Metrics for Expression 3, 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 17 to 9 computations (47.1% 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)

sample954.0ms (29.2%)

Results

657.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 457.0ms

ival-mult: 256.0ms (56.1% of total)

ival-<=: 126.0ms (27.6% of total)

ival-add: 51.0ms (11.2% of total)

const: 11.0ms (2.4% of total)

ival-and: 10.0ms (2.2% of total)

backward-pass: 2.0ms (0.4% of total)

Bogosity

preprocess42.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

648×	`fnmadd-define`
542×	`fnmsub-define`
538×	`fmsub-define`
384×	`fmm-def`
338×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	48	18
2	164	18
3	614	18
4	1508	18
5	2201	18
6	2305	18
0	4	6
1	15	6
2	26	6
3	35	6
4	49	6
5	77	6
6	83	6
0	83	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

Outputs
(+ (* x (* x x)) (* x x))
(fma x x (pow x 3))
(+ (* (neg x) (* (neg x) (neg x))) (* (neg x) (neg x)))
(- (square x) (pow x 3))
(neg (+ (* (neg x) (* (neg x) (neg x))) (* (neg x) (neg x))))
(fmsub x (square x) (square x))

explain80.0ms (2.5%)

FPErrors

Click to see full error table

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

Results

25.0ms

512×

valid

Compiler

Compiled 50 to 14 computations (72% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 8.0ms (71% of total)

ival-add: 3.0ms (26.6% of total)

const: 0.0ms (0% of total)

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

eval0.0ms (0%)

Compiler: Compiled 8 to 5 computations (37.5% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
▶	100.0%	(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))

Compiler

Compiled 18 to 9 computations (50% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	128	(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
✓	cost-diff	0	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 x (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))

Rules

42×	`-lowering-.f32`
42×	`-lowering-.f64`
40×	`fma-define`
28×	`fma-lowering-fma.f32`
28×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	27	27
2	39	27
3	62	27
4	66	27
0	66	27

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x (* x (+ x 1)))
x
(* x (+ x 1))
(+ x 1)
1
(+ (* x (* x x)) (* x x))
(* x (* x x))
x
(* x x)

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

localize33.0ms (1%)

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
✓	accuracy	100.0%	(*.f64 x (+.f64 x #s(literal 1 binary64)))

Results

22.0ms

256×

valid

Compiler

Compiled 37 to 9 computations (75.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 7.0ms (66.6% of total)

ival-add: 3.0ms (28.6% of total)

const: 0.0ms (0% of total)

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

series5.0ms (0.2%)

Counts

6 → 72

Calls

Call 1

Inputs
#<alt (* x (* x (+ x 1)))>
#<alt (* x (+ x 1))>
#<alt (+ x 1)>
#<alt (+ (* x (* x x)) (* x x))>
#<alt (* x (* x x))>
#<alt (* x x)>

Outputs
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<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 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<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

18 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(* x (* x (+ x 1)))
0.0ms	x	@	0	(* x (* x x))
0.0ms	x	@	0	(* x (* x (+ x 1)))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	-inf	(* x (* x (+ x 1)))

rewrite277.0ms (8.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2774×	`-lowering-.f32`
2774×	`-lowering-.f64`
1888×	`fma-lowering-fma.f32`
1888×	`fma-lowering-fma.f64`
1774×	`fmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	25
1	50	24
2	355	24
3	3416	24
0	8183	24

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 392

Calls

Call 1

Inputs
(* x (* x (+ x 1)))
(* x (+ x 1))
(+ x 1)
(+ (* x (* x x)) (* x x))
(* x (* x x))
(* x x)

Outputs
(+.f64 (.f64 x x) (.f64 x (*.f64 x x)))
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
(+.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64))))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x (+.f64 x #s(literal 1 binary64)))))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64))))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64))))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (-.f64 #s(literal 1 binary64) x)))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 x x (.f64 x (.f64 x x)))
(fma.f64 x (.f64 x x) (.f64 x x))
(fma.f64 x (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x x))) (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64))))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 x (*.f64 x x)))
(fma.f64 (.f64 x x) x (.f64 x x))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(fma.f64 (.f64 x x) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64))))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64))))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64))))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64))))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x x))) (/.f64 x (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64))))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)) (*.f64 x x))
(fma.f64 (/.f64 x x) (/.f64 (.f64 (.f64 x 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 (+.f64 x #s(literal -1 binary64)))))))
(fma.f64 (/.f64 (.f64 x x) x) (/.f64 (.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 (+.f64 x #s(literal -1 binary64)))))))
(fma.f64 (/.f64 (.f64 x (.f64 x x)) x) (/.f64 (.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 (+.f64 x #s(literal -1 binary64)))))))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x 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 (+.f64 x #s(literal -1 binary64)))))))
(fma.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x x))) x) (/.f64 x (.f64 x (+.f64 x #s(literal -1 binary64)))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(fma.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))))) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(fma.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x (.f64 x (.f64 x x))))) (neg.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(neg.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) x))))))))
(neg.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x (+.f64 x #s(literal -1 binary64)))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))))) (.f64 x (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (-.f64 #s(literal 1 binary64) x))) (.f64 (.f64 x (.f64 x x)) (-.f64 x (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal -1 binary64)) (.f64 x (.f64 x (+.f64 (*.f64 x x) #s(literal -1 binary64))))))
(/.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) x))))))
(/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64))))) (.f64 x (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) x)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))))) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x (+.f64 x #s(literal -1 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) (.f64 (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (-.f64 #s(literal 1 binary64) x))))) (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.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 x))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (-.f64 #s(literal 1 binary64) x))))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))))) (.f64 (.f64 x (.f64 x (+.f64 x #s(literal -1 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(/.f64 (.f64 x (.f64 x (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (+.f64 x #s(literal -1 binary64)))
(/.f64 (.f64 (.f64 x (.f64 x x)) (-.f64 x (.f64 x (.f64 x x)))) (.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) x))))
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(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x x) x)
(.f64 (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 2 binary64)))
(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)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 x))) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (exp.f64 (log.f64 x)) #s(literal 1 binary64)) (pow.f64 (exp.f64 (log.f64 x)) #s(literal 1 binary64)))

