MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f32`	`(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))`	oflow-rescue	132	0
↳	`(*.f32 x x)`	overflow	132
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	132
`log.f32`	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`	oflow-rescue	1	0
↳	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`	overflow	1
↳	`(*.f32 x x)`	overflow	132
↳	`(-.f32 (*.f32 x x) #s(literal 1 binary32))`	overflow	132

Confusion

	Predicted +	Predicted -
+	132	0
-	0	124

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	132	0	0
-	0	0	124

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	124
1	131
2	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

36.0ms

512×

valid

Compiler

Compiled 112 to 32 computations (71.4% saved)

Precisions

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

ival-log: 8.0ms (37.2% of total)

ival-mult: 4.0ms (18.6% of total)

ival-sqrt: 4.0ms (18.6% of total)

ival-sub: 3.0ms (14% of total)

ival-add: 3.0ms (14% of total)

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

exact: 0.0ms (0% of total)

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

preprocess279.0ms (5.7%)

Memory

-19.0MiB live, 267.0MiB allocated

Algorithm

1×	egg-herbie

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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.7%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify317.0ms (6.5%)

Memory

12.1MiB live, 164.1MiB 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))

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)

localize55.0ms (1.1%)

Memory

-22.5MiB live, 15.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(-.f32 (*.f32 x x) #s(literal 1 binary32))
accuracy	0.02734375	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))
accuracy	0.1348088616856756	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
accuracy	14.16854324510084	(sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))

Samples

14.0ms

256×

valid

Compiler

Compiled 68 to 16 computations (76.5% saved)

Precisions

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

ival-log: 2.0ms (22.7% of total)

ival-mult: 2.0ms (22.7% of total)

ival-sqrt: 2.0ms (22.7% of total)

ival-sub: 1.0ms (11.4% of total)

ival-add: 1.0ms (11.4% 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

14.3MiB live, 14.3MiB 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)))

simplify164.0ms (3.3%)

Memory

11.6MiB live, 164.3MiB allocated

Algorithm

1×	egg-herbie

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))

rewrite158.0ms (3.2%)

Memory

20.5MiB live, 211.3MiB allocated

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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eval152.0ms (3.1%)

Memory: -8.4MiB live, 156.5MiB allocated
Compiler: Compiled 8 015 to 1 574 computations (80.4% saved)

prune10.0ms (0.2%)

Memory

-8.8MiB live, 29.6MiB allocated

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	361	6	367
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	361	7	368

Accuracy

100.0%

Counts

368 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	29.0%	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
	16.6%	(log.f32 (+.f32 x (sqrt.f32 (/.f32 (exp.f32 (log.f32 (-.f32 (pow.f32 x #s(literal 6 binary32)) #s(literal 1 binary32)))) (exp.f32 (log.f32 (-.f32 (+.f32 (pow.f32 x #s(literal 4 binary32)) #s(literal 1 binary32)) (.f32 #s(literal -1 binary32) (.f32 x x)))))))))
✓	51.7%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
▶	98.4%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
▶	2.8%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (fma.f32 #s(literal 2 binary32) x (/.f32 #s(literal -1/2 binary32) x))))
▶	96.8%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
▶	96.3%	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))

Compiler

Compiled 131 to 109 computations (16.8% saved)

simplify230.0ms (4.7%)

Memory

23.8MiB live, 181.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	176
0	47	168
1	64	168
2	74	168
3	103	168
4	157	168
5	296	168
6	603	168
7	1146	168
8	2768	168
9	4506	168
10	5535	168
11	5975	168
12	6083	168
13	6162	168
14	6238	168
15	6960	168
16	7616	168
0	8048	168

Stop Event

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

Calls

Call 1

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

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

localize99.0ms (2%)

Memory

-17.5MiB live, 100.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(log.f32 x)
accuracy	0	(log.f32 #s(literal 2 binary32))
accuracy	0.26171875	(+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32)))
accuracy	0.9209823858731482	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f32 (log.f32 x) (log.f32 #s(literal 2 binary32))))
accuracy	0.02734375	(+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x)
accuracy	0.1348088616856756	(log.f32 (+.f32 (sqrt.f32 (fma.f32 x x #s(literal -1 binary32))) x))
accuracy	14.16854324510084	(sqrt.f32 (fma.f32 x x #s(literal -1 binary32)))
accuracy	31.447815394549213	(fma.f32 x x #s(literal -1 binary32))
accuracy	0	(/.f32 #s(literal -1/2 binary32) x)
accuracy	0.1348088616856756	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (fma.f32 #s(literal 2 binary32) x (/.f32 #s(literal -1/2 binary32) x))))
accuracy	0.438726463091674	#s(approx (+ x (sqrt (- (* x x) 1))) (fma.f32 #s(literal 2 binary32) x (/.f32 #s(literal -1/2 binary32) x)))
accuracy	30.143163347739332	(fma.f32 #s(literal 2 binary32) x (/.f32 #s(literal -1/2 binary32) x))
accuracy	0	(*.f32 #s(literal 2 binary32) x)
accuracy	0.1348088616856756	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x)))
accuracy	1.0813357134367645	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 2 binary32) x))
accuracy	0	(-.f32 x (/.f32 #s(literal 1/2 binary32) x))
accuracy	0.02734375	(+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x))))
accuracy	0.1348088616856756	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
accuracy	0.49204744448026705	#s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))

