Details

analyze47.0ms (3.3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
25%	25%	74.9%	0.1%	0%	0%	0%	5
30.8%	25%	56.2%	0.1%	18.7%	0%	0%	6
48%	37.5%	40.6%	0.1%	21.9%	0%	0%	7
60%	46.8%	31.2%	0.1%	21.9%	0%	0%	8
71.4%	54.6%	21.9%	0.1%	23.4%	0%	0%	9
78.6%	60.1%	16.4%	0.1%	23.4%	0%	0%	10
85.1%	64.4%	11.3%	0.1%	24.2%	0%	0%	11
88.9%	67.3%	8.4%	0.1%	24.2%	0%	0%	12

Compiler

Compiled 10 to 6 computations (40% saved)

sample705.0ms (49.5%)

Results

686.0ms	8256×	body	256	valid
7.0ms	92×	body	256	infinite

Bogosity

preprocess5.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

16×	`fma-def`
12×	`+-commutative`
4×	`*-commutative`
4×	`associate-+l+`
4×	`count-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	21	30
2	28	30
3	32	30
4	34	30
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify12.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

8×	`fma-def`
6×	`+-commutative`
2×	`*-commutative`
2×	`associate-+l+`
2×	`count-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	17	15
3	19	15
4	20	15

Stop Event

1×

saturated

Counts

1 → 3

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 21 to 9 computations (57.1% saved)

prune1.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

Counts

4 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0b	(fma.f64 x x (+.f64 y y))
▶	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)

Compiler

Compiled 17 to 9 computations (47.1% saved)

localize8.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	0.0b	(+.f64 (*.f64 x x) y)

Compiler

Compiled 19 to 5 computations (73.7% saved)

series4.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+.f64 (*.f64 x x) y)
0.0ms	x	@	0	(+.f64 (*.f64 x x) y)
0.0ms	x	@	0	(+.f64 (+.f64 (*.f64 x x) y) y)
0.0ms	y	@	0	(+.f64 (*.f64 x x) y)
0.0ms	y	@	-inf	(+.f64 (*.f64 x x) y)

rewrite64.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1934×	`add-sqr-sqrt`
1914×	`*-un-lft-identity`
1796×	`add-cube-cbrt`
1780×	`add-cbrt-cube`
174×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	162	24
2	2376	24

Stop Event

1×	node limit

Counts

2 → 75

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (/.f64 1 (-.f64 (.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (pow.f64 x 4) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 x 6) (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 x 4) (.f64 x (.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (neg.f64 (-.f64 (.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 x x y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 y y)) (cbrt.f64 y) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (.f64 x x)) y)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x x (+.f64 y y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 (fma.f64 x x y) y)) (/.f64 (.f64 y y) (-.f64 (fma.f64 x x y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x (+.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x x (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 x x (+.f64 y y))) (sqrt.f64 (fma.f64 x x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x (+.f64 y y))) (pow.f64 (cbrt.f64 (fma.f64 x x (+.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x (+.f64 y y))) 2) (cbrt.f64 (fma.f64 x x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y y)) (/.f64 1 (-.f64 (fma.f64 x x y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 x x y) y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y)))) (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y y)) (-.f64 (fma.f64 x x y) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (.f64 (+.f64 y y) (+.f64 y y))) (-.f64 (.f64 x x) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (-.f64 y (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 y y) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (+.f64 y y) (+.f64 y y)) (.f64 (.f64 x x) (+.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y y))) (neg.f64 (-.f64 (fma.f64 x x y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))) (neg.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x (+.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x x (+.f64 y y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x (+.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x (+.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x (+.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x (+.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x (+.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 x x (+.f64 y y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x x y) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 y y)) (cbrt.f64 y) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (.f64 x x)) (+.f64 y y))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (-.f64 (*.f64 x x) y)) (/.f64 (*.f64 y y) (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (/.f64 1 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 x x) y) (-.f64 (pow.f64 x 4) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x)))) (+.f64 (pow.f64 x 6) (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (-.f64 (*.f64 x x) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (*.f64 y y) (-.f64 (pow.f64 x 4) (*.f64 x (*.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 y y) (pow.f64 x 4)) (-.f64 y (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 y y))) (neg.f64 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 y y)) (cbrt.f64 y) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) y)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x x (+.f64 y y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 (fma.f64 x x y) y)) (/.f64 (*.f64 y y) (-.f64 (fma.f64 x x y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x (+.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x x (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x x (+.f64 y y))) (sqrt.f64 (fma.f64 x x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x (+.f64 y y))) (pow.f64 (cbrt.f64 (fma.f64 x x (+.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x (+.f64 y y))) 2) (cbrt.f64 (fma.f64 x x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (/.f64 1 (-.f64 (fma.f64 x x y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 x x y) y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y)))) (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (*.f64 y y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (fma.f64 x x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 (+.f64 y y) (+.f64 y y))) (-.f64 (*.f64 x x) (+.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (-.f64 y (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 y y) 3)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (+.f64 y y) (+.f64 y y)) (*.f64 (*.f64 x x) (+.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y))) (neg.f64 (-.f64 (fma.f64 x x y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))) (neg.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x (+.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x x (+.f64 y y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x (+.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x (+.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x (+.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x (+.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x (+.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x x (+.f64 y y))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x (+.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (+.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x x y) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 y y)) (cbrt.f64 y) (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) (+.f64 y y))))))

