Details

analyze70.0ms (3.2%)

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 (51%)

Results

1.0s	8256×	body	256	valid
68.0ms	385×	body	256	infinite

Bogosity

preprocess16.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

4×	`associate-/r*_binary64`
2×	`*-commutative_binary64`
2×	`count-2_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	13	20
2	18	20
3	22	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`associate-/r*_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`count-2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	12	10
3	14	10

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)

localize30.0ms (1.4%)

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)

series4.0ms (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))
1.0ms	x	@	-inf	(/.f64 (+.f64 x y) (+.f64 y y))

rewrite43.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

803×	`pow1_binary64`
753×	`add-log-exp_binary64`
752×	`log1p-expm1-u_binary64`
752×	`expm1-log1p-u_binary64`
737×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	142	10
2	2378	10

Stop Event

1×	node limit

Counts

1 → 33

Calls

Call 1

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

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

Outputs

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

simplify169.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

355×	`times-frac_binary64`
331×	`distribute-rgt-out_binary64`
310×	`log-prod_binary64`
309×	`distribute-rgt-in_binary64`
289×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	695
1	232	588
2	997	525
3	4731	525

Stop Event

1×	node limit

Counts

57 → 59

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

Outputs
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
1/2
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(fma.f64 1/2 (/.f64 x y) 1/2)
(-.f64 (+.f64 1 (*.f64 (+.f64 x y) (+.f64 y y))) 1)
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(*.f64 (+.f64 x y) (+.f64 y y))
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(*.f64 (+.f64 y y) (+.f64 x y))
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(.f64 (+.f64 y y) (.f64 (+.f64 x y) (+.f64 y y)))
(.f64 (+.f64 x y) (.f64 (*.f64 y y) 4))
(.f64 y (.f64 (+.f64 x y) (*.f64 y 4)))
(.f64 (.f64 (+.f64 x y) (+.f64 y y)) 1)
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(.f64 1 (.f64 (+.f64 x y) (+.f64 y y)))
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(.f64 (.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)) (pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)) 2))
(pow.f64 (*.f64 (+.f64 y y) (cbrt.f64 (+.f64 x y))) 3)
(.f64 (+.f64 x y) (.f64 8 (pow.f64 y 3)))
(.f64 (+.f64 x y) (.f64 (pow.f64 y 3) 8))
(.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)) 2) (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)))
(pow.f64 (*.f64 (+.f64 y y) (cbrt.f64 (+.f64 x y))) 3)
(.f64 (+.f64 x y) (.f64 8 (pow.f64 y 3)))
(.f64 (+.f64 x y) (.f64 (pow.f64 y 3) 8))
(.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)))
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(.f64 (sqrt.f64 (.f64 (+.f64 x y) (+.f64 y y))) (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 y y))))
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(.f64 (sqrt.f64 (+.f64 x y)) (sqrt.f64 (.f64 (+.f64 x y) (+.f64 y y))))
(.f64 (sqrt.f64 (.f64 (+.f64 x y) (+.f64 y y))) (sqrt.f64 (+.f64 x y)))
(.f64 (sqrt.f64 (.f64 y (*.f64 (+.f64 x y) 2))) (sqrt.f64 (+.f64 x y)))
(*.f64 (sqrt.f64 (/.f64 (+.f64 x y) (/.f64 1/2 y))) (sqrt.f64 (+.f64 x y)))
(*.f64 (neg.f64 (+.f64 x y)) (+.f64 y y))
(*.f64 (+.f64 x y) (neg.f64 (+.f64 y y)))
(.f64 (+.f64 x y) (.f64 -2 y))
(.f64 (+.f64 x y) (.f64 y -2))
(.f64 y (.f64 (+.f64 x y) -2))
(*.f64 1/2 (/.f64 (+.f64 x y) y))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 1) (.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)))
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 1) (sqrt.f64 (.f64 (+.f64 x y) (+.f64 y y))))
(.f64 (sqrt.f64 (.f64 (+.f64 x y) (+.f64 y y))) (sqrt.f64 (+.f64 x y)))
(.f64 (sqrt.f64 (.f64 y (*.f64 (+.f64 x y) 2))) (sqrt.f64 (+.f64 x y)))
(*.f64 (sqrt.f64 (/.f64 (+.f64 x y) (/.f64 1/2 y))) (sqrt.f64 (+.f64 x y)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (+.f64 y y)) (.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)))
(.f64 (.f64 (+.f64 y y) (cbrt.f64 (+.f64 x y))) (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) (+.f64 y y)))
(*.f64 (/.f64 (+.f64 x y) 2) (/.f64 (+.f64 y y) y))
(+.f64 x y)
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x y)) 2) 2) (/.f64 (cbrt.f64 (+.f64 x y)) y))
(*.f64 1/2 (/.f64 (+.f64 x y) y))
(*.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 2) (/.f64 (sqrt.f64 (+.f64 x y)) y))
(*.f64 1/2 (/.f64 (+.f64 x y) y))
(.f64 (/.f64 (+.f64 x y) (.f64 2 (pow.f64 y 3))) (fma.f64 y y 0))
(*.f64 1/2 (/.f64 (+.f64 x y) y))
(*.f64 (/.f64 (+.f64 x y) 0) 0)
0
(pow.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1)
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(pow.f64 (pow.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 3) 1/3)
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(pow.f64 (*.f64 (cbrt.f64 (+.f64 x y)) (+.f64 y y)) 3)
(pow.f64 (*.f64 (+.f64 y y) (cbrt.f64 (+.f64 x y))) 3)
(.f64 (+.f64 x y) (.f64 8 (pow.f64 y 3)))
(.f64 (+.f64 x y) (.f64 (pow.f64 y 3) 8))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 x y) (+.f64 y y))) 2)
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(pow.f64 (*.f64 2 (/.f64 y (+.f64 x y))) -1)
(*.f64 1/2 (/.f64 (+.f64 x y) y))
(neg.f64 (*.f64 (+.f64 x y) (+.f64 y y)))
(*.f64 (+.f64 x y) (neg.f64 (+.f64 y y)))
(.f64 (+.f64 x y) (.f64 -2 y))
(.f64 (+.f64 x y) (.f64 y -2))
(.f64 y (.f64 (+.f64 x y) -2))
(sqrt.f64 (*.f64 (pow.f64 (+.f64 x y) 2) (+.f64 y y)))
(sqrt.f64 (*.f64 (+.f64 y y) (pow.f64 (+.f64 x y) 2)))
(sqrt.f64 (.f64 y (.f64 2 (pow.f64 (+.f64 x y) 2))))
(log.f64 (pow.f64 (exp.f64 (+.f64 x y)) (+.f64 y y)))
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(cbrt.f64 (pow.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 3))
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(cbrt.f64 (/.f64 (pow.f64 (+.f64 x y) 3) (+.f64 y y)))
(expm1.f64 (log1p.f64 (*.f64 (+.f64 x y) (+.f64 y y))))
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(log1p.f64 (expm1.f64 (*.f64 (+.f64 x y) (+.f64 y y))))
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))
(exp.f64 (log.f64 (*.f64 (+.f64 x y) (+.f64 y y))))
(+.f64 1 (-.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 1))
(+.f64 (*.f64 (+.f64 x y) (+.f64 y y)) 0)
(.f64 y (.f64 (+.f64 x y) 2))
(/.f64 (+.f64 x y) (/.f64 1/2 y))