Samples

79.0ms

256×

valid

Compiler

Compiled 254 to 50 computations (80.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-mult: 29.0ms (44% of total)

ival-log: 21.0ms (31.8% of total)

ival-add: 6.0ms (9.1% of total)

ival-div: 4.0ms (6.1% of total)

ival-sqrt: 3.0ms (4.5% of total)

ival-sub: 2.0ms (3% of total)

exact: 1.0ms (1.5% of total)

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

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

series102.0ms (2.1%)

Memory

-5.2MiB live, 145.6MiB allocated

Counts

19 → 216

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
53.0ms	x	@	0	((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)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ (* 2 x) (/ -1/2 x)) (/ -1/2 x) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1) (log (+ x (sqrt (- (* x x) 1)))) (+ (log x) (log 2)) (log x) (log 2))
18.0ms	x	@	-inf	((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)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ (* 2 x) (/ -1/2 x)) (/ -1/2 x) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1) (log (+ x (sqrt (- (* x x) 1)))) (+ (log x) (log 2)) (log x) (log 2))
17.0ms	x	@	inf	((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)))) (+ x (sqrt (- (* x x) 1))) (* 2 x) (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ (* 2 x) (/ -1/2 x)) (/ -1/2 x) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1) (log (+ x (sqrt (- (* x x) 1)))) (+ (log x) (log 2)) (log x) (log 2))

Time

Variable

Point

Expression

53.0ms

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

18.0ms

-inf

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

17.0ms

inf

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

simplify155.0ms (3.2%)

Memory

-14.9MiB live, 162.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	169	2286
1	456	2186
2	1248	2101
3	3605	2025
0	8611	1939

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

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

rewrite386.0ms (7.9%)

Memory

20.4MiB live, 215.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	162
0	47	152
1	173	152
2	1184	152
0	8431	152

Stop Event

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

Counts

19 → 420

Calls

Call 1

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

Outputs
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eval168.0ms (3.4%)

Memory: -11.5MiB live, 107.4MiB allocated
Compiler: Compiled 11 487 to 1 986 computations (82.7% saved)

prune14.0ms (0.3%)

Memory

2.7MiB live, 41.5MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	630	2	632
Fresh	1	0	1
Picked	3	2	5
Done	0	1	1
Total	634	5	639

Accuracy

100.0%

Counts

639 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.7%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
✓	98.4%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
▶	98.4%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (-.f32 (*.f32 #s(literal 2 binary32) x) (/.f32 #s(literal 1/2 binary32) x))))
✓	96.8%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 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 38 to 33 computations (13.2% saved)

simplify377.0ms (7.7%)

Memory

25.3MiB live, 260.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	78
0	23	78
1	37	78
2	51	78
3	77	78
4	126	78
5	209	78
6	496	78
7	871	78
8	2314	78
9	3820	78
10	4801	78
11	5239	78
12	5473	78
13	5563	78
14	5644	78
15	6378	78
16	7190	78
17	7606	78
18	7691	78
19	7723	78
20	7737	78
0	8543	72

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

localize83.0ms (1.7%)

Memory

-13.2MiB live, 62.1MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(-.f32 (*.f32 #s(literal 2 binary32) x) (/.f32 #s(literal 1/2 binary32) x))
accuracy	0	(*.f32 #s(literal 2 binary32) x)
accuracy	0.1348088616856756	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (-.f32 (*.f32 #s(literal 2 binary32) x) (/.f32 #s(literal 1/2 binary32) x))))
accuracy	0.438726463091674	#s(approx (+ x (sqrt (- (* x x) 1))) (-.f32 (*.f32 #s(literal 2 binary32) x) (/.f32 #s(literal 1/2 binary32) 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	0.9209823858731482	#s(approx (log (+ x (sqrt (- (* x x) 1)))) (neg.f32 (log.f32 (/.f32 #s(literal 1/2 binary32) x))))

