Details

analyze62.0ms (1.9%)

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
37.5%	37.5%	62.4%	0.1%	0%	0%	0%	6
50.8%	50%	48.4%	0.1%	1.6%	0%	0%	7
60.8%	59.3%	38.2%	0.1%	2.3%	0%	0%	8
70.8%	67.1%	27.7%	0.1%	5.1%	0%	0%	9
77.3%	72.6%	21.3%	0.1%	6%	0%	0%	10
83.9%	76.9%	14.7%	0.1%	8.3%	0%	0%	11
87.7%	79.8%	11.2%	0.1%	8.9%	0%	0%	12

Compiler

Compiled 10 to 6 computations (40% saved)

sample1.1s (33.9%)

Results

1.1s	8254×	body	256	valid
31.0ms	359×	body	256	infinite
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Bogosity

preprocess21.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

50×	`fma-def_binary64`
7×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`associate-l_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	21	16
2	34	16
3	42	16
4	56	16
5	68	16
6	94	16
7	109	16
8	111	16
0	2	2
1	2	2

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1
0

Call 2

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

Outputs
(+.f64 (+.f64 (*.f64 x y) x) y)
(+.f64 y (fma.f64 x y x))
(+.f64 x (fma.f64 x y y))
(fma.f64 x (+.f64 y 1) y)
(+.f64 (+.f64 (*.f64 y x) y) x)
(+.f64 y (fma.f64 x y x))
(+.f64 x (fma.f64 x y y))
(fma.f64 x (+.f64 y 1) y)

Symmetry

(sort x y)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

48×	`fma-def_binary64`
6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`distribute-rgt-in_binary64`
4×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	25	8
3	35	8
4	45	8
5	58	8
6	80	8
7	102	8
8	109	8
9	110	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 15 to 7 computations (53.3% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 17 to 9 computations (47.1% saved)

localize37.0ms (1.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 4 computations (71.4% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(+.f64 x (fma.f64 x y y))
1.0ms	x	@	inf	(+.f64 x (fma.f64 x y y))
1.0ms	x	@	0	(+.f64 x (fma.f64 x y y))
1.0ms	y	@	-inf	(+.f64 x (fma.f64 x y y))
0.0ms	y	@	inf	(+.f64 x (fma.f64 x y y))

rewrite61.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

643×	`pow1_binary64`
599×	`add-log-exp_binary64`
599×	`log1p-expm1-u_binary64`
599×	`expm1-log1p-u_binary64`
585×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	110	8
2	1578	8

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

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

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

Outputs

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

simplify68.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

191×	`fma-neg_binary64`
155×	`fma-def_binary64`
45×	`unsub-neg_binary64`
44×	`cancel-sign-sub-inv_binary64`
38×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	210
1	51	174
2	115	166
3	299	166
4	600	166
5	871	166
6	939	166
7	944	166

Stop Event

1×

saturated

Counts

57 → 46

Calls

Call 1

Inputs
y
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(*.f64 (+.f64 1 y) x)
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(+.f64 y (.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x)))
(+.f64 y (.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x)))
(+.f64 y (.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x)))
x
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 (*.f64 (+.f64 1 x) y) x)
(*.f64 (+.f64 1 x) y)
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 (*.f64 (+.f64 1 x) y) x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y))
(+.f64 x (.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y)))
(+.f64 x (.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y)))
(+.f64 x (.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y)))

Outputs
y
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(*.f64 (+.f64 1 y) x)
(*.f64 (+.f64 y 1) x)
(fma.f64 y x x)
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(*.f64 (+.f64 y 1) x)
(fma.f64 y x x)
(+.f64 y (.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x)))
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(+.f64 y (.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x)))
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(+.f64 y (.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x)))
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
x
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(*.f64 (+.f64 1 x) y)
(*.f64 y (+.f64 1 x))
(fma.f64 y x y)
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y))
(*.f64 y (+.f64 1 x))
(fma.f64 y x y)
(+.f64 x (.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y)))
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(+.f64 x (.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y)))
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))
(+.f64 x (.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y)))
(+.f64 y (*.f64 (+.f64 y 1) x))
(fma.f64 (+.f64 y 1) x y)
(+.f64 y (fma.f64 y x x))

