Metrics for sqrt E (should all be same)

analyze0.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 10 to 8 computations (20% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

Operation ival-add, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

Operation ival-sqrt, time spent: 0.0ms, 0.0% of total-time

Operation ival-pow, time spent: 0.0ms, 0.0% of total-time

sample1.0s (15.4%)

Results

964.0ms	8254×	256	valid
0.0ms	1×	256	valid
0.0ms	1×	256	infinite

Precisions

Click to see histograms. Total time spent on operations: 352.0ms

Operation ival-pow, time spent: 218.0ms, 62.0% of total-time

Operation ival-sqrt, time spent: 74.0ms, 21.0% of total-time

Operation ival-add, time spent: 42.0ms, 12.0% of total-time

Operation const, time spent: 18.0ms, 5.0% of total-time

Bogosity

preprocess501.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

114×	`fma-define`
86×	`fma-neg`
56×	`associate-r`
52×	`unsub-neg`
28×	`distribute-rgt-neg-out`

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
137	-	3	(7.374300426770935e-160)	`(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))`
0	-	0	-	`2`
0	-	0	-	`(pow.f64 x 2)`
0	-	0	-	`(+.f64 (pow.f64 x 2) (pow.f64 x 2))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))`	uflow-rescue	76	0
↳	`(+.f64 (pow.f64 x 2) (pow.f64 x 2))`	underflow	76
↳	`(pow.f64 x 2)`	underflow	152
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))`	oflow-rescue	58	0
↳	`(+.f64 (pow.f64 x 2) (pow.f64 x 2))`	overflow	58
↳	`(pow.f64 x 2)`	overflow	116

Confusion

	Predicted +	Predicted -
+	134	3
-	0	119

Precision

1.0

Recall

0.9781021897810219

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	134	0	3
-	0	0	119

Precision?

1.0

Recall?

0.9781021897810219

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	88
1	25	56
2	54	56
3	171	56
4	322	56
5	397	56
6	413	56

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2)))
(neg.f64 (sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2))))

Outputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(hypot.f64 x x)
(neg.f64 (sqrt.f64 (+.f64 (pow.f64 (neg.f64 x) 2) (pow.f64 (neg.f64 x) 2))))
(neg.f64 (sqrt.f64 (*.f64 2 (pow.f64 (neg.f64 x) 2))))
(neg.f64 (hypot.f64 x x))

Symmetry

(abs x)

Compiler

Compiled 62 to 46 computations (25.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 372.0ms

Operation ival-sqrt, time spent: 221.0ms, 59.0% of total-time

Operation ival-add, time spent: 120.0ms, 32.0% of total-time

Operation ival-pow, time spent: 29.0ms, 8.0% of total-time

Operation const, time spent: 2.0ms, 1.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)

Compiler

Compiled 4 to 2 computations (50% saved)

localize29.0ms (0.4%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(hypot.f64 x x)

Compiler

Compiled 6 to 3 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

Operation composed, time spent: 13.0ms, 51.0% of total-time

Operation ival-mult, time spent: 9.0ms, 35.0% of total-time

Operation ival-sqrt, time spent: 2.0ms, 8.0% of total-time

Operation ival-add, time spent: 1.0ms, 4.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

series2.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (hypot.f64 x x)>

Outputs
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (.f64 -1 (.f64 x (sqrt.f64 2)))>
#<alt (.f64 -1 (.f64 x (sqrt.f64 2)))>
#<alt (.f64 -1 (.f64 x (sqrt.f64 2)))>
#<alt (.f64 -1 (.f64 x (sqrt.f64 2)))>

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt (+ (* x x) (* x x)))
1.0ms	x	@	inf	(sqrt (+ (* x x) (* x x)))
0.0ms	x	@	-inf	(sqrt (+ (* x x) (* x x)))

rewrite234.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`log1p-expm1-u`
801×	`expm1-log1p-u`
404×	`associate-r`
340×	`associate-l`
288×	`unpow-prod-down`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	46	13
2	482	7
3	5570	7

