Details

analyze202.0ms (7.8%)

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
12.5%	12.5%	87.4%	0.1%	0%	0%	0%	5
18.8%	18.7%	81.2%	0.1%	0%	0%	0%	6
43.8%	43.7%	56.2%	0.1%	0%	0%	0%	7
50%	50%	50%	0.1%	0%	0%	0%	8
67.2%	67.1%	32.8%	0.1%	0%	0%	0%	9
71.9%	71.8%	28.1%	0.1%	0%	0%	0%	10
82.4%	82.3%	17.6%	0.1%	0%	0%	0%	11
85.2%	85.1%	14.8%	0.1%	0%	0%	0%	12

Compiler

Compiled 10 to 7 computations (30% saved)

sample1.2s (45.6%)

Results

1.1s

8256×

body

256

valid

Bogosity

preprocess20.0ms (0.8%)

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)

simplify7.0ms (0.3%)

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
▶	0.0b	(*.f64 x (/.f64 y (+.f64 y 1)))
▶	10.1b	(/.f64 (*.f64 x 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)

series5.0ms (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	y	@	0	(*.f64 x (/.f64 y (+.f64 y 1)))
1.0ms	x	@	-inf	(*.f64 x (/.f64 y (+.f64 y 1)))

rewrite59.0ms (2.3%)

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)))))))

simplify85.0ms (3.3%)

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
✓	9.4b	(/.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	x	@	inf	(/.f64 (*.f64 x y) (+.f64 y 1))
0.0ms	y	@	0	(/.f64 (*.f64 x y) (+.f64 y 1))

rewrite82.0ms (3.2%)

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)))))))

simplify56.0ms (2.2%)

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))))

eval110.0ms (4.2%)

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

prune23.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	140	6	146

Error

Counts

146 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(*.f64 x (/.f64 y (+.f64 y 1)))
▶	29.7b	(-.f64 x (/.f64 x y))
▶	35.0b	(*.f64 y x)
✓	10.1b	(/.f64 (*.f64 x y) (+.f64 y 1))
	29.4b	x
▶	6.7b	(*.f64 (/.f64 y (/.f64 (+.f64 y 1) x)) 1)

Compiler

Compiled 44 to 29 computations (34.1% saved)

localize24.0ms (0.9%)

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

localize12.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 y 1) x)
✓	6.7b	(/.f64 y (/.f64 (+.f64 y 1) x))

Compiler

Compiled 29 to 18 computations (37.9% saved)

series9.0ms (0.4%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	(/.f64 y (/.f64 (+.f64 y 1) x))
1.0ms	x	@	-inf	(/.f64 (+.f64 y 1) x)
0.0ms	x	@	0	(/.f64 (+.f64 y 1) x)
0.0ms	y	@	inf	(/.f64 (+.f64 y 1) x)
0.0ms	y	@	0	(/.f64 y (/.f64 (+.f64 y 1) x))

rewrite97.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

925×	`pow1_binary64`
865×	`log1p-expm1-u_binary64`
865×	`expm1-log1p-u_binary64`
864×	`add-log-exp_binary64`
846×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	156	17
2	2314	17

Stop Event

1×	node limit

Counts

2 → 72

Calls

Call 1

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

Outputs

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

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

simplify57.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
459×	`times-frac_binary64`
414×	`distribute-lft-out--_binary64`
380×	`distribute-rgt-neg-in_binary64`
347×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	480
1	98	467
2	257	456
3	925	443
4	4176	436

Stop Event

1×	node limit

Counts

120 → 93

Calls

Call 1

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

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

localize66.0ms (2.5%)

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)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite77.0ms (3%)

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))))))

simplify26.0ms (1%)

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))

eval73.0ms (2.8%)

Compiler: Compiled 1786 to 1028 computations (42.4% saved)

prune27.0ms (1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	1	1
Picked	0	1	1
Done	0	4	4
Total	137	6	143

Error

Counts

143 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(*.f64 x (/.f64 y (+.f64 y 1)))
✓	29.7b	(-.f64 x (/.f64 x y))
✓	35.0b	(*.f64 y x)
✓	10.1b	(/.f64 (*.f64 x y) (+.f64 y 1))
	29.4b	x
✓	6.7b	(*.f64 (/.f64 y (/.f64 (+.f64 y 1) x)) 1)

Compiler

Compiled 44 to 29 computations (34.1% saved)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	5	5
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(*.f64 x (/.f64 y (+.f64 y 1)))
✓	29.7b	(-.f64 x (/.f64 x y))
✓	35.0b	(*.f64 y x)
✓	10.1b	(/.f64 (*.f64 x y) (+.f64 y 1))
	29.4b	x
✓	6.7b	(*.f64 (/.f64 y (/.f64 (+.f64 y 1) x)) 1)

