Metrics for sqrt B (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample965.0ms (64.8%)

Memory

-31.3MiB live, 753.7MiB allocated; 922ms collecting garbage

Samples

802.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 603.0ms

ival-sqrt: 509.0ms (84.4% of total)

ival-mult!: 93.0ms (15.4% of total)

adjust: 1.0ms (0.2% of total)

Bogosity

preprocess79.0ms (5.3%)

Memory

-27.0MiB live, 26.6MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	28	19
2	68	19
3	213	19
4	402	19
5	2482	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.4%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Symmetry

(abs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series3.0ms (0.2%)

Memory

7.1MiB live, 7.1MiB allocated; 0ms collecting garbage

Counts

5 → 5

Calls

Call 1

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

Outputs
#s(approx (sqrt (* (* 2 x) x)) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (* 2 x) x) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (* (* 2 x) x)) #s(hole binary64 (* -1 (* x (sqrt 2)))))

Calls

3 calls:

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

rewrite35.0ms (2.3%)

Memory

12.8MiB live, 58.8MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	61
0	22	60
1	48	60
0	150	51

Stop Event

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

Counts

10 → 58

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
#s(approx (sqrt (* (* 2 x) x)) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (* 2 x) x) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* 2 x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (* (* 2 x) x)) #s(hole binary64 (* -1 (* x (sqrt 2)))))

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

eval5.0ms (0.3%)

Memory: 11.5MiB live, 11.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 259 to 130 computations (49.8% saved)

prune4.0ms (0.2%)

Memory

9.5MiB live, 9.5MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	49	6	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	6	56

Accuracy

100.0%

Counts

56 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
	52.9%	(.f64 (pow.f64 (.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)))
▶	99.2%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
▶	53.4%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
▶	2.4%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 78 to 72 computations (7.7% saved)

series11.0ms (0.8%)

Memory

-26.5MiB live, 19.9MiB allocated; 5ms collecting garbage

Counts

15 → 14

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx x #s(hole binary64 x))
#s(approx (* (neg x) (sqrt 2)) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (* (+ x x) x) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt (* 2 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (sqrt (* 2 x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) #s(hole binary64 (* (pow x 2) (* (sqrt (/ 1 x)) (sqrt (/ 2 x))))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 x)))))
#s(approx (sqrt x) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 x))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))

Calls

3 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	((sqrt (+ (* x x) (* x x))) x (sqrt (* (* 2 x) x)) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (* (* 2 x) x)) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))
2.0ms	x	@	0	((sqrt (+ (* x x) (* x x))) x (sqrt (* (* 2 x) x)) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (* (* 2 x) x)) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))
2.0ms	x	@	-inf	((sqrt (+ (* x x) (* x x))) x (sqrt (* (* 2 x) x)) (* (sqrt 2) x) (sqrt 2) 2 (sqrt (* (* 2 x) x)) (* (neg x) (sqrt 2)) (neg x) (sqrt (* (+ x x) x)) (* (+ x x) x) (+ x x) (* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (sqrt x))

Time

Variable

Point

Expression

6.0ms

inf

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

2.0ms

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

2.0ms

-inf

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

rewrite85.0ms (5.7%)

Memory

14.7MiB live, 113.4MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	209
0	76	162
1	162	102
0	701	102

Stop Event

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

Counts

29 → 199

Calls

Call 1

Inputs
(hypot.f64 x x)
x
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 x)
(sqrt.f64 (*.f64 (+.f64 x x) x))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x x))
(sqrt.f64 x)
#s(approx (sqrt (+ (* x x) (* x x))) #s(hole binary64 (* x (sqrt 2))))
#s(approx x #s(hole binary64 x))
#s(approx (* (neg x) (sqrt 2)) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (neg x) #s(hole binary64 (* -1 x)))
#s(approx (* (+ x x) x) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) #s(hole binary64 (* (sqrt x) (sqrt (* 2 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (sqrt (* 2 x))))
#s(approx (sqrt x) #s(hole binary64 (sqrt x)))
#s(approx (* (sqrt (+ x x)) (sqrt x)) #s(hole binary64 (* (pow x 2) (* (sqrt (/ 1 x)) (sqrt (/ 2 x))))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 x)))))
#s(approx (sqrt x) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 x))))))
#s(approx (sqrt x) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))

