Metrics for Rust f64::acosh

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample845.0ms (18.6%)

Memory

-24.2MiB live, 652.2MiB allocated

Samples

585.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 448.0ms

ival-acosh: 406.0ms (90.6% of total)

ival->=: 30.0ms (6.7% of total)

exact: 8.0ms (1.8% of total)

ival-assert: 4.0ms (0.9% of total)

Bogosity

explain127.0ms (2.8%)

Memory

24.2MiB live, 184.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
135	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))`
0	-	-	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
0	-	-	`(*.f64 x x)`
0	-	-	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`
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	135	0
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	135
↳	`(*.f64 x x)`	overflow	135

Confusion

	Predicted +	Predicted -
+	135	0
-	0	121

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	135	0	0
-	0	0	121

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	121
1	135

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

49.0ms

512×

valid

Compiler

Compiled 79 to 25 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 20.0ms (54.7% of total)

ival-log: 6.0ms (16.4% of total)

ival-sqrt: 4.0ms (10.9% of total)

ival-sub: 3.0ms (8.2% of total)

ival-add: 2.0ms (5.5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess279.0ms (6.2%)

Memory

15.2MiB live, 276.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	10	7
2	14	7
3	17	7
4	21	7
5	28	7
6	35	7
0	7	9
0	12	9
1	21	9
2	25	9
3	40	9
4	71	9
5	132	9
6	298	9
7	578	9
8	2337	9
9	3439	9
10	4718	9
11	5410	9
12	5718	9
13	5904	9
14	6006	9
15	6325	9
16	6819	9
17	7862	9
0	8072	8

Stop Event

1×	iter limit
1×	node limit
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: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.9%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify357.0ms (7.9%)

Memory

-27.7MiB live, 266.6MiB 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	1	(-.f64 (*.f64 x x) #s(literal 1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33
0	12	33
1	21	33
2	25	33
3	40	33
4	71	33
5	132	33
6	298	33
7	578	33
8	2337	33
9	3439	33
10	4718	33
11	5410	33
12	5718	33
13	5904	33
14	6006	33
15	6325	33
16	6819	33
17	7862	33
0	8072	29

Stop Event

1×	iter limit
1×	node limit
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)

localize25.0ms (0.6%)

Memory

14.6MiB live, 51.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
accuracy	0.0	(*.f64 x x)
accuracy	0.00390625	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
accuracy	31.40983415103507	(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

19.0ms

256×

valid

Compiler

Compiled 35 to 9 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-sqrt: 5.0ms (39.2% of total)

ival-log: 3.0ms (23.5% of total)

ival-mult: 2.0ms (15.7% of total)

ival-sub: 1.0ms (7.8% of total)

ival-add: 1.0ms (7.8% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

5 → 39

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

Calls

3 calls:

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

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

2.0ms

-inf

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

2.0ms

inf

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

simplify188.0ms (4.2%)

Memory

4.1MiB live, 162.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	519
1	411	493
2	1170	486
3	3366	448
0	8112	426

Stop Event

1×	iter limit
1×	node limit

Counts

39 → 38

Calls

Call 1

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

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

rewrite274.0ms (6%)

Memory

-25.4MiB live, 256.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	31
0	12	31
1	49	31
2	322	31
3	3638	31
0	8656	27

