Details

analyze93.0ms (3.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
43.7%	56.2%	0.1%	7
50%	50%	0.1%	8
67.1%	32.8%	0.1%	9
71.8%	28.1%	0.1%	10
82.3%	17.6%	0.1%	11
85.1%	14.8%	0.1%	12

Compiler

Compiled 10 to 7 computations (30% saved)

sample1.1s (46.7%)

Results

1.1s

8256×

body

256

valid

preprocess16.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`associate-/l*_binary64`
4×	`associate-/r/_binary64`
2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	19	20
2	27	20
3	33	20
4	35	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify28.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	17	10
3	20	10
4	21	10

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

prune1.0ms (0.1%)

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
▶	6.3b	(/.f64 (*.f64 x y) (+.f64 y 1))
▶	0.0b	(*.f64 x (/.f64 y (+.f64 y 1)))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 20 to 12 computations (40% saved)

series6.0ms (0.2%)

Counts

2 → 36

Calls

9 calls:

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

rewrite60.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

822×	`pow1_binary64`
765×	`log1p-expm1-u_binary64`
765×	`expm1-log1p-u_binary64`
764×	`add-log-exp_binary64`
748×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	150	17
2	2065	17

Stop Event

1×	node limit

Counts

2 → 55

Calls

Call 1

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

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

Outputs

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

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

simplify90.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

667×	`times-frac_binary64`
436×	`sub-neg_binary64`
423×	`distribute-rgt-neg-in_binary64`
381×	`fma-neg_binary64`
280×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	437
1	136	413
2	372	400
3	1258	388
4	4804	388

Stop Event

1×	node limit

Counts

91 → 85

Calls

Call 1

Inputs
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(*.f64 y x)
(+.f64 (.f64 y x) (.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 (.f64 y x) (+.f64 (.f64 -1 (.f64 (pow.f64 y 2) x)) (.f64 (pow.f64 y 3) x)))
(+.f64 (.f64 y x) (+.f64 (.f64 -1 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 (pow.f64 y 3) x) (.f64 -1 (.f64 (pow.f64 y 4) x)))))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 x y)) x))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 x y)) x)))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 x y)) x))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 x y)) x)))
y
(+.f64 (*.f64 -1 (pow.f64 y 2)) y)
(+.f64 (*.f64 -1 (pow.f64 y 2)) (+.f64 (pow.f64 y 3) y))
(+.f64 (.f64 -1 (pow.f64 y 2)) (+.f64 (pow.f64 y 3) (+.f64 y (.f64 -1 (pow.f64 y 4)))))
1
(-.f64 1 (/.f64 1 y))
(-.f64 (+.f64 (/.f64 1 (pow.f64 y 2)) 1) (/.f64 1 y))
(-.f64 (+.f64 (/.f64 1 (pow.f64 y 2)) 1) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3))))
1
(-.f64 1 (/.f64 1 y))
(-.f64 (+.f64 (/.f64 1 (pow.f64 y 2)) 1) (/.f64 1 y))
(-.f64 (+.f64 (/.f64 1 (pow.f64 y 2)) 1) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3))))