simplify80.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

1460×	`associate-+l-`
1030×	`fma-def`
848×	`distribute-lft-in`
770×	`distribute-rgt-in`
636×	`unswap-sqr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	2527
1	418	2413
2	1670	2343
3	7448	2343

Stop Event

1×	node limit

Counts

123 → 95

Calls

Call 1

Inputs
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(*.f64 2 y)
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(+.f64 (*.f64 2 y) (pow.f64 x 2))
(-.f64 (exp.f64 (log1p.f64 (fma.f64 x x y))) 1)
(-.f64 (/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (*.f64 x x) y)))
(*.f64 (fma.f64 x x y) 1)
(*.f64 1 (fma.f64 x x y))
(*.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)))
(*.f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)))
(.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (/.f64 1 (-.f64 (*.f64 x x) y)))
(.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (*.f64 x x))))))
(/.f64 1 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (pow.f64 x 4) (.f64 y y))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 x 6) (pow.f64 y 3))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 x 4) (.f64 x (*.f64 x y)))))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (neg.f64 (-.f64 (.f64 x x) y)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))
(pow.f64 (fma.f64 x x y) 1)
(pow.f64 (hypot.f64 x (sqrt.f64 y)) 2)
(pow.f64 (cbrt.f64 (fma.f64 x x y)) 3)
(pow.f64 (pow.f64 (fma.f64 x x y) 3) 1/3)
(sqrt.f64 (pow.f64 (fma.f64 x x y) 2))
(log.f64 (exp.f64 (fma.f64 x x y)))
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x y))))
(cbrt.f64 (pow.f64 (fma.f64 x x y) 3))
(expm1.f64 (log1p.f64 (fma.f64 x x y)))
(exp.f64 (log.f64 (fma.f64 x x y)))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) 1))
(log1p.f64 (expm1.f64 (fma.f64 x x y)))
(fma.f64 x x y)
(fma.f64 1 (*.f64 x x) y)
(fma.f64 1 y (*.f64 x x))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (*.f64 x x))
(fma.f64 (cbrt.f64 (.f64 y y)) (cbrt.f64 y) (.f64 x x))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) y)
(-.f64 (exp.f64 (log1p.f64 (fma.f64 x x (+.f64 y y)))) 1)
(-.f64 (/.f64 (pow.f64 (fma.f64 x x y) 2) (-.f64 (fma.f64 x x y) y)) (/.f64 (*.f64 y y) (-.f64 (fma.f64 x x y) y)))
(*.f64 (fma.f64 x x (+.f64 y y)) 1)
(*.f64 1 (fma.f64 x x (+.f64 y y)))
(*.f64 (sqrt.f64 (fma.f64 x x (+.f64 y y))) (sqrt.f64 (fma.f64 x x (+.f64 y y))))
(*.f64 (cbrt.f64 (fma.f64 x x (+.f64 y y))) (pow.f64 (cbrt.f64 (fma.f64 x x (+.f64 y y))) 2))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x x (+.f64 y y))) 2) (cbrt.f64 (fma.f64 x x (+.f64 y y))))
(.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y y)) (/.f64 1 (-.f64 (fma.f64 x x y) y)))
(.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (-.f64 y (fma.f64 x x y))))))
(/.f64 1 (/.f64 (-.f64 (fma.f64 x x y) y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y))))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y)))) (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))))
(/.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y)) (-.f64 (fma.f64 x x y) y))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y)))))
(/.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 (fma.f64 x x y) 2) (.f64 y (fma.f64 x x y)))))
(/.f64 (-.f64 (pow.f64 x 4) (.f64 (+.f64 y y) (+.f64 y y))) (-.f64 (.f64 x x) (+.f64 y y)))
(/.f64 (-.f64 (*.f64 y y) (pow.f64 (fma.f64 x x y) 2)) (-.f64 y (fma.f64 x x y)))
(/.f64 (+.f64 (pow.f64 x 6) (pow.f64 (+.f64 y y) 3)) (+.f64 (pow.f64 x 4) (-.f64 (.f64 (+.f64 y y) (+.f64 y y)) (.f64 (*.f64 x x) (+.f64 y y)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y y))) (neg.f64 (-.f64 (fma.f64 x x y) y)))
(/.f64 (neg.f64 (+.f64 (pow.f64 y 3) (pow.f64 (fma.f64 x x y) 3))) (neg.f64 (+.f64 (pow.f64 (fma.f64 x x y) 2) (*.f64 y (-.f64 y (fma.f64 x x y))))))
(pow.f64 (fma.f64 x x (+.f64 y y)) 1)
(pow.f64 (sqrt.f64 (fma.f64 x x (+.f64 y y))) 2)
(pow.f64 (cbrt.f64 (fma.f64 x x (+.f64 y y))) 3)
(pow.f64 (pow.f64 (fma.f64 x x (+.f64 y y)) 3) 1/3)
(sqrt.f64 (pow.f64 (fma.f64 x x (+.f64 y y)) 2))
(log.f64 (exp.f64 (fma.f64 x x (+.f64 y y))))
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x (+.f64 y y)))))
(cbrt.f64 (pow.f64 (fma.f64 x x (+.f64 y y)) 3))
(expm1.f64 (log1p.f64 (fma.f64 x x (+.f64 y y))))
(exp.f64 (log.f64 (fma.f64 x x (+.f64 y y))))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x (+.f64 y y))) 1))
(log1p.f64 (expm1.f64 (fma.f64 x x (+.f64 y y))))
(fma.f64 x x (+.f64 y y))
(fma.f64 1 (*.f64 x x) (+.f64 y y))
(fma.f64 1 y (fma.f64 x x y))
(fma.f64 1 (fma.f64 x x y) y)
(fma.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)) y)
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (fma.f64 x x y))
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)) y)
(fma.f64 (cbrt.f64 (*.f64 y y)) (cbrt.f64 y) (fma.f64 x x y))
(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) (+.f64 y y))

