Details

analyze69.0ms (4.5%)

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
0%	0%	99.9%	0.1%	0%	0%	0%	5
0%	0%	99.9%	0.1%	0%	0%	0%	6
40.6%	40.6%	59.3%	0.1%	0%	0%	0%	7
46%	45.3%	53.1%	0.1%	1.6%	0%	0%	8
65.3%	63.2%	33.6%	0.1%	3.1%	0%	0%	9
69.5%	66%	28.9%	0.1%	5.1%	0%	0%	10
80.9%	75.1%	17.8%	0.1%	7%	0%	0%	11
83.6%	76.6%	15%	0.1%	8.3%	0%	0%	12

Compiler

Compiled 10 to 6 computations (40% saved)

sample961.0ms (63.2%)

Results

916.0ms	8256×	body	256	valid
33.0ms	408×	body	256	infinite

Bogosity

preprocess7.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

8×	`associate-/r*`
4×	`*-commutative`
4×	`count-2`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	14	38
2	19	38
3	23	38
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 y))
(/.f64 (+.f64 y x) (+.f64 x x))

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

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify12.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

4×	`associate-/r*`
2×	`*-commutative`
2×	`count-2`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	10	19
2	13	19
3	15	19

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 5 computations (44.4% saved)

localize6.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 17 to 5 computations (70.6% saved)

series3.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

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

rewrite57.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1820×	`add-sqr-sqrt`
1802×	`*-un-lft-identity`
1692×	`add-cube-cbrt`
1674×	`add-cbrt-cube`
174×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	162	19
2	2568	19

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (+.f64 x y) (/.f64 0 0)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x y) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 0 0) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 0 0) (.f64 (+.f64 x y) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 x y) (/.f64 0 0)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (+.f64 x y) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)) (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) (pow.f64 (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) 2) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (+.f64 x y)) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (/.f64 (+.f64 x y) y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 x y) 0) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 x y) (.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (+.f64 x y)) 1) (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (+.f64 x y)) 2) (/.f64 (sqrt.f64 (+.f64 x y)) 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 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (/.f64 0 0)) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 2) (/.f64 (cbrt.f64 (+.f64 x y)) y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (+.f64 x y) (/.f64 0 0)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (+.f64 x y) (/.f64 0 0)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (/.f64 y (+.f64 x y))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (.f64 (+.f64 x y) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (+.f64 x y) 2) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (+.f64 x y) (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (+.f64 x y) (/.f64 0 0)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (+.f64 x y) (/.f64 0 0))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (+.f64 x y) (/.f64 0 0))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (+.f64 x y) (/.f64 0 0))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x y) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 0 0) (+.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 0 0) (*.f64 (+.f64 x y) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (+.f64 x y) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x y)) (*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)) (*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) 2) (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (+.f64 x y)) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 (+.f64 x y) y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x y) 0) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x y) (*.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 1) (*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 2) (/.f64 (sqrt.f64 (+.f64 x y)) 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 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (/.f64 0 0)) (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 2) (/.f64 (cbrt.f64 (+.f64 x y)) y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (+.f64 x y) 2) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (+.f64 x y)) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 x y) (/.f64 0 0))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))))))

simplify18.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

44×	`*-commutative`
22×	`sqr-pow`
20×	`associate-*r/`
18×	`associate-*l/`
16×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	890
1	291	890

Stop Event

1×

unsound

Counts

58 → 48

Calls

Call 1

Inputs
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))) 1)
(*.f64 (+.f64 x y) (/.f64 0 0))
(*.f64 (/.f64 0 0) (+.f64 x y))
(.f64 (/.f64 0 0) (.f64 (+.f64 x y) (/.f64 0 0)))
(.f64 (.f64 (+.f64 x y) (/.f64 0 0)) 1)
(.f64 1 (.f64 (+.f64 x y) (/.f64 0 0)))
(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)))
(.f64 (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)) (*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)))
(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))
(.f64 (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) 2))
(.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) 2) (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))
(*.f64 (neg.f64 (+.f64 x y)) (/.f64 0 0))
(*.f64 1/2 (/.f64 (+.f64 x y) y))
(*.f64 (/.f64 (+.f64 x y) 0) 0)
(.f64 (/.f64 (+.f64 x y) (.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))
(.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 1) (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)))
(*.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 2) (/.f64 (sqrt.f64 (+.f64 x y)) y))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 1) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (/.f64 0 0)) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 2) (/.f64 (cbrt.f64 (+.f64 x y)) y))
(pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 1)
(pow.f64 (*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)) 2)
(pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) 3)
(pow.f64 (pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 3) 1/3)
(pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)
(neg.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))
(sqrt.f64 (*.f64 (pow.f64 (+.f64 x y) 2) (/.f64 0 0)))
(log.f64 (pow.f64 (exp.f64 (+.f64 x y)) (/.f64 0 0)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))))
(cbrt.f64 (pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 3))
(expm1.f64 (log1p.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))
(exp.f64 (log.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 x y) (/.f64 0 0))) 1))
(log1p.f64 (expm1.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))