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

eval5.0ms (0.3%)

Memory: 15.4MiB live, 15.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 243 to 152 computations (37.4% saved)

prune6.0ms (0.4%)

Memory

-36.1MiB live, 9.9MiB allocated; 3ms collecting garbage

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	1	1
Picked	0	5	5
Done	0	0	0
Total	57	7	64

Accuracy

100.0%

Counts

64 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	52.9%	(.f64 (pow.f64 (.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)))
✓	99.2%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	53.4%	(sqrt.f64 (*.f64 (+.f64 x x) x))
▶	5.4%	(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.4%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 45 to 42 computations (6.7% saved)

series46.0ms (3.1%)

Memory

12.1MiB live, 103.6MiB allocated; 6ms collecting garbage

Counts

9 → 11

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
#s(approx (* (+ x x) x) #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 (pow.f64 (.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
x
#s(literal 1/4 binary64)

Outputs
#s(approx (sqrt (* (+ x x) x)) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (+ x x) x) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) #s(hole binary64 (pow (exp (* 1/4 (+ (log 2) (* 2 (log x))))) 2)))
#s(approx (pow (* (+ x x) x) 1/4) #s(hole binary64 (exp (* 1/4 (+ (log 2) (* 2 (log x)))))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) #s(hole binary64 (pow (exp (* 1/4 (+ (log 2) (* -2 (log (/ 1 x)))))) 2)))
#s(approx (pow (* (+ x x) x) 1/4) #s(hole binary64 (exp (* 1/4 (+ (log 2) (* -2 (log (/ 1 x))))))))
#s(approx (sqrt (* (+ x x) x)) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) #s(hole binary64 (pow (exp (* 1/4 (+ (log 2) (* -2 (log (/ -1 x)))))) 2)))
#s(approx (pow (* (+ x x) x) 1/4) #s(hole binary64 (exp (* 1/4 (+ (log 2) (* -2 (log (/ -1 x))))))))

Calls

3 calls:

Time	Variable		Point	Expression
28.0ms	x	@	0	((sqrt (* (+ x x) x)) (* (+ x x) x) 2 (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) (pow (* (+ x x) x) 1/4) (* (+ x x) x) (+ x x) x 1/4)
9.0ms	x	@	-inf	((sqrt (* (+ x x) x)) (* (+ x x) x) 2 (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) (pow (* (+ x x) x) 1/4) (* (+ x x) x) (+ x x) x 1/4)
8.0ms	x	@	inf	((sqrt (* (+ x x) x)) (* (+ x x) x) 2 (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) (pow (* (+ x x) x) 1/4) (* (+ x x) x) (+ x x) x 1/4)

Time

Variable

Point

Expression

28.0ms

((sqrt (* (+ x x) x)) (* (+ x x) x) 2 (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) (pow (* (+ x x) x) 1/4) (* (+ x x) x) (+ x x) x 1/4)

9.0ms

-inf

((sqrt (* (+ x x) x)) (* (+ x x) x) 2 (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) (pow (* (+ x x) x) 1/4) (* (+ x x) x) (+ x x) x 1/4)

8.0ms

inf

((sqrt (* (+ x x) x)) (* (+ x x) x) 2 (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) (pow (* (+ x x) x) 1/4) (* (+ x x) x) (+ x x) x 1/4)

rewrite67.0ms (4.5%)

Memory

-24.0MiB live, 49.4MiB allocated; 49ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	239
0	62	200
0	235	194

