Details

analyze80.0ms (4.7%)

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)

sample1.1s (66.1%)

Results

1.0s	8256×	body	256	valid
84.0ms	384×	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)

simplify11.0ms (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)

prune2.0ms (0.1%)

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)

localize5.0ms (0.3%)

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
0.0ms	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))

rewrite79.0ms (4.7%)

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))))))))

simplify20.0ms (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

eval7.0ms (0.4%)

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
▶	35.7b	(/.f64 (*.f64 1/2 x) y)
▶	0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	27.6b	1/2
	62.5b	-1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize8.0ms (0.4%)

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

localize32.0ms (1.9%)

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
✓	35.7b	(/.f64 (*.f64 1/2 x) y)
✓	0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	27.6b	1/2
	62.5b	-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
✓	35.7b	(/.f64 (*.f64 1/2 x) y)
✓	0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	27.6b	1/2
	62.5b	-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
✓	35.7b	(/.f64 (*.f64 1/2 x) y)
✓	0b	(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
	27.6b	1/2
	62.5b	-1

Compiler

Compiled 22 to 18 computations (18.2% saved)

regimes15.0ms (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:

7.0ms	x
4.0ms	y
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)

regimes43.0ms (2.5%)

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:

21.0ms	y
20.0ms	x

Results

Error	Segments	Branch
13.6b	7	`x`
14.1b	7	`y`

Compiler

Compiled 15 to 11 computations (26.7% saved)

bsearch131.0ms (7.8%)

Algorithm

6×	binary-search

Steps

Time	Left	Right
40.0ms	4.3023224185163794e+33	1.5143553461023177e+46
3.0ms	1.9098212148262624e-8	2.2102729018809143e-8
31.0ms	1.525100029024799e-26	2.0360982254901208e-23
13.0ms	-4.601039712291361e-120	-3.145841034706576e-126
10.0ms	-9.457262009716957e-33	-5.892144329547457e-35
34.0ms	-3.3059953004713175e+146	-9.617899223066447e+133

Results

95.0ms	736×	body	256	valid
27.0ms	26×	body	256	infinite

Compiler

Compiled 566 to 469 computations (17.1% saved)

regimes7.0ms (0.4%)

Accuracy

Total -35.6b remaining (-129%)

Threshold costs -35.6b (-129%)

Counts

2 → 1

Calls

Call 1

Inputs
-1
1/2

Outputs
1/2

Calls

2 calls:

3.0ms	x
3.0ms	y

Results

Error	Segments	Branch
27.6b	1	`x`
27.6b	1	`y`

Compiler

Compiled 10 to 8 computations (20% saved)

simplify9.0ms (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 -609999999999999978330017587311431185238983037630721363837762635825875941993112069150381706960928428468436742444210708013139351926996992) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x -5799238496929023/93536104789177786765035829293842113257979682750464) 1/2 (if (<=.f64 x -3270774259330231/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x 8711228593176025/2722258935367507707706996859454145691648) 1/2 (if (<=.f64 x 3022314549036573/151115727451828646838272) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x 68000000000000001113715910357104459776) 1/2 (/.f64 (.f64 1/2 x) y)))))))
1/2
-1

Outputs
(+.f64 1/2 (/.f64 (*.f64 1/2 x) y))
(if (<=.f64 x -609999999999999978330017587311431185238983037630721363837762635825875941993112069150381706960928428468436742444210708013139351926996992) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x -5799238496929023/93536104789177786765035829293842113257979682750464) 1/2 (if (<=.f64 x -3270774259330231/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x 8711228593176025/2722258935367507707706996859454145691648) 1/2 (if (<=.f64 x 3022314549036573/151115727451828646838272) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x 68000000000000001113715910357104459776) 1/2 (/.f64 (.f64 1/2 x) y)))))))
(if (<=.f64 x -609999999999999978330017587311431185238983037630721363837762635825875941993112069150381706960928428468436742444210708013139351926996992) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x -5799238496929023/93536104789177786765035829293842113257979682750464) 1/2 (if (<=.f64 x -3270774259330231/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x 8711228593176025/2722258935367507707706996859454145691648) 1/2 (if (or (<=.f64 x 3022314549036573/151115727451828646838272) (not (<=.f64 x 68000000000000001113715910357104459776))) (/.f64 (*.f64 1/2 x) y) 1/2)))))
(if (<=.f64 x -609999999999999978330017587311431185238983037630721363837762635825875941993112069150381706960928428468436742444210708013139351926996992) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x -5799238496929023/93536104789177786765035829293842113257979682750464) 1/2 (if (or (<=.f64 x -3270774259330231/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (not (or (<=.f64 x 8711228593176025/2722258935367507707706996859454145691648) (and (not (<=.f64 x 3022314549036573/151115727451828646838272)) (<=.f64 x 68000000000000001113715910357104459776))))) (/.f64 (.f64 1/2 x) y) 1/2)))
(if (<=.f64 x -609999999999999978330017587311431185238983037630721363837762635825875941993112069150381706960928428468436742444210708013139351926996992) (/.f64 (.f64 1/2 x) y) (if (<=.f64 x -5799238496929023/93536104789177786765035829293842113257979682750464) 1/2 (if (or (<=.f64 x -3270774259330231/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (and (not (<=.f64 x 8711228593176025/2722258935367507707706996859454145691648)) (or (<=.f64 x 3022314549036573/151115727451828646838272) (not (<=.f64 x 68000000000000001113715910357104459776))))) (/.f64 (.f64 1/2 x) y) 1/2)))
(if (or (<=.f64 x -609999999999999978330017587311431185238983037630721363837762635825875941993112069150381706960928428468436742444210708013139351926996992) (not (or (<=.f64 x -5799238496929023/93536104789177786765035829293842113257979682750464) (and (not (<=.f64 x -3270774259330231/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656)) (or (<=.f64 x 8711228593176025/2722258935367507707706996859454145691648) (and (not (<=.f64 x 3022314549036573/151115727451828646838272)) (<=.f64 x 68000000000000001113715910357104459776))))))) (/.f64 (*.f64 1/2 x) y) 1/2)
(if (or (<=.f64 x -609999999999999978330017587311431185238983037630721363837762635825875941993112069150381706960928428468436742444210708013139351926996992) (and (not (<=.f64 x -5799238496929023/93536104789177786765035829293842113257979682750464)) (or (<=.f64 x -3270774259330231/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (and (not (<=.f64 x 8711228593176025/2722258935367507707706996859454145691648)) (or (<=.f64 x 3022314549036573/151115727451828646838272) (not (<=.f64 x 68000000000000001113715910357104459776))))))) (/.f64 (*.f64 1/2 x) y) 1/2)
1/2
-1

Compiler

Compiled 50 to 40 computations (20% saved)

soundness39.0ms (2.3%)

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)

end65.0ms (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

analyze80.0ms (4.7%)

sample1.1s (66.1%)

preprocess5.0ms (0.3%)

simplify11.0ms (0.7%)

eval0.0ms (0%)

prune2.0ms (0.1%)

localize5.0ms (0.3%)

series3.0ms (0.2%)

rewrite79.0ms (4.7%)

simplify20.0ms (1.2%)

eval7.0ms (0.4%)

prune7.0ms (0.4%)

localize8.0ms (0.4%)

localize32.0ms (1.9%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes15.0ms (0.9%)

regimes43.0ms (2.5%)

bsearch131.0ms (7.8%)

regimes7.0ms (0.4%)

simplify9.0ms (0.5%)

soundness39.0ms (2.3%)

end65.0ms (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