Stop Event

1×	node limit

Counts

1 → 104

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(+.f64 (+.f64 (/.f64 0 0) 1) -1)
(+.f64 0 (/.f64 0 0))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (.f64 (/.f64 0 0) (pow.f64 x 2)) (.f64 (/.f64 0 0) (pow.f64 x 2)))
(+.f64 (.f64 (pow.f64 x 2) (/.f64 0 0)) (.f64 (pow.f64 x 2) (/.f64 0 0)))
(-.f64 (+.f64 (/.f64 0 0) 1) 1)
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
(.f64 x (.f64 x 2))
(.f64 x (.f64 (*.f64 x 2) 1))
(.f64 x (.f64 (*.f64 x 2) (/.f64 0 0)))
(*.f64 (pow.f64 x 2) 2)
(.f64 (pow.f64 x 2) (.f64 (.f64 x 2) (.f64 x 2)))
(*.f64 (/.f64 0 0) (/.f64 0 0))
(*.f64 (/.f64 0 0) 1)
(*.f64 (/.f64 0 0) (log.f64 (E.f64)))
(*.f64 (/.f64 0 0) (pow.f64 1 1/3))
(*.f64 (/.f64 0 0) (pow.f64 1 1/2))
(*.f64 1 (/.f64 0 0))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x 2)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 4)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (*.f64 x 2)))
(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(*.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 x 2)))
(*.f64 0 (/.f64 1 0))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 (pow.f64 x 2) (/.f64 0 0)))
(*.f64 (pow.f64 (cbrt.f64 x) 4) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))
(.f64 (.f64 x 2) x)
(*.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(*.f64 4 (pow.f64 x 4))
(*.f64 (pow.f64 1 1/3) (/.f64 0 0))
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))
(.f64 (.f64 (/.f64 0 0) x) (*.f64 x 2))
(.f64 (.f64 (/.f64 0 0) 2) (pow.f64 x 2))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (cbrt.f64 x) 4))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2))
(.f64 (.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))
(/.f64 0 0)
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (.f64 2 (pow.f64 x 6))) (.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 0 0) 1) 3) 1) (+.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) (+.f64 1 (+.f64 (/.f64 0 0) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) 1) (+.f64 (+.f64 (/.f64 0 0) 1) 1))
(/.f64 (.f64 (/.f64 0 0) (.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 1/3)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 1/9)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 6)
(pow.f64 (/.f64 0 0) 4)
(pow.f64 (/.f64 0 0) 9)
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 (/.f64 0 0) 5)
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 0 0))) 2)) (cbrt.f64 (log.f64 (/.f64 0 0))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
(sqrt.f64 (/.f64 0 0))
(fabs.f64 (/.f64 0 0))
(fabs.f64 (neg.f64 (/.f64 0 0)))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(exp.f64 (log.f64 (/.f64 0 0)))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
(fma.f64 x x (pow.f64 x 2))
(fma.f64 1 (pow.f64 x 2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4) (pow.f64 x 2))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2) (pow.f64 x 2))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (pow.f64 x 2))

simplify21.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

84×	`*-commutative`
32×	`associate-r`
28×	`associate-l`
20×	`count-2`
18×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	222	12884902958
1	581	12884902958

