Metrics for Hyperbolic arcsine

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze84.0ms (1%)

Memory

-24.1MiB live, 92.2MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
50%	50%	50%	0%	0%	0%	0%	4
62.5%	62.5%	37.5%	0%	0%	0%	0%	5
68.8%	68.7%	31.2%	0%	0%	0%	0%	6
71.9%	71.8%	28.1%	0%	0%	0%	0%	7
73.4%	73.4%	26.5%	0%	0%	0%	0%	8
74.2%	74.2%	25.8%	0%	0%	0%	0%	9
74.6%	74.6%	25.4%	0%	0%	0%	0%	10
74.8%	74.8%	25.2%	0%	0%	0%	0%	11
74.9%	74.9%	25.1%	0%	0%	0%	0%	12

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample2.7s (31.7%)

Memory

29.5MiB live, 3 413.2MiB allocated

Samples

1.2s	4 422×	1	valid
828.0ms	1 591×	2	valid
377.0ms	2 243×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 2.1s

ival-log: 1.2s (60.2% of total)

ival-hypot: 492.0ms (23.9% of total)

ival-add: 214.0ms (10.4% of total)

adjust: 99.0ms (4.8% of total)

ival-true: 6.0ms (0.3% of total)

exact: 5.0ms (0.2% of total)

ival-assert: 3.0ms (0.1% of total)

Bogosity

explain191.0ms (2.2%)

Memory

4.6MiB live, 429.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
130	-	-	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`
65	-	-	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`
65	-	-	`(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f64`	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`	sensitivity	130	0
`+.f64`	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`	cancellation	65	0
`sqrt.f64`	`(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))`	oflow-rescue	65	0
↳	`(*.f64 x x)`	overflow	65
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	65

Confusion

	Predicted +	Predicted -
+	226	0
-	1	29

Precision

0.9955947136563876

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	226	0	0
-	1	0	29

Precision?

0.9955947136563876

Recall?

1.0

Freqs

test

number	freq
0	29
1	194
2	33

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

62.0ms	288×	1	valid
45.0ms	94×	2	valid
10.0ms	130×	0	valid

Compiler

Compiled 80 to 25 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-log: 41.0ms (46.4% of total)

ival-hypot: 23.0ms (26% of total)

ival-add: 10.0ms (11.3% of total)

adjust: 9.0ms (10.2% of total)

ival-mult: 5.0ms (5.7% of total)

ival-true: 1.0ms (1.1% of total)

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

exact: 0.0ms (0% of total)

preprocess20.0ms (0.2%)

Memory

-5.4MiB live, 37.9MiB allocated

Algorithm

1×	egg-herbie

Rules

30×	`distribute-lft-neg-in`
28×	`sub-neg`
26×	`associate--r+`
24×	`neg-mul-1`
22×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	23	19
2	48	19
3	88	19
4	137	19
5	184	19
6	211	19
7	214	19
0	7	9
0	12	9
1	16	9
0	16	8

Stop Event

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

Calls

Call 1

Inputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))

Outputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))

Compiler

Compiled 10 to 7 computations (30% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	16.2%	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify3.0ms (0%)

Memory

8.5MiB live, 8.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
cost-diff	0	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
cost-diff	128	(+.f64 (*.f64 x x) #s(literal 1 binary64))

Rules

8×	`lower-+.f32`
4×	`lift-+.f64`
4×	`lower-+.f64`
4×	`+-commutative`
2×	`lift-sqrt.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	12	33
1	16	33
0	16	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
x
(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)

Outputs
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
(+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)
x
(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(fma.f64 x x #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)

localize62.0ms (0.7%)

Memory

24.0MiB live, 142.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	15.058889021023464	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy	15.173777103314602	(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))
accuracy	30.335731504438908	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))

Samples

27.0ms	144×	1	valid
22.0ms	47×	2	valid
5.0ms	65×	0	valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 43.0ms

ival-log: 20.0ms (46.5% of total)

ival-hypot: 11.0ms (25.6% of total)

adjust: 5.0ms (11.6% of total)

ival-add: 4.0ms (9.3% of total)

ival-mult: 2.0ms (4.7% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.2%)

Memory

-43.4MiB live, 14.2MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6)))) (taylor 0 x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2))))))) (taylor 0 x) (#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* 1/2 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8))))) (taylor 0 x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (* -1 (log (/ 1 x)))) (taylor inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4))) (taylor inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4))) (taylor inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 2 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))) (taylor inf x) (#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))) (taylor inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) #s(literal 1 binary64)) (patch (+.f64 (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log 1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#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.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#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.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) (patch (log.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x)) (taylor -inf x) (#s(alt (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) (patch (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) (patch (sqrt.f64 (+.f64 (.f64 x x) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
9.0ms	x	@	0	((+ (* x x) 1) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)) (* x x))
2.0ms	x	@	inf	((+ (* x x) 1) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)) (* x x))
1.0ms	x	@	-inf	((+ (* x x) 1) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)) (* x x))

Time

Variable

Point

Expression

9.0ms

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

2.0ms

inf

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

1.0ms

-inf

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

simplify154.0ms (1.8%)

Memory

-4.1MiB live, 188.0MiB allocated

Algorithm

1×	egg-herbie

Rules

11 038×	`lower-fma.f64`
11 038×	`lower-fma.f32`
4 124×	`lower-+.f64`
4 124×	`lower-+.f32`
2 226×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	525
1	353	517
2	931	509
3	2896	479
4	6990	479
0	8034	448

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 58

Calls

Call 1

Inputs
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(pow x 2)
(pow x 2)
(pow x 2)
(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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(pow x 2)
(pow x 2)
(pow x 2)
(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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(fma.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (log.f64 x)) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (log.f64 x)) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)) (log.f64 x)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal 1/2 binary64) x))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(fma.f64 #s(literal 2 binary64) x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64)) x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(-.f64 x (/.f64 #s(literal -1/2 binary64) x))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) x)
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(fma.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (neg.f64 (log.f64 (neg.f64 x))) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (neg.f64 (log.f64 (neg.f64 x))) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (neg.f64 (log.f64 (neg.f64 x))) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x))) (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (log.f64 #s(literal 1/2 binary64))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
(-.f64 (-.f64 (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (log.f64 #s(literal 1/2 binary64))) (neg.f64 (log.f64 (neg.f64 x)))))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) x) x))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 (-.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) x) x))) (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 6 binary64)))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) x)
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(neg.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite158.0ms (1.9%)

Memory

46.1MiB live, 238.8MiB allocated

Rules

6 062×	`lower-fma.f64`
6 062×	`lower-fma.f32`
3 598×	`lower-*.f32`
3 596×	`lower-*.f64`
2 994×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	31
0	12	31
1	44	31
2	297	31
3	3155	31
0	8738	27

Stop Event

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

Counts

5 → 363

Calls

Call 1

Inputs
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(*.f64 x x)

Outputs
(.f64 (exp.f64 (log.f64 (fma.f64 (.f64 (*.f64 x x) x) x #s(literal -1 binary64)))) (exp.f64 (neg.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64))))))
(.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x))) (exp.f64 (neg.f64 (log1p.f64 (.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)))))))
(.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (*.f64 x x) x) x #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) (.f64 (.f64 x x) x) (fma.f64 (.f64 (*.f64 x x) x) x #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) #s(literal -1 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x) (.f64 (.f64 x x) x)) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x)) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 (*.f64 x x) x) x) x) x)))))
(*.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) x #s(literal -1 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x) #s(literal -1 binary64))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x) #s(literal 1 binary64)) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) x) x)) (.f64 x x) (.f64 #s(literal -1 binary64) (.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (fma.f64 x x #s(literal -1 binary64)))))) #s(literal 1 binary64)) (pow.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 x x) x)) x (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x)))) #s(literal 1 binary64)))
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(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
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eval85.0ms (1%)

Memory: -16.2MiB live, 104.8MiB allocated
Compiler: Compiled 12 006 to 1 625 computations (86.5% saved)

prune96.0ms (1.1%)