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 19 to 5 computations (73.7% saved)

series5.0ms (0.2%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+.f64 (+.f64 (*.f64 x y) x) y)
0.0ms	x	@	inf	(+.f64 (+.f64 (*.f64 x y) x) y)
0.0ms	y	@	inf	(+.f64 (+.f64 (*.f64 x y) x) y)
0.0ms	x	@	inf	(+.f64 (*.f64 x y) x)
0.0ms	y	@	0	(+.f64 (+.f64 (*.f64 x y) x) y)

rewrite74.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

905×	`pow1_binary64`
846×	`add-log-exp_binary64`
846×	`log1p-expm1-u_binary64`
846×	`expm1-log1p-u_binary64`
828×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	142	13
2	2247	13

Stop Event

1×	node limit

Counts

2 → 78

Calls

Call 1

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

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

Outputs

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

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

simplify86.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

199×	`fma-neg_binary64`
163×	`fma-def_binary64`
45×	`unsub-neg_binary64`
44×	`cancel-sign-sub-inv_binary64`
31×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	284
1	57	284
2	128	280
3	277	280
4	569	280
5	839	280
6	916	280
7	921	280

Stop Event

1×

saturated

Counts

126 → 92

Calls

Call 1

Inputs
y
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(*.f64 (+.f64 1 y) x)
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(+.f64 y (.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x)))
(+.f64 y (.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x)))
(+.f64 y (.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x)))
x
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 (*.f64 (+.f64 1 x) y) x)
(*.f64 (+.f64 1 x) y)
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 (*.f64 (+.f64 1 x) y) x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y))
(+.f64 x (.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y)))
(+.f64 x (.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y)))
(+.f64 x (.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y)))
(*.f64 (+.f64 1 y) x)
(*.f64 (+.f64 1 y) x)
(*.f64 (+.f64 1 y) x)
(*.f64 (+.f64 1 y) x)
(*.f64 (+.f64 1 y) x)
(*.f64 (+.f64 1 y) x)
(*.f64 (+.f64 1 y) x)
(*.f64 (+.f64 1 y) x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
x
(+.f64 (*.f64 y x) x)
(+.f64 (*.f64 y x) x)
(+.f64 (*.f64 y x) x)
(*.f64 y x)
(+.f64 (*.f64 y x) x)
(+.f64 (*.f64 y x) x)
(+.f64 (*.f64 y x) x)
(*.f64 y x)
(+.f64 (*.f64 y x) x)
(+.f64 (*.f64 y x) x)
(+.f64 (*.f64 y x) x)