Stop Event

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

Counts

20 → 36

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
#s(approx (* (+ x x) x) #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 (pow.f64 (.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
x
#s(literal 1/4 binary64)
#s(approx (sqrt (* (+ x x) x)) #s(hole binary64 (* x (sqrt 2))))
#s(approx (* (+ x x) x) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) #s(hole binary64 (pow (exp (* 1/4 (+ (log 2) (* 2 (log x))))) 2)))
#s(approx (pow (* (+ x x) x) 1/4) #s(hole binary64 (exp (* 1/4 (+ (log 2) (* 2 (log x)))))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) #s(hole binary64 (pow (exp (* 1/4 (+ (log 2) (* -2 (log (/ 1 x)))))) 2)))
#s(approx (pow (* (+ x x) x) 1/4) #s(hole binary64 (exp (* 1/4 (+ (log 2) (* -2 (log (/ 1 x))))))))
#s(approx (sqrt (* (+ x x) x)) #s(hole binary64 (* -1 (* x (sqrt 2)))))
#s(approx (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) #s(hole binary64 (pow (exp (* 1/4 (+ (log 2) (* -2 (log (/ -1 x)))))) 2)))
#s(approx (pow (* (+ x x) x) 1/4) #s(hole binary64 (exp (* 1/4 (+ (log 2) (* -2 (log (/ -1 x))))))))

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

eval3.0ms (0.2%)

Memory: 4.2MiB live, 4.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 272 to 108 computations (60.3% saved)

prune2.0ms (0.1%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	24	1	25
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	25	7	32

Accuracy

100.0%

Counts

32 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.9%	(pow.f64 (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	100.0%	(hypot.f64 x x)
✓	99.2%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	53.4%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	5.4%	(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.4%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 43 to 43 computations (0% saved)

series68.0ms (4.6%)

Memory

10.8MiB live, 59.7MiB allocated; 5ms collecting garbage

Counts

7 → 9

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
x
#s(literal 1/4 binary64)
#s(literal 2 binary64)

Outputs
#s(approx (pow (pow (* (+ x x) x) 1/4) 2) #s(hole binary64 (pow (exp (* 1/4 (+ (log 2) (* 2 (log x))))) 2)))
#s(approx (pow (* (+ x x) x) 1/4) #s(hole binary64 (exp (* 1/4 (+ (log 2) (* 2 (log x)))))))
#s(approx (* (+ x x) x) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (pow (pow (* (+ x x) x) 1/4) 2) #s(hole binary64 (pow (exp (* 1/4 (+ (log 2) (* -2 (log (/ 1 x)))))) 2)))
#s(approx (pow (* (+ x x) x) 1/4) #s(hole binary64 (exp (* 1/4 (+ (log 2) (* -2 (log (/ 1 x))))))))
#s(approx (pow (pow (* (+ x x) x) 1/4) 2) #s(hole binary64 (pow (exp (* 1/4 (+ (log 2) (* -2 (log (/ -1 x)))))) 2)))
#s(approx (pow (* (+ x x) x) 1/4) #s(hole binary64 (exp (* 1/4 (+ (log 2) (* -2 (log (/ -1 x))))))))

Calls

3 calls:

Time	Variable		Point	Expression
53.0ms	x	@	inf	((pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (+ x x) x) (+ x x) x 1/4 2)
8.0ms	x	@	-inf	((pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (+ x x) x) (+ x x) x 1/4 2)
7.0ms	x	@	0	((pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (+ x x) x) (+ x x) x 1/4 2)

Time

Variable

Point

Expression

53.0ms

inf

((pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (+ x x) x) (+ x x) x 1/4 2)

8.0ms

-inf

((pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (+ x x) x) (+ x x) x 1/4 2)

7.0ms

((pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (+ x x) x) (+ x x) x 1/4 2)

rewrite31.0ms (2.1%)

Memory

1.1MiB live, 46.5MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	176
0	53	174
0	209	168

