Metrics for sqrt C (should all be same)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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)

sample658.0ms (60.1%)

Memory

-0.8MiB live, 728.8MiB allocated; 244ms collecting garbage

Samples

443.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 263.0ms

ival-mult!: 190.0ms (72.3% of total)

ival-sqrt: 71.0ms (27% of total)

adjust: 2.0ms (0.8% of total)

Bogosity

preprocess79.0ms (7.2%)

Memory

-16.6MiB live, 27.9MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	33	19
2	105	19
3	213	19
4	780	19
5	4039	19

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.3%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Symmetry

(abs x)

Compiler

Compiled 10 to 10 computations (0% saved)

series3.0ms (0.3%)

Memory

4.7MiB live, 4.7MiB allocated; 0ms collecting garbage

Counts

5 → 5

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 #s(literal 2 binary64) (.f64 x x))
#s(literal 2 binary64)
(*.f64 x x)
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 (* x x) #s(hole binary64 (pow x 2)))
#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 x) x)
1.0ms	x	@	inf	((sqrt (* 2 (* x x))) (* 2 (* x x)) 2 (* x x) x)
1.0ms	x	@	0	((sqrt (* 2 (* x x))) (* 2 (* x x)) 2 (* x x) x)

rewrite31.0ms (2.9%)

Memory

42.1MiB live, 42.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	61
0	22	60
1	50	57
0	179	51

Stop Event

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

Counts

10 → 94

Calls

Call 1

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

eval14.0ms (1.3%)

Memory: -28.0MiB live, 17.2MiB allocated; 6ms collecting garbage
Compiler: Compiled 433 to 200 computations (53.8% saved)

prune4.0ms (0.4%)

Memory

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

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Accuracy

100.0%

Counts

91 → 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)

series7.0ms (0.7%)

Memory

14.2MiB live, 14.2MiB allocated; 0ms 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
3.0ms	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	@	-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))

Time

Variable

Point

Expression

3.0ms

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

-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))

rewrite68.0ms (6.2%)

Memory

-8.3MiB live, 51.0MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	209
0	76	162
1	165	102
0	659	102

Stop Event

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

Counts

29 → 175

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

eval8.0ms (0.7%)

Memory: -36.7MiB live, 9.8MiB allocated; 3ms collecting garbage
Compiler: Compiled 228 to 145 computations (36.4% saved)

prune3.0ms (0.3%)

Memory

4.9MiB live, 4.9MiB allocated; 0ms collecting garbage

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	1	1
Picked	0	5	5
Done	0	0	0
Total	53	7	60

Accuracy

100.0%

Counts

60 → 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) #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 44 to 41 computations (6.8% saved)

series44.0ms (4%)

Memory

13.8MiB live, 58.0MiB allocated; 5ms collecting garbage

Counts

9 → 12

Calls

Call 1

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

Calls

3 calls:

Time	Variable		Point	Expression
25.0ms	x	@	0	((sqrt (+ 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)
11.0ms	x	@	inf	((sqrt (+ 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) 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

25.0ms

((sqrt (+ 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)

11.0ms

inf

((sqrt (+ 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) 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)

rewrite29.0ms (2.7%)

Memory

22.1MiB live, 22.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	244
0	65	209
0	241	203

Stop Event

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

Counts

21 → 35

Calls

Call 1

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

Outputs
(pow.f64 #s(approx (+ x x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (+ x x) #s(literal 2 binary64)))
#s(approx (+ 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 (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))
(.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)) (sqrt.f64 (+.f64 x x)))
#s(approx (+ x x) (+.f64 x x))
#s(approx (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) (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)
#s(approx (sqrt (+ x x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x))
#s(approx (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) (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)) (neg.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) x)) x)))
#s(approx (* (pow (* (+ x x) x) 1/4) (pow (* (+ x x) x) 1/4)) (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: 2.9MiB live, 2.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 288 to 111 computations (61.5% saved)

prune2.0ms (0.2%)

Memory

2.6MiB live, 2.6MiB allocated; 0ms collecting garbage

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	25	8	33

Accuracy

100.0%

Counts

33 → 8

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))
▶	7.0%	(sqrt.f64 #s(approx (+ x x) (+.f64 x x)))
✓	5.4%	(sqrt.f64 #s(approx (+ 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 47 to 47 computations (0% saved)

series26.0ms (2.4%)