Outputs
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))) 1)
0
(*.f64 (+.f64 x y) (/.f64 0 0))
0
(*.f64 (/.f64 0 0) (+.f64 x y))
0
(.f64 (/.f64 0 0) (.f64 (+.f64 x y) (/.f64 0 0)))
0
(.f64 (.f64 (+.f64 x y) (/.f64 0 0)) 1)
0
(.f64 1 (.f64 (+.f64 x y) (/.f64 0 0)))
0
(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)))
(pow.f64 (*.f64 0 (sqrt.f64 (+.f64 x y))) 2)
(.f64 (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)) (*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)))
(pow.f64 (*.f64 0 (sqrt.f64 (+.f64 x y))) 2)
(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))
(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 0 (cbrt.f64 (+.f64 x y))))
(.f64 (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) 2))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 3) 0)
(.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) 2) (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 3) 0)
(*.f64 (neg.f64 (+.f64 x y)) (/.f64 0 0))
-1
(*.f64 1/2 (/.f64 (+.f64 x y) y))
(*.f64 (/.f64 (+.f64 x y) 0) 0)
0
(.f64 (/.f64 (+.f64 x y) (.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))
(*.f64 (/.f64 (/.f64 (+.f64 x y) 2) (pow.f64 y 3)) (fma.f64 y y 0))
(.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 1) (.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)))
(pow.f64 (*.f64 0 (sqrt.f64 (+.f64 x y))) 2)
(*.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 2) (/.f64 (sqrt.f64 (+.f64 x y)) y))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 1) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))
(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 0 (cbrt.f64 (+.f64 x y))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (/.f64 0 0)) (.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)))
(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 0 (cbrt.f64 (+.f64 x y))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 2) (/.f64 (cbrt.f64 (+.f64 x y)) y))
(pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 1)
0
(pow.f64 (*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 0 0)) 2)
(pow.f64 (*.f64 0 (sqrt.f64 (+.f64 x y))) 2)
(pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (/.f64 0 0)) 3)
(*.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 3) 0)
(pow.f64 (pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 3) 1/3)
0
(pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)
(/.f64 0 (*.f64 2 (/.f64 y (+.f64 x y))))
(neg.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))
-1
(sqrt.f64 (*.f64 (pow.f64 (+.f64 x y) 2) (/.f64 0 0)))
(sqrt.f64 (*.f64 0 (pow.f64 (+.f64 x y) 2)))
(log.f64 (pow.f64 (exp.f64 (+.f64 x y)) (/.f64 0 0)))
(*.f64 0 (log.f64 (exp.f64 (+.f64 x y))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (+.f64 x y) (/.f64 0 0)))))
0
(cbrt.f64 (pow.f64 (*.f64 (+.f64 x y) (/.f64 0 0)) 3))
0
(expm1.f64 (log1p.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))
0
(exp.f64 (log.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))
0
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 x y) (/.f64 0 0))) 1))
0
(log1p.f64 (expm1.f64 (*.f64 (+.f64 x y) (/.f64 0 0))))
0

eval9.0ms (0.6%)

Compiler: Compiled 483 to 282 computations (41.6% saved)

prune8.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Error

Counts

49 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	35.3b	(/.f64 (*.f64 1/2 x) y)
▶	0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	27.2b	1/2
	62.4b	-1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize13.0ms (0.9%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 1/2 x) y)

Compiler

Compiled 20 to 13 computations (35% saved)

series4.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (*.f64 1/2 x) y)
1.0ms	x	@	inf	(/.f64 (*.f64 1/2 x) y)
1.0ms	y	@	inf	(/.f64 (*.f64 1/2 x) y)
1.0ms	y	@	0	(/.f64 (*.f64 1/2 x) y)
0.0ms	x	@	-inf	(/.f64 (*.f64 1/2 x) y)

rewrite88.0ms (5.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1584×	`add-sqr-sqrt`
1564×	`*-un-lft-identity`
1466×	`add-cube-cbrt`
1448×	`add-cbrt-cube`
1434×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	147	13
2	1916	13