Outputs
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 (/.f64 y (+.f64 y 1)) x)
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 (/.f64 y (+.f64 y 1)) x)
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 (/.f64 y (+.f64 y 1)) x)
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 (/.f64 y (+.f64 y 1)) x)
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 (/.f64 y (+.f64 y 1)) x)
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 (/.f64 y (+.f64 y 1)) x)
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 (/.f64 y (+.f64 y 1)) x)
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 (/.f64 y (+.f64 y 1)) x)
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 (/.f64 y (+.f64 y 1)) x)
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 (/.f64 y (+.f64 y 1)) x)
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 (/.f64 y (+.f64 y 1)) x)
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 (/.f64 y (+.f64 y 1)) x)
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 y (/.f64 x (+.f64 y 1)))
(*.f64 y x)
(+.f64 (.f64 y x) (.f64 -1 (*.f64 (pow.f64 y 2) x)))
(fma.f64 y x (neg.f64 (.f64 x (.f64 y y))))
(.f64 x (-.f64 y (.f64 y y)))
(+.f64 (.f64 y x) (+.f64 (.f64 -1 (.f64 (pow.f64 y 2) x)) (.f64 (pow.f64 y 3) x)))
(fma.f64 y x (fma.f64 -1 (.f64 x (.f64 y y)) (*.f64 x (pow.f64 y 3))))
(fma.f64 y x (.f64 x (.f64 (*.f64 y y) (+.f64 -1 y))))
(.f64 x (.f64 y (-.f64 (fma.f64 y y 1) y)))
(+.f64 (.f64 y x) (+.f64 (.f64 -1 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 (pow.f64 y 3) x) (.f64 -1 (.f64 (pow.f64 y 4) x)))))
(fma.f64 y x (fma.f64 -1 (.f64 x (.f64 y y)) (fma.f64 (pow.f64 y 3) x (neg.f64 (*.f64 x (pow.f64 y 4))))))
(fma.f64 y x (-.f64 (.f64 x (.f64 (.f64 y y) (+.f64 -1 y))) (.f64 x (pow.f64 y 4))))
(.f64 x (-.f64 (.f64 y (-.f64 (fma.f64 y y 1) y)) (pow.f64 y 4)))
(.f64 x (.f64 (fma.f64 y y 1) (-.f64 y (*.f64 y y))))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(fma.f64 -1 (/.f64 x y) x)
(-.f64 x (/.f64 x y))
(+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 x y)) x))
(+.f64 (fma.f64 -1 (/.f64 x y) x) (/.f64 x (*.f64 y y)))
(+.f64 x (-.f64 (/.f64 x (*.f64 y y)) (/.f64 x y)))
(-.f64 x (-.f64 (/.f64 x y) (/.f64 x (*.f64 y y))))
(-.f64 (/.f64 x (*.f64 y y)) (-.f64 (/.f64 x y) x))
(+.f64 (-.f64 x (/.f64 x y)) (/.f64 x (*.f64 y y)))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 x y)) x)))
(fma.f64 -1 (/.f64 x (pow.f64 y 3)) (+.f64 (fma.f64 -1 (/.f64 x y) x) (/.f64 x (*.f64 y y))))
(-.f64 (+.f64 x (-.f64 (/.f64 x (*.f64 y y)) (/.f64 x y))) (/.f64 x (pow.f64 y 3)))
(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 -1 y)) (/.f64 x (.f64 y y)))) (/.f64 x y))
(+.f64 x (-.f64 (/.f64 (-.f64 x (/.f64 x y)) (*.f64 y y)) (/.f64 x y)))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(fma.f64 -1 (/.f64 x y) x)
(-.f64 x (/.f64 x y))
(+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 x y)) x))
(+.f64 (fma.f64 -1 (/.f64 x y) x) (/.f64 x (*.f64 y y)))