simplify286.0ms (8.8%)

Algorithm

1×	egg-herbie

Rules

4556×	`-lowering-.f32`
4556×	`-lowering-.f64`
2478×	`cube-prod`
2370×	`/-lowering-/.f32`
2370×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	298
1	49	255
2	86	255
3	246	255
4	1419	255
5	2607	255
6	4013	255
7	5013	255
8	5894	255
9	6287	255
10	6566	255
11	6797	255
12	7039	255
13	7144	255
14	7949	255
0	8008	255

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(pow x 2)
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
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)))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(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
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 x))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 x))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 x))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
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)))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 x))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 x))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(* (pow x 2) (+ 1 x))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 (.f64 x x) (+.f64 x #s(literal 1 binary64)))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.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)
(pow x 2)
(*.f64 x x)

eval59.0ms (1.8%)

Compiler: Compiled 13195 to 856 computations (93.5% saved)

prune34.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	486	2	488
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	487	3	490

Accuracy

100.0%

Counts

490 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
✓	100.0%	(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
▶	98.3%	(*.f64 x x)

Compiler

Compiled 20 to 12 computations (40% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
✓	cost-diff	(*.f64 x x)

Rules

46×	`fma-define`
42×	`-lowering-.f32`
42×	`-lowering-.f64`
28×	`fma-lowering-fma.f32`
28×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
1	12	16
2	23	16
3	44	16
4	74	16
5	80	16
0	80	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x x)
x
(* (+ x 1) (* x x))
(+ x 1)
x
1
(* x x)

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

localize24.0ms (0.7%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
✓	accuracy	100.0%	(*.f64 x x)

Results

16.0ms

256×

valid

Compiler

Compiled 21 to 6 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 4.0ms (67.1% of total)

ival-add: 1.0ms (16.8% of total)

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (* x x)>
#<alt (* (+ x 1) (* x x))>
#<alt (+ x 1)>

Outputs
#<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)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (* (pow x 2) (+ 1 x))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (pow x 3)>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt (* (pow x 3) (+ 1 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* (+ x 1) (* x x))
0.0ms	x	@	inf	(* (+ x 1) (* x x))
0.0ms	x	@	-inf	(* (+ x 1) (* x x))
0.0ms	x	@	0	(* x x)
0.0ms	x	@	inf	(* x x)

rewrite372.0ms (11.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3798×	`/-lowering-/.f32`
3798×	`/-lowering-/.f64`
2608×	`-lowering-.f32`
2608×	`-lowering-.f64`
1648×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	26	11
2	150	11
3	1286	11
0	8531	11

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 239

Calls

Call 1

Inputs
(* x x)
(* (+ x 1) (* x x))
(+ x 1)