Stop Event

1×

unsound

Counts

116 → 134

Calls

Call 1

Inputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
(+.f64 (+.f64 (/.f64 0 0) 1) -1)
(+.f64 0 (/.f64 0 0))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (.f64 (/.f64 0 0) (pow.f64 x 2)) (.f64 (/.f64 0 0) (pow.f64 x 2)))
(+.f64 (.f64 (pow.f64 x 2) (/.f64 0 0)) (.f64 (pow.f64 x 2) (/.f64 0 0)))
(-.f64 (+.f64 (/.f64 0 0) 1) 1)
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
(.f64 x (.f64 x 2))
(.f64 x (.f64 (*.f64 x 2) 1))
(.f64 x (.f64 (*.f64 x 2) (/.f64 0 0)))
(*.f64 (pow.f64 x 2) 2)
(.f64 (pow.f64 x 2) (.f64 (.f64 x 2) (.f64 x 2)))
(*.f64 (/.f64 0 0) (/.f64 0 0))
(*.f64 (/.f64 0 0) 1)
(*.f64 (/.f64 0 0) (log.f64 (E.f64)))
(*.f64 (/.f64 0 0) (pow.f64 1 1/3))
(*.f64 (/.f64 0 0) (pow.f64 1 1/2))
(*.f64 1 (/.f64 0 0))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x 2)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 4)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (*.f64 x 2)))
(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(*.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 x 2)))
(*.f64 0 (/.f64 1 0))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 (pow.f64 x 2) (/.f64 0 0)))
(*.f64 (pow.f64 (cbrt.f64 x) 4) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))
(.f64 (.f64 x 2) x)
(*.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(*.f64 4 (pow.f64 x 4))
(*.f64 (pow.f64 1 1/3) (/.f64 0 0))
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
(*.f64 (pow.f64 2 1/2) x)
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))
(.f64 (.f64 (/.f64 0 0) x) (*.f64 x 2))
(.f64 (.f64 (/.f64 0 0) 2) (pow.f64 x 2))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (cbrt.f64 x) 4))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2))
(.f64 (.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))
(/.f64 0 0)
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (.f64 2 (pow.f64 x 6))) (.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 0 0) 1) 3) 1) (+.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) (+.f64 1 (+.f64 (/.f64 0 0) 1))))
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) 1) (+.f64 (+.f64 (/.f64 0 0) 1) 1))
(/.f64 (.f64 (/.f64 0 0) (.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 1/3)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 1/9)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 6)
(pow.f64 (/.f64 0 0) 4)
(pow.f64 (/.f64 0 0) 9)
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 (/.f64 0 0) 5)
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 0 0))) 2)) (cbrt.f64 (log.f64 (/.f64 0 0))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
(sqrt.f64 (/.f64 0 0))
(fabs.f64 (/.f64 0 0))
(fabs.f64 (neg.f64 (/.f64 0 0)))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(exp.f64 (log.f64 (/.f64 0 0)))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
(fma.f64 x x (pow.f64 x 2))
(fma.f64 1 (pow.f64 x 2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4) (pow.f64 x 2))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2) (pow.f64 x 2))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (pow.f64 x 2))