(+.f64 x (-.f64 (/.f64 x (*.f64 y y)) (/.f64 x y)))
(-.f64 x (-.f64 (/.f64 x y) (/.f64 x (*.f64 y y))))
(-.f64 (/.f64 x (*.f64 y y)) (-.f64 (/.f64 x y) x))
(+.f64 (-.f64 x (/.f64 x y)) (/.f64 x (*.f64 y y)))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 x y)) x)))
(fma.f64 -1 (/.f64 x (pow.f64 y 3)) (+.f64 (fma.f64 -1 (/.f64 x y) x) (/.f64 x (*.f64 y y))))
(-.f64 (+.f64 x (-.f64 (/.f64 x (*.f64 y y)) (/.f64 x y))) (/.f64 x (pow.f64 y 3)))
(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 -1 y)) (/.f64 x (.f64 y y)))) (/.f64 x y))
(+.f64 x (-.f64 (/.f64 (-.f64 x (/.f64 x y)) (*.f64 y y)) (/.f64 x y)))
y
(+.f64 (*.f64 -1 (pow.f64 y 2)) y)
(fma.f64 -1 (*.f64 y y) y)
(-.f64 y (*.f64 y y))
(+.f64 (*.f64 -1 (pow.f64 y 2)) (+.f64 (pow.f64 y 3) y))
(fma.f64 -1 (*.f64 y y) (+.f64 y (pow.f64 y 3)))
(+.f64 y (.f64 (.f64 y y) (+.f64 -1 y)))
(*.f64 y (-.f64 (fma.f64 y y 1) y))
(+.f64 (.f64 -1 (pow.f64 y 2)) (+.f64 (pow.f64 y 3) (+.f64 y (.f64 -1 (pow.f64 y 4)))))
(fma.f64 -1 (*.f64 y y) (+.f64 (pow.f64 y 3) (+.f64 y (neg.f64 (pow.f64 y 4)))))
(+.f64 (-.f64 y (pow.f64 y 4)) (.f64 (.f64 y y) (+.f64 -1 y)))
(-.f64 (*.f64 y (-.f64 (fma.f64 y y 1) y)) (pow.f64 y 4))
(.f64 (fma.f64 y y 1) (-.f64 y (.f64 y y)))
1
(-.f64 1 (/.f64 1 y))
(+.f64 1 (/.f64 -1 y))
(-.f64 (+.f64 (/.f64 1 (pow.f64 y 2)) 1) (/.f64 1 y))
(+.f64 (/.f64 1 (*.f64 y y)) (-.f64 1 (/.f64 1 y)))
(+.f64 1 (-.f64 (/.f64 (/.f64 1 y) y) (/.f64 1 y)))
(+.f64 1 (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 -1 y)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 y 2)) 1) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3))))
(-.f64 (+.f64 1 (/.f64 1 (*.f64 y y))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3))))
(+.f64 1 (-.f64 (/.f64 (/.f64 1 y) y) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))))
(+.f64 (+.f64 1 (/.f64 -1 y)) (-.f64 (/.f64 1 (*.f64 y y)) (/.f64 1 (pow.f64 y 3))))
(+.f64 1 (+.f64 (/.f64 1 (*.f64 y y)) (+.f64 (/.f64 -1 y) (/.f64 -1 (pow.f64 y 3)))))
(+.f64 (+.f64 1 (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 -1 y))) (/.f64 -1 (pow.f64 y 3)))
1
(-.f64 1 (/.f64 1 y))
(+.f64 1 (/.f64 -1 y))
(-.f64 (+.f64 (/.f64 1 (pow.f64 y 2)) 1) (/.f64 1 y))
(+.f64 (/.f64 1 (*.f64 y y)) (-.f64 1 (/.f64 1 y)))
(+.f64 1 (-.f64 (/.f64 (/.f64 1 y) y) (/.f64 1 y)))
(+.f64 1 (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 -1 y)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 y 2)) 1) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3))))
(-.f64 (+.f64 1 (/.f64 1 (*.f64 y y))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3))))
(+.f64 1 (-.f64 (/.f64 (/.f64 1 y) y) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))))
(+.f64 (+.f64 1 (/.f64 -1 y)) (-.f64 (/.f64 1 (*.f64 y y)) (/.f64 1 (pow.f64 y 3))))
(+.f64 1 (+.f64 (/.f64 1 (*.f64 y y)) (+.f64 (/.f64 -1 y) (/.f64 -1 (pow.f64 y 3)))))
(+.f64 (+.f64 1 (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 -1 y))) (/.f64 -1 (pow.f64 y 3)))

