Details

analyze116.0ms (6.4%)

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)

sample1.2s (64.4%)

Results

1.1s	8256×	body	256	valid
55.0ms	432×	body	256	infinite

Bogosity

preprocess5.0ms (0.3%)

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)

simplify13.0ms (0.7%)

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

0.01%

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.01%	(/.f64 (+.f64 x y) (+.f64 y y))

Compiler

Compiled 9 to 5 computations (44.4% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.01%	(/.f64 (+.f64 x y) (+.f64 y y))

Compiler

Compiled 17 to 5 computations (70.6% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite90.0ms (5%)

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))))))))

simplify19.0ms (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

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 (0.5%)

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

prune7.0ms (0.4%)

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
▶	55.44%	(/.f64 (*.f64 1/2 x) y)
▶	0%	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	44.09%	1/2
	97.45%	-1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize8.0ms (0.4%)

Compiler: Compiled 20 to 13 computations (35% saved)

localize31.0ms (1.8%)

Compiler: Compiled 13 to 8 computations (38.5% 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	1	1
Done	1	1
Total	4	4

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	55.44%	(/.f64 (*.f64 1/2 x) y)
✓	0%	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	44.09%	1/2
	97.45%	-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
✓	55.44%	(/.f64 (*.f64 1/2 x) y)
✓	0%	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	44.09%	1/2
	97.45%	-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
✓	55.44%	(/.f64 (*.f64 1/2 x) y)
✓	0%	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	44.09%	1/2
	97.45%	-1

Compiler

Compiled 22 to 18 computations (18.2% saved)

regimes46.0ms (2.6%)

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:

37.0ms	y
4.0ms	x
3.0ms	(/.f64 (+.f64 x y) (+.f64 y y))

Results

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

Compiler

Compiled 38 to 24 computations (36.8% saved)

regimes60.0ms (3.3%)

Counts

3 → 7

Calls

Call 1

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

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

Calls

2 calls:

46.0ms	x
13.0ms	y

Results

Error	Segments	Branch
24.57%	7	`x`
26.55%	3	`y`

Compiler

Compiled 15 to 11 computations (26.7% saved)

bsearch70.0ms (3.9%)

Algorithm

6×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.0926898793757327e+120	1.544867553080983e+123
14.0ms	2.6822701866798318e+20	6.029097742767463e+23
5.0ms	9.292661732659066e-70	1.2349979784433808e-69
12.0ms	-5.362972718797129e-109	-7.805673419949276e-111
13.0ms	-3.0503359942137826e-99	-2.4262563222483245e-101
12.0ms	-7.304386560435108e-11	-7.403496726869021e-15

Results

60.0ms	656×	body	256	valid
2.0ms	19×	body	256	infinite

Compiler

Compiled 506 to 419 computations (17.2% saved)

regimes45.0ms (2.5%)

Accuracy

Total -34.9b remaining (-123.7%)

Threshold costs -34.9b (-123.7%)

Counts

2 → 1

Calls

Call 1

Inputs
-1
1/2

Outputs
1/2

Calls

2 calls:

41.0ms	y
3.0ms	x

Results

Error	Segments	Branch
44.09%	1	`x`
44.09%	1	`y`

Compiler

Compiled 10 to 8 computations (20% saved)

simplify10.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

16×	`not-or`
14×	`not-not`
14×	`if-not`
10×	`if-if-or-not`
6×	`not-and`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	30	124
1	37	124
2	40	124
3	46	120
4	53	120
5	63	116
6	70	116
7	75	116
8	77	116
9	78	116

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(if (<=.f64 x -5694524180712749/4951760157141521099596496896) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x -492525077454931/19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408) 1/2 (if (<=.f64 x -1374996415083717/2644223875160994395807661232131084159313618731857124877138595181097623164945245383300756841758861139390364848100093433217024) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x 2331202670670875/1942668892225729070919461906823518906642406839052139521251812409738904285205208498176) 1/2 (if (<=.f64 x 1100000000000000000000) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x 1100000000000000064010013281761302985241469286014969649878700236824391796249753075020876231741171986355949424328897986560) 1/2 (/.f64 (.f64 1/2 x) y)))))))
1/2
-1