Memory

-8.6MiB live, 37.9MiB allocated; 3ms collecting garbage

Counts

9 → 12

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ x x)) #s(hole binary64 (sqrt (* 2 x))))
#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 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 (sqrt (+ x x)) #s(hole binary64 (* x (sqrt (/ 2 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 (sqrt (+ x x)) #s(hole binary64 (* -1 (* x (sqrt (/ 2 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
11.0ms	x	@	0	((sqrt (+ x x)) (+ x x) (+ x x) x (pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (+ x x) x) 1/4 2)
7.0ms	x	@	inf	((sqrt (+ x x)) (+ x x) (+ x x) x (pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (+ x x) x) 1/4 2)
7.0ms	x	@	-inf	((sqrt (+ x x)) (+ x x) (+ x x) x (pow (pow (* (+ x x) x) 1/4) 2) (pow (* (+ x x) x) 1/4) (* (+ x x) x) 1/4 2)

Time

Variable

Point

Expression

11.0ms

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

7.0ms

inf

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

7.0ms

-inf

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

rewrite33.0ms (3%)

Memory

-26.4MiB live, 22.4MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	224
0	66	221
0	237	215

Stop Event

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

Counts

21 → 33

Calls

Call 1

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

eval3.0ms (0.2%)

Memory: 2.7MiB live, 2.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 215 to 119 computations (44.7% saved)

prune3.0ms (0.3%)

Memory

7.6MiB live, 7.6MiB allocated; 0ms collecting garbage

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	0	0
Picked	0	2	2
Done	0	6	6
Total	28	8	36

Accuracy

100.0%

Counts

36 → 8

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))
✓	7.0%	(sqrt.f64 #s(approx (+ x x) (+.f64 x x)))
✓	5.4%	(sqrt.f64 #s(approx (+ 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 93 to 78 computations (16.1% saved)

regimes12.0ms (1.1%)

Memory

18.4MiB live, 18.4MiB allocated; 0ms collecting garbage

Counts

10 → 1

Calls

Call 1

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

4 calls:

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

Results

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

Compiler

Compiled 12 to 12 computations (0% saved)

regimes12.0ms (1.1%)

Memory

-35.0MiB live, 11.2MiB allocated; 2ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

4 calls:

5.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
3.0ms	x
2.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
2.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 12 to 12 computations (0% saved)

regimes5.0ms (0.5%)

Memory

16.4MiB live, 16.4MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

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

Outputs
(sqrt.f64 #s(approx (+ x x) (+.f64 x x)))

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
7.0%	1	`(*.f64 x x)`
7.0%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
7.0%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
7.0%	1	`x`

Compiler

Compiled 12 to 12 computations (0% saved)

regimes4.0ms (0.4%)

Memory

6.2MiB live, 6.2MiB allocated; 0ms 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) #s(literal 2 binary64)))

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 12 to 12 computations (0% saved)

derivations7.0ms (0.6%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 17 to 16 computations (5.9% saved)

preprocess35.0ms (3.2%)

Memory: 14.5MiB live, 60.6MiB allocated; 3ms collecting garbage
Remove: (abs x)
Compiler: Compiled 64 to 63 computations (1.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample658.0ms (60.1%)

preprocess79.0ms (7.2%)

series3.0ms (0.3%)

rewrite31.0ms (2.9%)

eval14.0ms (1.3%)

prune4.0ms (0.4%)

series7.0ms (0.7%)

rewrite68.0ms (6.2%)

eval8.0ms (0.7%)

prune3.0ms (0.3%)

series44.0ms (4%)

rewrite29.0ms (2.7%)

eval3.0ms (0.2%)

prune2.0ms (0.2%)

series26.0ms (2.4%)

rewrite33.0ms (3%)

eval3.0ms (0.2%)

prune3.0ms (0.3%)

regimes12.0ms (1.1%)

regimes12.0ms (1.1%)

regimes5.0ms (0.5%)

regimes4.0ms (0.4%)

derivations7.0ms (0.6%)

preprocess35.0ms (3.2%)

end0.0ms (0%)

Profiling