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.9b	(/.f64 (*.f64 x y) (+.f64 y 1))

Compiler

Compiled 18 to 9 computations (50% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite63.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

854×	`pow1_binary64`
797×	`log1p-expm1-u_binary64`
797×	`expm1-log1p-u_binary64`
796×	`add-log-exp_binary64`
780×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	150	10
2	2126	10

Stop Event

1×	node limit

Counts

1 → 43

Calls

Call 1

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

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

Outputs

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

simplify57.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
459×	`times-frac_binary64`
413×	`distribute-lft-out--_binary64`
375×	`distribute-rgt-neg-in_binary64`
347×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	294
1	94	281
2	254	270
3	922	257
4	4184	250

Stop Event

1×	node limit

Counts

67 → 59

Calls

Call 1

Inputs
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(*.f64 y x)
(+.f64 (.f64 y x) (.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 (.f64 y x) (+.f64 (.f64 -1 (.f64 (pow.f64 y 2) x)) (.f64 (pow.f64 y 3) x)))
(+.f64 (.f64 y x) (+.f64 (.f64 -1 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 (pow.f64 y 3) x) (.f64 -1 (.f64 (pow.f64 y 4) x)))))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 x y)) x))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 x y)) x)))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 x y)) x))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 x y)) x)))

Outputs
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(*.f64 y x)
(+.f64 (.f64 y x) (.f64 -1 (*.f64 (pow.f64 y 2) x)))
(fma.f64 y x (neg.f64 (.f64 x (.f64 y y))))
(.f64 x (+.f64 (neg.f64 (.f64 y y)) y))
(.f64 y (-.f64 x (.f64 y x)))
(+.f64 (.f64 y x) (+.f64 (.f64 -1 (.f64 (pow.f64 y 2) x)) (.f64 (pow.f64 y 3) x)))
(fma.f64 y x (fma.f64 -1 (.f64 x (.f64 y y)) (*.f64 x (pow.f64 y 3))))
(fma.f64 y x (.f64 x (+.f64 (neg.f64 (.f64 y y)) (pow.f64 y 3))))
(.f64 x (+.f64 y (.f64 (*.f64 y y) (+.f64 -1 y))))
(.f64 x (fma.f64 (.f64 y y) (+.f64 y -1) y))
(+.f64 (.f64 y x) (+.f64 (.f64 -1 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 (pow.f64 y 3) x) (.f64 -1 (.f64 (pow.f64 y 4) x)))))
(fma.f64 y x (fma.f64 -1 (.f64 x (.f64 y y)) (fma.f64 (pow.f64 y 3) x (neg.f64 (*.f64 x (pow.f64 y 4))))))
(fma.f64 y x (-.f64 (.f64 x (+.f64 (neg.f64 (.f64 y y)) (pow.f64 y 3))) (*.f64 x (pow.f64 y 4))))
(.f64 x (+.f64 (-.f64 y (.f64 y y)) (-.f64 (pow.f64 y 3) (pow.f64 y 4))))
(.f64 x (.f64 (fma.f64 y y 1) (-.f64 y (*.f64 y y))))
(.f64 (-.f64 x (.f64 y x)) (+.f64 y (pow.f64 y 3)))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(fma.f64 -1 (/.f64 x y) x)
(-.f64 x (/.f64 x y))
(+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 x y)) x))
(+.f64 (fma.f64 -1 (/.f64 x y) x) (/.f64 x (*.f64 y y)))
(+.f64 x (-.f64 (/.f64 x (*.f64 y y)) (/.f64 x y)))
(-.f64 (/.f64 x (*.f64 y y)) (-.f64 (/.f64 x y) x))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 x y)) x)))
(fma.f64 -1 (/.f64 x (pow.f64 y 3)) (+.f64 (fma.f64 -1 (/.f64 x y) x) (/.f64 x (*.f64 y y))))
(-.f64 (+.f64 x (-.f64 (/.f64 x (*.f64 y y)) (/.f64 x y))) (/.f64 x (pow.f64 y 3)))
(+.f64 (-.f64 x (/.f64 x y)) (-.f64 (/.f64 x (*.f64 y y)) (/.f64 x (pow.f64 y 3))))
(+.f64 (-.f64 x (/.f64 x y)) (/.f64 (-.f64 x (/.f64 x y)) (*.f64 y y)))
(.f64 (+.f64 1 (/.f64 -1 y)) (+.f64 x (/.f64 x (.f64 y y))))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(fma.f64 -1 (/.f64 x y) x)
(-.f64 x (/.f64 x y))
(+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 x y)) x))
(+.f64 (fma.f64 -1 (/.f64 x y) x) (/.f64 x (*.f64 y y)))
(+.f64 x (-.f64 (/.f64 x (*.f64 y y)) (/.f64 x y)))
(-.f64 (/.f64 x (*.f64 y y)) (-.f64 (/.f64 x y) x))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 x y)) x)))
(fma.f64 -1 (/.f64 x (pow.f64 y 3)) (+.f64 (fma.f64 -1 (/.f64 x y) x) (/.f64 x (*.f64 y y))))
(-.f64 (+.f64 x (-.f64 (/.f64 x (*.f64 y y)) (/.f64 x y))) (/.f64 x (pow.f64 y 3)))
(+.f64 (-.f64 x (/.f64 x y)) (-.f64 (/.f64 x (*.f64 y y)) (/.f64 x (pow.f64 y 3))))
(+.f64 (-.f64 x (/.f64 x y)) (/.f64 (-.f64 x (/.f64 x y)) (*.f64 y y)))
(.f64 (+.f64 1 (/.f64 -1 y)) (+.f64 x (/.f64 x (.f64 y y))))

eval90.0ms (3.8%)