Memory

-20.8MiB live, 140.5MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	412	9	421
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	413	9	422

Accuracy

100.0%

Counts

422 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	4.8%	(log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
	16.2%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
▶	25.0%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
	10.7%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
▶	25.9%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
	25.6%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
▶	24.2%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
▶	52.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
▶	51.2%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))

Compiler

Compiled 184 to 114 computations (38% saved)

simplify165.0ms (1.9%)

Memory

28.0MiB live, 66.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
cost-diff	0	(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
cost-diff	0	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
cost-diff	0	(-.f64 x (/.f64 #s(literal -1/2 binary64) x))
cost-diff	0	#s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))
cost-diff	0	(+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))
cost-diff	0	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
cost-diff	0	(*.f64 #s(literal 2 binary64) x)
cost-diff	0	#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
cost-diff	0	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
cost-diff	0	(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))

Rules

2 896×	`lower-fma.f32`
2 890×	`lower-fma.f64`
1 352×	`lower-*.f32`
1 344×	`lower-*.f64`
844×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	243
0	53	243
1	82	243
2	125	239
3	209	239
4	404	239
5	809	239
6	2677	239
7	3157	239
8	3835	239
9	4068	239
10	4161	239
11	4177	239
12	4187	239
13	4414	239
14	4694	239
15	4694	239
16	4694	239
17	4694	239
18	4696	239
0	4696	226

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
#s(literal 3/40 binary64)
(*.f64 x x)
x
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64))
#s(literal -1/6 binary64)
(*.f64 x x)
x
#s(literal 1 binary64)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
(+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))
x
#s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 x (/.f64 #s(literal -1/2 binary64) x))
(/.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(literal 1/8 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)

Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))
#s(literal 3/40 binary64)
(*.f64 x x)
x
#s(literal -1/6 binary64)
#s(literal 1 binary64)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64))
#s(literal -1/6 binary64)
(*.f64 x x)
x
#s(literal 1 binary64)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
(log.f64 (+.f64 #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) x))
(+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))
(+.f64 #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) x)
x
#s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 x (/.f64 #s(literal -1/2 binary64) x))
(/.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
#s(literal 1/8 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)

localize170.0ms (2%)

Memory

-6.8MiB live, 224.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.03515625	(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
accuracy	0.26218151831628256	(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
accuracy	30.335731504438908	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
accuracy	46.95697307397985	#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
accuracy	0	(-.f64 x (/.f64 #s(literal -1/2 binary64) x))
accuracy	15.058889021023464	(+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))
accuracy	30.335731504438908	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
accuracy	47.689286016545594	#s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	30.335731504438908	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
accuracy	47.451335082255746	#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
accuracy	0	(*.f64 x x)
accuracy	0.05078125	(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)
accuracy	0.08984375	(fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64))
accuracy	31.25726651868536	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
accuracy	0.0390625	(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
accuracy	0.0546875	(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
accuracy	0.06640625	(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
accuracy	30.368239587418874	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))

Samples

74.0ms	144×	1	valid
49.0ms	47×	2	valid
20.0ms	65×	0	valid

Compiler

Compiled 183 to 28 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 110.0ms

ival-mult: 20.0ms (18.2% of total)

ival-log: 20.0ms (18.2% of total)

const: 15.0ms (13.7% of total)

ival-add: 15.0ms (13.7% of total)

ival-div: 13.0ms (11.8% of total)

ival-hypot: 12.0ms (10.9% of total)

adjust: 10.0ms (9.1% of total)

ival-sub: 3.0ms (2.7% of total)

exact: 1.0ms (0.9% of total)

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

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

series20.0ms (0.2%)

Memory

-6.8MiB live, 29.2MiB allocated

Counts

20 → 240

Calls

Call 1

Inputs
#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x) (patch (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (.f64 #s(literal 2 binary64) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ ( x x) 1))) (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())
#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ x (sqrt (+ ( x x) 1))) (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())
#s(alt (log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))) (patch (log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))) #<representation binary64>) () ())
#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())
#s(alt (-.f64 x (/.f64 #s(literal -1/2 binary64) x)) (patch (-.f64 x (/.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())
#s(alt (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ ( x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))) #<representation binary64>) () ())
#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ x (sqrt (+ ( x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) (patch (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6)))) (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
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#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.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (.f64 #s(literal 2 binary64) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ ( x x) 1))) (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#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.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (.f64 #s(literal 2 binary64) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ ( x x) 1))) (*.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ x (sqrt (+ ( x x) 1))) (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ x (sqrt (+ ( x x) 1))) (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ x (sqrt (+ ( x x) 1))) (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x)) (taylor -inf x) (#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (.f64 #s(literal 2 binary64) x)) (patch #s(approx (+ x (sqrt (+ ( x x) 1))) (*.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) x) (patch (.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ (log 1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))) (patch (log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))) (patch (log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))) #<representation binary64>) () ())) ())
#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.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))) (patch (log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))) #<representation binary64>) () ())) ())
#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.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))) (patch (log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x)) (taylor -inf x) (#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) (patch #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal -1/2 binary64) x)) (patch (-.f64 x (/.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal -1/2 binary64) x)) (patch (-.f64 x (/.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal -1/2 binary64) x)) (patch (-.f64 x (/.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 #s(literal -1/2 binary64) x)) (patch (-.f64 x (/.f64 #s(literal -1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log 1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ ( x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ ( x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))) #<representation binary64>) () ())) ())
#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.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ ( x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))) #<representation binary64>) () ())) ())
#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.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ ( x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ x (sqrt (+ ( x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ x (sqrt (+ ( x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ x (sqrt (+ ( x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x)) (taylor -inf x) (#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x)) (patch #s(approx (+ x (sqrt (+ ( x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) (patch (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) (patch (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) (patch (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) (patch (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt -1/2 (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/8 (/ 1 (pow x 2))) 1/2) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/8 (/ 1 (pow x 2))) 1/2) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/8 (/ 1 (pow x 2))) 1/2) (taylor -inf x) (#s(alt (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (patch (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1/8 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/8 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/8 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 1/8 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (patch (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

inf

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

3.0ms

-inf

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

2.0ms

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

simplify160.0ms (1.9%)

Memory

45.1MiB live, 233.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14 074×	`lower-fma.f64`
14 074×	`lower-fma.f32`
4 144×	`lower-*.f64`
4 144×	`lower-*.f32`
2 380×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	162	2274
1	432	2180
2	1178	2179
3	3627	2109
0	8697	1991

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 230

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
1
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))
(+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))
-1/6
(- (* 3/40 (pow x 2)) 1/6)
(- (* 3/40 (pow x 2)) 1/6)
(- (* 3/40 (pow x 2)) 1/6)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
1
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* -1/6 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(/ 1/2 x)
(/ (+ 1/2 (pow x 2)) x)
(/ (+ 1/2 (pow x 2)) x)
(/ (+ 1/2 (pow x 2)) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(/ 1/8 (pow x 3))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/ 1/8 (pow x 2))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 3/40 (pow x 5))
(* (pow x 5) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 3/40 (pow x 4))
(* (pow x 4) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 3/40 (pow x 2))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/40 (* 1/6 (/ 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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(* 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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(/ -1/2 x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
-1/2
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (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)))))
(* 3/40 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 3/40)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 3/40 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 3/40 (/ 1 (pow x 4))))))
(* 3/40 (pow x 4))
(* (pow x 4) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 3/40 (pow x 2))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/40 (* 1/6 (/ 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)))))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1/6 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/6))
(pow x 2)
(pow x 2)
(pow x 2)
(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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) 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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
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 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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(/ -1/2 x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
-1/2
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))

Outputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/6 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))
(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))
(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
-1/6
#s(literal -1/6 binary64)
(- (* 3/40 (pow x 2)) 1/6)
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(- (* 3/40 (pow x 2)) 1/6)
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(- (* 3/40 (pow x 2)) 1/6)
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/6 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (* -1/6 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (* -1/6 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(fma.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (pow x 2)) x)
(/.f64 (fma.f64 x x #s(literal 1/2 binary64)) x)
(/ (+ 1/2 (pow x 2)) x)
(/.f64 (fma.f64 x x #s(literal 1/2 binary64)) x)
(/ (+ 1/2 (pow x 2)) x)
(/.f64 (fma.f64 x x #s(literal 1/2 binary64)) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(/ 1/8 (pow x 3))
(/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 (*.f64 x x) x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 (*.f64 x x) x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 (*.f64 x x) x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (log.f64 x)) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (log.f64 x)) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(-.f64 (+.f64 (+.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (log.f64 x)) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)))
(* 3/40 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 3/40 binary64))
(* (pow x 5) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
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(-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x))) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
(-.f64 (+.f64 (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x))) (log.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 (.f64 (.f64 x x) x) x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1/2 binary64))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) x)
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(neg.f64 (+.f64 (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)) x))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(-.f64 x (/.f64 #s(literal -1/2 binary64) x))
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(-.f64 x (/.f64 #s(literal -1/2 binary64) x))
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(-.f64 x (/.f64 #s(literal -1/2 binary64) x))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x))) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
(-.f64 (+.f64 (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x))) (log.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 (.f64 (.f64 x x) x) x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1/2 binary64))) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))

rewrite421.0ms (5%)

Memory

-180.7MiB live, 298.1MiB allocated

Rules

6 428×	`lower-fma.f32`
6 422×	`lower-fma.f64`
4 654×	`lower-/.f32`
4 648×	`lower-/.f64`
3 862×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	220
0	53	220
1	195	220
2	1443	220
0	8281	207

Stop Event

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

Counts

20 → 502

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 #s(literal -1/6 binary64) (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
(+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))))
#s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))
(-.f64 x (/.f64 #s(literal -1/2 binary64) x))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))

Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) #s(literal -1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64))))
(.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)) x) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)))))
(.f64 (.f64 x (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (.f64 x x) #s(literal -1 binary64))))
(.f64 (.f64 x (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)))))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(.f64 x (fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))) (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x) (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x) (-.f64 (.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x)) (.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x) (.f64 #s(literal 1 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 #s(literal 1 binary64) x) (-.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x) (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x)) (.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) #s(literal 3 binary64)) (pow.f64 (.f64 x #s(literal 1 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) (.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) (-.f64 (.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64))) (.f64 (.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) (.f64 x #s(literal 1 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) #s(literal 3 binary64))) (fma.f64 (.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1 binary64)) (-.f64 (.f64 (.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) (.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x))) (.f64 (.f64 x #s(literal 1 binary64)) (.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) #s(literal -1 binary64)) x)) (neg.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)) x)) (neg.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) #s(literal -1 binary64)))) (neg.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (.f64 x (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)))) (neg.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) #s(literal -1 binary64)) x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 x x) x) #s(literal 1 binary64)) x) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x))))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 x x) #s(literal -1 binary64))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal -1 binary64)))
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(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/8 binary64))
(.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) x)))
(.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))
(pow.f64 (.f64 (.f64 x x) #s(literal 8 binary64)) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1/8 binary64) x))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (/.f64 #s(literal 1/8 binary64) x)) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 x x) #s(literal 8 binary64))))
(/.f64 (/.f64 #s(literal 1/8 binary64) x) (*.f64 x #s(literal 1 binary64)))
(/.f64 (/.f64 #s(literal 1/8 binary64) x) x)
(/.f64 #s(literal -1/8 binary64) (neg.f64 (neg.f64 (*.f64 (neg.f64 x) x))))
(/.f64 #s(literal -1/8 binary64) (*.f64 (neg.f64 x) x))
(/.f64 #s(literal 1/8 binary64) (neg.f64 (*.f64 (neg.f64 x) x)))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (.f64 (.f64 x x) #s(literal 8 binary64)))))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 8 binary64)))
(neg.f64 (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 x x) #s(literal 8 binary64))) #s(literal -1 binary64)))

eval103.0ms (1.2%)

Memory: 8.3MiB live, 159.5MiB allocated
Compiler: Compiled 19 004 to 2 039 computations (89.3% saved)

prune75.0ms (0.9%)

Memory

-15.2MiB live, 148.6MiB allocated

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	807	3	810
Fresh	1	3	4
Picked	1	4	5
Done	0	0	0
Total	809	10	819

Accuracy

100.0%

Counts

819 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
	4.8%	(log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
▶	16.2%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
✓	25.0%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
▶	10.7%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
✓	25.9%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
▶	25.6%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)))
✓	24.2%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
▶	52.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)))
✓	51.2%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
▶	53.3%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 164 to 100 computations (39% saved)

simplify13.0ms (0.1%)

Memory

17.3MiB live, 17.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
cost-diff	0	(+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)
cost-diff	0	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
cost-diff	0	#s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64))
cost-diff	0	(/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)
cost-diff	0	#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))
cost-diff	0	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)))
cost-diff	0	#s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))
cost-diff	0	(+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)))
cost-diff	0	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
cost-diff	0	(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)
cost-diff	0	(fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x))
cost-diff	0	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)))
cost-diff	320	(*.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (+ (* (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))

Rules

330×	`lower-fma.f32`
324×	`lower-fma.f64`
248×	`lower-*.f32`
238×	`lower-*.f64`
148×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	248
0	57	239
1	91	239
2	154	237
3	298	237
4	481	237
5	518	237
6	521	237
0	521	232

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
x
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)))
(fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))
(*.f64 x x)
x
#s(literal 3/40 binary64)
#s(literal -1/6 binary64)
(*.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
(+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)))
x
#s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))
#s(literal 1 binary64)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))
(/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)
#s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
x
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
(+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
x
#s(literal 1 binary64)

Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
x
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x) x x))
(fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x))
(fma.f64 (.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x) x x)
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)
(.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)
(.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(*.f64 x x)
x
#s(literal 3/40 binary64)
#s(literal -1/6 binary64)
(*.f64 #s(literal 1 binary64) x)
x
#s(literal 1 binary64)
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
(log.f64 (+.f64 #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) x))
(+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)))
(+.f64 #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) x)
x
#s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))
#s(literal 1 binary64)
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))
(/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)
#s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
x
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
(+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
x
#s(literal 1 binary64)

localize388.0ms (4.6%)

Memory

19.1MiB live, 174.7MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	15.058889021023464	(+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)
accuracy	15.173777103314602	(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
accuracy	30.335731504438908	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
accuracy	0.03515625	(/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)
accuracy	30.335731504438908	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)))
accuracy	32.57981551903193	#s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64))
accuracy	46.95697307397985	#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))
accuracy	15.058889021023464	(+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)))
accuracy	29.918239034613244	#s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))
accuracy	30.335731504438908	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
accuracy	0.06640625	(fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))
accuracy	0.09765625	(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)
accuracy	0.23828125	(.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)
accuracy	30.368239587418874	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)))
accuracy	0.0390625	(.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)
accuracy	30.368239587418874	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))
accuracy	30.448453260021147	#s(approx (+ (* (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64))

Samples

205.0ms	144×	1	valid
50.0ms	47×	2	valid
15.0ms	65×	0	valid

Compiler

Compiled 194 to 31 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 233.0ms

ival-mult: 85.0ms (36.5% of total)

const: 63.0ms (27.1% of total)

ival-log: 39.0ms (16.8% of total)

adjust: 13.0ms (5.6% of total)

ival-add: 13.0ms (5.6% of total)

ival-hypot: 12.0ms (5.2% of total)

ival-div: 6.0ms (2.6% of total)

ival-sub: 2.0ms (0.9% of total)

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

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

exact: 0.0ms (0% of total)

series83.0ms (1%)