Stop Event

1×	node limit

Counts

1 → 41

Calls

Call 1

Inputs
(/.f64 (*.f64 1/2 x) y)

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

Outputs

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

simplify51.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1384×	`associate-+r+`
1278×	`associate-+l+`
1062×	`associate-*r/`
844×	`*-commutative`
672×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	107	1071
1	268	1023
2	1038	1023
3	4443	1023

Stop Event

1×	node limit

Counts

65 → 47

Calls

Call 1

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

Outputs
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) 1)
(*.f64 1/2 (/.f64 x y))
(.f64 1/2 (.f64 x (/.f64 1 y)))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 x y))
(*.f64 1/2 (/.f64 1 (/.f64 y x)))
(*.f64 1/2 (/.f64 x y))
(.f64 x (.f64 1/2 (/.f64 1 y)))
(*.f64 1/2 (/.f64 x y))
(.f64 (.f64 1/2 x) (/.f64 1 y))
(*.f64 1/2 (/.f64 x y))
(.f64 (.f64 1/2 (/.f64 x y)) 1)
(*.f64 1/2 (/.f64 x y))
(.f64 1 (.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(.f64 (sqrt.f64 (.f64 1/2 x)) (.f64 (sqrt.f64 (.f64 1/2 x)) (/.f64 1 y)))
(*.f64 1/2 (/.f64 x y))
(.f64 (sqrt.f64 (.f64 1/2 (/.f64 x y))) (sqrt.f64 (*.f64 1/2 (/.f64 x y))))
(*.f64 1/2 (/.f64 x y))
(.f64 (pow.f64 (cbrt.f64 (.f64 1/2 x)) 2) (.f64 (cbrt.f64 (.f64 1/2 x)) (/.f64 1 y)))
(*.f64 1/2 (/.f64 x y))
(.f64 (cbrt.f64 (.f64 1/2 (/.f64 x y))) (pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 2))
(*.f64 1/2 (/.f64 x y))
(.f64 (pow.f64 (cbrt.f64 (.f64 1/2 (/.f64 x y))) 2) (cbrt.f64 (*.f64 1/2 (/.f64 x y))))
(*.f64 1/2 (/.f64 x y))
(.f64 (/.f64 1 y) (.f64 1/2 x))
(*.f64 1/2 (/.f64 x y))
(.f64 (.f64 x -1/2) (/.f64 1 (neg.f64 y)))
(*.f64 1/2 (/.f64 x y))
(.f64 (/.f64 1 (sqrt.f64 y)) (/.f64 (.f64 1/2 x) (sqrt.f64 y)))
(*.f64 (/.f64 1 (sqrt.f64 y)) (/.f64 1/2 (/.f64 (sqrt.f64 y) x)))
(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 1/2 (sqrt.f64 y)))
(*.f64 x (/.f64 (/.f64 1/2 (sqrt.f64 y)) (sqrt.f64 y)))
(.f64 (/.f64 1 (cbrt.f64 (.f64 y y))) (/.f64 (*.f64 1/2 x) (cbrt.f64 y)))
(/.f64 (.f64 1 (/.f64 1/2 (/.f64 (cbrt.f64 y) x))) (cbrt.f64 (.f64 y y)))
(.f64 (/.f64 1/2 (cbrt.f64 (.f64 y y))) (/.f64 x (cbrt.f64 y)))
(/.f64 (.f64 1/2 (/.f64 x (cbrt.f64 y))) (cbrt.f64 (.f64 y y)))
(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 1/2 (sqrt.f64 y)))
(*.f64 (/.f64 1 (sqrt.f64 y)) (/.f64 1/2 (/.f64 (sqrt.f64 y) x)))
(*.f64 x (/.f64 (/.f64 1/2 (sqrt.f64 y)) (sqrt.f64 y)))
(*.f64 (/.f64 1/2 y) x)
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 1/2 (sqrt.f64 y)) (/.f64 x (sqrt.f64 y)))
(*.f64 (/.f64 1 (sqrt.f64 y)) (/.f64 1/2 (/.f64 (sqrt.f64 y) x)))
(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 1/2 (sqrt.f64 y)))
(*.f64 x (/.f64 (/.f64 1/2 (sqrt.f64 y)) (sqrt.f64 y)))