Outputs
y
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (fma.f64 y x x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (fma.f64 y x x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (fma.f64 y x x))
(*.f64 (+.f64 1 y) x)
(fma.f64 y x x)
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (fma.f64 y x x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (fma.f64 y x x))
(+.f64 y (*.f64 (+.f64 1 y) x))
(+.f64 y (fma.f64 y x x))
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(fma.f64 y x x)
(+.f64 y (.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x)))
(+.f64 y (fma.f64 y x x))
(+.f64 y (.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x)))
(+.f64 y (fma.f64 y x x))
(+.f64 y (.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x)))
(+.f64 y (fma.f64 y x x))
x
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 y (fma.f64 y x x))
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 y (fma.f64 y x x))
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 y (fma.f64 y x x))
(*.f64 (+.f64 1 x) y)
(*.f64 y (+.f64 1 x))
(fma.f64 y x y)
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 y (fma.f64 y x x))
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 y (fma.f64 y x x))
(+.f64 (*.f64 (+.f64 1 x) y) x)
(+.f64 y (fma.f64 y x x))
(.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y))
(*.f64 y (+.f64 1 x))
(fma.f64 y x y)
(+.f64 x (.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y)))
(+.f64 y (fma.f64 y x x))
(+.f64 x (.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y)))
(+.f64 y (fma.f64 y x x))
(+.f64 x (.f64 -1 (.f64 (-.f64 (*.f64 -1 x) 1) y)))
(+.f64 y (fma.f64 y x x))
(*.f64 (+.f64 1 y) x)
(fma.f64 y x x)
(*.f64 (+.f64 1 y) x)
(fma.f64 y x x)
(*.f64 (+.f64 1 y) x)
(fma.f64 y x x)
(*.f64 (+.f64 1 y) x)
(fma.f64 y x x)
(*.f64 (+.f64 1 y) x)
(fma.f64 y x x)
(*.f64 (+.f64 1 y) x)
(fma.f64 y x x)
(*.f64 (+.f64 1 y) x)
(fma.f64 y x x)
(*.f64 (+.f64 1 y) x)
(fma.f64 y x x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(fma.f64 y x x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(fma.f64 y x x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(fma.f64 y x x)
(.f64 -1 (.f64 (-.f64 (*.f64 -1 y) 1) x))
(fma.f64 y x x)
x
(+.f64 (*.f64 y x) x)
(fma.f64 y x x)
(+.f64 (*.f64 y x) x)
(fma.f64 y x x)
(+.f64 (*.f64 y x) x)
(fma.f64 y x x)
(*.f64 y x)
(+.f64 (*.f64 y x) x)
(fma.f64 y x x)
(+.f64 (*.f64 y x) x)
(fma.f64 y x x)
(+.f64 (*.f64 y x) x)
(fma.f64 y x x)
(*.f64 y x)
(+.f64 (*.f64 y x) x)
(fma.f64 y x x)
(+.f64 (*.f64 y x) x)
(fma.f64 y x x)
(+.f64 (*.f64 y x) x)
(fma.f64 y x x)

eval56.0ms (1.7%)

Compiler: Compiled 1711 to 593 computations (65.3% saved)

prune50.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	135	5	140

Error

Counts

140 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.7b	(*.f64 (+.f64 1 x) y)
✓	0.0b	(+.f64 (+.f64 (*.f64 x y) x) y)
▶	27.1b	(*.f64 (+.f64 1 y) x)
	36.2b	y
	34.0b	x

Compiler

Compiled 29 to 19 computations (34.5% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 x) y)

Compiler

Compiled 13 to 8 computations (38.5% saved)

series34.0ms (1%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
30.0ms	y	@	inf	(*.f64 (+.f64 1 x) y)
1.0ms	y	@	0	(*.f64 (+.f64 1 x) y)
1.0ms	y	@	-inf	(*.f64 (+.f64 1 x) y)
0.0ms	x	@	0	(*.f64 (+.f64 1 x) y)
0.0ms	x	@	-inf	(*.f64 (+.f64 1 x) y)

rewrite57.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

604×	`pow1_binary64`
560×	`add-log-exp_binary64`
560×	`log1p-expm1-u_binary64`
560×	`expm1-log1p-u_binary64`
549×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1520	7

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

Inputs
(*.f64 (+.f64 1 x) y)

Outputs

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

simplify17.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
4×	`associate-r_binary64`
4×	`associate-l_binary64`
3×	`*-lft-identity_binary64`
3×	`*-rgt-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	54
1	8	54
2	12	54
3	16	54
4	22	54
5	28	54
6	41	54
7	45	54
8	47	54

Stop Event

1×

saturated

Counts

31 → 22

Calls

Call 1

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

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

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 y) x)

Compiler

Compiled 13 to 8 computations (38.5% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	y	@	0	(*.f64 (+.f64 1 y) x)
0.0ms	x	@	-inf	(*.f64 (+.f64 1 y) x)
0.0ms	x	@	inf	(*.f64 (+.f64 1 y) x)
0.0ms	x	@	0	(*.f64 (+.f64 1 y) x)
0.0ms	y	@	-inf	(*.f64 (+.f64 1 y) x)

rewrite49.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

604×	`pow1_binary64`
560×	`add-log-exp_binary64`
560×	`log1p-expm1-u_binary64`
560×	`expm1-log1p-u_binary64`
549×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1520	7

Stop Event

1×	node limit

Counts

1 → 19

Calls

Call 1

Inputs
(*.f64 (+.f64 1 y) x)