Stop Event

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

Counts

5 → 328

Calls

Call 1

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

Outputs
(.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (exp.f64 (neg.f64 (log1p.f64 (.f64 x x)))))
(*.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (exp.f64 (neg.f64 (log1p.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))))))
(*.f64 (exp.f64 (log1p.f64 x)) (exp.f64 (log.f64 (-.f64 x #s(literal 1 binary64)))))
(*.f64 (exp.f64 (log.f64 (-.f64 x #s(literal 1 binary64)))) (exp.f64 (log1p.f64 x)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 x x)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(.f64 (.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (/.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/4 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/4 binary64)))
(*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (pow.f64 (neg.f64 (fma.f64 x x #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 (neg.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) #s(literal -1 binary64)))
(.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(*.f64 (-.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x #s(literal 1 binary64)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(.f64 (fma.f64 x x #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 #s(literal -1 binary64) (*.f64 x x))) #s(literal -1 binary64)))
(*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (fma.f64 x x #s(literal -1 binary64))))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 2 binary64))))
(pow.f64 (/.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 #s(literal -1 binary64) (.f64 x x))) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 2 binary64))
(pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 (exp.f64 (log.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))) (exp.f64 (log.f64 (neg.f64 (fma.f64 x x #s(literal 1 binary64))))))
(/.f64 (exp.f64 (log.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))))) (exp.f64 (+.f64 (log.f64 #s(literal -1 binary64)) (log1p.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (exp.f64 (log1p.f64 (*.f64 x x))))
(/.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (exp.f64 (log.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (.f64 #s(literal -1 binary64) (.f64 x x))))))
(/.f64 (exp.f64 (log.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (exp.f64 (log1p.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))) (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (*.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(/.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 x x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (*.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(/.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (-.f64 x #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal 1 binary64))) (-.f64 x #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -2 binary64))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -2 binary64))) (+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -3 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (pow.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) (-.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 x #s(literal 1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 18 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (.f64 (sqrt.f64 (fma.f64 x x #s(literal 1 binary64))) (sqrt.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (.f64 (sqrt.f64 (fma.f64 x x (+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64)))
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eval100.0ms (2.2%)

Memory: 5.8MiB live, 77.1MiB allocated
Compiler: Compiled 8 294 to 1 611 computations (80.6% saved)

prune6.0ms (0.1%)

Memory

25.0MiB live, 25.0MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	361	4	365
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	362	4	366

Accuracy

100.0%

Counts

366 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.9%	(log.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
▶	48.9%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
▶	99.7%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
▶	99.5%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))

Compiler

Compiled 47 to 34 computations (27.7% saved)

simplify241.0ms (5.3%)

Memory

-4.1MiB live, 151.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	141
0	38	130
1	53	130
2	78	130
3	124	130
4	231	130
5	696	130
6	2320	130
7	5880	130
8	7886	130
0	8006	130

Stop Event

1×	iter limit
1×	node limit
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 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
(+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))
x
#s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(log.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(sqrt.f64 x)
x
(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
#s(literal -1 binary64)

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

localize136.0ms (3%)

Memory

-4.5MiB live, 122.3MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 x)
accuracy	0.00390625	(log.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
accuracy	0.08984375	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
accuracy	31.40983415103507	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	0.0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0.0	(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
accuracy	0.00390625	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
accuracy	31.40983415103507	(sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	0.0	(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
accuracy	0.0	(+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))
accuracy	0.00390625	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
accuracy	0.23711491837715837	#s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))
accuracy	0.0	(*.f64 #s(literal 2 binary64) x)
accuracy	0.00390625	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
accuracy	0.32138688845194996	#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))

Samples

83.0ms

256×

valid

Compiler

Compiled 127 to 23 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-mult: 35.0ms (49.1% of total)

ival-log: 22.0ms (30.9% of total)

ival-add: 5.0ms (7% of total)

ival-sqrt: 5.0ms (7% of total)

ival-div: 2.0ms (2.8% of total)

ival-sub: 2.0ms (2.8% of total)

exact: 1.0ms (1.4% of total)

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

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

series7.0ms (0.2%)

Memory

8.2MiB live, 8.2MiB allocated

Counts

14 → 52

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

Outputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(/ -1/2 x)
(/ (- (pow x 2) 1/2) x)
-1
(- (pow x 2) 1)
(sqrt x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (+ 1 (pow (sqrt -1) 2))))
(* -1 (* x (- (+ 1 (pow (sqrt -1) 2)) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) (pow (sqrt -1) 2)))))
(* -1 (* x (- (+ 1 (+ (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4))) (pow (sqrt -1) 2))) (* 1/2 (/ 1 (pow x 2))))))
(+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x)))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (pow (sqrt -1) 2))))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	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))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1) (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) (log (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1)))) (sqrt x))
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))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1) (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) (log (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1)))) (sqrt x))
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))) (sqrt (- (* x x) 1)) (- x (/ 1/2 x)) (log (+ (sqrt (+ (* x x) -1)) x)) (+ (sqrt (+ (* x x) -1)) x) (sqrt (+ (* x x) -1)) (+ (* x x) -1) (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) (log (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1)))) (sqrt x))

