Metrics for Hyperbolic arcsine

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze107.0ms (3.3%)

Memory

-6.2MiB live, 199.7MiB 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)

sample2.1s (65.2%)

Memory

38.0MiB live, 3 449.0MiB allocated

Samples

893.0ms	4 350×	1	valid
728.0ms	1 501×	2	valid
242.0ms	2 153×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-log: 746.0ms (49.3% of total)

ival-hypot: 524.0ms (34.6% of total)

ival-add: 126.0ms (8.3% of total)

adjust: 103.0ms (6.8% of total)

ival-true: 7.0ms (0.5% of total)

exact: 6.0ms (0.4% of total)

ival-assert: 4.0ms (0.3% of total)

Bogosity

explain3.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
2	-	-	`(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
1	-	-	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`
1	-	-	`(log.f64 (+.f64 x (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
`sqrt.f64`	`(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))`	oflow-rescue	2	0
↳	`(*.f64 x x)`	overflow	2
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	2
`+.f64`	`(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))`	cancellation	1	0
`log.f64`	`(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	4	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	4	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	4

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

1.0ms	4×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 112 to 32 computations (71.4% saved)

Precisions

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

adjust: 0.0ms (0% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

preprocess16.0ms (0.5%)

Memory

-11.4MiB live, 27.7MiB allocated

Algorithm

1×	egg-herbie

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 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	3.7%	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify3.0ms (0.1%)

Memory

4.9MiB live, 4.9MiB 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))

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)

localize1.0ms (0%)

Memory

2.6MiB live, 2.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	15.173045271963	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))))
accuracy	15.399345286536569	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy	29.535680296021333	(sqrt.f64 (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

0.0ms	2×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 68 to 16 computations (76.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

adjust: 0.0ms (0% of total)

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

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

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

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

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.2%)

Memory

13.1MiB live, 13.1MiB 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
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	@	0	((+ (* 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

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

((+ (* 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))

simplify125.0ms (3.8%)

Memory

3.6MiB live, 161.8MiB allocated

Algorithm

1×	egg-herbie

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

rewrite164.0ms (5%)

Memory

-21.9MiB live, 254.3MiB allocated

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
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eval9.0ms (0.3%)

Memory: 22.4MiB live, 22.3MiB allocated
Compiler: Compiled 9 003 to 1 683 computations (81.3% saved)

prune1.0ms (0%)

Memory

3.6MiB live, 3.6MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	415	6	421
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	416	6	422

Accuracy

100.0%

Counts

422 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.4%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (neg.f64 x))))
▶	18.1%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
	25.0%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
▶	50.6%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
▶	3.6%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) #s(literal 1 binary64)))
▶	25.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x))

Compiler

Compiled 62 to 60 computations (3.2% saved)

simplify31.0ms (1%)

Memory

-20.4MiB live, 18.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	146
0	36	146
1	50	146
2	60	146
3	69	146
4	73	146
5	83	146
6	140	146
7	279	146
8	390	146
9	521	146
10	619	146
11	751	146
12	823	146
13	847	146
14	855	146
0	855	135

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize2.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 3 binary64))
accuracy	0.25	(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
accuracy	47.65601335686612	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x))
accuracy	0	(neg.f64 x)
accuracy	15.173045271963	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (neg.f64 x))))
accuracy	15.399345286536569	(+.f64 x #s(approx (sqrt (+ (* x x) 1)) (neg.f64 x)))
accuracy	47.57225458109196	#s(approx (sqrt (+ (* x x) 1)) (neg.f64 x))
accuracy	15.173045271963	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
accuracy	15.399345286536569	(+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64)))
accuracy	45.884716206097714	#s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))
accuracy	15.173045271963	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) #s(literal 1 binary64)))
accuracy	45.8871883987225	#s(approx (+ x (sqrt (+ (* x x) 1))) #s(literal 1 binary64))
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	15.173045271963	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
accuracy	31.061826823668213	#s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x))

Samples

1.0ms	2×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 184 to 35 computations (81% saved)

Precisions

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

adjust: 0.0ms (0% of total)