Outputs
y
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
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(fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) (+.f64 y y))
(+.f64 (fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) y) y)
(+.f64 y (fma.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x)) y))

localize6.0ms (0.4%)

Compiler: Compiled 13 to 4 computations (69.2% saved)

eval17.0ms (1.2%)

Compiler: Compiled 1273 to 469 computations (63.2% saved)

prune13.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	93	4	97

Error

Counts

97 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(fma.f64 x x (+.f64 y y))
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
▶	36.1b	(+.f64 (*.f64 x x) y)
▶	19.9b	(+.f64 y y)

Compiler

Compiled 29 to 16 computations (44.8% saved)

localize3.0ms (0.2%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (*.f64 x x) y)

Compiler

Compiled 12 to 4 computations (66.7% saved)

eval7.0ms (0.5%)

Compiler: Compiled 415 to 169 computations (59.3% saved)

prune8.0ms (0.5%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	38	7	45

Error

Counts

45 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(fma.f64 x x (+.f64 y y))
▶	36.1b	(fma.f64 x x y)
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	36.1b	(+.f64 (*.f64 x x) y)
✓	19.9b	(+.f64 y y)
▶	42.9b	(*.f64 x x)
	55.2b	y

Compiler

Compiled 43 to 24 computations (44.2% saved)

localize3.0ms (0.2%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize3.0ms (0.2%)

Compiler: Compiled 8 to 3 computations (62.5% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune3.0ms (0.2%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	5	5
Total	7	7

Error

Counts

7 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(fma.f64 x x (+.f64 y y))
✓	36.1b	(fma.f64 x x y)
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	36.1b	(+.f64 (*.f64 x x) y)
✓	19.9b	(+.f64 y y)
✓	42.9b	(*.f64 x x)
	55.2b	y

Compiler

Compiled 43 to 24 computations (44.2% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.2%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	6	6
Total	7	7