Samples

61.0ms

256×

valid

Compiler

Compiled 111 to 27 computations (75.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 39.0ms (73.3% of total)

ival-log: 5.0ms (9.4% of total)

ival-div: 2.0ms (3.8% of total)

ival-sub: 2.0ms (3.8% of total)

ival-sqrt: 2.0ms (3.8% of total)

ival-add: 1.0ms (1.9% of total)

ival-neg: 1.0ms (1.9% of total)

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

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

exact: 0.0ms (0% of total)

series58.0ms (1.2%)

Memory

18.3MiB live, 105.1MiB allocated

Counts

8 → 96

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

Calls

3 calls:

Time

Variable

Point

Expression

33.0ms

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

13.0ms

-inf

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

9.0ms

inf

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

simplify162.0ms (3.3%)

Memory

1.9MiB live, 190.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	139	859
1	372	811
2	969	794
3	2724	762
4	6239	762
0	8280	737

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

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)
(/ -1/2 x)
(/ (- (* 2 (pow x 2)) 1/2) x)
(/ (- (* 2 (pow x 2)) 1/2) x)
(/ (- (* 2 (pow x 2)) 1/2) x)
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 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))))
(* -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)
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- 2 (* 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)))))
(* 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 (+ (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)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 2)))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 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)

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

rewrite188.0ms (3.8%)

Memory

9.7MiB live, 161.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	70
0	23	70
1	88	68
2	651	68
3	7451	68
0	8219	62

Stop Event

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

Counts

8 → 310

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

Outputs
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eval121.0ms (2.5%)

Memory: -14.7MiB live, 127.0MiB allocated
Compiler: Compiled 6 791 to 1 489 computations (78.1% saved)

prune10.0ms (0.2%)

Memory

-3.8MiB live, 33.0MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	443	0	443
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	443	5	448

Accuracy

100.0%

Counts

448 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.7%	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
✓	98.4%	(log.f32 (+.f32 x #s(approx (sqrt (- (* x x) 1)) (-.f32 x (/.f32 #s(literal 1/2 binary32) x)))))
✓	98.4%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (-.f32 (*.f32 #s(literal 2 binary32) x) (/.f32 #s(literal 1/2 binary32) x))))
✓	96.8%	(log.f32 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f32 #s(literal 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 123 to 86 computations (30.1% saved)

regimes13.0ms (0.3%)

Memory

-17.8MiB live, 20.1MiB allocated

Counts

9 → 1

Calls

Call 1

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

Calls

3 calls:

6.0ms	(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))
3.0ms	x
3.0ms	(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
98.4%	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

17.2MiB live, 17.2MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs

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

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

Calls

3 calls:

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

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)

regimes4.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
96.8%	1	`x`
96.8%	1	`(log.f32 (+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32)))))`
96.8%	1	`(+.f32 x (sqrt.f32 (-.f32 (*.f32 x x) #s(literal 1 binary32))))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify86.0ms (1.8%)

Memory

-12.9MiB live, 73.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	30	43
2	39	43
3	46	43
4	51	43
5	53	43

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

#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))) (*.f32 #s(literal 2 binary32) x)))

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

soundness433.0ms (8.9%)

Memory

-14.0MiB live, 297.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	162
0	47	152
1	173	152
2	1184	152
0	8431	152
0	150	559
1	411	533
2	1146	526
3	3331	488
4	7979	488
0	8531	459

Stop Event

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

Compiler

Compiled 35 to 30 computations (14.3% saved)

preprocess184.0ms (3.8%)

Memory: 21.9MiB live, 94.9MiB allocated
Compiler: Compiled 82 to 60 computations (26.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample772.0ms (15.8%)

explain100.0ms (2%)

preprocess279.0ms (5.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify317.0ms (6.5%)

localize55.0ms (1.1%)

series6.0ms (0.1%)

simplify164.0ms (3.3%)

rewrite158.0ms (3.2%)

eval152.0ms (3.1%)

prune10.0ms (0.2%)

simplify230.0ms (4.7%)

localize99.0ms (2%)

series102.0ms (2.1%)

simplify155.0ms (3.2%)

rewrite386.0ms (7.9%)

eval168.0ms (3.4%)

prune14.0ms (0.3%)

simplify377.0ms (7.7%)

localize83.0ms (1.7%)

series58.0ms (1.2%)

simplify162.0ms (3.3%)

rewrite188.0ms (3.8%)

eval121.0ms (2.5%)

prune10.0ms (0.2%)

regimes13.0ms (0.3%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

simplify86.0ms (1.8%)

soundness433.0ms (8.9%)

preprocess184.0ms (3.8%)

end0.0ms (0%)

Profiling