Time

Variable

Point

Expression

4.0ms

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

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

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

simplify388.0ms (8.6%)

Memory

-31.4MiB live, 90.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	211	802
1	590	671
2	1840	625
0	5395	600

Stop Event

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

Counts

52 → 51

Calls

Call 1

Inputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(* 2 x)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(/ -1/2 x)
(/ (- (pow x 2) 1/2) x)
-1
(- (pow x 2) 1)
(sqrt x)
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(+ (log -1/2) (log (/ -1 x)))
(+ (log -1/2) (+ (log (/ -1 x)) (* 1/4 (/ 1 (pow x 2)))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))
(+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)
(* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(* -1 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (+ 1 (pow (sqrt -1) 2))))
(* -1 (* x (- (+ 1 (pow (sqrt -1) 2)) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) (pow (sqrt -1) 2)))))
(* -1 (* x (- (+ 1 (+ (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4))) (pow (sqrt -1) 2))) (* 1/2 (/ 1 (pow x 2))))))
(+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x)))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (pow (sqrt -1) 2))))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

Outputs
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/6 binary64) (+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 3/40 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/8 binary64) x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) x) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x) x (sqrt.f64 #s(literal -1 binary64))))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ (- (pow x 2) 1/2) x)
(-.f64 x (/.f64 #s(literal 1/2 binary64) x))
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(sqrt x)
(sqrt.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 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) x) x))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (.f64 x x)) #s(literal 3/32 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x) #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) x)
x
(* x (- 1 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) x x)
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) #s(literal 1 binary64) x)
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(*.f64 (fma.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) 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)) (/.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))))))
(+.f64 (+.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (log.f64 (/.f64 #s(literal -1 binary64) 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 (+.f64 (/.f64 #s(literal 5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64)))) (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)
(/ (+ 1/2 (* 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 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))
(/.f64 (-.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (*.f64 x x)) #s(literal -1/8 binary64)) x) x) #s(literal 1/2 binary64)) (neg.f64 x))
(* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/128 binary64) (.f64 x x)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)) x (neg.f64 x))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))
(neg.f64 (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x) #s(literal 1 binary64) x))
(* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))
(neg.f64 (fma.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x x))
(* -1 (* x (- (* 1/2 (/ 1 (pow x 2))) 1)))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (*.f64 x x)) x x)
(* -1 (* x (+ 1 (pow (sqrt -1) 2))))
#s(literal 0 binary64)
(* -1 (* x (- (+ 1 (pow (sqrt -1) 2)) (* 1/2 (/ 1 (pow x 2))))))
(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(* -1 (* x (+ 1 (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) (pow (sqrt -1) 2)))))
(neg.f64 (.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) x) #s(literal 1 binary64)))
(* -1 (* x (- (+ 1 (+ (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4))) (pow (sqrt -1) 2))) (* 1/2 (/ 1 (pow x 2))))))
(.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x))) (neg.f64 x))
(+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal 0 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x)))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (pow (sqrt -1) 2))))))
(-.f64 (-.f64 (log.f64 #s(literal 0 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal -1/2 binary64) #s(literal 0 binary64)))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(-.f64 (-.f64 (+.f64 (/.f64 (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 0 binary64)) #s(literal -1/12 binary64)) (pow.f64 x #s(literal 4 binary64))) (log.f64 #s(literal 0 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal -1/2 binary64) #s(literal 0 binary64)))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) #s(literal 0 binary64)) #s(literal 75 binary64) (/.f64 #s(literal 45 binary64) #s(literal 0 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/720 binary64) (-.f64 (-.f64 (+.f64 (/.f64 (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 0 binary64)) #s(literal -1/12 binary64)) (pow.f64 x #s(literal 4 binary64))) (log.f64 #s(literal 0 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal -1/2 binary64) #s(literal 0 binary64))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)

rewrite255.0ms (5.6%)