Memory

-20.6MiB live, 16.6MiB allocated

Counts

20 → 240

Calls

Call 1

Inputs
#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x) (patch (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1 binary64) x) (patch (.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x))) (patch #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)) (patch (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) (patch (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) #<representation binary64>) () ())
#s(alt (log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)))) (patch (log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))) (patch (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))) #<representation binary64>) () ())
#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)) (patch #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x) (patch (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x) #<representation binary64>) () ())
#s(alt #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) (patch #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (patch (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) #<representation binary64>) () ())
#s(alt (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) (patch #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) #<representation binary64>) () ())) ())
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#s(alt (* -1 x) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) (patch #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log 1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))) #<representation binary64>) () ())) ())
#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.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))) #<representation binary64>) () ())) ())
#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.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))) (patch (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)) (patch #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)) (patch #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)) (patch #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x)) (taylor -inf x) (#s(alt #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)) (patch #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x) (patch (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x) (patch (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x) (patch (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x) (patch (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt -1/2 (taylor -inf x) (#s(alt #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) (patch #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/8 (/ 1 (pow x 2))) 1/2) (taylor -inf x) (#s(alt #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) (patch #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/8 (/ 1 (pow x 2))) 1/2) (taylor -inf x) (#s(alt #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) (patch #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/8 (/ 1 (pow x 2))) 1/2) (taylor -inf x) (#s(alt #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) (patch #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (log 1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (patch (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (patch (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#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.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (patch (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#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.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (patch (log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x)) (taylor -inf x) (#s(alt (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 3/40 (pow x 3)) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 3/40))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 3/40))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 3/40))) (taylor -inf x) (#s(alt (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (patch (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 3/40 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

72.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

simplify300.0ms (3.5%)

Memory

2.4MiB live, 117.5MiB allocated

Algorithm

1×	egg-herbie

Rules

14 330×	`lower-fma.f64`
14 330×	`lower-fma.f32`
3 958×	`lower-+.f64`
3 958×	`lower-+.f32`
3 728×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	161	2460
1	438	2378
2	1175	2376
3	3673	2292
0	8391	2167

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 219

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
1
(+ 1 (* -1/6 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))
(+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))
x
x
x
x
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* -1/6 (pow x 2))
(* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))
(* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))
(* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(/ 1/8 (pow x 3))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/ 1/8 (pow x 2))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(* -1/6 x)
(* x (- (* 3/40 (pow x 2)) 1/6))
(* x (- (* 3/40 (pow x 2)) 1/6))
(* x (- (* 3/40 (pow x 2)) 1/6))
-1/6
(- (* 3/40 (pow x 2)) 1/6)
(- (* 3/40 (pow x 2)) 1/6)
(- (* 3/40 (pow x 2)) 1/6)
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 3/40 (pow x 5))
(* (pow x 5) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 3/40 (pow x 4))
(* (pow x 4) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
x
x
x
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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 3/40 (pow x 5))
(* (pow x 5) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 3/40 (pow x 4))
(* (pow x 4) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 3/40 (* 1/6 (/ 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))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(/ -1/2 x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
(/ (- (* 1/8 (/ 1 (pow x 2))) 1/2) x)
-1/2
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* 3/40 (pow x 3))
(* (pow x 3) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 3) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 3) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* 3/40 (pow x 2))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/40 (* 1/6 (/ 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)))))
(* 3/40 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 3/40)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 3/40 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 3/40 (/ 1 (pow x 4))))))
(* 3/40 (pow x 4))
(* (pow x 4) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
x
x
x
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)))))
(* 3/40 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 3/40)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 3/40 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 3/40 (/ 1 (pow x 4))))))
(* 3/40 (pow x 4))
(* (pow x 4) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 3/40 (* 1/6 (/ 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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(+ (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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(/ -1/2 x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
-1/2
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(+ (log 1/2) (log (/ -1 x)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
(/ -1/2 x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* 3/40 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 3/40)))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 3/40)))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 3/40)))
(* 3/40 (pow x 2))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))

Outputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/6 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))
(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))
(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64))
x
x
x
x
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* -1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/6 binary64))
(* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))
(.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x)
(* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))
(.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x)
(* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))
(.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(fma.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(/ 1/8 (pow x 3))
(/.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 (*.f64 x x) x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 (*.f64 x x) x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 (*.f64 x x) x))
(/ 1/8 (pow x 2))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))
(/ (+ 1/8 (* -1/2 (pow x 2))) (pow x 2))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(fma.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(* -1/6 x)
(*.f64 #s(literal -1/6 binary64) x)
(* x (- (* 3/40 (pow x 2)) 1/6))
(.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)
(* x (- (* 3/40 (pow x 2)) 1/6))
(.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)
(* x (- (* 3/40 (pow x 2)) 1/6))
(.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)
-1/6
#s(literal -1/6 binary64)
(- (* 3/40 (pow x 2)) 1/6)
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(- (* 3/40 (pow x 2)) 1/6)
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(- (* 3/40 (pow x 2)) 1/6)
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (log.f64 x)) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
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(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
(-.f64 (+.f64 (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x))) (log.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 (.f64 (.f64 x x) x) x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1/2 binary64))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) x)
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(neg.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x))) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
(-.f64 (+.f64 (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x))) (log.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 (.f64 (.f64 x x) x) x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1/2 binary64))) x)
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(- (* 1/8 (/ 1 (pow x 2))) 1/2)
(-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64))
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x))) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
(-.f64 (+.f64 (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (+.f64 (log.f64 (/.f64 #s(literal -1 binary64) x)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x))) (log.f64 #s(literal 1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) (.f64 (.f64 (.f64 x x) x) x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1/2 binary64))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) x)
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(neg.f64 (fma.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* 3/40 (pow x 3))
(.f64 (.f64 (*.f64 x x) x) #s(literal 3/40 binary64))
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 3/40)))
(.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 3/40)))
(.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)
(* -1 (* (pow x 3) (- (* 1/6 (/ 1 (pow x 2))) 3/40)))
(.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)
(* 3/40 (pow x 2))
(.f64 #s(literal 3/40 binary64) (.f64 x x))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))

rewrite312.0ms (3.7%)

Memory

16.0MiB live, 137.7MiB allocated

Rules

8 960×	`lower-fma.f32`
8 954×	`lower-fma.f64`
4 090×	`lower-*.f32`
4 080×	`lower-*.f64`
4 034×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	233
0	57	224
1	217	222
2	1355	222
0	8316	213

Stop Event

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

Counts

20 → 450

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)
#s(approx (+ (* (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) x)
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)))
(fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x))
(.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
(+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)))
#s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)))
#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x))
(/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)
#s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64))
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
(+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
(.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))

Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))
(.f64 (.f64 #s(approx (+ (* (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x) #s(literal 1 binary64))
(.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)
(.f64 #s(literal 1 binary64) (.f64 #s(approx (+ (* (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))
(.f64 x #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)))
(.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 x))
(*.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 1 binary64))
(pow.f64 x #s(literal 1 binary64))
(/.f64 (neg.f64 x) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(/.f64 x #s(literal 1 binary64))
(neg.f64 (neg.f64 x))
(-.f64 #s(literal 0 binary64) (neg.f64 x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
x
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) (*.f64 x x) x))
(.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) (.f64 x x) x) x) (/.f64 (.f64 x (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) x #s(literal -1 binary64))) (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x #s(literal -1 binary64))))
(.f64 (.f64 x (fma.f64 (.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) (.f64 (.f64 x x) x)) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) x #s(literal -1 binary64))))
(.f64 (.f64 x (fma.f64 (.f64 (.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) (.f64 (.f64 x x) x)) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 (.f64 (.f64 x x) x) x) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x)))))
(.f64 (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) (.f64 x x) x) (-.f64 x (.f64 (.f64 (.f64 x x) x) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 (.f64 (.f64 x x) x) (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))))))
(.f64 (neg.f64 (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) (.f64 x x) x) (.f64 x (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) x #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 x (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x #s(literal -1 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) (.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64))) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 (.f64 x x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) x)) x (.f64 x (-.f64 x (.f64 (.f64 (.f64 x x) x) (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)))))))))
(.f64 (.f64 (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) (.f64 x x) x) (.f64 x (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x #s(literal -1 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) (.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64))) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (neg.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x)) (.f64 (*.f64 x x) x))))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x)) (.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64))) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (.f64 x x) x) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64))) (.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) x)) x (.f64 x (-.f64 x (.f64 (.f64 (.f64 x x) x) (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))))))))
(.f64 (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) x) x #s(literal 1 binary64)) x)
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) x) (.f64 x x) x))
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(/.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 #s(literal 9/1600 binary64) (.f64 x x)) (.f64 x x))) (-.f64 #s(literal -1/6 binary64) (.f64 #s(literal 3/40 binary64) (.f64 x x))))
(/.f64 (neg.f64 (fma.f64 #s(literal 9/1600 binary64) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1/36 binary64))) (neg.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal 1/6 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 27/64000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64))) (neg.f64 (+.f64 #s(literal 1/36 binary64) (fma.f64 (.f64 #s(literal 9/1600 binary64) (.f64 x x)) (.f64 x x) (.f64 (.f64 (neg.f64 x) x) #s(literal -1/80 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 27/64000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64))) (neg.f64 (fma.f64 (.f64 #s(literal 9/1600 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/80 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)))))
(/.f64 (fma.f64 #s(literal 9/1600 binary64) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1/36 binary64)) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal 1/6 binary64)))
(/.f64 (fma.f64 (.f64 #s(literal 27/64000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64)) (+.f64 #s(literal 1/36 binary64) (fma.f64 (.f64 #s(literal 9/1600 binary64) (.f64 x x)) (.f64 x x) (.f64 (.f64 (neg.f64 x) x) #s(literal -1/80 binary64)))))
(/.f64 (fma.f64 (.f64 #s(literal 27/64000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64)) (fma.f64 (.f64 #s(literal 9/1600 binary64) (.f64 x x)) (.f64 x x) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/80 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal -1/6 binary64) (.f64 #s(literal 3/40 binary64) (.f64 x x))) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 #s(literal 9/1600 binary64) (.f64 x x)) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/36 binary64) (fma.f64 (.f64 #s(literal 9/1600 binary64) (.f64 x x)) (.f64 x x) (.f64 (.f64 (neg.f64 x) x) #s(literal -1/80 binary64)))) (fma.f64 (.f64 #s(literal 27/64000 binary64) (.f64 (.f64 x x) x)) (.f64 (.f64 x x) x) #s(literal -1/216 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))))
(fma.f64 (*.f64 #s(literal 3/40 binary64) x) x #s(literal -1/6 binary64))
(fma.f64 (.f64 (.f64 #s(literal 9/1600 binary64) (.f64 x x)) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 (/.f64 #s(literal 1/36 binary64) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal 1/6 binary64)))))
(fma.f64 (.f64 #s(literal 3/40 binary64) (.f64 x x)) #s(literal 1 binary64) #s(literal -1/6 binary64))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 3/40 binary64) (.f64 x x)) #s(literal -1/6 binary64))
(fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))
(fma.f64 x (*.f64 #s(literal 3/40 binary64) x) #s(literal -1/6 binary64))
(-.f64 (/.f64 #s(literal 1/36 binary64) (-.f64 #s(literal -1/6 binary64) (.f64 #s(literal 3/40 binary64) (.f64 x x)))) (/.f64 (.f64 (.f64 #s(literal 9/1600 binary64) (.f64 x x)) (.f64 x x)) (-.f64 #s(literal -1/6 binary64) (.f64 #s(literal 3/40 binary64) (.f64 x x)))))
(-.f64 (/.f64 (.f64 (.f64 #s(literal 9/1600 binary64) (.f64 x x)) (.f64 x x)) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal 1/6 binary64))) (/.f64 #s(literal 1/36 binary64) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal 1/6 binary64))))
(+.f64 (/.f64 (.f64 (.f64 #s(literal 9/1600 binary64) (.f64 x x)) (.f64 x x)) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal 1/6 binary64))) (neg.f64 (/.f64 #s(literal 1/36 binary64) (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal 1/6 binary64)))))
(+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 3/40 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal 3/40 binary64) (.f64 x x)) #s(literal -1/6 binary64))

eval178.0ms (2.1%)

Memory: 11.1MiB live, 83.8MiB allocated
Compiler: Compiled 16 514 to 1 787 computations (89.2% saved)

prune207.0ms (2.4%)

Memory

-14.7MiB live, 107.2MiB allocated

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	667	2	669
Fresh	1	0	1
Picked	1	4	5
Done	0	4	4
Total	669	10	679

Accuracy

100.0%

Counts

679 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	4.8%	(log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))
✓	16.2%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
✓	25.0%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
✓	10.7%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
✓	25.9%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
✓	25.6%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)))
✓	24.2%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
▶	52.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))
✓	51.2%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
✓	53.3%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 99 to 57 computations (42.4% saved)

simplify275.0ms (3.2%)

Memory

-26.8MiB live, 82.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
cost-diff	0	(/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
cost-diff	576	(log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))
cost-diff	896	(-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)
cost-diff	0	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))

Rules

16 562×	`lower-fma.f32`
16 556×	`lower-fma.f64`
2 256×	`lower-*.f32`
2 252×	`lower-*.f64`
1 936×	`lower-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	114
0	32	121
1	56	115
2	98	87
3	212	86
4	375	86
5	563	86
6	1209	86
7	2597	86
8	4302	86
9	5803	86
10	7959	86
0	8091	86

Stop Event

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

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))
(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
#s(literal 3/40 binary64)
(*.f64 x x)
x
#s(literal -1/6 binary64)
(.f64 (.f64 x x) x)
(log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))
(/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
(-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x))
(fma.f64 x x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(*.f64 x x)
(-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))

Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x))
(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)
(fma.f64 (.f64 (.f64 x x) x) (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))
#s(literal 3/40 binary64)
(*.f64 x x)
x
#s(literal -1/6 binary64)
(.f64 (.f64 x x) x)
(log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))
(neg.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))
(/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
(/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
(-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x))
#s(literal 1 binary64)
(fma.f64 x x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(*.f64 x x)
(-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))

localize301.0ms (3.5%)

Memory

9.8MiB live, 122.8MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	14.268456641594375	(-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)
accuracy	15.173777103314602	(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
accuracy	29.788921962542844	(-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x))
accuracy	30.335731504438908	(log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))
accuracy	0.04296875	(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)
accuracy	0.06640625	(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
accuracy	0.08203125	(.f64 (.f64 x x) x)
accuracy	30.368239587418874	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))

Samples

134.0ms	47×	2	valid
76.0ms	204×	1	valid
1.0ms	5×	0	valid

Compiler

Compiled 114 to 20 computations (82.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 193.0ms

ival-log: 82.0ms (42.5% of total)

adjust: 60.0ms (31.1% of total)

ival-hypot: 13.0ms (6.7% of total)

ival-mult: 10.0ms (5.2% of total)

const: 10.0ms (5.2% of total)

ival-add: 9.0ms (4.7% of total)

ival-sub: 5.0ms (2.6% of total)