Error

Counts

7 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(fma.f64 x x (+.f64 y y))
✓	36.1b	(fma.f64 x x y)
✓	0.0b	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	36.1b	(+.f64 (*.f64 x x) y)
✓	19.9b	(+.f64 y y)
✓	42.9b	(*.f64 x x)
	55.2b	y

Compiler

Compiled 43 to 24 computations (44.2% saved)

regimes23.0ms (1.6%)

Counts

7 → 1

Calls

Call 1

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

Outputs
(fma.f64 x x (+.f64 y y))

Calls

4 calls:

8.0ms	y
6.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
5.0ms	x
3.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0b	1	`x`
0b	1	`y`
0b	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
0b	1	`(*.f64 x x)`

Compiler

Compiled 51 to 20 computations (60.8% saved)

regimes20.0ms (1.4%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

5.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
5.0ms	x
5.0ms	y
3.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
0.0b	1	`(*.f64 x x)`

Compiler

Compiled 45 to 19 computations (57.8% saved)

regimes102.0ms (7.1%)

Counts

4 → 5

Calls

Call 1

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

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

Calls

3 calls:

64.0ms	x
29.0ms	y
7.0ms	(*.f64 x x)

Results

Error	Segments	Branch
8.5b	5	`x`
12.3b	7	`y`
9.6b	2	`(*.f64 x x)`

Compiler

Compiled 25 to 12 computations (52% saved)

bsearch50.0ms (3.5%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
15.0ms	1.0077788670667209e+58	1.6085318147613663e+69
14.0ms	1.5816189790784366e+33	2.540794532495887e+40
1.0ms	4.240017206146851e-9	4.634485819190561e-9
20.0ms	-3959754369.181858	-85.94079834191292

Results

45.0ms

464×

body

256

valid

Compiler

Compiled 420 to 270 computations (35.7% saved)

regimes69.0ms (4.8%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

3 calls:

49.0ms	y
11.0ms	x
8.0ms	(*.f64 x x)

Results

Error	Segments	Branch
10.2b	3	`x`
12.5b	7	`y`
10.7b	2	`(*.f64 x x)`

Compiler

Compiled 20 to 11 computations (45% saved)

bsearch29.0ms (2%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
15.0ms	1.0077788670667209e+58	1.6085318147613663e+69
14.0ms	-4.424563889212398e+36	-2.9480902405787764e+31

Results

26.0ms

304×

body

256

valid

Compiler

Compiled 242 to 161 computations (33.5% saved)

regimes20.0ms (1.4%)

Accuracy

Total -23.1b remaining (-59.5%)

Threshold costs -23.1b (-59.5%)

Counts

2 → 3

Calls

Call 1

Inputs
y
(*.f64 x x)

Outputs
(*.f64 x x)
y
(*.f64 x x)

Calls

3 calls:

9.0ms	x
6.0ms	(*.f64 x x)
4.0ms	y

Results

Error	Segments	Branch
38.8b	3	`x`
42.9b	1	`y`
39.0b	2	`(*.f64 x x)`

Compiler

Compiled 17 to 10 computations (41.2% saved)

bsearch21.0ms (1.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
15.0ms	8.389423521555319e-90	3.3743145086188854e-74
6.0ms	-5.9444503496069495e-99	-3.064102954471696e-99

Results

19.0ms

224×

body

256

valid

Compiler

Compiled 154 to 107 computations (30.5% saved)

simplify10.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

10×	`if-if-or-not`
8×	`not-or`
8×	`if-not`
6×	`not-not`
4×	`+-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	190
1	47	190
2	50	184
3	56	180
4	60	180
5	65	180
6	66	180
7	67	180

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(fma.f64 x x (+.f64 y y))
(+.f64 (+.f64 (*.f64 x x) y) y)
(if (<=.f64 x -230000000) (+.f64 (.f64 x x) y) (if (<=.f64 x 5440166188265831/1208925819614629174706176) (+.f64 y y) (if (<=.f64 x 25000000000000000155002161260194579873792) (+.f64 (.f64 x x) y) (if (<=.f64 x 10200000000000000458291345205943223728140067627070180556800) (+.f64 y y) (+.f64 (*.f64 x x) y)))))
(if (<=.f64 x -34999999999999999824515341456769024) (.f64 x x) (if (<=.f64 x 10200000000000000458291345205943223728140067627070180556800) (+.f64 y y) (.f64 x x)))
(if (<=.f64 x -6402826006914103/1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153613775207124697088) (.f64 x x) (if (<=.f64 x 2776783146697183/533996758980227520598755426542388028650676130589163192486760401955554931445160137505740521734144) y (.f64 x x)))
y

