Metrics for Expression 2, p15

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
100%	25%	0%	75%	0%	0%	0%	1

Compiler

Compiled 13 to 8 computations (38.5% saved)

Precisions

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

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

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

ival-<=: 0.0ms (0% of total)

sample738.0ms (32%)

Results

503.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 241.0ms

ival-add: 77.0ms (31.9% of total)

ival-mult: 76.0ms (31.5% of total)

ival-<=: 61.0ms (25.3% of total)

ival-and: 15.0ms (6.2% of total)

const: 10.0ms (4.1% of total)

backward-pass: 3.0ms (1.2% of total)

Bogosity

preprocess59.0ms (2.6%)

Algorithm

2×	egg-herbie

Rules

368×	`fnmadd-define`
268×	`fnmsub-define`
268×	`fmsub-define`
260×	`sum3-define`
216×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	30	12
2	98	12
3	357	12
4	817	12
5	1273	12
6	1321	12
0	3	4
1	8	4
2	13	4
3	19	4
4	23	4
5	33	4
6	35	4
0	35	4

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ x (* x x))

Outputs
(+ x (* x x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))

Call 2

Inputs
(+ x (* x x))
(+ (neg x) (* (neg x) (neg x)))
(neg (+ (neg x) (* (neg x) (neg x))))

Outputs
(+ x (* x x))
(fma x x x)
(+ (neg x) (* (neg x) (neg x)))
(- (square x) x)
(neg (+ (neg x) (* (neg x) (neg x))))
(- x (square x))

explain48.0ms (2.1%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(*.f64 x x)`
-	-	`(+.f64 x (*.f64 x x))`

Results

30.0ms

512×

valid

Compiler

Compiled 28 to 11 computations (60.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 9.0ms (73.4% of total)

ival-add: 3.0ms (24.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 x (*.f64 x x))

Compiler

Compiled 6 to 3 computations (50% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 x (*.f64 x x))

Rules

22×	`-lowering-.f32`
22×	`-lowering-.f64`
18×	`fma-define`
14×	`fma-lowering-fma.f32`
14×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	7
1	8	7
2	13	7
3	19	7
4	23	7
5	33	7
6	35	7
0	35	7

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ x (* x x))
x
(* x x)

Outputs
(+ x (* x x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))
x
(* x x)
(*.f64 x x)

localize19.0ms (0.8%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x (*.f64 x x))
✓	accuracy	100.0%	(*.f64 x x)

Results

14.0ms

256×

valid

Compiler

Compiled 11 to 4 computations (63.6% saved)

Precisions

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

ival-mult: 2.0ms (49.9% of total)

ival-add: 1.0ms (25% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0.1%)

Counts

2 → 24

Calls

Call 1

Inputs
#<alt (+ x (* x x))>
#<alt (* x x)>

Outputs
#<alt x>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

6 calls:

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

rewrite524.0ms (22.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2676×	`/-lowering-/.f32`
2676×	`/-lowering-/.f64`
2172×	`-lowering-.f32`
2172×	`-lowering-.f64`
2110×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	6
1	22	6
2	174	6
3	1751	6
0	8576	6

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 134

Calls

Call 1

Inputs
(+ x (* x x))
(* x x)

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

simplify401.0ms (17.4%)

Algorithm

1×	egg-herbie

Rules

5040×	`-lowering-.f32`
5040×	`-lowering-.f64`
2514×	`cube-prod`
2280×	`/-lowering-/.f32`
2280×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	88
1	27	65
2	48	65
3	94	65
4	172	65
5	1089	65
6	2548	65
7	3400	65
8	4613	65
9	5808	65
10	6247	65
11	6482	65
12	6690	65
13	6905	65
14	7262	65
0	8052	65

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

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

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

eval69.0ms (3%)

Compiler: Compiled 5482 to 411 computations (92.5% saved)

prune16.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	157	2	159

Accuracy

100.0%

Counts

159 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 x (*.f64 x x))
▶	98.2%	x

Compiler

Compiled 8 to 4 computations (50% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
x

Outputs
x

localize8.0ms (0.3%)

Results

5.0ms

256×

valid

Compiler

Compiled 3 to 2 computations (33.3% saved)

Precisions

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series0.0ms (0%)

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite13.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	1	1
Total	2	2

Accuracy

100.0%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 x (*.f64 x x))
✓	98.2%	x

Compiler

Compiled 15 to 7 computations (53.3% saved)

regimes5.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(+.f64 x (*.f64 x x))

Calls

2 calls:

3.0ms	x
2.0ms	(+.f64 x (*.f64 x x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(+.f64 x (*.f64 x x))`

Compiler

Compiled 8 to 4 computations (50% saved)

regimes1.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
98.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	6
1	4	6

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(+.f64 x (*.f64 x x))
x

soundness351.0ms (15.2%)

Rules

5040×	`-lowering-.f32`
5040×	`-lowering-.f64`
2514×	`cube-prod`
2280×	`/-lowering-/.f32`
2280×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	88
1	27	65
2	48	65
3	94	65
4	172	65
5	1089	65
6	2548	65
7	3400	65
8	4613	65
9	5808	65
10	6247	65
11	6482	65
12	6690	65
13	6905	65
14	7262	65
0	8052	65

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 9 to 4 computations (55.6% saved)

preprocess27.0ms (1.2%)

Compiler: Compiled 38 to 20 computations (47.4% saved)

Expression 2, p15

analyze0.0ms (0%)

sample738.0ms (32%)

preprocess59.0ms (2.6%)

explain48.0ms (2.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.3%)

localize19.0ms (0.8%)

series1.0ms (0.1%)

rewrite524.0ms (22.7%)

simplify401.0ms (17.4%)

eval69.0ms (3%)

prune16.0ms (0.7%)

simplify5.0ms (0.2%)

localize8.0ms (0.3%)

series0.0ms (0%)

rewrite13.0ms (0.6%)

simplify4.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes5.0ms (0.2%)

regimes1.0ms (0.1%)

simplify7.0ms (0.3%)

soundness351.0ms (15.2%)

preprocess27.0ms (1.2%)

end0.0ms (0%)

Profiling