Stop Event

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

Counts

16 → 27

Calls

Call 1

Inputs
(pow.f64 (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64))
(*.f64 (+.f64 x x) x)
(+.f64 x x)
x
#s(literal 1/4 binary64)
#s(literal 2 binary64)
#s(approx (pow (pow (* (+ x x) x) 1/4) 2) #s(hole binary64 (pow (exp (* 1/4 (+ (log 2) (* 2 (log x))))) 2)))
#s(approx (pow (* (+ x x) x) 1/4) #s(hole binary64 (exp (* 1/4 (+ (log 2) (* 2 (log x)))))))
#s(approx (* (+ x x) x) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (pow (pow (* (+ x x) x) 1/4) 2) #s(hole binary64 (pow (exp (* 1/4 (+ (log 2) (* -2 (log (/ 1 x)))))) 2)))
#s(approx (pow (* (+ x x) x) 1/4) #s(hole binary64 (exp (* 1/4 (+ (log 2) (* -2 (log (/ 1 x))))))))
#s(approx (pow (pow (* (+ x x) x) 1/4) 2) #s(hole binary64 (pow (exp (* 1/4 (+ (log 2) (* -2 (log (/ -1 x)))))) 2)))
#s(approx (pow (* (+ x x) x) 1/4) #s(hole binary64 (exp (* 1/4 (+ (log 2) (* -2 (log (/ -1 x))))))))

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

eval2.0ms (0.2%)

Memory: 5.7MiB live, 5.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 169 to 101 computations (40.2% saved)

prune3.0ms (0.2%)

Memory

6.8MiB live, 6.8MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	20	7	27

Accuracy

100.0%

Counts

27 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.9%	(pow.f64 (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
✓	100.0%	(hypot.f64 x x)
✓	99.2%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	53.4%	(sqrt.f64 (*.f64 (+.f64 x x) x))
✓	5.4%	(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
✓	99.3%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
✓	2.4%	#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 86 to 73 computations (15.1% saved)

regimes13.0ms (0.9%)

Memory

-19.6MiB live, 26.3MiB allocated; 3ms collecting garbage

Counts

9 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (* (+ x x) x) #s(literal 2 binary64)))
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x))
#s(approx (sqrt (* (* 2 x) x)) (*.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (+.f64 x x) x))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(hypot.f64 x x)
(pow.f64 (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(.f64 (pow.f64 (.f64 (+.f64 x x) x) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 x x) x) #s(literal 1/4 binary64)))

Outputs
(hypot.f64 x x)

Calls

3 calls:

7.0ms	x
3.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
3.0ms	(.f64 (.f64 #s(literal 2 binary64) x) x)

Results

Accuracy	Segments	Branch
100.0%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
100.0%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
100.0%	1	`x`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes7.0ms (0.5%)

Memory

18.8MiB live, 18.8MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	x
2.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
2.0ms	(.f64 (.f64 #s(literal 2 binary64) x) x)

Results

Accuracy	Segments	Branch
99.3%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
99.3%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
99.3%	1	`x`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes10.0ms (0.7%)

Memory

-33.7MiB live, 14.4MiB allocated; 7ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
1.0ms	x
1.0ms	(.f64 (.f64 #s(literal 2 binary64) x) x)

Results

Accuracy	Segments	Branch
5.4%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
5.4%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
5.4%	1	`x`

Compiler

Compiled 10 to 10 computations (0% saved)

derivations6.0ms (0.4%)

Memory

15.8MiB live, 15.8MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 14 to 14 computations (0% saved)

preprocess33.0ms (2.2%)

Memory: 30.5MiB live, 68.9MiB allocated; 13ms collecting garbage
Remove: (abs x)
Compiler: Compiled 53 to 53 computations (0% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample965.0ms (64.8%)

preprocess79.0ms (5.3%)

series3.0ms (0.2%)

rewrite35.0ms (2.3%)

eval5.0ms (0.3%)

prune4.0ms (0.2%)

series11.0ms (0.8%)

rewrite85.0ms (5.7%)

eval5.0ms (0.3%)

prune6.0ms (0.4%)

series46.0ms (3.1%)

rewrite67.0ms (4.5%)

eval3.0ms (0.2%)

prune2.0ms (0.1%)

series68.0ms (4.6%)

rewrite31.0ms (2.1%)

eval2.0ms (0.2%)

prune3.0ms (0.2%)

regimes13.0ms (0.9%)

regimes7.0ms (0.5%)

regimes10.0ms (0.7%)

derivations6.0ms (0.4%)

preprocess33.0ms (2.2%)

end0.0ms (0%)

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