(.f64 (/.f64 1/2 (cbrt.f64 (.f64 y y))) (/.f64 x (cbrt.f64 y)))
(/.f64 (.f64 1 (/.f64 1/2 (/.f64 (cbrt.f64 y) x))) (cbrt.f64 (.f64 y y)))
(/.f64 (.f64 1/2 (/.f64 x (cbrt.f64 y))) (cbrt.f64 (.f64 y y)))
(*.f64 (/.f64 x 1) (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(.f64 (/.f64 x (cbrt.f64 (.f64 y y))) (/.f64 1/2 (cbrt.f64 y)))
(/.f64 (.f64 1 (/.f64 1/2 (/.f64 (cbrt.f64 y) x))) (cbrt.f64 (.f64 y y)))
(.f64 (/.f64 1/2 (cbrt.f64 (.f64 y y))) (/.f64 x (cbrt.f64 y)))
(/.f64 (.f64 1/2 (/.f64 x (cbrt.f64 y))) (cbrt.f64 (.f64 y y)))
(.f64 (/.f64 (sqrt.f64 (.f64 1/2 x)) 1) (/.f64 (sqrt.f64 (*.f64 1/2 x)) y))
(*.f64 1/2 (/.f64 x y))
(.f64 (/.f64 (sqrt.f64 (.f64 1/2 x)) (cbrt.f64 (.f64 y y))) (/.f64 (sqrt.f64 (.f64 1/2 x)) (cbrt.f64 y)))
(/.f64 (.f64 1 (/.f64 1/2 (/.f64 (cbrt.f64 y) x))) (cbrt.f64 (.f64 y y)))
(.f64 (/.f64 1/2 (cbrt.f64 (.f64 y y))) (/.f64 x (cbrt.f64 y)))
(/.f64 (.f64 1/2 (/.f64 x (cbrt.f64 y))) (cbrt.f64 (.f64 y y)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 1/2 x)) 2) 1) (/.f64 (cbrt.f64 (*.f64 1/2 x)) y))
(*.f64 1/2 (/.f64 x y))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 1/2 x)) 2) (sqrt.f64 y)) (/.f64 (cbrt.f64 (*.f64 1/2 x)) (sqrt.f64 y)))
(*.f64 (/.f64 1 (sqrt.f64 y)) (/.f64 1/2 (/.f64 (sqrt.f64 y) x)))
(*.f64 (/.f64 x (sqrt.f64 y)) (/.f64 1/2 (sqrt.f64 y)))
(*.f64 x (/.f64 (/.f64 1/2 (sqrt.f64 y)) (sqrt.f64 y)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 1/2 x)) 2) (cbrt.f64 (.f64 y y))) (cbrt.f64 (.f64 1/2 (/.f64 x y))))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 1/2 x)) 2) (cbrt.f64 (.f64 1/2 (/.f64 x y)))) (cbrt.f64 (.f64 y y)))
(.f64 (cbrt.f64 (.f64 1/2 (/.f64 x y))) (/.f64 (pow.f64 (cbrt.f64 (.f64 1/2 x)) 2) (cbrt.f64 (.f64 y y))))
(pow.f64 (*.f64 1/2 (/.f64 x y)) 1)
(*.f64 1/2 (/.f64 x y))
(pow.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)
(*.f64 1/2 (/.f64 x y))
(pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 3)
(*.f64 1/2 (/.f64 x y))
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3) 1/3)
(*.f64 1/2 (/.f64 x y))
(pow.f64 (/.f64 (/.f64 y 1/2) x) -1)
(*.f64 1/2 (/.f64 x y))
(neg.f64 (/.f64 (*.f64 1/2 x) (neg.f64 y)))
(*.f64 1/2 (/.f64 x y))
(sqrt.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 2))
(*.f64 1/2 (/.f64 x y))
(log.f64 (exp.f64 (*.f64 1/2 (/.f64 x y))))
(*.f64 1/2 (/.f64 x y))
(cbrt.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3))
(*.f64 1/2 (/.f64 x y))
(expm1.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y))))
(*.f64 1/2 (/.f64 x y))
(exp.f64 (log.f64 (*.f64 1/2 (/.f64 x y))))
(*.f64 1/2 (/.f64 x y))
(exp.f64 (.f64 (log.f64 (.f64 1/2 (/.f64 x y))) 1))
(*.f64 1/2 (/.f64 x y))
(log1p.f64 (expm1.f64 (*.f64 1/2 (/.f64 x y))))
(*.f64 1/2 (/.f64 x y))

localize6.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (*.f64 1/2 x) y)