Outputs

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

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
4×	`associate-r_binary64`
4×	`associate-l_binary64`
3×	`*-lft-identity_binary64`
3×	`*-rgt-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	54
1	11	54
2	16	54
3	22	54
4	28	54
5	41	54
6	45	54
7	47	54

Stop Event

1×

saturated

Counts

31 → 23

Calls

Call 1

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

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

eval11.0ms (0.3%)

Compiler: Compiled 333 to 144 computations (56.8% saved)

prune30.0ms (0.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	44	6	50

Error

Counts

50 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	28.7b	(*.f64 (+.f64 1 x) y)
✓	0.0b	(+.f64 (+.f64 (*.f64 x y) x) y)
	36.2b	y
✓	27.1b	(*.f64 (+.f64 1 y) x)
▶	55.2b	(*.f64 y x)
	34.0b	x

Compiler

Compiled 34 to 22 computations (35.3% saved)

localize3.0ms (0.1%)

Compiler: Compiled 7 to 3 computations (57.1% saved)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	3	3
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	28.7b	(*.f64 (+.f64 1 x) y)
✓	0.0b	(+.f64 (+.f64 (*.f64 x y) x) y)
	36.2b	y
✓	27.1b	(*.f64 (+.f64 1 y) x)
✓	55.2b	(*.f64 y x)
	34.0b	x

Compiler

Compiled 34 to 22 computations (35.3% saved)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	0	0
Done	4	4
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	28.7b	(*.f64 (+.f64 1 x) y)
✓	0.0b	(+.f64 (+.f64 (*.f64 x y) x) y)
	36.2b	y
✓	27.1b	(*.f64 (+.f64 1 y) x)
✓	55.2b	(*.f64 y x)
	34.0b	x

Compiler

Compiled 34 to 22 computations (35.3% saved)

regimes98.0ms (3%)

Counts

8 → 1

Calls

Call 1

Inputs
y
y
x
(*.f64 y x)
(*.f64 (+.f64 1 x) y)
(*.f64 (+.f64 1 y) x)
(+.f64 (+.f64 (*.f64 x y) x) y)
(+.f64 x (fma.f64 x y y))

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

Calls

3 calls:

74.0ms	x
11.0ms	(+.f64 (+.f64 (*.f64 x y) x) y)
11.0ms	y

Results

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

Compiler

Compiled 46 to 23 computations (50% saved)

regimes66.0ms (2%)

Counts

7 → 1

Calls

Call 1

Inputs
y
y
x
(*.f64 y x)
(*.f64 (+.f64 1 x) y)
(*.f64 (+.f64 1 y) x)
(+.f64 (+.f64 (*.f64 x y) x) y)

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

Calls

3 calls:

39.0ms	y
13.0ms	(+.f64 (+.f64 (*.f64 x y) x) y)
11.0ms	x

Results

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

Compiler

Compiled 40 to 21 computations (47.5% saved)

regimes187.0ms (5.8%)

Counts

6 → 4

Calls

Call 1

Inputs
y
y
x
(*.f64 y x)
(*.f64 (+.f64 1 x) y)
(*.f64 (+.f64 1 y) x)

Outputs
(*.f64 (+.f64 1 y) x)
(*.f64 (+.f64 1 x) y)
x
(*.f64 (+.f64 1 x) y)

Calls

2 calls:

121.0ms	x
63.0ms	y

Results

Error	Segments	Branch
5.8b	6	`x`
4.9b	4	`y`

Compiler

Compiled 24 to 13 computations (45.8% saved)

bsearch128.0ms (3.9%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
42.0ms	6.286880263735206e-85	1.0419243550166809e-82
56.0ms	4.158584108004265e-112	1.375443421780725e-108
29.0ms	2.9705343794959834e-152	8.742543113224253e-152

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes155.0ms (4.8%)

Counts

5 → 5

Calls

Call 1

Inputs
y
y
x
(*.f64 y x)
(*.f64 (+.f64 1 x) y)

Outputs
(*.f64 y x)
x
(*.f64 (+.f64 1 x) y)
x
(*.f64 (+.f64 1 x) y)

Calls

2 calls:

96.0ms	y
57.0ms	x

Results

Error	Segments	Branch
11.4b	6	`x`
5.1b	5	`y`

Compiler

Compiled 19 to 10 computations (47.4% saved)

bsearch168.0ms (5.2%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
28.0ms	6.286880263735206e-85	1.0419243550166809e-82
60.0ms	4.158584108004265e-112	1.375443421780725e-108
28.0ms	2.9705343794959834e-152	8.742543113224253e-152
51.0ms	-1188055.149700893	-2.8613762525451886e-15

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes148.0ms (4.6%)

Counts

4 → 5

Calls

Call 1

Inputs
y
y
x
(*.f64 y x)

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

Calls

2 calls:

88.0ms	y
58.0ms	x

Results

Error	Segments	Branch
11.9b	7	`x`
10.3b	5	`y`

Compiler

Compiled 14 to 7 computations (50% saved)

bsearch168.0ms (5.2%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
30.0ms	4.429036703158842e-59	5.964990923607549e-57
35.0ms	4.158584108004265e-112	1.375443421780725e-108
33.0ms	2.9705343794959834e-152	8.742543113224253e-152
69.0ms	-1188055.149700893	-2.8613762525451886e-15

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes94.0ms (2.9%)

Counts

3 → 4

Calls

Call 1

Inputs
y
y
x

Outputs
x
y
x
y

Calls

2 calls:

52.0ms	x
41.0ms	y

Results

Error	Segments	Branch
13.0b	6	`x`
12.5b	4	`y`

Compiler

Compiled 11 to 6 computations (45.5% saved)

bsearch55.0ms (1.7%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
16.0ms	4.429036703158842e-59	5.964990923607549e-57
17.0ms	4.158584108004265e-112	1.375443421780725e-108
22.0ms	2.9705343794959834e-152	8.742543113224253e-152

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes7.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
y
y

Outputs
y

Calls

2 calls:

3.0ms	x
3.0ms	y

Results

Error	Segments	Branch
36.2b	1	`x`
36.2b	1	`y`

Compiler

Compiled 10 to 6 computations (40% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	157
1	44	157

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 x (fma.f64 x y y))
(+.f64 (+.f64 (*.f64 x y) x) y)
(if (<=.f64 y 7006678206161509/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) (.f64 (+.f64 1 y) x) (if (<=.f64 y 2252027368499193/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) (.f64 (+.f64 1 x) y) (if (<=.f64 y 5500393365391537/8749002899132047697490008908470485461412677723572849745703082425639811996797503692894052708092215296) x (*.f64 (+.f64 1 x) y))))
(if (<=.f64 y -637832251726215/536870912) (.f64 y x) (if (<=.f64 y 7006678206161509/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) x (if (<=.f64 y 2252027368499193/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) (.f64 (+.f64 1 x) y) (if (<=.f64 y 5500393365391537/8749002899132047697490008908470485461412677723572849745703082425639811996797503692894052708092215296) x (*.f64 (+.f64 1 x) y)))))
(if (<=.f64 y -637832251726215/536870912) (*.f64 y x) (if (<=.f64 y 7006678206161509/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) x (if (<=.f64 y 2252027368499193/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) y (if (<=.f64 y 5008275519214037/113078212145816597093331040047546785012958969400039613319782796882727665664) x y))))
(if (<=.f64 y 7006678206161509/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) x (if (<=.f64 y 2252027368499193/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) y (if (<=.f64 y 5008275519214037/113078212145816597093331040047546785012958969400039613319782796882727665664) x y)))
y

