Details

analyze186.0ms (14%)

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
90.8%	9.1%	0.1%	13
92.3%	7.6%	0.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample796.0ms (60.1%)

Results

784.0ms

8256×

body

128

valid

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess17.0ms (1.3%)

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

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify9.0ms (0.7%)

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

prune3.0ms (0.2%)

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

Counts

3 → 2

Alt Table

Status	Error	Program
	6.0b	(/.f64 (*.f64 x y) (+.f64 y 1))
▶	0.0b	(*.f64 x (/.f64 y (+.f64 y 1)))

Compiler

Compiled 52 to 34 computations (34.6% saved)

localize4.0ms (0.3%)

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)))

series7.0ms (0.5%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	(/.f64 y (+.f64 y 1))
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)))

rewrite44.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

822×	`pow1_binary64`
765×	`log1p-expm1-u_binary64`
765×	`expm1-log1p-u_binary64`
77×	`add-sqr-sqrt_binary64`
75×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	150	17
2	2054	17

Stop Event

1×	node limit

Counts

2 → 59

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

Outputs

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

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

simplify43.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

667×	`times-frac_binary64`
381×	`fma-neg_binary64`
280×	`associate-l_binary64`
272×	`cancel-sign-sub-inv_binary64`
231×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	437
1	136	413
2	372	400
3	1260	388
4	4655	388

Stop Event

1×	node limit

Counts

95 → 89

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

prune48.0ms (3.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	89	2	91

Error

Counts

91 → 2

Alt Table

Status	Error	Program
▶	6.0b	(/.f64 (*.f64 x y) (+.f64 y 1))
✓	0.0b	(*.f64 x (/.f64 y (+.f64 y 1)))

Compiler

Compiled 1020 to 625 computations (38.7% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.7b	(/.f64 (*.f64 x y) (+.f64 y 1))

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	y	@	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))

rewrite46.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

797×	`log1p-expm1-u_binary64`
797×	`expm1-log1p-u_binary64`
77×	`add-sqr-sqrt_binary64`
75×	`*-un-lft-identity_binary64`
75×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	150	10
2	2114	10

Stop Event

1×	node limit

Counts

1 → 45

Calls

Call 1

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

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

Outputs

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

simplify34.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

705×	`fma-def_binary64`
459×	`times-frac_binary64`
287×	`fma-neg_binary64`
262×	`sub-neg_binary64`
243×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	294
1	94	281
2	254	270
3	924	257
4	4068	257

Stop Event

1×	node limit

Counts

69 → 61

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

prune27.0ms (2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	61	2	63

Error

Counts

63 → 2

Alt Table

Status	Error	Program
✓	6.0b	(/.f64 (*.f64 x y) (+.f64 y 1))
✓	0.0b	(*.f64 x (/.f64 y (+.f64 y 1)))

Compiler

Compiled 741 to 422 computations (43% saved)

regimes16.0ms (1.2%)

Accuracy

Total 0.0b remaining (51.4%)

Threshold costs 0.0b (51.4%)

Counts

7 → 1

Compiler

Compiled 46 to 25 computations (45.7% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	10

Stop Event

1×

saturated

Calls

Call 1

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

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

end38.0ms (2.9%)

Stop Event

1×

done

Compiler

Compiled 36 to 24 computations (33.3% saved)

Details

analyze186.0ms (14%)

sample796.0ms (60.1%)

preprocess17.0ms (1.3%)

simplify9.0ms (0.7%)

prune3.0ms (0.2%)

localize4.0ms (0.3%)

series7.0ms (0.5%)

rewrite44.0ms (3.3%)

simplify43.0ms (3.2%)

prune48.0ms (3.6%)

localize4.0ms (0.3%)

series2.0ms (0.1%)

rewrite46.0ms (3.5%)

simplify34.0ms (2.5%)

prune27.0ms (2%)

regimes16.0ms (1.2%)

simplify2.0ms (0.2%)

end38.0ms (2.9%)

Profiling