Compiler

Compiled 44 to 29 computations (34.1% saved)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	5	5
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(*.f64 x (/.f64 y (+.f64 y 1)))
✓	29.7b	(-.f64 x (/.f64 x y))
✓	35.0b	(*.f64 y x)
✓	10.1b	(/.f64 (*.f64 x y) (+.f64 y 1))
	29.4b	x
✓	6.7b	(*.f64 (/.f64 y (/.f64 (+.f64 y 1) x)) 1)

Compiler

Compiled 44 to 29 computations (34.1% saved)

regimes20.0ms (0.8%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	y
6.0ms	x
5.0ms	(/.f64 (*.f64 x y) (+.f64 y 1))

Results

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

Compiler

Compiled 49 to 29 computations (40.8% saved)

regimes73.0ms (2.8%)

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:

58.0ms	x
14.0ms	y

Results

Error	Segments	Branch
22.7b	7	`x`
2.2b	3	`y`

Compiler

Compiled 17 to 9 computations (47.1% saved)

bsearch48.0ms (1.8%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
30.0ms	1.1926242047658488e-6	2.0344160612957536
17.0ms	-11.62750023525451	-0.2884979389380311

Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes39.0ms (1.5%)

Accuracy

Total -59.0b remaining (-2192.5%)

Threshold costs -59.0b (-2192.5%)

Counts

2 → 3

Calls

Call 1

Inputs
x
(*.f64 y x)

Outputs
x
(*.f64 y x)
x

Calls

2 calls:

26.0ms	x
11.0ms	y

Results

Error	Segments	Branch
22.7b	7	`x`
2.7b	3	`y`

Compiler

Compiled 12 to 7 computations (41.7% saved)

bsearch36.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
19.0ms	1.1926242047658488e-6	2.0344160612957536
18.0ms	-11.62750023525451	-0.2884979389380311

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify6.0ms (0.2%)

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	19	59
1	26	59
2	32	59
3	36	59
4	39	59
5	40	59

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(*.f64 x (/.f64 y (+.f64 y 1)))
(if (<=.f64 y -6545700715842821/562949953421312) (-.f64 x (/.f64 x y)) (if (<=.f64 y 5632008571245309/4722366482869645213696) (*.f64 y x) (-.f64 x (/.f64 x y))))
(if (<=.f64 y -6545700715842821/562949953421312) x (if (<=.f64 y 5632008571245309/4722366482869645213696) (*.f64 y x) x))
x

Outputs
(*.f64 x (/.f64 y (+.f64 y 1)))
(if (<=.f64 y -6545700715842821/562949953421312) (-.f64 x (/.f64 x y)) (if (<=.f64 y 5632008571245309/4722366482869645213696) (*.f64 y x) (-.f64 x (/.f64 x y))))
(if (<=.f64 y -6545700715842821/562949953421312) (-.f64 x (/.f64 x y)) (if (<=.f64 y 5632008571245309/4722366482869645213696) (*.f64 x y) (-.f64 x (/.f64 x y))))
(if (<=.f64 y -6545700715842821/562949953421312) x (if (<=.f64 y 5632008571245309/4722366482869645213696) (*.f64 y x) x))
(if (<=.f64 y -6545700715842821/562949953421312) x (if (<=.f64 y 5632008571245309/4722366482869645213696) (*.f64 x y) x))
x

Compiler

Compiled 50 to 28 computations (44% saved)

soundness8.0ms (0.3%)

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)

end34.0ms (1.3%)

Compiler: Compiled 44 to 21 computations (52.3% saved)

Details

analyze202.0ms (7.8%)

sample1.2s (45.6%)

preprocess20.0ms (0.8%)

simplify7.0ms (0.3%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize9.0ms (0.4%)

series5.0ms (0.2%)

rewrite59.0ms (2.3%)

simplify85.0ms (3.3%)

localize7.0ms (0.3%)

series2.0ms (0.1%)

rewrite82.0ms (3.2%)

simplify56.0ms (2.2%)

eval110.0ms (4.2%)

prune23.0ms (0.9%)

localize24.0ms (0.9%)

localize12.0ms (0.5%)

series9.0ms (0.4%)

rewrite97.0ms (3.7%)

simplify57.0ms (2.2%)

localize66.0ms (2.5%)

series3.0ms (0.1%)

rewrite77.0ms (3%)

simplify26.0ms (1%)

eval73.0ms (2.8%)

prune27.0ms (1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes20.0ms (0.8%)

regimes73.0ms (2.8%)

bsearch48.0ms (1.8%)

regimes39.0ms (1.5%)

bsearch36.0ms (1.4%)

simplify6.0ms (0.2%)

soundness8.0ms (0.3%)

end34.0ms (1.3%)

Profiling