Memory

12.1MiB live, 141.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	121
0	38	110
1	141	110
2	906	110
0	8565	110

Stop Event

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

Counts

14 → 506

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

Outputs
(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 (.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(*.f64 (neg.f64 x) #s(literal -2 binary64))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) x)
(.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))
(*.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal -2 binary64) x) #s(literal -1 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))
(/.f64 (neg.f64 x) #s(literal -1/2 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x))
(/.f64 x #s(literal 1/2 binary64))
(neg.f64 (*.f64 #s(literal -2 binary64) x))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -2 binary64) x))
(/.f64 (-.f64 (.f64 (log.f64 (-.f64 (.f64 x x) (pow.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))) (log.f64 (-.f64 (.f64 x x) (pow.f64 #s(approx (sqrt (- ( x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64))))) (.f64 (log.f64 (-.f64 x #s(approx (sqrt (- ( x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))) (log.f64 (-.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))))) (+.f64 (log.f64 (-.f64 (.f64 x x) (pow.f64 #s(approx (sqrt (- ( x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))) (log.f64 (-.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))))
(/.f64 (-.f64 (.f64 (log.f64 (+.f64 (pow.f64 #s(approx (sqrt (- ( x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (+.f64 (pow.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (.f64 (log.f64 (fma.f64 #s(approx (sqrt (- ( x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x) (.f64 x x))) (log.f64 (fma.f64 #s(approx (sqrt (- ( x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x) (.f64 x x))))) (+.f64 (log.f64 (+.f64 (pow.f64 #s(approx (sqrt (- ( x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (fma.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x) (*.f64 x x)))))
(/.f64 (-.f64 (pow.f64 (log.f64 (-.f64 (.f64 x x) (pow.f64 #s(approx (sqrt (- ( x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (log.f64 (-.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))) #s(literal 3 binary64))) (fma.f64 (log.f64 (-.f64 (.f64 x x) (pow.f64 #s(approx (sqrt (- ( x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))) (log.f64 (-.f64 (.f64 x x) (pow.f64 #s(approx (sqrt (- ( x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))) (fma.f64 (log.f64 (-.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))) (log.f64 (-.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))))) (.f64 (log.f64 (-.f64 (.f64 x x) (pow.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))) (log.f64 (-.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))))))
(/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 (pow.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal 3 binary64)) (pow.f64 (log.f64 (fma.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x) (.f64 x x))) #s(literal 3 binary64))) (fma.f64 (log.f64 (+.f64 (pow.f64 #s(approx (sqrt (- ( x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (+.f64 (pow.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (log.f64 (fma.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x) (.f64 x x))) (log.f64 (fma.f64 #s(approx (sqrt (- ( x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x) (.f64 x x))) (.f64 (log.f64 (+.f64 (pow.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (fma.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) (-.f64 #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x))) x) (*.f64 x x)))))))
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(neg.f64 (/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/2 binary64))) (neg.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))))))
(fma.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) x)
(fma.f64 (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/4 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 x #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal 1 binary64)))) x)
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))) x)
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) x)
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))) x)
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64))) x)
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (pow.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) x)
(fma.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) x)
(fma.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))) x)
(fma.f64 (sqrt.f64 x) (neg.f64 (neg.f64 (sqrt.f64 x))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #s(literal -1 binary64)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))))
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 #s(literal 1 binary64) x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 (*.f64 x x) (pow.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64)) (neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))
(fma.f64 x (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(fma.f64 x #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))
(-.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) (/.f64 (*.f64 x x) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)))
(+.f64 (/.f64 (*.f64 x x) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))
(+.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) (neg.f64 (/.f64 (*.f64 x x) (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))))
(+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)
(+.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal 1 binary64))))) (.f64 (log.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (log.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))) (+.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (log.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))
(/.f64 (-.f64 (.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))) (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal -1 binary64))))) (.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)))) (+.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))) (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))))
(/.f64 (-.f64 (.f64 (log.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) (log.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/2 binary64))))) (.f64 (log.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))) (log.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))))) (+.f64 (log.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) (log.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) #s(literal 3 binary64)) (pow.f64 (log.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) #s(literal 3 binary64))) (fma.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (fma.f64 (log.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (log.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))) (*.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (log.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))))
(/.f64 (-.f64 (pow.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))) #s(literal 3 binary64)) (pow.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) #s(literal 3 binary64))) (fma.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))) (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))) (fma.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)) (*.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))) (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))))))
(/.f64 (-.f64 (pow.f64 (log.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (log.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))) #s(literal 3 binary64))) (fma.f64 (log.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) (log.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) (fma.f64 (log.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))) (log.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))) (*.f64 (log.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) (log.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))))))))
(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))))
(-.f64 (log.f64 (fma.f64 (neg.f64 x) x (fma.f64 x x #s(literal -1 binary64)))) (log.f64 (neg.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))
(-.f64 (log.f64 (fma.f64 #s(literal -1 binary64) (fma.f64 x x #s(literal -1 binary64)) (*.f64 x x))) (log.f64 (neg.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))))
(-.f64 (log.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/2 binary64))))) (log.f64 (neg.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))))))
(-.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (log.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))))
(-.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))) (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x)))
(-.f64 (log.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) (log.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64)))))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))))
(+.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (neg.f64 (log.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))))
(+.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))) (log.f64 (pow.f64 (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) #s(literal -1 binary64))))
(+.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))) (neg.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))))
(+.f64 (log.f64 (fma.f64 x x (fma.f64 (neg.f64 x) x #s(literal -1 binary64)))) (log.f64 (pow.f64 (-.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x) #s(literal -1 binary64))))
(+.f64 (log.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) (neg.f64 (log.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))))))
(+.f64 (log.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3/2 binary64)))) (log.f64 (pow.f64 (fma.f64 x (-.f64 x (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))) (fma.f64 x x #s(literal -1 binary64))) #s(literal -1 binary64))))
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/4 binary64)) (sqrt.f64 x))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) (pow.f64 #s(literal 1 binary64) #s(literal 1/4 binary64)))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/8 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(sqrt.f64 x)
(fabs.f64 (neg.f64 (sqrt.f64 x)))
(fabs.f64 (sqrt.f64 x))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))

