Metrics for sqrt C (should all be same)

start0.0ms (0%)

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

analyze1.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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)

sample1.1s (45.2%)

Memory

-0.6MiB live, 688.7MiB allocated; 328ms collecting garbage

Samples

604.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 356.0ms

ival-mult: 247.0ms (69.3% of total)

ival-sqrt: 94.0ms (26.4% of total)

exact: 9.0ms (2.5% of total)

adjust: 3.0ms (0.8% of total)

ival-assert: 3.0ms (0.8% of total)

Bogosity

explain99.0ms (4.1%)

Memory

21.4MiB live, 113.5MiB allocated; 17ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
126	-	2	(5.587807455199186e-158)	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(.f64 #s(literal 2 binary64) (.f64 x x))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	uflow-rescue	63	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	underflow	63
↳	`(*.f64 x x)`	underflow	63
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	oflow-rescue	61	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	overflow	61
↳	`(*.f64 x x)`	overflow	61

Confusion

	Predicted +	Predicted -
+	124	2
-	0	130

Precision

1.0

Recall

0.9841269841269841

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	124	0	2
-	0	0	130

Precision?

1.0

Recall?

0.9841269841269841

Freqs

test

number	freq
0	132
1	124

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

44.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 13.0ms (66.3% of total)

ival-sqrt: 5.0ms (25.5% of total)

ival-true: 1.0ms (5.1% of total)

exact: 1.0ms (5.1% of total)

adjust: 0.0ms (0% of total)

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

preprocess582.0ms (24.3%)

Memory

16.1MiB live, 204.2MiB allocated; 46ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	28	19
2	90	19
3	185	19
4	578	19
5	1314	19
6	4975	19
0	5	6
0	8	6
1	18	6
2	61	6
3	182	6
4	501	6
5	1234	6
6	4730	6
7	7915	6
0	8495	3

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.7%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

series7.0ms (0.3%)

Memory

6.5MiB live, 6.5MiB 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
3.0ms	x	@	inf	((sqrt (* 2 (* x x))) (* 2 (* x x)) 2 (* x x) x)
2.0ms	x	@	0	((sqrt (* 2 (* x x))) (* 2 (* x x)) 2 (* x x) x)
2.0ms	x	@	-inf	((sqrt (* 2 (* x x))) (* 2 (* x x)) 2 (* x x) x)

rewrite61.0ms (2.6%)

Memory

-0.4MiB live, 45.2MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	60
1	44	54
0	165	49

Stop Event

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

Counts

10 → 65

Calls

Call 1

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

eval78.0ms (3.3%)

Memory: -8.2MiB live, 46.2MiB allocated; 14ms collecting garbage
Compiler: Compiled 563 to 158 computations (71.9% saved)

prune5.0ms (0.2%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Accuracy

100.0%

Counts

68 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	99.1%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	54.7%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 20 to 17 computations (15% saved)

series109.0ms (4.5%)

Memory

-36.9MiB live, 8.3MiB allocated; 6ms collecting garbage

Counts

9 → 11

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
101.0ms	x	@	0	((* (sqrt 2) x) (sqrt 2) 2 x (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (sqrt (+ (* x x) (* x x))))
5.0ms	x	@	-inf	((* (sqrt 2) x) (sqrt 2) 2 x (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (sqrt (+ (* x x) (* x x))))
2.0ms	x	@	inf	((* (sqrt 2) x) (sqrt 2) 2 x (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (sqrt (+ (* x x) (* x x))))

Time

Variable

Point

Expression

101.0ms

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

5.0ms

-inf

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

2.0ms

inf

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

rewrite36.0ms (1.5%)

Memory

6.7MiB live, 6.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	126
0	109	117

Stop Event

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

Counts

20 → 44

Calls

Call 1

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

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

eval7.0ms (0.3%)

Memory: 4.6MiB live, 4.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 377 to 95 computations (74.8% saved)

prune6.0ms (0.2%)

Memory

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

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	53	4	57

Accuracy

100.0%

Counts

57 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	99.1%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	54.7%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 20 to 16 computations (20% saved)

series5.0ms (0.2%)

Memory

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

Counts

5 → 8

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x x))
(+.f64 x x)
x
(sqrt.f64 x)

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (+ x x) x (sqrt x))
1.0ms	x	@	inf	((* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (+ x x) x (sqrt x))
1.0ms	x	@	0	((* (sqrt (+ x x)) (sqrt x)) (sqrt (+ x x)) (+ x x) x (sqrt x))

rewrite31.0ms (1.3%)

Memory

5.3MiB live, 5.3MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	81
0	89	81

Stop Event

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

Counts

13 → 24

Calls

Call 1

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

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

eval4.0ms (0.2%)

Memory: 2.6MiB live, 2.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 267 to 76 computations (71.5% saved)

prune5.0ms (0.2%)

Memory

3.0MiB live, 3.0MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	28	4	32

Accuracy

100.0%

Counts

32 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	99.1%	(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	54.7%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 47 to 31 computations (34% saved)

regimes12.0ms (0.5%)

Memory

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

Counts

5 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

3.0ms	x
3.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
3.0ms	(sqrt.f64 (.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 15 to 12 computations (20% saved)

regimes69.0ms (2.9%)

Memory

-31.9MiB live, 14.4MiB allocated; 7ms collecting garbage

Accuracy

Total -28.9b remaining (-6714.7%)

Threshold costs -28.9b (-6714.7%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

50.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
3.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(.f64 #s(literal 2 binary64) (.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 15 to 12 computations (20% saved)

simplify166.0ms (6.9%)

Memory

-2.4MiB live, 43.7MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	10	7
3	16	7
4	48	7
5	370	7
6	3460	7

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations4.0ms (0.2%)

Memory

2.0MiB live, 2.0MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 7 to 5 computations (28.6% saved)

preprocess23.0ms (1%)

Memory: 24.8MiB live, 24.8MiB allocated; 0ms collecting garbage
Remove: (abs x)
Compiler: Compiled 32 to 24 computations (25% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.0ms (0%)

sample1.1s (45.2%)

explain99.0ms (4.1%)

preprocess582.0ms (24.3%)

eval0.0ms (0%)

prune1.0ms (0%)

series7.0ms (0.3%)

rewrite61.0ms (2.6%)

eval78.0ms (3.3%)

prune5.0ms (0.2%)

series109.0ms (4.5%)

rewrite36.0ms (1.5%)

eval7.0ms (0.3%)

prune6.0ms (0.2%)

series5.0ms (0.2%)

rewrite31.0ms (1.3%)

eval4.0ms (0.2%)

prune5.0ms (0.2%)

regimes12.0ms (0.5%)

regimes69.0ms (2.9%)

simplify166.0ms (6.9%)

derivations4.0ms (0.2%)

preprocess23.0ms (1%)

end0.0ms (0%)

Profiling