Compiler: Compiled 1654 to 986 computations (40.4% saved)

prune71.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	141	5	146

Error

Counts

146 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	6.3b	(/.f64 (*.f64 x y) (+.f64 y 1))
▶	30.8b	(*.f64 y x)
	32.3b	x
▶	0.1b	(/.f64 x (/.f64 (+.f64 y 1) y))
▶	32.7b	(-.f64 x (/.f64 x y))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize7.0ms (0.3%)

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

localize11.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 x y))

Compiler

Compiled 12 to 4 computations (66.7% saved)

series6.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	(-.f64 x (/.f64 x y))
1.0ms	x	@	inf	(-.f64 x (/.f64 x y))
1.0ms	x	@	0	(-.f64 x (/.f64 x y))
1.0ms	y	@	0	(-.f64 x (/.f64 x y))
1.0ms	y	@	inf	(-.f64 x (/.f64 x y))

rewrite160.0ms (6.8%)

Algorithm

1×	batch-egg-rewrite

Rules

726×	`pow1_binary64`
678×	`add-log-exp_binary64`
678×	`log1p-expm1-u_binary64`
678×	`expm1-log1p-u_binary64`
663×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	116	7
2	1789	7

Stop Event

1×	node limit

Counts

1 → 36

Calls

Call 1

Inputs
(-.f64 x (/.f64 x y))

Outputs

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

simplify29.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

148×	`fma-def_binary64`
74×	`fma-neg_binary64`
28×	`distribute-rgt-in_binary64`
25×	`distribute-lft-in_binary64`
23×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	218
1	32	218
2	67	155
3	132	155
4	223	155
5	385	155
6	621	155
7	649	155

Stop Event

1×

saturated

Counts

60 → 44

Calls

Call 1

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

Outputs
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(.f64 -1 (.f64 (-.f64 (/.f64 1 y) 1) x))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(.f64 -1 (.f64 (-.f64 (/.f64 1 y) 1) x))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(.f64 -1 (.f64 (-.f64 (/.f64 1 y) 1) x))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(.f64 -1 (.f64 (-.f64 (/.f64 1 y) 1) x))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(*.f64 -1 (/.f64 x y))
(neg.f64 (/.f64 x y))
(/.f64 (neg.f64 x) y)
(+.f64 x (*.f64 -1 (/.f64 x y)))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(+.f64 x (*.f64 -1 (/.f64 x y)))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(+.f64 x (*.f64 -1 (/.f64 x y)))
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(*.f64 (-.f64 1 (/.f64 1 y)) x)
(*.f64 x (-.f64 1 (/.f64 1 y)))
(-.f64 x (/.f64 x y))

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 y 1) y)
✓	0.1b	(/.f64 x (/.f64 (+.f64 y 1) y))

Compiler

Compiled 20 to 12 computations (40% saved)

series3.0ms (0.1%)

Counts

2 → 36

Calls

9 calls:

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

rewrite75.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

926×	`pow1_binary64`
866×	`log1p-expm1-u_binary64`
866×	`expm1-log1p-u_binary64`
865×	`add-log-exp_binary64`
847×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	156	17
2	2315	17

Stop Event

1×	node limit

Counts

2 → 72

Calls

Call 1

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

Outputs

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

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

simplify56.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
459×	`times-frac_binary64`
415×	`distribute-lft-out--_binary64`
378×	`distribute-rgt-neg-in_binary64`
347×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	363
1	97	350
2	257	339
3	928	326
4	4189	319