ival-div: 3.0ms (1.6% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated

Counts

11 → 132

Calls

Call 1

Inputs
#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) (patch (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (patch (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) #<representation binary64>) () ())
#s(alt (log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))) (patch (log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (patch (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6)))) (taylor 0 x) (#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) (patch (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/6 (pow x 2)))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) (patch (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) (patch (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6)))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) (patch (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) #<representation binary64>) () ())) ())
#s(alt -1/6 (taylor 0 x) (#s(alt (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 3/40 (pow x 2)) 1/6) (taylor 0 x) (#s(alt (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 3/40 (pow x 2)) 1/6) (taylor 0 x) (#s(alt (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
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#s(alt (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x) (taylor inf x) (#s(alt (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (+ (log 1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)) #<representation binary64>) () ())) ())
#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)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)) #<representation binary64>) () ())) ())
#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)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)) #<representation binary64>) () ())) ())
#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)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (patch #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)) #<representation binary64>) () ())) ())
#s(alt (* 3/40 (pow x 5)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) (patch (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 3/40))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) (patch (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 3/40 (/ 1 (pow x 4)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) (patch (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 3/40 (/ 1 (pow x 4)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) (patch (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x) #<representation binary64>) () ())) ())
#s(alt (* 3/40 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (patch (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (patch (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (patch (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor -inf x) (#s(alt (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (patch (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ (log 1/2) (log (/ -1 x))) (taylor -inf x) (#s(alt (log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))) (patch (log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))) #<representation binary64>) () ())) ())
#s(alt (- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))) (patch (log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))) #<representation binary64>) () ())) ())
#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.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))) (patch (log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))) #<representation binary64>) () ())) ())
#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.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))) (patch (log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))) #<representation binary64>) () ())) ())
#s(alt (/ -1/2 x) (taylor -inf x) (#s(alt (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (patch (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (patch (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (patch (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (patch (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (patch (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -2 x) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))) (taylor -inf x) (#s(alt (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (patch (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (+ (* 3/40 (* x x)) -1/6) (* (* x x) x)) x) (+ (* 3/40 (* x x)) -1/6) (* x x) (- (+ (* x x) 1) (* x x)) (log (/ (- (+ (* x x) 1) (* x x)) (- (sqrt (+ (* x x) 1)) x))) (/ (- (+ (* x x) 1) (* x x)) (- (sqrt (+ (* x x) 1)) x)) (+ (* x x) 1) (* (* x x) x) (sqrt (+ (* x x) 1)) (- (sqrt (+ (* x x) 1)) x))

1.0ms

-inf

((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (+ (* 3/40 (* x x)) -1/6) (* (* x x) x)) x) (+ (* 3/40 (* x x)) -1/6) (* x x) (- (+ (* x x) 1) (* x x)) (log (/ (- (+ (* x x) 1) (* x x)) (- (sqrt (+ (* x x) 1)) x))) (/ (- (+ (* x x) 1) (* x x)) (- (sqrt (+ (* x x) 1)) x)) (+ (* x x) 1) (* (* x x) x) (sqrt (+ (* x x) 1)) (- (sqrt (+ (* x x) 1)) x))

1.0ms

((log (+ x (sqrt (+ (* x x) 1)))) (+ (* (+ (* 3/40 (* x x)) -1/6) (* (* x x) x)) x) (+ (* 3/40 (* x x)) -1/6) (* x x) (- (+ (* x x) 1) (* x x)) (log (/ (- (+ (* x x) 1) (* x x)) (- (sqrt (+ (* x x) 1)) x))) (/ (- (+ (* x x) 1) (* x x)) (- (sqrt (+ (* x x) 1)) x)) (+ (* x x) 1) (* (* x x) x) (sqrt (+ (* x x) 1)) (- (sqrt (+ (* x x) 1)) x))

simplify159.0ms (1.9%)

Memory

-21.6MiB live, 134.0MiB allocated

Algorithm

1×	egg-herbie

Rules

10 342×	`lower-fma.f64`
10 342×	`lower-fma.f32`
3 080×	`lower-*.f64`
3 080×	`lower-*.f32`
2 526×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	1089
1	435	1054
2	1177	1052
3	3636	1013
4	6838	1013
0	8095	954

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 128

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
-1/6
(- (* 3/40 (pow x 2)) 1/6)
(- (* 3/40 (pow x 2)) 1/6)
(- (* 3/40 (pow x 2)) 1/6)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
1
1
1
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/8 (pow x 2)))) 1)))
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 3/40 (pow x 5))
(* (pow x 5) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 3/40 (pow x 2))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
1
1
1
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x)
(+ (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)))))
(* 3/40 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 3/40)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 3/40 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 3/40 (/ 1 (pow x 4))))))
(* 3/40 (pow x 2))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
1
1
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 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(* -2 x)
(* -1 (* x (+ 2 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(* -1 (* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))

Outputs
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
-1/6
#s(literal -1/6 binary64)
(- (* 3/40 (pow x 2)) 1/6)
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(- (* 3/40 (pow x 2)) 1/6)
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(- (* 3/40 (pow x 2)) 1/6)
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 3/40 (pow x 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 3/40 (* -5/112 (pow x 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/112 binary64) (.f64 x x) #s(literal 3/40 binary64)) (.f64 x x) #s(literal -1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* -1/8 (pow x 2)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* -1/8 (pow x 2)))))
(fma.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/16 (pow x 2)) 1/8)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/16 binary64) (.f64 x x) #s(literal -1/8 binary64)) (.f64 x x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/8 (pow x 2)))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (log.f64 x)) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (log.f64 x)) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(-.f64 (+.f64 (+.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (log.f64 x)) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)))
(* 3/40 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 3/40 binary64))
(* (pow x 5) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 3/40 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -3/40 binary64)) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (+ 3/40 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -3/40 binary64)) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* 3/40 (pow x 2))
(.f64 #s(literal 3/40 binary64) (.f64 x x))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
(+ (log 2) (* -1 (log (/ 1 x))))
(+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (*.f64 x x)) (log.f64 x)) (log.f64 #s(literal 2 binary64)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))) (/ 3/32 (pow x 4)))
(-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (log.f64 x)) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))) (/ 3/32 (pow x 4)))
(-.f64 (+.f64 (+.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (log.f64 x)) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 2 binary64) x (/.f64 #s(literal 1/2 binary64) x))
(* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(fma.f64 #s(literal 2 binary64) x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))
(* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(fma.f64 #s(literal 2 binary64) x (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
x
(* x (+ 1 (* 1/2 (/ 1 (pow x 2)))))
(-.f64 x (/.f64 #s(literal -1/2 binary64) x))
(* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4))))
(+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) x)
(* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4))))
(+.f64 (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x)
(/.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x)
(/.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64)))) x)
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (neg.f64 (log.f64 (neg.f64 x))) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (neg.f64 (log.f64 (neg.f64 x))) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (+.f64 (log.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x))) (neg.f64 (log.f64 (neg.f64 x)))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
(-.f64 (-.f64 (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (log.f64 #s(literal 1/2 binary64))) (neg.f64 (log.f64 (neg.f64 x)))))
(* 3/40 (pow x 5))
(*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 3/40 binary64))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 3/40)))
(.f64 (-.f64 #s(literal 3/40 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 3/40 (/ 1 (pow x 4))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -3/40 binary64)) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 3/40 (/ 1 (pow x 4))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)) #s(literal -3/40 binary64)) (/.f64 #s(literal 1/6 binary64) (*.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* 3/40 (pow x 2))
(.f64 #s(literal 3/40 binary64) (.f64 x x))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(* (pow x 2) (- 3/40 (* 1/6 (/ 1 (pow x 2)))))
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
(+ (log 1/2) (log (/ -1 x)))
(+.f64 (neg.f64 (log.f64 (neg.f64 x))) (log.f64 #s(literal 1/2 binary64)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (neg.f64 (log.f64 (neg.f64 x))) (log.f64 #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (+.f64 (+.f64 (log.f64 #s(literal 1/2 binary64)) (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x))) (neg.f64 (log.f64 (neg.f64 x)))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
(-.f64 (-.f64 (/.f64 #s(literal 3/32 binary64) (.f64 (.f64 (.f64 x x) x) x)) (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) (log.f64 #s(literal 1/2 binary64))) (neg.f64 (log.f64 (neg.f64 x)))))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(* -1 (/ (- 1/2 (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (* 1/8 (/ 1 (pow x 2)))) x))
(/.f64 (-.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x x))) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) x) x))) x)
(* -1 (/ (- (+ 1/2 (/ 1/16 (pow x 4))) (+ (* 1/8 (/ 1 (pow x 2))) (* 5/128 (/ 1 (pow x 6))))) x))
(/.f64 (-.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/16 binary64) (.f64 (.f64 (.f64 x x) x) x))) (-.f64 (/.f64 #s(literal -5/128 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(pow x 3)
(.f64 (.f64 x x) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* 1/2 (/ 1 (pow x 2))))))
(-.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(* -1 (* x (- (+ 1 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(-.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x) x)
(* -1 (* x (- (+ 1 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(neg.f64 (+.f64 (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)) x))
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* -1 (* x (+ 2 (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -2 binary64) x (/.f64 #s(literal -1/2 binary64) x))
(* -1 (* x (- (+ 2 (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 4)))))
(fma.f64 #s(literal -2 binary64) x (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1/8 binary64) (*.f64 x x))) x))
(* -1 (* x (- (+ 2 (+ (* 1/2 (/ 1 (pow x 2))) (* 1/16 (/ 1 (pow x 6))))) (/ 1/8 (pow x 4)))))
(neg.f64 (fma.f64 #s(literal 2 binary64) x (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) x (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x))))

rewrite232.0ms (2.7%)