Outputs
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(if (<=.f64 x -5694524180712749/4951760157141521099596496896) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x -492525077454931/19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408) 1/2 (if (<=.f64 x -1374996415083717/2644223875160994395807661232131084159313618731857124877138595181097623164945245383300756841758861139390364848100093433217024) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x 2331202670670875/1942668892225729070919461906823518906642406839052139521251812409738904285205208498176) 1/2 (if (<=.f64 x 1100000000000000000000) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x 1100000000000000064010013281761302985241469286014969649878700236824391796249753075020876231741171986355949424328897986560) 1/2 (/.f64 (.f64 1/2 x) y)))))))
(if (<=.f64 x -5694524180712749/4951760157141521099596496896) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x -492525077454931/19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408) 1/2 (if (<=.f64 x -1374996415083717/2644223875160994395807661232131084159313618731857124877138595181097623164945245383300756841758861139390364848100093433217024) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x 2331202670670875/1942668892225729070919461906823518906642406839052139521251812409738904285205208498176) 1/2 (if (or (<=.f64 x 1100000000000000000000) (not (<=.f64 x 1100000000000000064010013281761302985241469286014969649878700236824391796249753075020876231741171986355949424328897986560))) (/.f64 (*.f64 1/2 x) y) 1/2)))))
(if (<=.f64 x -5694524180712749/4951760157141521099596496896) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x -492525077454931/19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408) 1/2 (if (or (<=.f64 x -1374996415083717/2644223875160994395807661232131084159313618731857124877138595181097623164945245383300756841758861139390364848100093433217024) (not (or (<=.f64 x 2331202670670875/1942668892225729070919461906823518906642406839052139521251812409738904285205208498176) (and (not (<=.f64 x 1100000000000000000000)) (<=.f64 x 1100000000000000064010013281761302985241469286014969649878700236824391796249753075020876231741171986355949424328897986560))))) (/.f64 (.f64 1/2 x) y) 1/2)))
(if (<=.f64 x -5694524180712749/4951760157141521099596496896) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x -492525077454931/19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408) 1/2 (if (or (<=.f64 x -1374996415083717/2644223875160994395807661232131084159313618731857124877138595181097623164945245383300756841758861139390364848100093433217024) (and (not (<=.f64 x 2331202670670875/1942668892225729070919461906823518906642406839052139521251812409738904285205208498176)) (or (<=.f64 x 1100000000000000000000) (not (<=.f64 x 1100000000000000064010013281761302985241469286014969649878700236824391796249753075020876231741171986355949424328897986560))))) (/.f64 (.f64 1/2 x) y) 1/2)))
(if (or (<=.f64 x -5694524180712749/4951760157141521099596496896) (not (or (<=.f64 x -492525077454931/19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408) (and (not (<=.f64 x -1374996415083717/2644223875160994395807661232131084159313618731857124877138595181097623164945245383300756841758861139390364848100093433217024)) (or (<=.f64 x 2331202670670875/1942668892225729070919461906823518906642406839052139521251812409738904285205208498176) (and (not (<=.f64 x 1100000000000000000000)) (<=.f64 x 1100000000000000064010013281761302985241469286014969649878700236824391796249753075020876231741171986355949424328897986560))))))) (/.f64 (*.f64 1/2 x) y) 1/2)
(if (or (<=.f64 x -5694524180712749/4951760157141521099596496896) (and (not (<=.f64 x -492525077454931/19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408)) (or (<=.f64 x -1374996415083717/2644223875160994395807661232131084159313618731857124877138595181097623164945245383300756841758861139390364848100093433217024) (and (not (<=.f64 x 2331202670670875/1942668892225729070919461906823518906642406839052139521251812409738904285205208498176)) (or (<=.f64 x 1100000000000000000000) (not (<=.f64 x 1100000000000000064010013281761302985241469286014969649878700236824391796249753075020876231741171986355949424328897986560))))))) (/.f64 (*.f64 1/2 x) y) 1/2)
1/2
-1

Compiler

Compiled 50 to 40 computations (20% saved)

soundness28.0ms (1.5%)

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)

end69.0ms (3.9%)

Compiler: Compiled 44 to 34 computations (22.7% saved)

Iter	Nodes	Cost
0	30	124
1	37	124
2	40	124
3	46	120
4	53	120
5	63	116
6	70	116
7	75	116
8	77	116
9	78	116

Iter	Nodes	Cost
0	30	124
1	37	124
2	40	124
3	46	120
4	53	120
5	63	116
6	70	116
7	75	116
8	77	116
9	78	116

Details

analyze116.0ms (6.4%)

sample1.2s (64.4%)

preprocess5.0ms (0.3%)

simplify13.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.3%)

series3.0ms (0.1%)

rewrite90.0ms (5%)

simplify19.0ms (1.1%)

eval9.0ms (0.5%)

prune7.0ms (0.4%)

localize8.0ms (0.4%)

localize31.0ms (1.8%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes46.0ms (2.6%)

regimes60.0ms (3.3%)

bsearch70.0ms (3.9%)

regimes45.0ms (2.5%)

simplify10.0ms (0.5%)

soundness28.0ms (1.5%)

end69.0ms (3.9%)

Profiling

Iter	Nodes	Cost
0	30	124
1	37	124
2	40	124
3	46	120
4	53	120
5	63	116
6	70	116
7	75	116
8	77	116
9	78	116