Stop Event

1×	node limit

Counts

108 → 91

Calls

Call 1

Inputs
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 (*.f64 y x) (+.f64 1 y))
(*.f64 y x)
(+.f64 (.f64 y x) (.f64 -1 (*.f64 (pow.f64 y 2) x)))
(+.f64 (.f64 y x) (+.f64 (.f64 -1 (.f64 (pow.f64 y 2) x)) (.f64 (pow.f64 y 3) x)))
(+.f64 (.f64 y x) (+.f64 (.f64 -1 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 (pow.f64 y 3) x) (.f64 -1 (.f64 (pow.f64 y 4) x)))))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 x y)) x))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 x y)) x)))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 x y)) x))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 x y)) x)))
(/.f64 1 y)
(+.f64 (/.f64 1 y) 1)
(+.f64 (/.f64 1 y) 1)
(+.f64 (/.f64 1 y) 1)
1
(+.f64 (/.f64 1 y) 1)
(+.f64 (/.f64 1 y) 1)
(+.f64 (/.f64 1 y) 1)
1
(+.f64 (/.f64 1 y) 1)
(+.f64 (/.f64 1 y) 1)
(+.f64 (/.f64 1 y) 1)

Outputs
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(/.f64 (*.f64 y x) (+.f64 1 y))
(/.f64 y (/.f64 (+.f64 y 1) x))
(/.f64 (*.f64 y x) (+.f64 y 1))
(*.f64 x (/.f64 y (+.f64 y 1)))
(*.f64 y (/.f64 x (+.f64 y 1)))
(*.f64 y x)
(+.f64 (.f64 y x) (.f64 -1 (*.f64 (pow.f64 y 2) x)))
(fma.f64 y x (neg.f64 (.f64 x (.f64 y y))))
(.f64 x (+.f64 y (neg.f64 (.f64 y y))))
(.f64 x (-.f64 y (.f64 y y)))
(*.f64 x (fma.f64 y (neg.f64 y) y))
(.f64 y (-.f64 x (.f64 y x)))
(+.f64 (.f64 y x) (+.f64 (.f64 -1 (.f64 (pow.f64 y 2) x)) (.f64 (pow.f64 y 3) x)))
(fma.f64 y x (fma.f64 -1 (.f64 x (.f64 y y)) (*.f64 x (pow.f64 y 3))))
(fma.f64 y x (.f64 x (+.f64 (neg.f64 (.f64 y y)) (pow.f64 y 3))))
(.f64 x (+.f64 y (.f64 (*.f64 y y) (+.f64 y -1))))
(.f64 x (fma.f64 (.f64 y y) (+.f64 y -1) y))
(+.f64 (.f64 y x) (+.f64 (.f64 -1 (.f64 (pow.f64 y 2) x)) (+.f64 (.f64 (pow.f64 y 3) x) (.f64 -1 (.f64 (pow.f64 y 4) x)))))
(fma.f64 y x (fma.f64 -1 (.f64 x (.f64 y y)) (fma.f64 (pow.f64 y 3) x (neg.f64 (*.f64 x (pow.f64 y 4))))))
(fma.f64 y x (-.f64 (.f64 x (+.f64 (neg.f64 (.f64 y y)) (pow.f64 y 3))) (*.f64 x (pow.f64 y 4))))
(.f64 x (+.f64 (-.f64 y (.f64 y y)) (-.f64 (pow.f64 y 3) (pow.f64 y 4))))
(.f64 (fma.f64 y y 1) (.f64 x (fma.f64 y (neg.f64 y) y)))
(.f64 (-.f64 x (.f64 y x)) (+.f64 y (pow.f64 y 3)))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(fma.f64 -1 (/.f64 x y) x)
(-.f64 x (/.f64 x y))
(+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 x y)) x))
(+.f64 (fma.f64 -1 (/.f64 x y) x) (/.f64 x (*.f64 y y)))
(+.f64 (-.f64 x (/.f64 x y)) (/.f64 x (*.f64 y y)))
(+.f64 x (-.f64 (/.f64 x (*.f64 y y)) (/.f64 x y)))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 x y)) x)))
(fma.f64 -1 (/.f64 x (pow.f64 y 3)) (+.f64 (fma.f64 -1 (/.f64 x y) x) (/.f64 x (*.f64 y y))))
(-.f64 (+.f64 (-.f64 x (/.f64 x y)) (/.f64 x (*.f64 y y))) (/.f64 x (pow.f64 y 3)))
(+.f64 x (-.f64 (.f64 (+.f64 (/.f64 -1 y) 1) (/.f64 x (.f64 y y))) (/.f64 x y)))
(+.f64 x (-.f64 (/.f64 (-.f64 x (/.f64 x y)) (*.f64 y y)) (/.f64 x y)))
(.f64 (+.f64 1 (/.f64 -1 y)) (+.f64 x (/.f64 x (.f64 y y))))
x
(+.f64 (*.f64 -1 (/.f64 x y)) x)
(fma.f64 -1 (/.f64 x y) x)
(-.f64 x (/.f64 x y))
(+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 x y)) x))
(+.f64 (fma.f64 -1 (/.f64 x y) x) (/.f64 x (*.f64 y y)))
(+.f64 (-.f64 x (/.f64 x y)) (/.f64 x (*.f64 y y)))
(+.f64 x (-.f64 (/.f64 x (*.f64 y y)) (/.f64 x y)))
(+.f64 (.f64 -1 (/.f64 x (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (.f64 -1 (/.f64 x y)) x)))
(fma.f64 -1 (/.f64 x (pow.f64 y 3)) (+.f64 (fma.f64 -1 (/.f64 x y) x) (/.f64 x (*.f64 y y))))
(-.f64 (+.f64 (-.f64 x (/.f64 x y)) (/.f64 x (*.f64 y y))) (/.f64 x (pow.f64 y 3)))
(+.f64 x (-.f64 (.f64 (+.f64 (/.f64 -1 y) 1) (/.f64 x (.f64 y y))) (/.f64 x y)))
(+.f64 x (-.f64 (/.f64 (-.f64 x (/.f64 x y)) (*.f64 y y)) (/.f64 x y)))
(.f64 (+.f64 1 (/.f64 -1 y)) (+.f64 x (/.f64 x (.f64 y y))))
(/.f64 1 y)
(+.f64 (/.f64 1 y) 1)
(+.f64 1 (/.f64 1 y))
(+.f64 (/.f64 1 y) 1)
(+.f64 1 (/.f64 1 y))
(+.f64 (/.f64 1 y) 1)
(+.f64 1 (/.f64 1 y))
1
(+.f64 (/.f64 1 y) 1)
(+.f64 1 (/.f64 1 y))
(+.f64 (/.f64 1 y) 1)
(+.f64 1 (/.f64 1 y))
(+.f64 (/.f64 1 y) 1)
(+.f64 1 (/.f64 1 y))
1
(+.f64 (/.f64 1 y) 1)
(+.f64 1 (/.f64 1 y))
(+.f64 (/.f64 1 y) 1)
(+.f64 1 (/.f64 1 y))
(+.f64 (/.f64 1 y) 1)
(+.f64 1 (/.f64 1 y))