Memory

26.5MiB live, 304.1MiB allocated

Rules

7 294×	`lower-fma.f32`
7 288×	`lower-fma.f64`
3 906×	`lower-/.f32`
3 904×	`lower-/.f64`
3 516×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	106
0	32	100
1	136	82
2	1094	75
0	8791	75

Stop Event

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

Counts

11 → 596

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))
(fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x)
(fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64))
(*.f64 x x)
(-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x))
(log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))
(/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
(fma.f64 x x #s(literal 1 binary64))
(.f64 (.f64 x x) x)
(sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))
(-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)

Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x))
(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (-.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (*.f64 x x)))))
(.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (neg.f64 x) x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (*.f64 (neg.f64 x) x) x)))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) x (.f64 x (-.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (*.f64 x x))))))))
(.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (*.f64 (neg.f64 x) x) x)))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 (neg.f64 x) x) x) (.f64 (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x))))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) x (.f64 x (-.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (*.f64 x x)))))))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) (/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x)))) (.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))))) (+.f64 (/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) (/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) (fma.f64 (/.f64 (.f64 x x) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) (.f64 (/.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) (/.f64 (.f64 x x) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (*.f64 x x) (neg.f64 x)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (-.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x))))) (neg.f64 (-.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x)))))
(/.f64 (neg.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (neg.f64 x) x) x))) (neg.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (neg.f64 x) x) x)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)))) (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) x (.f64 x (-.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x))))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 (.f64 x x) x) x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x)) (.f64 x x))) (.f64 (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (*.f64 x x) (neg.f64 x))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (-.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x)))) (-.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (neg.f64 x) x) x)) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (neg.f64 x) x) x))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 x x (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 (neg.f64 x) x) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) x (.f64 x (-.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x) (neg.f64 x)))
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(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x))) (.f64 (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (-.f64 x (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) (.f64 (.f64 (.f64 x x) x) x) (.f64 (.f64 (.f64 (neg.f64 x) x) x) (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)))) (fma.f64 (.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64))) (.f64 (.f64 (.f64 x x) x) x)) (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x)) (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) x) (fma.f64 (*.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x)))
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(fma.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (.f64 x x)))
(-.f64 (/.f64 (fma.f64 x x (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)) (.f64 (.f64 x x) x))) (/.f64 (.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (fma.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)) (.f64 (*.f64 x x) x))))
(-.f64 (/.f64 x #s(literal -1 binary64)) (/.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64)))
(-.f64 (/.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)) x)
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x (fma.f64 x x #s(literal 1 binary64)))) (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) x) x) (fma.f64 x x (fma.f64 x x #s(literal 1 binary64)))) (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)) (.f64 (.f64 x x) (fma.f64 x x (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (/.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)) (.f64 (*.f64 x x) (fma.f64 x x (fma.f64 x x #s(literal 1 binary64)))))) (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))
(-.f64 (/.f64 (.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (fma.f64 x x #s(literal 1 binary64))))) (/.f64 (.f64 (.f64 x x) x) (*.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (fma.f64 x x #s(literal 1 binary64))))))
(-.f64 (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) #s(literal 1 binary64)) (/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (*.f64 x x)) #s(literal 1 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)) (/.f64 (/.f64 (.f64 (*.f64 x x) x) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)))
(-.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)) x)
(-.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (*.f64 x x)))
(-.f64 (/.f64 (.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (.f64 (*.f64 x x) x) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (fma.f64 x x #s(literal 1 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)
(+.f64 (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))) (neg.f64 x))
(+.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64)) (neg.f64 x))
(+.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (neg.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (*.f64 x x))))
(+.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)) (.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) (*.f64 x x)))
(+.f64 (/.f64 (.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (fma.f64 x x #s(literal 1 binary64)))) (neg.f64 (/.f64 (.f64 (*.f64 x x) x) (fma.f64 x (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x) (fma.f64 x x #s(literal 1 binary64))))))
(+.f64 (neg.f64 x) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(+.f64 (neg.f64 x) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (neg.f64 x))

eval171.0ms (2%)

Memory: -12.5MiB live, 259.8MiB allocated
Compiler: Compiled 31 316 to 2 924 computations (90.7% saved)

prune103.0ms (1.2%)

Memory

20.9MiB live, 257.4MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	896	1	897
Fresh	0	0	0
Picked	1	1	2
Done	1	7	8
Total	898	9	907

Accuracy

100.0%

Counts

907 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	17.0%	(neg.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))
✓	16.2%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
✓	25.0%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
✓	10.7%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
✓	25.6%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)))
✓	24.2%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
✓	52.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))
✓	51.2%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
✓	53.3%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 239 to 101 computations (57.7% saved)

regimes16.0ms (0.2%)

Memory

-10.5MiB live, 31.5MiB allocated

Counts

16 → 3

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)))
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)))
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
(neg.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))
(log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x)) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))))
(log.f64 (/.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) (*.f64 x x)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))

Outputs

(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x)))

#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 (*.f64 x x) x) x))

(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))

Calls

3 calls:

6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
5.0ms	x
4.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
99.8%	3	`x`
87.1%	3	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`
87.1%	3	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes5.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated

Counts

13 → 3

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)))
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)))
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
(neg.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) x)))

Outputs

(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))

#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 (*.f64 x x) x) x))

(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
99.6%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Memory

8.0MiB live, 8.0MiB allocated

Counts

9 → 3

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)))
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(approx (- (/ 1/8 (* x x)) 1/2) #s(literal -1/2 binary64)) x)))

Outputs

(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))

#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (*.f64 x x) #s(literal -1/6 binary64)) (*.f64 (*.f64 x x) x) x))

(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.5%	3	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes8.0ms (0.1%)

Memory

-21.9MiB live, 17.4MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)))
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))

Outputs

#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (*.f64 #s(approx (+ (* (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))

(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))

Calls

3 calls:

3.0ms	x
2.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
2.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
75.2%	2	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`
75.2%	2	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`
75.7%	2	`x`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes7.0ms (0.1%)

Memory

18.3MiB live, 18.3MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)))
(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))

Outputs

#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (*.f64 #s(approx (+ (* (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))

(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))

Calls

3 calls:

2.0ms	x
2.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
2.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
59.1%	2	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`
59.1%	2	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`
59.6%	2	`x`

Compiler

Compiled 21 to 14 computations (33.3% saved)

regimes8.0ms (0.1%)

Memory

-22.6MiB live, 16.2MiB allocated

Accuracy

Total -1.5b remaining (-4.9%)

Threshold costs -1.5b (-4.9%)

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (*.f64 x x) x) x))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal 3/40 binary64) #s(literal -1/6 binary64)) x) x) x (.f64 #s(literal 1 binary64) x)))

Outputs
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))

Calls

3 calls:

3.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
2.0ms	x
2.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
53.3%	1	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`
53.3%	1	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`
53.3%	1	`x`

Compiler

Compiled 21 to 14 computations (33.3% saved)

bsearch49.0ms (0.6%)

Memory

9.0MiB live, 47.9MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
34.0ms	0.00019493158565729167	6371.557083399013
13.0ms	-24.220841576636452	-2.990536921739895e-8