Outputs
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(*.f64 x (sqrt.f64 2))
(*.f64 x -2)
(.f64 -1 (.f64 x (sqrt.f64 2)))
(*.f64 x -2)
(.f64 -1 (.f64 x (sqrt.f64 2)))
(*.f64 x -2)
(.f64 -1 (.f64 x (sqrt.f64 2)))
(*.f64 x -2)
(.f64 -1 (.f64 x (sqrt.f64 2)))
(*.f64 x -2)
(+.f64 (pow.f64 x 2) (pow.f64 x 2))
-2
(+.f64 (+.f64 (/.f64 0 0) 1) -1)
-2
(+.f64 0 (/.f64 0 0))
-2
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
-2
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
-2
(+.f64 (.f64 (/.f64 0 0) (pow.f64 x 2)) (.f64 (/.f64 0 0) (pow.f64 x 2)))
-2
(+.f64 (.f64 (pow.f64 x 2) (/.f64 0 0)) (.f64 (pow.f64 x 2) (/.f64 0 0)))
-2
(-.f64 (+.f64 (/.f64 0 0) 1) 1)
-2
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
-2
(.f64 x (.f64 x 2))
-2
(.f64 x (.f64 (*.f64 x 2) 1))
-2
(.f64 x (.f64 (*.f64 x 2) (/.f64 0 0)))
-2
(*.f64 (pow.f64 x 2) 2)
-2
(.f64 (pow.f64 x 2) (.f64 (.f64 x 2) (.f64 x 2)))
-2
(*.f64 (/.f64 0 0) (/.f64 0 0))
-2
(*.f64 (/.f64 0 0) 1)
-2
(*.f64 (/.f64 0 0) (log.f64 (E.f64)))
-2
(*.f64 (/.f64 0 0) (pow.f64 1 1/3))
-2
(*.f64 (/.f64 0 0) (pow.f64 1 1/2))
-2
(*.f64 1 (/.f64 0 0))
-2
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x 2)))
(.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x -2)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x)))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x 2)))
(.f64 (cbrt.f64 x) (.f64 (*.f64 x -2) (pow.f64 (cbrt.f64 x) -2)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 4)))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) -2) (pow.f64 (cbrt.f64 x) -2)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (*.f64 x 2)))
(.f64 (pow.f64 (cbrt.f64 x) -2) (.f64 (*.f64 x -2) (cbrt.f64 x)))
(.f64 (sqrt.f64 x) (pow.f64 (.f64 x 2) 1/2))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x -2)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x 2)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 x -2)))
(*.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))
(.f64 (sqrt.f64 x) (.f64 -2 (pow.f64 x 3/2)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (*.f64 x 2)))
(.f64 (sqrt.f64 x) (.f64 (*.f64 x -2) (sqrt.f64 x)))
(*.f64 0 (/.f64 1 0))
-2
(*.f64 2 (pow.f64 x 2))
-2
(.f64 2 (.f64 (pow.f64 x 2) (/.f64 0 0)))
-2
(*.f64 (pow.f64 (cbrt.f64 x) 4) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) -2) (pow.f64 (cbrt.f64 x) -2)))
(*.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (sqrt.f64 x) (.f64 -2 (pow.f64 x 3/2)))
(.f64 (.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))
-2
(.f64 (.f64 x 2) x)
-2
(*.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x)))
(*.f64 4 (pow.f64 x 4))
-2
(*.f64 (pow.f64 1 1/3) (/.f64 0 0))
-2
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
-2
(*.f64 (pow.f64 2 1/2) x)
(*.f64 x -2)
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x -2)
(.f64 (.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))
(.f64 (sqrt.f64 x) (.f64 -2 (pow.f64 x 3/2)))
(.f64 (.f64 (/.f64 0 0) x) (*.f64 x 2))
-2
(.f64 (.f64 (/.f64 0 0) 2) (pow.f64 x 2))
-2
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (pow.f64 (cbrt.f64 x) 4))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) -2) (pow.f64 (cbrt.f64 x) -2)))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 4)) (pow.f64 (cbrt.f64 x) 2))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) -2) (pow.f64 (cbrt.f64 x) -2)))
(.f64 (.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (.f64 -2 (pow.f64 x 3/2)))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))
(.f64 -2 (.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x)))
(/.f64 1 (/.f64 0 0))
-2
(/.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))
-2
(/.f64 0 0)
-2
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 -2 (cbrt.f64 (pow.f64 x -2)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (.f64 2 (pow.f64 x 6))) (.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))
-2
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 -2 (sqrt.f64 (pow.f64 x -2)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))
-2
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))
-2
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))
-2
(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 0 0) 1) 3) 1) (+.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) (+.f64 1 (+.f64 (/.f64 0 0) 1))))
-2
(/.f64 (-.f64 (*.f64 (+.f64 (/.f64 0 0) 1) (+.f64 (/.f64 0 0) 1)) 1) (+.f64 (+.f64 (/.f64 0 0) 1) 1))
-2
(/.f64 (.f64 (/.f64 0 0) (.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
-2
(pow.f64 (/.f64 0 0) 1)
-2
(pow.f64 (/.f64 0 0) 1/2)
-2
(pow.f64 (/.f64 0 0) 2)
-2
(pow.f64 (/.f64 0 0) 1/3)
-2
(pow.f64 (/.f64 0 0) 3)
-2
(pow.f64 (/.f64 0 0) 1/9)
(pow.f64 -2 1/9)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 -2 2/3)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 -2 1/6)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 -2 1/4)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 -2 3/2)
(pow.f64 (/.f64 0 0) 6)
64
(pow.f64 (/.f64 0 0) 4)
-2
(pow.f64 (/.f64 0 0) 9)
512
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 -2 4/3)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 -2 5/2)
(pow.f64 (/.f64 0 0) 5)
32
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
-2
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 0 0))) 2)) (cbrt.f64 (log.f64 (/.f64 0 0))))
-2
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
-2
(sqrt.f64 (/.f64 0 0))
-2
(fabs.f64 (/.f64 0 0))
-2
(fabs.f64 (neg.f64 (/.f64 0 0)))
-2
(log.f64 (exp.f64 (/.f64 0 0)))
-2
(cbrt.f64 (/.f64 0 0))
-2
(expm1.f64 (log1p.f64 (/.f64 0 0)))
-2
(log1p.f64 (expm1.f64 (/.f64 0 0)))
-2
(exp.f64 (log.f64 (/.f64 0 0)))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
-2
(fma.f64 x x (pow.f64 x 2))
-2
(fma.f64 1 (pow.f64 x 2) (pow.f64 x 2))
(pow.f64 x -2)
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 4) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) -2) (pow.f64 (cbrt.f64 x) -2) (pow.f64 x -2))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (pow.f64 x 2))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (pow.f64 x -2))
(fma.f64 (pow.f64 (cbrt.f64 x) 4) (pow.f64 (cbrt.f64 x) 2) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) -2) (pow.f64 (cbrt.f64 x) -2) (pow.f64 x -2))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (pow.f64 x -2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (pow.f64 x 2))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (pow.f64 x -2))

eval26.0ms (0.4%)

Compiler: Compiled 1066 to 850 computations (20.3% saved)

prune96.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	129	5	134
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	129	6	135