Outputs
(fma.f64 x x (+.f64 y y))
(+.f64 (+.f64 (*.f64 x x) y) y)
(+.f64 y (+.f64 y (*.f64 x x)))
(if (<=.f64 x -230000000) (+.f64 (.f64 x x) y) (if (<=.f64 x 5440166188265831/1208925819614629174706176) (+.f64 y y) (if (<=.f64 x 25000000000000000155002161260194579873792) (+.f64 (.f64 x x) y) (if (<=.f64 x 10200000000000000458291345205943223728140067627070180556800) (+.f64 y y) (+.f64 (*.f64 x x) y)))))
(if (<=.f64 x -230000000) (+.f64 y (.f64 x x)) (if (<=.f64 x 5440166188265831/1208925819614629174706176) (+.f64 y y) (if (or (<=.f64 x 25000000000000000155002161260194579873792) (not (<=.f64 x 10200000000000000458291345205943223728140067627070180556800))) (+.f64 y (.f64 x x)) (+.f64 y y))))
(if (or (<=.f64 x -230000000) (not (or (<=.f64 x 5440166188265831/1208925819614629174706176) (not (or (<=.f64 x 25000000000000000155002161260194579873792) (not (<=.f64 x 10200000000000000458291345205943223728140067627070180556800))))))) (+.f64 y (*.f64 x x)) (+.f64 y y))
(if (or (<=.f64 x -230000000) (not (or (<=.f64 x 5440166188265831/1208925819614629174706176) (and (not (<=.f64 x 25000000000000000155002161260194579873792)) (<=.f64 x 10200000000000000458291345205943223728140067627070180556800))))) (+.f64 y (*.f64 x x)) (+.f64 y y))
(if (or (<=.f64 x -230000000) (and (not (<=.f64 x 5440166188265831/1208925819614629174706176)) (or (<=.f64 x 25000000000000000155002161260194579873792) (not (<=.f64 x 10200000000000000458291345205943223728140067627070180556800))))) (+.f64 y (*.f64 x x)) (+.f64 y y))
(if (<=.f64 x -34999999999999999824515341456769024) (.f64 x x) (if (<=.f64 x 10200000000000000458291345205943223728140067627070180556800) (+.f64 y y) (.f64 x x)))
(if (<=.f64 x -6402826006914103/1231312693637327475383720003129487931408741852202045208373384168882678805359287831606695820465153613775207124697088) (.f64 x x) (if (<=.f64 x 2776783146697183/533996758980227520598755426542388028650676130589163192486760401955554931445160137505740521734144) y (.f64 x x)))
y

Compiler

Compiled 84 to 49 computations (41.7% saved)

soundness36.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

8×	`fma-def`
6×	`+-commutative`
2×	`*-commutative`
2×	`associate-+l+`
2×	`count-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	17	15
3	19	15
4	20	15

Stop Event

1×

saturated

Compiler

Compiled 22 to 8 computations (63.6% saved)

end48.0ms (3.4%)

Compiler: Compiled 74 to 33 computations (55.4% saved)

Details

analyze47.0ms (3.3%)

sample705.0ms (49.5%)

preprocess5.0ms (0.3%)

simplify12.0ms (0.9%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize8.0ms (0.6%)

series4.0ms (0.3%)

rewrite64.0ms (4.5%)

simplify80.0ms (5.6%)

localize6.0ms (0.4%)

eval17.0ms (1.2%)

prune13.0ms (0.9%)

localize3.0ms (0.2%)

localize4.0ms (0.3%)

eval7.0ms (0.5%)

prune8.0ms (0.5%)

localize3.0ms (0.2%)

localize3.0ms (0.2%)

eval0.0ms (0%)

prune3.0ms (0.2%)

eval0.0ms (0%)

prune2.0ms (0.2%)

regimes23.0ms (1.6%)

regimes20.0ms (1.4%)

regimes102.0ms (7.1%)

bsearch50.0ms (3.5%)

regimes69.0ms (4.8%)

bsearch29.0ms (2%)

regimes20.0ms (1.4%)

bsearch21.0ms (1.5%)

simplify10.0ms (0.7%)

soundness36.0ms (2.5%)

end48.0ms (3.4%)

Profiling