Metrics for sqrt E (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 10 to 6 computations (40% saved)

sample847.0ms (36.1%)

Memory

28.7MiB live, 712.7MiB allocated; 761ms collecting garbage

Samples

631.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 209.0ms

ival-pow2: 108.0ms (51.8% of total)

ival-sqrt: 52.0ms (24.9% of total)

ival-add: 38.0ms (18.2% of total)

ival-true: 6.0ms (2.9% of total)

ival-assert: 3.0ms (1.4% of total)

adjust: 2.0ms (1% of total)

Bogosity

explain96.0ms (4.1%)

Memory

-26.2MiB live, 85.0MiB allocated; 88ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
121	-	4	(-3.222238778852059e-157)	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
0	-	0	-	`(pow.f64 x #s(literal 2 binary64))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	oflow-rescue	62	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	overflow	62
↳	`(pow.f64 x #s(literal 2 binary64))`	overflow	124
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`	uflow-rescue	55	0
↳	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`	underflow	55
↳	`(pow.f64 x #s(literal 2 binary64))`	underflow	110

Confusion

	Predicted +	Predicted -
+	117	4
-	0	135

Precision

1.0

Recall

0.9669421487603306

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	117	0	4
-	0	0	135

Precision?

1.0

Recall?

0.9669421487603306

Freqs

test

number	freq
0	139
1	117

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 52 to 19 computations (63.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-pow2: 8.0ms (53.7% of total)

ival-sqrt: 3.0ms (20.1% of total)

ival-add: 2.0ms (13.4% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess168.0ms (7.2%)

Memory

3.8MiB live, 143.7MiB allocated; 25ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	11	13
2	33	13
3	112	13
4	272	13
5	890	13
6	4745	13
0	5	8
0	8	6
1	12	6
2	28	6
3	80	6
4	244	6
5	826	6
6	5361	6
0	8499	3

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Outputs
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(hypot.f64 x x)

Compiler

Compiled 8 to 5 computations (37.5% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.7%	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))

Compiler

Compiled 8 to 5 computations (37.5% saved)

series4.0ms (0.2%)

Memory

5.0MiB live, 5.0MiB allocated; 0ms collecting garbage

Counts

5 → 5

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)

Outputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
x
(* -1 (* x (sqrt 2)))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)
1.0ms	x	@	0	((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)
1.0ms	x	@	-inf	((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)

Time

Variable

Point

Expression

1.0ms

inf

((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)

1.0ms

((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)

1.0ms

-inf

((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (pow x 2) x 2)

simplify147.0ms (6.2%)

Memory

25.2MiB live, 114.4MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	18	18
2	50	18
3	125	18
4	398	18
5	1308	18
6	4899	18
0	8087	18

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 4

Calls

Call 1

Inputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
x
(* -1 (* x (sqrt 2)))

Outputs
(* x (sqrt 2))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(pow x 2)
(*.f64 x x)
x
(* -1 (* x (sqrt 2)))
(*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))

rewrite44.0ms (1.9%)

Memory

0.3MiB live, 45.9MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	20
0	8	12
1	29	8
0	204	8

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

5 → 20

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)

Outputs
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
#s(literal 2 binary64)
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
x
#s(literal 2 binary64)

eval8.0ms (0.3%)

Memory: -45.8MiB live, 5.7MiB allocated; 11ms collecting garbage
Compiler: Compiled 321 to 95 computations (70.4% saved)

prune14.0ms (0.6%)

Memory

17.6MiB live, 17.6MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	5	35

Accuracy

99.6%

Counts

35 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	21.5%	(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
▶	56.7%	(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) (.f64 (.f64 x x) #s(literal 2 binary64))))
▶	5.7%	(sqrt.f64 #s(literal 2 binary64))
▶	52.8%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	48.7%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 112 to 86 computations (23.2% saved)

series8.0ms (0.3%)

Memory

13.1MiB live, 13.1MiB allocated; 0ms collecting garbage

Counts

22 → 10

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) (.f64 (.f64 x x) #s(literal 2 binary64))))
#s(approx (+ (pow x 2) (pow x 2)) (.f64 (.f64 x x) #s(literal 2 binary64)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow.f64 x #s(literal 6 binary64))
#s(literal 6 binary64)
(sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 0 binary64)
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)

Outputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
x
(* -1 (* x (sqrt 2)))
(* (pow x 3) (sqrt 2))
(* 2 (pow x 6))
(pow x 6)
(pow x 4)
(* -1 (* (pow x 3) (sqrt 2)))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (* (* x x) 2) (* x x) x 2 (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* x (sqrt 2)) (sqrt (+ (pow x 2) (pow x 2))) (* x (neg (sqrt 2))) (neg (sqrt 2)) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)
3.0ms	x	@	-inf	((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (* (* x x) 2) (* x x) x 2 (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* x (sqrt 2)) (sqrt (+ (pow x 2) (pow x 2))) (* x (neg (sqrt 2))) (neg (sqrt 2)) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)
2.0ms	x	@	0	((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (* (* x x) 2) (* x x) x 2 (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* x (sqrt 2)) (sqrt (+ (pow x 2) (pow x 2))) (* x (neg (sqrt 2))) (neg (sqrt 2)) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)

Time

Variable

Point

Expression

3.0ms

inf

((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (* (* x x) 2) (* x x) x 2 (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* x (sqrt 2)) (sqrt (+ (pow x 2) (pow x 2))) (* x (neg (sqrt 2))) (neg (sqrt 2)) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)

3.0ms

-inf

((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (* (* x x) 2) (* x x) x 2 (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* x (sqrt 2)) (sqrt (+ (pow x 2) (pow x 2))) (* x (neg (sqrt 2))) (neg (sqrt 2)) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)

2.0ms

((sqrt (+ (pow x 2) (pow x 2))) (+ (pow x 2) (pow x 2)) (* (* x x) 2) (* x x) x 2 (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* x (sqrt 2)) (sqrt (+ (pow x 2) (pow x 2))) (* x (neg (sqrt 2))) (neg (sqrt 2)) (/ (sqrt (* 2 (pow x 6))) (sqrt (+ 0 (pow x 4)))) (sqrt (* 2 (pow x 6))) (* 2 (pow x 6)) (pow x 6) 6 (sqrt (+ 0 (pow x 4))) (+ 0 (pow x 4)) 0 (pow x 4) 4)

simplify155.0ms (6.6%)

Memory

-1.4MiB live, 129.8MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	42
1	36	42
2	91	42
3	243	42
4	737	42
5	2526	42
6	6091	42
0	8829	42

Stop Event

1×	iter limit
1×	node limit

Counts

10 → 9

Calls

Call 1

Inputs
(* x (sqrt 2))
(* 2 (pow x 2))
(pow x 2)
x
(* -1 (* x (sqrt 2)))
(* (pow x 3) (sqrt 2))
(* 2 (pow x 6))
(pow x 6)
(pow x 4)
(* -1 (* (pow x 3) (sqrt 2)))

Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (pow x 2))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(pow x 2)
(*.f64 x x)
x
(* -1 (* x (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 x))
(* (pow x 3) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* 2 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 2 binary64))
(pow x 6)
(pow.f64 x #s(literal 6 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* -1 (* (pow x 3) (sqrt 2)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))

rewrite67.0ms (2.8%)

Memory

9.8MiB live, 63.8MiB allocated; 36ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	122
0	39	94
1	111	70
0	723	70

Stop Event

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

Counts

22 → 270

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) (.f64 (.f64 x x) #s(literal 2 binary64))))
#s(approx (+ (pow x 2) (pow x 2)) (.f64 (.f64 x x) #s(literal 2 binary64)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
(*.f64 x (sqrt.f64 #s(literal 2 binary64)))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))
(pow.f64 x #s(literal 6 binary64))
#s(literal 6 binary64)
(sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64))))
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 0 binary64)
(pow.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)

Outputs
(*.f64 (pow.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(pow.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
#s(approx (+ (pow x 2) (pow x 2)) #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (sqrt.f64 (neg.f64 (pow.f64 x #s(literal 8 binary64)))) (sqrt.f64 (neg.f64 (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (pow.f64 x #s(literal 12 binary64))) (sqrt.f64 (pow.f64 x #s(literal 8 binary64))))
(neg.f64 (*.f64 (neg.f64 x) x))
(neg.f64 (*.f64 x (neg.f64 x)))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 4 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
x
#s(literal 2 binary64)
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 x x)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 (.f64 x x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (fabs.f64 x))
(pow.f64 #s(literal 2 binary64) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (neg.f64 (.f64 x x))))
(/.f64 (sqrt.f64 #s(literal 0 binary64)) (sqrt.f64 #s(literal 0 binary64)))
(/.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (.f64 x x)))
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(fma.f64 x (pow.f64 x #s(literal 3 binary64)) #s(literal 0 binary64))
(-.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 8 binary64)) (neg.f64 (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (.f64 (neg.f64 (.f64 x x)) (*.f64 x x)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 2 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(+.f64 (/.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 8 binary64))) (pow.f64 x #s(literal 4 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))))
(+.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 4 binary64)

eval41.0ms (1.8%)