eval111.0ms (2.4%)

Memory: -15.1MiB live, 142.4MiB allocated
Compiler: Compiled 15 337 to 2 275 computations (85.2% saved)

prune9.0ms (0.2%)

Memory

26.2MiB live, 26.2MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	627	1	628
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	627	5	632

Accuracy

100.0%

Counts

632 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	48.9%	(log.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
✓	48.9%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	99.7%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
▶	0.6%	(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
✓	99.5%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))

Compiler

Compiled 62 to 45 computations (27.4% saved)

simplify150.0ms (3.3%)

Memory

3.7MiB live, 156.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
0	12	22
1	19	22
2	32	22
3	57	22
4	150	22
5	530	22
6	1933	22
7	5376	22
0	8778	20

Stop Event

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

Calls

Call 1

Inputs
(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
#s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64))
#s(literal 0 binary64)

Outputs
(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
#s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64))
#s(literal 0 binary64)

localize28.0ms (0.6%)

Memory

-11.2MiB live, 62.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.00390625	(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
accuracy	62.57965205647025	#s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64))

Samples

22.0ms

256×

valid

Compiler

Compiled 28 to 12 computations (57.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-log: 7.0ms (43.1% of total)

ival-sqrt: 4.0ms (24.6% of total)

ival-mult: 3.0ms (18.5% of total)

ival-add: 2.0ms (12.3% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
#s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64))

Outputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x)))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (pow (sqrt -1) 2))))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(* -1 (* x (+ 1 (pow (sqrt -1) 2))))
(* -1 (* x (- (+ 1 (pow (sqrt -1) 2)) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) (pow (sqrt -1) 2)))))
(* -1 (* x (- (+ 1 (+ (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4))) (pow (sqrt -1) 2))) (* 1/2 (/ 1 (pow x 2))))))

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

-inf

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

0.0ms

inf

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

0.0ms

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

simplify88.0ms (1.9%)

Memory

-5.9MiB live, 118.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	146	477
1	411	354
2	1302	320
0	3760	310

Stop Event

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

Counts

24 → 24

Calls

Call 1

Inputs
(log (sqrt -1))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(sqrt -1)
(+ x (sqrt -1))
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(+ (log 2) (* -1 (log (/ 1 x))))
(- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(* 2 x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x)))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (pow (sqrt -1) 2))))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(* -1 (* x (+ 1 (pow (sqrt -1) 2))))
(* -1 (* x (- (+ 1 (pow (sqrt -1) 2)) (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) (pow (sqrt -1) 2)))))
(* -1 (* x (- (+ 1 (+ (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4))) (pow (sqrt -1) 2))) (* 1/2 (/ 1 (pow x 2))))))

Outputs
(log (sqrt -1))
(log.f64 (sqrt.f64 #s(literal -1 binary64)))
(+ (log (sqrt -1)) (/ x (sqrt -1)))
(+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
(+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/6 binary64) (+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
(+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 #s(literal 3/40 binary64) x) (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal 1/6 binary64) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ x (sqrt -1))
(+.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) x) #s(literal 1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (sqrt.f64 #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 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))
(+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))
(-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) x) x))
(- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))
(-.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 #s(literal 2 binary64))) (/.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (.f64 x x)) #s(literal 3/32 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1/4 binary64) (.f64 x x)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (- 2 (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x)
(* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))
(.f64 (-.f64 #s(literal 2 binary64) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) x) x)) x)
(* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))
(.f64 (-.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) x)
(+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x))))
(-.f64 (log.f64 #s(literal 0 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x)))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (* -1 (log (/ -1 x)))) (* 1/2 (/ 1 (* (pow x 2) (+ 1 (pow (sqrt -1) 2))))))
(-.f64 (-.f64 (log.f64 #s(literal 0 binary64)) (log.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal -1/2 binary64) #s(literal 0 binary64)))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(-.f64 (-.f64 (+.f64 (/.f64 (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 0 binary64)) #s(literal -1/12 binary64)) (pow.f64 x #s(literal 4 binary64))) (log.f64 #s(literal 0 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal -1/2 binary64) #s(literal 0 binary64)))
(- (+ (log (+ 1 (pow (sqrt -1) 2))) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (* 3 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2)))) (pow x 4))) (* -1/720 (/ (+ (* 45 (/ 1 (+ 1 (pow (sqrt -1) 2)))) (+ (* 45 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 2))) (* 30 (/ 1 (pow (+ 1 (pow (sqrt -1) 2)) 3))))) (pow x 6)))))) (/ 1/2 (* (pow x 2) (+ 1 (pow (sqrt -1) 2)))))
(fma.f64 (/.f64 (fma.f64 (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)) #s(literal 90 binary64) (/.f64 #s(literal 30 binary64) #s(literal 0 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/720 binary64) (-.f64 (-.f64 (+.f64 (/.f64 (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 0 binary64)) #s(literal -1/12 binary64)) (pow.f64 x #s(literal 4 binary64))) (log.f64 #s(literal 0 binary64))) (log.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal -1/2 binary64) #s(literal 0 binary64))))
(* -1 (* x (+ 1 (pow (sqrt -1) 2))))
#s(literal 0 binary64)
(* -1 (* x (- (+ 1 (pow (sqrt -1) 2)) (* 1/2 (/ 1 (pow x 2))))))
(.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) x)
(* -1 (* x (+ 1 (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) (pow (sqrt -1) 2)))))
(.f64 (neg.f64 x) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal -1/2 binary64)) x) x))
(* -1 (* x (- (+ 1 (+ (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4))) (pow (sqrt -1) 2))) (* 1/2 (/ 1 (pow x 2))))))
(.f64 (neg.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))) x)

rewrite261.0ms (5.7%)