eval54.0ms (2.3%)

Compiler: Compiled 1580 to 834 computations (47.2% saved)

prune22.0ms (0.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	135	5	140

Error

Counts

140 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	6.3b	(/.f64 (*.f64 x y) (+.f64 y 1))
✓	30.8b	(*.f64 y x)
	32.3b	x
✓	0.1b	(/.f64 x (/.f64 (+.f64 y 1) y))
✓	32.7b	(-.f64 x (/.f64 x y))

Compiler

Compiled 33 to 21 computations (36.4% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	4	4
Total	5	5

Error

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	6.3b	(/.f64 (*.f64 x y) (+.f64 y 1))
✓	30.8b	(*.f64 y x)
	32.3b	x
✓	0.1b	(/.f64 x (/.f64 (+.f64 y 1) y))
✓	32.7b	(-.f64 x (/.f64 x y))

Compiler

Compiled 33 to 21 computations (36.4% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	4	4
Total	5	5

Error

Counts

5 → 5

Alt Table

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Status	Error	Program
✓	6.3b	(/.f64 (*.f64 x y) (+.f64 y 1))
✓	30.8b	(*.f64 y x)
	32.3b	x
✓	0.1b	(/.f64 x (/.f64 (+.f64 y 1) y))
✓	32.7b	(-.f64 x (/.f64 x y))

Compiler

Compiled 33 to 21 computations (36.4% saved)

regimes17.0ms (0.7%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	y
5.0ms	(/.f64 (*.f64 x y) (+.f64 y 1))
5.0ms	x

Results

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

Compiler

Compiled 47 to 27 computations (42.6% saved)

regimes10.0ms (0.4%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	y
4.0ms	x

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`y`

Compiler

Compiled 24 to 13 computations (45.8% saved)

regimes42.0ms (1.8%)