Memory: 3.7MiB live, 48.1MiB allocated; 26ms collecting garbage
Compiler: Compiled 3 687 to 692 computations (81.2% saved)

prune14.0ms (0.6%)

Memory

-26.9MiB live, 20.5MiB allocated; 5ms collecting garbage

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	225	3	228
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	226	7	233

Accuracy

99.9%

Counts

233 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.0%	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
✓	56.7%	(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) (.f64 (.f64 x x) #s(literal 2 binary64))))
✓	5.7%	(sqrt.f64 #s(literal 2 binary64))
▶	52.8%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
✓	52.8%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
▶	48.5%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
✓	48.7%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 81 to 58 computations (28.4% saved)

series13.0ms (0.5%)

Memory

14.9MiB live, 14.9MiB allocated; 0ms collecting garbage

Counts

13 → 11

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 x (neg.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
x
(neg.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 x (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(sqrt.f64 x)
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)

Outputs
(* x (sqrt 2))
(* -2 (/ x (sqrt 2)))
x
(* 2 (/ x (sqrt 2)))
(sqrt x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((sqrt (+ (pow x 2) (pow x 2))) (* x (neg (/ 2 (sqrt 2)))) x (neg (/ 2 (sqrt 2))) (/ 2 (sqrt 2)) 2 (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* x (/ 2 (sqrt 2))) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x))
4.0ms	x	@	0	((sqrt (+ (pow x 2) (pow x 2))) (* x (neg (/ 2 (sqrt 2)))) x (neg (/ 2 (sqrt 2))) (/ 2 (sqrt 2)) 2 (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* x (/ 2 (sqrt 2))) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x))
3.0ms	x	@	inf	((sqrt (+ (pow x 2) (pow x 2))) (* x (neg (/ 2 (sqrt 2)))) x (neg (/ 2 (sqrt 2))) (/ 2 (sqrt 2)) 2 (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* x (/ 2 (sqrt 2))) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x))

Time

Variable

Point

Expression

5.0ms

-inf

((sqrt (+ (pow x 2) (pow x 2))) (* x (neg (/ 2 (sqrt 2)))) x (neg (/ 2 (sqrt 2))) (/ 2 (sqrt 2)) 2 (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* x (/ 2 (sqrt 2))) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x))

4.0ms

((sqrt (+ (pow x 2) (pow x 2))) (* x (neg (/ 2 (sqrt 2)))) x (neg (/ 2 (sqrt 2))) (/ 2 (sqrt 2)) 2 (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* x (/ 2 (sqrt 2))) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x))

3.0ms

inf

((sqrt (+ (pow x 2) (pow x 2))) (* x (neg (/ 2 (sqrt 2)))) x (neg (/ 2 (sqrt 2))) (/ 2 (sqrt 2)) 2 (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (* x (/ 2 (sqrt 2))) (* (sqrt x) (sqrt (* 2 x))) (sqrt x) (sqrt (* 2 x)) (* 2 x))

simplify28.0ms (1.2%)

Memory

25.1MiB live, 25.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	51
1	58	51
2	159	51
0	400	51

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

11 → 10

Calls

Call 1

Inputs
(* x (sqrt 2))
(* -2 (/ x (sqrt 2)))
x
(* 2 (/ x (sqrt 2)))
(sqrt x)
(* (sqrt x) (sqrt 2))
(* 2 x)
(* -1 (* x (sqrt 2)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))

Outputs
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* -2 (/ x (sqrt 2)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal -2 binary64))
x
(* 2 (/ x (sqrt 2)))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))
(sqrt x)
(sqrt.f64 x)
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (sqrt 2)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 (sqrt.f64 #s(literal -2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))

rewrite61.0ms (2.6%)

Memory

-12.5MiB live, 34.2MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	73
0	25	61
1	66	53
0	285	53

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

13 → 72

Calls

Call 1

Inputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 x (neg.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
x
(neg.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 x (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(sqrt.f64 x)
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 #s(literal 2 binary64) x)

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

eval13.0ms (0.6%)

Memory: 11.6MiB live, 11.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 422 to 270 computations (81% saved)

prune65.0ms (2.8%)