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

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

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

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

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

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

const: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

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

series14.0ms (0.4%)

Memory

-17.4MiB live, 25.8MiB allocated

Counts

15 → 180

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (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))) (sqrt (+ (* x x) 1)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (pow x 3) -1/6) x) (pow x 3))
1.0ms	x	@	inf	((log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (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))) (sqrt (+ (* x x) 1)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (pow x 3) -1/6) x) (pow x 3))
1.0ms	x	@	0	((log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (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))) (sqrt (+ (* x x) 1)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (pow x 3) -1/6) x) (pow x 3))

Time

Variable

Point

Expression

2.0ms

-inf

((log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (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))) (sqrt (+ (* x x) 1)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (pow x 3) -1/6) x) (pow x 3))

1.0ms

inf

((log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (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))) (sqrt (+ (* x x) 1)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (pow x 3) -1/6) x) (pow x 3))

1.0ms

((log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (* 2 x) (log (+ x (sqrt (+ (* x x) 1)))) (+ x (sqrt (+ (* x x) 1))) (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))) (sqrt (+ (* x x) 1)) (neg x) (log (+ x (sqrt (+ (* x x) 1)))) (+ (* (pow x 3) -1/6) x) (pow x 3))

simplify150.0ms (4.6%)

Memory

26.8MiB live, 219.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	130	1838
1	361	1750
2	986	1744
3	3093	1668
4	7810	1668
0	8391	1581

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 172

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))))
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)))))))
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
(+ 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 x)
(* -1 x)
(* -1 x)
(* -1 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 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(+ (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))))
(+ (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))))
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 x)
(* -1 x)
(* -1 x)
(* -1 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)))
(* -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))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(+ (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))
(+ (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 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)))))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(+ (log 1/2) (log (/ -1 x)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
(* -1/6 (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)))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

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

rewrite220.0ms (6.7%)

Memory

-11.9MiB live, 277.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	137
0	36	137
1	112	137
2	698	137
3	7462	137
0	8304	126

Stop Event

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

Counts

15 → 315

Calls

Call 1

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

Outputs
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval9.0ms (0.3%)

Memory: -17.2MiB live, 21.9MiB allocated
Compiler: Compiled 9 202 to 1 268 computations (86.2% saved)

prune1.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	486	1	487
Fresh	0	1	1
Picked	1	4	5
Done	0	0	0
Total	487	6	493

Accuracy

100.0%

Counts

493 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	1.4%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (neg.f64 x))))
✓	18.1%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
▶	25.0%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
✓	50.6%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
✓	3.6%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) #s(literal 1 binary64)))
▶	25.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x))

Compiler

Compiled 33 to 30 computations (9.1% saved)

simplify5.0ms (0.2%)

Memory

10.3MiB live, 10.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal -1/2 binary64) x)
cost-diff	0	#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x))
cost-diff	0	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
cost-diff	-5824	(.f64 (.f64 x x) x)
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x)
cost-diff	0	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	66
0	22	66
1	31	60
2	42	60
3	47	60
4	49	60
5	55	60
6	55	60
7	77	60
8	78	60
9	79	60
0	79	57

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize1.0ms (0%)

Memory

2.9MiB live, 2.9MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal -1/2 binary64) x)
accuracy	15.173045271963	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
accuracy	47.34275912664416	#s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x))
accuracy	0	(.f64 (.f64 x x) x)
accuracy	0	(*.f64 x x)
accuracy	0.25	(fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x)
accuracy	47.65601335686612	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x))

Samples

1.0ms	2×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 93 to 24 computations (74.2% saved)

Precisions

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

adjust: 0.0ms (0% of total)

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

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

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

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

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

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

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

const: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series7.0ms (0.2%)

Memory

15.9MiB live, 15.9MiB allocated

Counts

7 → 84

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify110.0ms (3.4%)

Memory

-1.0MiB live, 154.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	109	675
1	297	629
2	780	628
3	2373	620
4	5791	620
0	8141	591