Counts

3 → 3

Calls

Call 1

Inputs
x
(*.f64 y x)
(-.f64 x (/.f64 x y))

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

Calls

2 calls:

30.0ms	x
10.0ms	y

Results

Error	Segments	Branch
22.8b	9	`x`
1.1b	3	`y`

Compiler

Compiled 17 to 9 computations (47.1% saved)

bsearch36.0ms (1.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	1.607625927258275e-8	25.213549419601623
18.0ms	-218.53919179681262	-5.086466952169019e-6

Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes38.0ms (1.6%)

Accuracy

Total -59.9b remaining (-3704.2%)

Threshold costs -59.9b (-3704.2%)

Counts

2 → 3

Calls

Call 1

Inputs
x
(*.f64 y x)

Outputs
x
(*.f64 y x)
x

Calls

2 calls:

27.0ms	x
10.0ms	y

Results

Error	Segments	Branch
22.8b	9	`x`
1.6b	3	`y`

Compiler

Compiled 12 to 7 computations (41.7% saved)

bsearch39.0ms (1.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
21.0ms	1.607625927258275e-8	25.213549419601623
18.0ms	-218.53919179681262	-5.086466952169019e-6

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	69
1	28	69
2	34	69
3	38	69
4	41	69
5	42	69

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 x (/.f64 (+.f64 y 1) y))
(if (<=.f64 y -7689164240171677/35184372088832) (-.f64 x (/.f64 x y)) (if (<=.f64 y 607343903670137/37778931862957161709568) (*.f64 y x) (-.f64 x (/.f64 x y))))
(if (<=.f64 y -7689164240171677/35184372088832) x (if (<=.f64 y 607343903670137/37778931862957161709568) (*.f64 y x) x))
x

Outputs
(*.f64 x (/.f64 y (+.f64 y 1)))
(/.f64 x (/.f64 (+.f64 y 1) y))
(if (<=.f64 y -7689164240171677/35184372088832) (-.f64 x (/.f64 x y)) (if (<=.f64 y 607343903670137/37778931862957161709568) (*.f64 y x) (-.f64 x (/.f64 x y))))
(if (<=.f64 y -7689164240171677/35184372088832) (-.f64 x (/.f64 x y)) (if (<=.f64 y 607343903670137/37778931862957161709568) (*.f64 x y) (-.f64 x (/.f64 x y))))
(if (<=.f64 y -7689164240171677/35184372088832) x (if (<=.f64 y 607343903670137/37778931862957161709568) (*.f64 y x) x))
(if (<=.f64 y -7689164240171677/35184372088832) x (if (<=.f64 y 607343903670137/37778931862957161709568) (*.f64 x y) x))
x

Compiler

Compiled 59 to 34 computations (42.4% saved)

soundness9.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	17	10
3	20	10
4	21	10

Stop Event

1×

saturated

Compiler

Compiled 18 to 12 computations (33.3% saved)

end35.0ms (1.5%)

Compiler: Compiled 51 to 25 computations (51% saved)

Details

analyze93.0ms (3.9%)

sample1.1s (46.7%)

preprocess16.0ms (0.7%)

simplify28.0ms (1.2%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize9.0ms (0.4%)

series6.0ms (0.2%)

rewrite60.0ms (2.5%)

simplify90.0ms (3.8%)

localize7.0ms (0.3%)

series2.0ms (0.1%)

rewrite63.0ms (2.7%)

simplify57.0ms (2.4%)

eval90.0ms (3.8%)

prune71.0ms (3%)

localize7.0ms (0.3%)

localize11.0ms (0.5%)

series6.0ms (0.3%)

rewrite160.0ms (6.8%)

simplify29.0ms (1.2%)

localize10.0ms (0.4%)

series3.0ms (0.1%)

rewrite75.0ms (3.1%)

simplify56.0ms (2.3%)

eval54.0ms (2.3%)

prune22.0ms (0.9%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes17.0ms (0.7%)

regimes10.0ms (0.4%)

regimes42.0ms (1.8%)

bsearch36.0ms (1.5%)

regimes38.0ms (1.6%)

bsearch39.0ms (1.6%)

simplify7.0ms (0.3%)

soundness9.0ms (0.4%)

end35.0ms (1.5%)

Profiling