Memory

-65.6MiB live, 6.4MiB allocated; 20ms collecting garbage

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	0	0
Picked	3	0	3
Done	0	4	4
Total	94	6	100

Accuracy

100.0%

Counts

100 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.7%	(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) (.f64 (.f64 x x) #s(literal 2 binary64))))
✓	5.7%	(sqrt.f64 #s(literal 2 binary64))
▶	48.7%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
▶	52.9%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
✓	52.8%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	48.7%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 73 to 52 computations (28.8% saved)

series12.0ms (0.5%)

Memory

8.8MiB live, 8.8MiB allocated; 0ms collecting garbage

Counts

10 → 7

Calls

Call 1

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

Outputs
(* x (sqrt 2))
(* 2 (/ x (sqrt 2)))
(* 2 x)
x
(* -2 (/ x (sqrt 2)))
(* -2 x)
(* -1 (* x (sqrt 2)))

Calls

3 calls:

Time

Variable

Point

Expression

7.0ms

((sqrt (+ (pow x 2) (pow x 2))) (/ (* 2 x) (sqrt 2)) (* 2 x) 2 x (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (/ (* x -2) (sqrt 2)) (* x -2) -2)

2.0ms

-inf

((sqrt (+ (pow x 2) (pow x 2))) (/ (* 2 x) (sqrt 2)) (* 2 x) 2 x (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (/ (* x -2) (sqrt 2)) (* x -2) -2)

2.0ms

inf

((sqrt (+ (pow x 2) (pow x 2))) (/ (* 2 x) (sqrt 2)) (* 2 x) 2 x (sqrt 2) (sqrt (+ (pow x 2) (pow x 2))) (/ (* x -2) (sqrt 2)) (* x -2) -2)

simplify173.0ms (7.4%)

Memory

40.2MiB live, 126.9MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	27	28
2	54	28
3	90	28
4	195	28
5	878	28
6	5242	28
0	8684	28

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 6

Calls

Call 1

Inputs
(* x (sqrt 2))
(* 2 (/ x (sqrt 2)))
(* 2 x)
x
(* -2 (/ x (sqrt 2)))
(* -2 x)
(* -1 (* x (sqrt 2)))

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

rewrite37.0ms (1.6%)

Memory

-26.9MiB live, 19.6MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	53
0	18	49
1	52	41
0	260	41

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

10 → 46

Calls

Call 1

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

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

eval6.0ms (0.2%)

Memory: 6.6MiB live, 6.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 076 to 175 computations (83.7% saved)

prune5.0ms (0.2%)

Memory

6.4MiB live, 6.4MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	63	6	69

Accuracy

100.0%

Counts

69 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.7%	(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) (.f64 (.f64 x x) #s(literal 2 binary64))))
✓	5.7%	(sqrt.f64 #s(literal 2 binary64))
	52.9%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (+.f64 x x) (sqrt.f64 #s(literal 2 binary64))))
✓	48.7%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
✓	52.8%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
✓	48.7%	#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 220 to 100 computations (54.5% saved)

regimes15.0ms (0.6%)

Memory

13.9MiB live, 13.9MiB allocated; 0ms collecting garbage

Counts

12 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) (.f64 (.f64 x x) #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (+.f64 x x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (+.f64 #s(literal 0 binary64) (pow.f64 x #s(literal 4 binary64)))))

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))

Calls

4 calls:

4.0ms	x
3.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
3.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
3.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
80.2%	3	`(pow.f64 x #s(literal 2 binary64))`
80.2%	3	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
80.2%	3	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
99.4%	2	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes4.0ms (0.2%)

Memory

3.8MiB live, 3.8MiB allocated; 0ms collecting garbage

Counts

9 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) (.f64 (.f64 x x) #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (+.f64 x x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (*.f64 #s(literal 2 binary64) x) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (*.f64 x #s(literal -2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (/.f64 #s(literal 2 binary64) (sqrt.f64 #s(literal 2 binary64))))))

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (+.f64 x x) (sqrt.f64 #s(literal 2 binary64))))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.4%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0.1%)

Memory

2.7MiB live, 2.7MiB allocated; 0ms collecting garbage

Counts

4 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(approx (+ (pow x 2) (pow x 2)) (.f64 (.f64 x x) #s(literal 2 binary64))))

Outputs
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes39.0ms (1.6%)

Memory

-43.3MiB live, 14.8MiB allocated; 9ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Outputs
(sqrt.f64 #s(literal 2 binary64))
#s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64))))