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 81

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 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
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)))))))
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(+ (log 2) (* -1 (log (/ 1 x))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* 1/4 (/ 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))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(+ (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)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)
(+ (log 1/2) (log (/ -1 x)))
(- (+ (log 1/2) (log (/ -1 x))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (* 1/4 (/ 1 (pow x 2))))
(- (+ (log 1/2) (+ (log (/ -1 x)) (/ 3/32 (pow x 4)))) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))
(* -1/6 (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)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(+ (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)
(/ -1/2 x)
(/ -1/2 x)
(/ -1/2 x)

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

rewrite149.0ms (4.5%)

Memory

13.3MiB live, 209.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	62
0	22	56
1	76	56
2	484	56
3	4981	56
0	8098	53

Stop Event

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

Counts

7 → 142

Calls

Call 1

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

Outputs
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eval4.0ms (0.1%)

Memory: -30.1MiB live, 9.0MiB allocated
Compiler: Compiled 3 402 to 642 computations (81.1% saved)

prune1.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	223	6	229

Accuracy

100.0%

Counts

229 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	1.4%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) (neg.f64 x))))
✓	18.1%	(log.f64 (+.f64 x #s(approx (sqrt (+ (* x x) 1)) #s(literal 1 binary64))))
✓	25.0%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (/.f64 #s(literal -1/2 binary64) x)))
✓	50.6%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
✓	3.6%	(log.f64 #s(approx (+ x (sqrt (+ (* x x) 1))) #s(literal 1 binary64)))
✓	25.5%	#s(approx (log (+ x (sqrt (+ (* x x) 1)))) (fma.f64 (.f64 (.f64 x x) x) #s(literal -1/6 binary64) x))

Compiler

Compiled 82 to 62 computations (24.4% saved)

regimes0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 8 to 6 computations (25% saved)

end0.0ms (0%)

Memory

0.0MiB live, 0.0MiB allocated

Calls

1 calls:

0.0ms

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

Iter	Nodes	Cost
0	25	146
0	36	146
1	50	146
2	60	146
3	69	146
4	73	146
5	83	146
6	140	146
7	279	146
8	390	146
9	521	146
10	619	146
11	751	146
12	823	146
13	847	146
14	855	146
0	855	135

Iter	Nodes	Cost
0	16	66
0	22	66
1	31	60
2	42	60
3	47	60
4	49	60
5	55	60
6	55	60
7	77	60
8	78	60
9	79	60
0	79	57

Iter	Nodes	Cost
0	25	146
0	36	146
1	50	146
2	60	146
3	69	146
4	73	146
5	83	146
6	140	146
7	279	146
8	390	146
9	521	146
10	619	146
11	751	146
12	823	146
13	847	146
14	855	146
0	855	135

Iter	Nodes	Cost
0	16	66
0	22	66
1	31	60
2	42	60
3	47	60
4	49	60
5	55	60
6	55	60
7	77	60
8	78	60
9	79	60
0	79	57

start0.0ms (0%)

analyze107.0ms (3.3%)

sample2.1s (65.2%)

explain3.0ms (0.1%)

preprocess16.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize1.0ms (0%)

series6.0ms (0.2%)

simplify125.0ms (3.8%)

rewrite164.0ms (5%)

eval9.0ms (0.3%)

prune1.0ms (0%)

simplify31.0ms (1%)

localize2.0ms (0.1%)

series14.0ms (0.4%)

simplify150.0ms (4.6%)

rewrite220.0ms (6.7%)

eval9.0ms (0.3%)

prune1.0ms (0%)

simplify5.0ms (0.2%)

localize1.0ms (0%)

series7.0ms (0.2%)

simplify110.0ms (3.4%)

rewrite149.0ms (4.5%)

eval4.0ms (0.1%)

prune1.0ms (0%)

regimes0.0ms (0%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	25	146
0	36	146
1	50	146
2	60	146
3	69	146
4	73	146
5	83	146
6	140	146
7	279	146
8	390	146
9	521	146
10	619	146
11	751	146
12	823	146
13	847	146
14	855	146
0	855	135

Iter	Nodes	Cost
0	16	66
0	22	66
1	31	60
2	42	60
3	47	60
4	49	60
5	55	60
6	55	60
7	77	60
8	78	60
9	79	60
0	79	57