Memory

16.4MiB live, 218.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
0	12	21
1	50	21
2	343	21
3	3843	21
0	8422	19

Stop Event

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

Counts

2 → 2

Calls

Call 1

Inputs
(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
#s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64))

Outputs
(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
#s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64))

eval6.0ms (0.1%)

Memory: -29.0MiB live, 7.6MiB allocated
Compiler: Compiled 661 to 154 computations (76.7% saved)

prune3.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	25	5	30

Accuracy

100.0%

Counts

30 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	48.9%	(log.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))
✓	48.9%	(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
✓	99.7%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
✓	0.6%	(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
✓	99.5%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))

Compiler

Compiled 133 to 84 computations (36.8% saved)

regimes8.0ms (0.2%)

Memory

17.2MiB live, 17.2MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
(log.f64 (+.f64 (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))) x))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(log.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64)))))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.7%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes8.0ms (0.2%)

Memory

-37.1MiB live, 10.3MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))

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

Calls

3 calls:

5.0ms	x
1.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
1.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.5%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes4.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))

Outputs
(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))

Calls

3 calls:

1.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
1.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
1.0ms	x

Results

Accuracy	Segments	Branch
0.6%	1	`x`
0.6%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
0.6%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify54.0ms (1.2%)

Memory

11.3MiB live, 49.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	39
1	39	39
2	60	39
3	106	39
4	222	39
5	756	39
6	2152	39
7	5824	39
8	7585	39

Stop Event

1×	node limit

Calls

Call 1

Inputs

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

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

(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))

Outputs
(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) (-.f64 x (/.f64 #s(literal 1/2 binary64) x)))))
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x)))
(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) (*.f64 #s(literal 2 binary64) x)))
(log.f64 #s(approx (+ (* (sqrt x) (sqrt x)) (sqrt (+ (* x x) -1))) #s(literal 0 binary64)))

soundness453.0ms (10%)

Memory

28.3MiB live, 416.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	31
0	12	31
1	49	31
2	322	31
3	3638	31
0	8656	27
0	211	802
1	590	671
2	1840	625
0	5395	600
0	150	519
1	411	493
2	1170	486
3	3366	448
0	8112	426

Stop Event

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

Compiler

Compiled 85 to 47 computations (44.7% saved)

preprocess116.0ms (2.6%)

Memory: -38.7MiB live, 91.7MiB allocated
Compiler: Compiled 136 to 80 computations (41.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample845.0ms (18.6%)

explain127.0ms (2.8%)

preprocess279.0ms (6.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify357.0ms (7.9%)

localize25.0ms (0.6%)

series5.0ms (0.1%)

simplify188.0ms (4.2%)

rewrite274.0ms (6%)

eval100.0ms (2.2%)

prune6.0ms (0.1%)

simplify241.0ms (5.3%)

localize136.0ms (3%)

series7.0ms (0.2%)

simplify388.0ms (8.6%)

rewrite255.0ms (5.6%)

eval111.0ms (2.4%)

prune9.0ms (0.2%)

simplify150.0ms (3.3%)

localize28.0ms (0.6%)

series1.0ms (0%)

simplify88.0ms (1.9%)

rewrite261.0ms (5.7%)

eval6.0ms (0.1%)

prune3.0ms (0.1%)

regimes8.0ms (0.2%)

regimes8.0ms (0.2%)

regimes4.0ms (0.1%)

simplify54.0ms (1.2%)

soundness453.0ms (10%)

preprocess116.0ms (2.6%)

end0.0ms (0%)

Profiling