Calls

4 calls:

34.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
1.0ms	x
1.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
1.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
52.8%	1	`(pow.f64 x #s(literal 2 binary64))`
52.8%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
52.8%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
54.8%	2	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes4.0ms (0.2%)

Memory

9.1MiB live, 9.1MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))

Outputs
(sqrt.f64 #s(literal 2 binary64))

Calls

4 calls:

1.0ms	x
1.0ms	(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))
1.0ms	(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))
1.0ms	(pow.f64 x #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
5.7%	1	`(pow.f64 x #s(literal 2 binary64))`
5.7%	1	`(+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64)))`
5.7%	1	`(sqrt.f64 (+.f64 (pow.f64 x #s(literal 2 binary64)) (pow.f64 x #s(literal 2 binary64))))`
5.7%	1	`x`

Compiler

Compiled 19 to 13 computations (31.6% saved)

bsearch14.0ms (0.6%)

Memory

16.5MiB live, 16.5MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	-1.8174149497926452e-291	5.569508350748552e-308

Samples

7.0ms

160×

valid

Compiler

Compiled 221 to 188 computations (14.9% saved)

Precisions

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

ival-pow2: 2.0ms (51.5% of total)

ival-add: 1.0ms (25.7% of total)

ival-sqrt: 1.0ms (25.7% of total)

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

adjust: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.8174149497926452e-291	5.569508350748552e-308

Compiler

Compiled 301 to 228 computations (24.3% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.8174149497926452e-291	5.569508350748552e-308

Compiler

Compiled 281 to 218 computations (22.4% saved)

bsearch18.0ms (0.8%)

Memory

-35.7MiB live, 10.4MiB allocated; 4ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	-5.901682878617649e-206	-5.273136891989275e-208

Samples

13.0ms

112×

valid

Compiler

Compiled 116 to 106 computations (8.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sqrt: 9.0ms (81.8% of total)

ival-pow2: 1.0ms (9.1% of total)

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

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

adjust: 0.0ms (0% of total)

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

simplify49.0ms (2.1%)

Memory

25.4MiB live, 68.7MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	98
1	36	98
2	57	98
3	114	98
4	280	98
5	1500	98
6	5245	98

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (+.f64 x x) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(literal 2 binary64))

Outputs
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) (.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 #s(literal 2 binary64) x))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (+.f64 x x) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (/.f64 (+.f64 x x) (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64))))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -20240225330731/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -7229475734293037/180736893357325919804742965901096183254486650358500961579737723575212405143116703993975930943694719806137463391890175780999890999416217020648099397663164550811570949854893831716648452639533025774320471006645409943407034368 binary64)) (sqrt.f64 #s(literal 2 binary64)) #s(approx (sqrt (+ (pow x 2) (pow x 2))) (*.f64 x (sqrt.f64 #s(literal 2 binary64)))))
(sqrt.f64 #s(literal 2 binary64))

derivations92.0ms (3.9%)

Memory

-7.2MiB live, 91.1MiB allocated; 14ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 110 to 27 computations (75.5% saved)

preprocess81.0ms (3.5%)

Memory: -7.1MiB live, 39.3MiB allocated; 5ms collecting garbage
Compiler: Compiled 236 to 64 computations (72.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample847.0ms (36.1%)

explain96.0ms (4.1%)

preprocess168.0ms (7.2%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.2%)

simplify147.0ms (6.2%)

rewrite44.0ms (1.9%)

eval8.0ms (0.3%)

prune14.0ms (0.6%)

series8.0ms (0.3%)

simplify155.0ms (6.6%)

rewrite67.0ms (2.8%)

eval41.0ms (1.8%)

prune14.0ms (0.6%)

series13.0ms (0.5%)

simplify28.0ms (1.2%)

rewrite61.0ms (2.6%)

eval13.0ms (0.6%)

prune65.0ms (2.8%)

series12.0ms (0.5%)

simplify173.0ms (7.4%)

rewrite37.0ms (1.6%)

eval6.0ms (0.2%)

prune5.0ms (0.2%)

regimes15.0ms (0.6%)

regimes4.0ms (0.2%)

regimes2.0ms (0.1%)

regimes39.0ms (1.6%)

regimes4.0ms (0.2%)

bsearch14.0ms (0.6%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch18.0ms (0.8%)

simplify49.0ms (2.1%)

derivations92.0ms (3.9%)

preprocess81.0ms (3.5%)

end0.0ms (0%)

Profiling