Outputs
(+.f64 x (fma.f64 x y y))
(+.f64 (+.f64 (*.f64 x y) x) y)
(+.f64 y (+.f64 x (*.f64 x y)))
(if (<=.f64 y 7006678206161509/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) (.f64 (+.f64 1 y) x) (if (<=.f64 y 2252027368499193/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) (.f64 (+.f64 1 x) y) (if (<=.f64 y 5500393365391537/8749002899132047697490008908470485461412677723572849745703082425639811996797503692894052708092215296) x (*.f64 (+.f64 1 x) y))))
(if (<=.f64 y 7006678206161509/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) (.f64 x (+.f64 y 1)) (if (<=.f64 y 2252027368499193/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) (.f64 y (+.f64 x 1)) (if (<=.f64 y 5500393365391537/8749002899132047697490008908470485461412677723572849745703082425639811996797503692894052708092215296) x (*.f64 y (+.f64 x 1)))))
(if (<=.f64 y -637832251726215/536870912) (.f64 y x) (if (<=.f64 y 7006678206161509/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) x (if (<=.f64 y 2252027368499193/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) (.f64 (+.f64 1 x) y) (if (<=.f64 y 5500393365391537/8749002899132047697490008908470485461412677723572849745703082425639811996797503692894052708092215296) x (*.f64 (+.f64 1 x) y)))))
(if (<=.f64 y -637832251726215/536870912) (.f64 x y) (if (<=.f64 y 7006678206161509/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) x (if (<=.f64 y 2252027368499193/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) (.f64 y (+.f64 x 1)) (if (<=.f64 y 5500393365391537/8749002899132047697490008908470485461412677723572849745703082425639811996797503692894052708092215296) x (*.f64 y (+.f64 x 1))))))
(if (<=.f64 y -637832251726215/536870912) (*.f64 y x) (if (<=.f64 y 7006678206161509/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) x (if (<=.f64 y 2252027368499193/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) y (if (<=.f64 y 5008275519214037/113078212145816597093331040047546785012958969400039613319782796882727665664) x y))))
(if (<=.f64 y -637832251726215/536870912) (*.f64 x y) (if (<=.f64 y 7006678206161509/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) x (if (<=.f64 y 2252027368499193/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) y (if (<=.f64 y 5008275519214037/113078212145816597093331040047546785012958969400039613319782796882727665664) x y))))
(if (<=.f64 y 7006678206161509/235872651551346334515097161311766805682307576276027526773512893765351510149509303255382920323603672971341773439422740306235661539370299539535089640714543502728087207936) x (if (<=.f64 y 2252027368499193/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) y (if (<=.f64 y 5008275519214037/113078212145816597093331040047546785012958969400039613319782796882727665664) x y)))
y

Compiler

Compiled 126 to 78 computations (38.1% saved)

soundness12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

48×	`fma-def_binary64`
6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`distribute-rgt-in_binary64`
4×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	25	8
3	35	8
4	45	8
5	58	8
6	80	8
7	102	8
8	109	8
9	110	8

Stop Event

1×

saturated

Compiler

Compiled 35 to 19 computations (45.7% saved)

end68.0ms (2.1%)

Remove: (sort x y)
Compiler: Compiled 130 to 72 computations (44.6% saved)

Details

analyze62.0ms (1.9%)

sample1.1s (33.9%)

preprocess21.0ms (0.6%)

simplify10.0ms (0.3%)

eval1.0ms (0%)

prune2.0ms (0%)

localize37.0ms (1.1%)

series4.0ms (0.1%)

rewrite61.0ms (1.9%)

simplify68.0ms (2.1%)

localize6.0ms (0.2%)

series5.0ms (0.2%)

rewrite74.0ms (2.3%)

simplify86.0ms (2.6%)

eval56.0ms (1.7%)

prune50.0ms (1.5%)

localize6.0ms (0.2%)

series34.0ms (1%)

rewrite57.0ms (1.8%)

simplify17.0ms (0.5%)

localize7.0ms (0.2%)

series3.0ms (0.1%)

rewrite49.0ms (1.5%)

simplify10.0ms (0.3%)

eval11.0ms (0.3%)

prune30.0ms (0.9%)

localize3.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes98.0ms (3%)

regimes66.0ms (2%)

regimes187.0ms (5.8%)

bsearch128.0ms (3.9%)

regimes155.0ms (4.8%)

bsearch168.0ms (5.2%)

regimes148.0ms (4.6%)

bsearch168.0ms (5.2%)

regimes94.0ms (2.9%)

bsearch55.0ms (1.7%)

regimes7.0ms (0.2%)

simplify10.0ms (0.3%)

soundness12.0ms (0.4%)

end68.0ms (2.1%)

Profiling