Accuracy

100.0%

Counts

135 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
▶	6.9%	(.f64 (.f64 x 2) x)
▶	99.3%	(*.f64 (sqrt.f64 2) x)
▶	2.5%	(*.f64 x -2)
▶	5.3%	512
▶	5.3%	32

Compiler

Compiled 42 to 32 computations (23.8% saved)

localize77.0ms (1.1%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 27 to 19 computations (29.6% saved)

Precisions

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

Operation ival-mult, time spent: 9.0ms, 61.0% of total-time

Operation ival-sqrt, time spent: 4.0ms, 27.0% of total-time

Operation const, time spent: 2.0ms, 14.0% of total-time

series1.0ms (0%)

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (*.f64 (sqrt.f64 2) x)>

Outputs
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>
#<alt (*.f64 x (sqrt.f64 2))>

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(* (sqrt 2) x)
0.0ms	x	@	0	(* (sqrt 2) x)
0.0ms	x	@	inf	(* (sqrt 2) x)

rewrite63.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

946×	`associate-r`
804×	`associate-l`
488×	`unpow-prod-down`
296×	`log-prod`
286×	`cbrt-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	67	14
2	729	14

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)

Outputs
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) -1)
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 8)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(/.f64 (-.f64 (pow.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 3) 1) (+.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 1 (.f64 (sqrt.f64 2) x))) (+.f64 1 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1))))
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 1 (.f64 (sqrt.f64 2) x))) 1) (+.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (*.f64 (sqrt.f64 8) (pow.f64 x 3)) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 (sqrt.f64 2) x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))) 2)) (cbrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (sqrt.f64 2) x)))) (sqrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(fabs.f64 (*.f64 (sqrt.f64 2) x))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (*.f64 (sqrt.f64 8) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 (sqrt.f64 2) x))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x))) 2))

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1406×	`cancel-sign-sub-inv`
1112×	`distribute-lft-out`
852×	`sub-neg`
758×	`times-frac`
598×	`div-sub`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	778
1	161	760
2	401	745
3	1618	745
4	3913	745

Stop Event

1×	node limit

Counts

37 → 34

Calls

Call 1

Inputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) -1)
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 8)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(/.f64 (-.f64 (pow.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 3) 1) (+.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 1 (.f64 (sqrt.f64 2) x))) (+.f64 1 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1))))
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 1 (.f64 (sqrt.f64 2) x))) 1) (+.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(pow.f64 (*.f64 (sqrt.f64 8) (pow.f64 x 3)) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (E.f64) (log.f64 (*.f64 (sqrt.f64 2) x)))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))) 2)) (cbrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (sqrt.f64 2) x)))) (sqrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(fabs.f64 (*.f64 (sqrt.f64 2) x))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (*.f64 (sqrt.f64 8) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 (sqrt.f64 2) x))) 1/3))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x))) 2))

Outputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) -1)
(*.f64 x (sqrt.f64 2))
(+.f64 0 (*.f64 (sqrt.f64 2) x))
(*.f64 x (sqrt.f64 2))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 8)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 8)))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 2 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))))
(*.f64 2 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))))
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(*.f64 x (sqrt.f64 2))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 3) 1) (+.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 1 (.f64 (sqrt.f64 2) x))) (+.f64 1 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1))))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (.f64 x (sqrt.f64 2))) 3) -1) (fma.f64 (+.f64 1 (.f64 x (sqrt.f64 2))) (+.f64 1 (.f64 x (sqrt.f64 2))) (+.f64 1 (+.f64 1 (.f64 x (sqrt.f64 2))))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (sqrt.f64 2) 1) 3)) (fma.f64 (fma.f64 x (sqrt.f64 2) 1) (fma.f64 x (sqrt.f64 2) 1) (+.f64 2 (*.f64 x (sqrt.f64 2)))))
(/.f64 (+.f64 -1 (pow.f64 (fma.f64 x (sqrt.f64 2) 1) 3)) (+.f64 1 (*.f64 (fma.f64 x (sqrt.f64 2) 1) (fma.f64 x (sqrt.f64 2) 2))))
(/.f64 (-.f64 (.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) (+.f64 1 (.f64 (sqrt.f64 2) x))) 1) (+.f64 (+.f64 1 (.f64 (sqrt.f64 2) x)) 1))
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(*.f64 x (sqrt.f64 2))
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 2 (pow.f64 x 2)) 1/2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (*.f64 (sqrt.f64 8) (pow.f64 x 3)) 1/3)
(cbrt.f64 (*.f64 (sqrt.f64 8) (pow.f64 x 3)))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(*.f64 x (sqrt.f64 2))
(pow.f64 (E.f64) (log.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))) 2)) (cbrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))) 2)) (cbrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (sqrt.f64 2) x)))) (sqrt.f64 (log.f64 (.f64 (sqrt.f64 2) x))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2))))) (sqrt.f64 (log.f64 (.f64 x (sqrt.f64 2)))))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(*.f64 x (sqrt.f64 2))
(fabs.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 x (sqrt.f64 2))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(*.f64 x (sqrt.f64 2))
(cbrt.f64 (*.f64 (sqrt.f64 8) (pow.f64 x 3)))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (sqrt.f64 2) x))) 3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (.f64 3 (log.f64 (*.f64 (sqrt.f64 2) x))) 1/3))
(*.f64 x (sqrt.f64 2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (sqrt.f64 2) x))) 2))
(*.f64 x (sqrt.f64 2))