Compiler

Compiled 13 to 8 computations (38.5% saved)

eval54.0ms (3.5%)

Compiler: Compiled 1050 to 656 computations (37.5% saved)

prune14.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	94	4	98

Error

Counts

98 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	35.3b	(/.f64 (*.f64 1/2 x) y)
✓	0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	27.2b	1/2
	62.4b	-1

Compiler

Compiled 22 to 18 computations (18.2% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

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

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	35.3b	(/.f64 (*.f64 1/2 x) y)
✓	0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	27.2b	1/2
	62.4b	-1

Compiler

Compiled 22 to 18 computations (18.2% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

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

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	35.3b	(/.f64 (*.f64 1/2 x) y)
✓	0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	27.2b	1/2
	62.4b	-1

Compiler

Compiled 22 to 18 computations (18.2% saved)

regimes13.0ms (0.9%)

Counts

5 → 1

Calls

Call 1

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

Outputs
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))

Calls

3 calls:

5.0ms	y
4.0ms	x
3.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

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

Compiler

Compiled 38 to 24 computations (36.8% saved)

regimes24.0ms (1.6%)

Counts

3 → 3

Calls

Call 1

Inputs
-1
1/2
(/.f64 (*.f64 1/2 x) y)

Outputs
1/2
(/.f64 (*.f64 1/2 x) y)
1/2

Calls

2 calls:

13.0ms	x
10.0ms	y

Results

Error	Segments	Branch
17.7b	3	`x`
12.0b	3	`y`

Compiler

Compiled 15 to 11 computations (26.7% saved)

bsearch43.0ms (2.8%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
13.0ms	7.150189468666401e-20	4.371705542813904e-16
30.0ms	-7.517856632164755e-12	-2.0628342210571377e-20

Results

39.0ms	272×	body	256	valid
0.0ms	2×	body	256	infinite

Compiler

Compiled 218 to 179 computations (17.9% saved)

regimes8.0ms (0.5%)

Accuracy

Total -36.0b remaining (-132.4%)

Threshold costs -36.0b (-132.4%)

Counts

2 → 1

Calls

Call 1

Inputs
-1
1/2

Outputs
1/2

Calls

2 calls:

3.0ms	y
3.0ms	x

Results

Error	Segments	Branch
27.2b	1	`x`
27.2b	1	`y`

Compiler

Compiled 10 to 8 computations (20% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative`
2×	`if-if-or-not`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	54
1	25	54

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(if (<=.f64 y -8473828473128839/332306998946228968225951765070086144) 1/2 (if (<=.f64 y 5981525981032121/83076749736557242056487941267521536) (/.f64 (*.f64 1/2 x) y) 1/2))
1/2
-1

Outputs
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(if (<=.f64 y -8473828473128839/332306998946228968225951765070086144) 1/2 (if (<=.f64 y 5981525981032121/83076749736557242056487941267521536) (/.f64 (*.f64 1/2 x) y) 1/2))
1/2
-1

Compiler

Compiled 32 to 26 computations (18.8% saved)

soundness17.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

44×	`*-commutative`
22×	`sqr-pow`
20×	`associate-*r/`
18×	`associate-*l/`
16×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	890
1	291	890

Stop Event

1×

unsound

Compiler

Compiled 16 to 12 computations (25% saved)

end27.0ms (1.7%)

Compiler: Compiled 26 to 20 computations (23.1% saved)

Details

analyze69.0ms (4.5%)

sample961.0ms (63.2%)

preprocess7.0ms (0.5%)

simplify12.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.4%)

series3.0ms (0.2%)

rewrite57.0ms (3.7%)

simplify18.0ms (1.2%)

eval9.0ms (0.6%)

prune8.0ms (0.5%)

localize13.0ms (0.9%)

series4.0ms (0.2%)

rewrite88.0ms (5.8%)

simplify51.0ms (3.4%)

localize6.0ms (0.4%)

eval54.0ms (3.5%)

prune14.0ms (0.9%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes13.0ms (0.9%)

regimes24.0ms (1.6%)

bsearch43.0ms (2.8%)

regimes8.0ms (0.5%)

simplify5.0ms (0.3%)

soundness17.0ms (1.1%)

end27.0ms (1.7%)

Profiling