Samples

15.0ms

288×

valid

Compiler

Compiled 517 to 297 computations (42.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-hypot: 5.0ms (49.9% of total)

ival-log: 3.0ms (29.9% of total)

ival-add: 1.0ms (10% of total)

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

exact: 0.0ms (0% of total)

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

bsearch4.0ms (0%)

Memory

6.0MiB live, 6.0MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.00019493158565729167	6371.557083399013
2.0ms	-24.220841576636452	-2.990536921739895e-8

Samples

1.0ms

16×

valid

Compiler

Compiled 463 to 261 computations (43.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

exact: 0.0ms (0% of total)

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

bsearch26.0ms (0.3%)

Memory

-33.2MiB live, 21.0MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.00019493158565729167	6371.557083399013
1.0ms	-24.220841576636452	-2.990536921739895e-8

Samples

7.0ms

128×

valid

Compiler

Compiled 427 to 243 computations (43.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-hypot: 2.0ms (46% of total)

ival-add: 1.0ms (23% of total)

ival-log: 1.0ms (23% of total)

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

exact: 0.0ms (0% of total)

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

bsearch4.0ms (0%)

Memory

5.9MiB live, 5.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	0.00019493158565729167	6371.557083399013

Samples

2.0ms

32×

valid

Compiler

Compiled 139 to 90 computations (35.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-hypot: 1.0ms (93.1% of total)

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

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

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

exact: 0.0ms (0% of total)

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

bsearch5.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
5.0ms	0.00019493158565729167	6371.557083399013

Samples

2.0ms

48×

valid

Compiler

Compiled 139 to 90 computations (35.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-log: 1.0ms (62.2% of total)

ival-hypot: 1.0ms (62.2% of total)

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

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

exact: 0.0ms (0% of total)

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

simplify8.0ms (0.1%)

Memory

14.5MiB live, 14.5MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
14×	`*-commutative_binary64`
12×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	294
1	74	294
2	85	294
3	93	294
4	99	294
5	101	294

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal -2589569785738035/2251799813685248 binary64)) (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))) (if (<=.f64 x #s(literal 4728779608739021/4503599627370496 binary64)) #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (log.f64 (+.f64 x #s(approx (sqrt (+ ( x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))))
(if (<=.f64 x #s(literal -3039929748475085/2251799813685248 binary64)) (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x))) (if (<=.f64 x #s(literal 4728779608739021/4503599627370496 binary64)) #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (log.f64 (+.f64 x #s(approx (sqrt (+ ( x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))))
(if (<=.f64 x #s(literal -3039929748475085/2251799813685248 binary64)) (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x))) (if (<=.f64 x #s(literal 3039929748475085/2251799813685248 binary64)) #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (log.f64 #s(approx (+ x (sqrt (+ ( x x) 1))) (*.f64 #s(literal 2 binary64) x)))))
(if (<=.f64 x #s(literal 5/4 binary64)) #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x))))
(if (<=.f64 x #s(literal 3602879701896397/2251799813685248 binary64)) #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) (log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)))))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))

Outputs
(if (<=.f64 x #s(literal -2589569785738035/2251799813685248 binary64)) (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))) (if (<=.f64 x #s(literal 4728779608739021/4503599627370496 binary64)) #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (log.f64 (+.f64 x #s(approx (sqrt (+ ( x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))))
(if (<=.f64 x #s(literal -2589569785738035/2251799813685248 binary64)) (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 (-.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x))) (if (<=.f64 x #s(literal 4728779608739021/4503599627370496 binary64)) #s(approx (log (+ x (sqrt (+ ( x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (log.f64 (+.f64 #s(approx (sqrt (+ ( x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) x))))
(if (<=.f64 x #s(literal -3039929748475085/2251799813685248 binary64)) (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x))) (if (<=.f64 x #s(literal 4728779608739021/4503599627370496 binary64)) #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (log.f64 (+.f64 x #s(approx (sqrt (+ ( x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x)))))))
(if (<=.f64 x #s(literal -3039929748475085/2251799813685248 binary64)) (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x))) (if (<=.f64 x #s(literal 4728779608739021/4503599627370496 binary64)) #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (log.f64 (+.f64 #s(approx (sqrt (+ ( x x) 1)) (-.f64 x (/.f64 #s(literal -1/2 binary64) x))) x))))
(if (<=.f64 x #s(literal -3039929748475085/2251799813685248 binary64)) (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x))) (if (<=.f64 x #s(literal 3039929748475085/2251799813685248 binary64)) #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (fma.f64 #s(literal 3/40 binary64) (.f64 x x) #s(literal -1/6 binary64)) (.f64 (.f64 x x) x) x)) (log.f64 #s(approx (+ x (sqrt (+ ( x x) 1))) (*.f64 #s(literal 2 binary64) x)))))
(if (<=.f64 x #s(literal 5/4 binary64)) #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) (log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x))))
(if (<=.f64 x #s(literal 3602879701896397/2251799813685248 binary64)) #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) (log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal 3602879701896397/2251799813685248 binary64)) #s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x)) (log.f64 (+.f64 #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)) x)))
#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (.f64 #s(approx (+ ( (+ (* 3/40 (* x x)) -1/6) (* x x)) 1) #s(literal 1 binary64)) x))

soundness785.0ms (9.2%)

Memory

8.0MiB live, 677.6MiB allocated

Rules

14 074×	`lower-fma.f64`
14 074×	`lower-fma.f32`
11 038×	`lower-fma.f64`
11 038×	`lower-fma.f32`
8 960×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	525
1	353	517
2	931	509
3	2896	479
4	6990	479
0	8034	448
0	34	220
0	53	220
1	195	220
2	1443	220
0	8281	207
0	162	2274
1	432	2180
2	1178	2179
3	3627	2109
0	8697	1991
0	39	233
0	57	224
1	217	222
2	1355	222
0	8316	213

Stop Event

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

Compiler

Compiled 393 to 196 computations (50.1% saved)

preprocess157.0ms (1.8%)

Memory: -16.7MiB live, 142.7MiB allocated
Compiler: Compiled 358 to 132 computations (63.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	39	248
0	57	239
1	91	239
2	154	237
3	298	237
4	481	237
5	518	237
6	521	237
0	521	232

Iter	Nodes	Cost
0	39	248
0	57	239
1	91	239
2	154	237
3	298	237
4	481	237
5	518	237
6	521	237
0	521	232

start0.0ms (0%)

analyze84.0ms (1%)

sample2.7s (31.7%)

explain191.0ms (2.2%)

preprocess20.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize62.0ms (0.7%)

series13.0ms (0.2%)

simplify154.0ms (1.8%)

rewrite158.0ms (1.9%)

eval85.0ms (1%)

prune96.0ms (1.1%)

simplify165.0ms (1.9%)

localize170.0ms (2%)

series20.0ms (0.2%)

simplify160.0ms (1.9%)

rewrite421.0ms (5%)

eval103.0ms (1.2%)

prune75.0ms (0.9%)

simplify13.0ms (0.1%)

localize388.0ms (4.6%)

series83.0ms (1%)

simplify300.0ms (3.5%)

rewrite312.0ms (3.7%)

eval178.0ms (2.1%)

prune207.0ms (2.4%)

simplify275.0ms (3.2%)

localize301.0ms (3.5%)

series8.0ms (0.1%)

simplify159.0ms (1.9%)

rewrite232.0ms (2.7%)

eval171.0ms (2%)

prune103.0ms (1.2%)

regimes16.0ms (0.2%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes8.0ms (0.1%)

bsearch49.0ms (0.6%)

bsearch4.0ms (0%)

bsearch26.0ms (0.3%)

bsearch4.0ms (0%)

bsearch5.0ms (0.1%)

simplify8.0ms (0.1%)

soundness785.0ms (9.2%)

preprocess157.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	39	248
0	57	239
1	91	239
2	154	237
3	298	237
4	481	237
5	518	237
6	521	237
0	521	232