eval31.0ms (0.5%)

Compiler: Compiled 403 to 346 computations (14.1% saved)

prune9.0ms (0.1%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	34	6	40

Accuracy

100.0%

Counts

40 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	6.9%	(.f64 (.f64 x 2) x)
✓	99.3%	(*.f64 (sqrt.f64 2) x)
✓	2.5%	(*.f64 x -2)
✓	5.3%	512
✓	5.3%	32

Compiler

Compiled 49 to 35 computations (28.6% saved)

regimes19.0ms (0.3%)

Counts

7 → 1

Calls

Call 1

Inputs
32
512
(*.f64 x -2)
(.f64 (.f64 x 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))

Outputs
(hypot.f64 x x)

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
5.0ms	x
4.0ms	(+.f64 (pow.f64 x 2) (pow.f64 x 2))
4.0ms	(pow.f64 x 2)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))`
100.0%	1	`(+.f64 (pow.f64 x 2) (pow.f64 x 2))`
100.0%	1	`(pow.f64 x 2)`

Compiler

Compiled 23 to 17 computations (26.1% saved)

regimes4.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
32
512
(*.f64 x -2)
(.f64 (.f64 x 2) x)

Outputs
(.f64 (.f64 x 2) x)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
6.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.1%)

Accuracy

Total -2.1b remaining (-3.5%)

Threshold costs -2.1b (-3.5%)

Counts

3 → 1

Calls

Call 1

Inputs
32
512
(*.f64 x -2)

Outputs
32

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
5.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	12	33

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(.f64 (.f64 x 2) x)
32

Outputs
(hypot.f64 x x)
(.f64 (.f64 x 2) x)
(.f64 x (.f64 x 2))
32

Compiler

Compiled 12 to 8 computations (33.3% saved)

soundness4.4s (66.3%)

Rules

801×	`log1p-expm1-u`
801×	`expm1-log1p-u`
404×	`associate-r`
340×	`associate-l`
288×	`unpow-prod-down`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	12884902958
1	581	12884902958
0	6	13
1	46	13
2	482	7
3	5570	7
0	15	88
1	25	56
2	54	56
3	171	56
4	322	56
5	397	56
6	413	56

Stop Event

1×	saturated
1×	node limit
1×	unsound

Compiler

Compiled 342 to 97 computations (71.6% saved)

end0.0ms (0%)

preprocess33.0ms (0.5%)

Remove: (abs x)
Compiler: Compiled 70 to 42 computations (40% saved)

analyze0.0ms (0%)

sample1.0s (15.4%)

preprocess501.0ms (7.5%)

eval0.0ms (0%)

prune2.0ms (0%)

localize29.0ms (0.4%)

series2.0ms (0%)

rewrite234.0ms (3.5%)

simplify21.0ms (0.3%)

eval26.0ms (0.4%)

prune96.0ms (1.4%)

localize77.0ms (1.1%)

series1.0ms (0%)

rewrite63.0ms (0.9%)

simplify64.0ms (1%)

eval31.0ms (0.5%)

prune9.0ms (0.1%)

regimes19.0ms (0.3%)

regimes4.0ms (0.1%)

regimes6.0ms (0.1%)

simplify3.0ms (0%)

soundness4.4s (66.3%)

end0.0ms (0%)

preprocess33.0ms (0.5%)

Profiling