Outputs
(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 (-.f64 #s(literal 0 binary64) x) #s(literal 2 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))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(+.f64 (.f64 x x) (.f64 x (*.f64 x x)))
(+.f64 (.f64 x (.f64 x x)) (*.f64 x x))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (-.f64 (.f64 x (.f64 x x)) (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x (.f64 x x)) (.f64 x x))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (-.f64 #s(literal 1 binary64) x)))) (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (-.f64 #s(literal 1 binary64) x)))))
(fma.f64 x x (.f64 x (.f64 x x)))
(fma.f64 x (.f64 x x) (.f64 x x))
(fma.f64 (.f64 x x) x (.f64 x x))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 x (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 x (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)) (*.f64 x x))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)) (*.f64 x x))
(/.f64 x (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))
(/.f64 (*.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 x x)) (.f64 (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))) (-.f64 (.f64 x (.f64 x x)) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (-.f64 #s(literal 1 binary64) x))) (.f64 (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))) (.f64 x (*.f64 x (-.f64 #s(literal 1 binary64) x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 x #s(literal -1 binary64)) (.f64 x x)) (.f64 (.f64 x x) (-.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (+.f64 x #s(literal -1 binary64)) (.f64 x x)) (.f64 (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x x))))
(/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (/.f64 (+.f64 x #s(literal -1 binary64)) (.f64 x x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (+.f64 (*.f64 x x) #s(literal -1 binary64))))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (-.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.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 x))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (*.f64 x x))))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (-.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 x x)))
(/.f64 (.f64 (.f64 x x) (+.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (-.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))) (.f64 x x)) (-.f64 (+.f64 x #s(literal -1 binary64)) (*.f64 x x)))
(/.f64 (.f64 (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal 1 binary64)) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (.f64 x (.f64 x (+.f64 (.f64 x x) #s(literal -1 binary64)))) (+.f64 (.f64 x x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))
(/.f64 (.f64 (.f64 x (.f64 x (+.f64 x #s(literal 1 binary64)))) (-.f64 (.f64 x (.f64 x x)) (.f64 x x))) (-.f64 (.f64 x (.f64 x x)) (*.f64 x x)))
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(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))))))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (*.f64 x x) #s(literal 1 binary64))) (+.f64 x #s(literal -1 binary64)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (.f64 x x) #s(literal 1 binary64)))))
(.f64 (+.f64 (.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 #s(literal -1 binary64)))))
(.f64 (+.f64 (.f64 (.f64 x x) (+.f64 x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(.f64 (-.f64 (.f64 (.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64)))) (/.f64 (.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64)))) (/.f64 (+.f64 x #s(literal -1 binary64)) (.f64 x x)))) (/.f64 #s(literal -1 binary64) (.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64)))) (/.f64 (+.f64 x #s(literal -1 binary64)) (.f64 x x))) (+.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64))) (/.f64 (.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 x #s(literal -1 binary64)))))))
(.f64 (.f64 (+.f64 (.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64)))) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (/.f64 x (+.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x x)) #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) #s(literal 1 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64)) (+.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (-.f64 #s(literal 1 binary64) x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) x))) (+.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) x))
(.f64 (/.f64 (+.f64 (.f64 x x) #s(literal -1 binary64)) (+.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) #s(literal 1 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 x #s(literal -1 binary64)))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (*.f64 x x)) #s(literal -1 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal -1/2 binary64)))

simplify273.0ms (8.4%)

Algorithm

1×	egg-herbie

Rules

4600×	`-lowering-.f32`
4600×	`-lowering-.f64`
2216×	`cube-prod`
2110×	`fma-define`
1756×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	138
1	39	116
2	71	116
3	166	116
4	932	116
5	3043	116
6	3701	116
7	4684	116
8	5682	116
9	6480	116
10	6845	116
11	7037	116
12	7202	116
13	7373	116
0	8044	116

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(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)
(pow x 2)
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(* (pow x 2) (+ 1 x))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(pow x 3)
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
(* (pow x 3) (+ 1 (/ 1 x)))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))

Outputs
(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)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 2) (+ 1 x))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(pow x 3)
(.f64 x (.f64 x x))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
(* (pow x 3) (+ 1 (/ 1 x)))
(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))

eval31.0ms (1%)

Compiler: Compiled 6745 to 692 computations (89.7% saved)

prune29.0ms (0.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	297	3	300

Accuracy

100.0%

Counts

300 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))
✓	100.0%	(.f64 x (.f64 x (+.f64 x #s(literal 1 binary64))))
✓	98.3%	(*.f64 x x)

Compiler

Compiled 47 to 21 computations (55.3% saved)

regimes4.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 12 to 5 computations (58.3% saved)

regimes2.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 x x)

Outputs
(*.f64 x x)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
98.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	14	17

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness701.0ms (21.5%)

Rules

4556×	`-lowering-.f32`
4556×	`-lowering-.f64`
2774×	`-lowering-.f32`
2774×	`-lowering-.f64`
2478×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	15	6
2	26	6
3	35	6
4	49	6
5	77	6
6	83	6
0	83	6
0	8	25
1	50	24
2	355	24
3	3416	24
0	8183	24
0	14	298
1	49	255
2	86	255
3	246	255
4	1419	255
5	2607	255
6	4013	255
7	5013	255
8	5894	255
9	6287	255
10	6566	255
11	6797	255
12	7039	255
13	7144	255
14	7949	255
0	8008	255

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	saturated

Compiler

Compiled 54 to 29 computations (46.3% saved)

preprocess34.0ms (1%)

Compiler: Compiled 72 to 32 computations (55.6% saved)

Expression 3, p15

analyze0.0ms (0%)

sample954.0ms (29.2%)

preprocess42.0ms (1.3%)

explain80.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.2%)

localize33.0ms (1%)

series5.0ms (0.2%)

rewrite277.0ms (8.5%)

simplify286.0ms (8.8%)

eval59.0ms (1.8%)

prune34.0ms (1%)

simplify6.0ms (0.2%)

localize24.0ms (0.7%)

series0.0ms (0%)

rewrite372.0ms (11.4%)

simplify273.0ms (8.4%)

eval31.0ms (1%)

prune29.0ms (0.9%)

regimes4.0ms (0.1%)

regimes2.0ms (0.1%)

regimes1.0ms (0%)

simplify7.0ms (0.2%)

soundness701.0ms (21.5%)

preprocess34.0ms (1%)

end0.0ms (0%)

Profiling