eval10.0ms (0.5%)

Compiler: Compiled 598 to 190 computations (68.2% saved)

prune11.0ms (0.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	54	5	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	5	60

Error

Counts

60 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	61.7b	(+.f64 x y)
▶	0b	(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
▶	36.8b	(*.f64 1/2 (/.f64 x y))
	27.3b	1/2
	62.2b	0

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 13 to 6 computations (53.8% saved)

series4.0ms (0.2%)

Counts

1 → 0

Calls

6 calls:

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

rewrite43.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

653×	`pow1_binary64`
606×	`add-log-exp_binary64`
606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
594×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	127	7
2	1609	7

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(*.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 y x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 y (.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 1/2 x) y)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 1/2 x)) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 1/2 x) 1) y)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 1/2 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 1/2 x) (sqrt.f64 y)) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (neg.f64 x) 1/2) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 1/2 (neg.f64 x)) (neg.f64 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 (pow.f64 (.f64 1/2 (/.f64 x y)) 3) 1/3)))) (#(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 (sqrt.f64 (.f64 1/2 (/.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (/.f64 x y) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.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 log1p.f64 (expm1.f64 (.f64 1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.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 y x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 y (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 x) y)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 1/2 x)) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 1/2 x) 1) y)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 1/2 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 1/2 x) (sqrt.f64 y)) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 x) 1/2) (neg.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1/2 (neg.f64 x)) (neg.f64 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 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3) 1/3)))) (#(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 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.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 log1p.f64 (expm1.f64 (*.f64 1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/2 (/.f64 x y))))))))

simplify33.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

701×	`log-prod_binary64`
583×	`fma-def_binary64`
436×	`associate-l_binary64`
397×	`associate-r_binary64`
322×	`log-div_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	56	260
1	142	200
2	511	140
3	3974	140

Stop Event

1×	node limit

Counts

20 → 23

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) 1)
(/.f64 1/2 (/.f64 y x))
(/.f64 1 (/.f64 y (*.f64 1/2 x)))
(/.f64 (*.f64 1/2 x) y)
(/.f64 (neg.f64 (*.f64 1/2 x)) (neg.f64 y))
(/.f64 (/.f64 (*.f64 1/2 x) 1) y)
(/.f64 (/.f64 (*.f64 1/2 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))
(/.f64 (/.f64 (*.f64 1/2 x) (sqrt.f64 y)) (sqrt.f64 y))
(/.f64 (*.f64 (neg.f64 x) 1/2) (neg.f64 y))
(/.f64 (*.f64 1/2 (neg.f64 x)) (neg.f64 y))
(pow.f64 (*.f64 1/2 (/.f64 x y)) 1)
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 3)
(pow.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)
(sqrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))
(log.f64 (pow.f64 (exp.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))))
(log1p.f64 (expm1.f64 (*.f64 1/2 (/.f64 x y))))
(exp.f64 (log.f64 (*.f64 1/2 (/.f64 x y))))

Outputs
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) 1)
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(/.f64 1/2 (/.f64 y x))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(/.f64 1 (/.f64 y (*.f64 1/2 x)))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(/.f64 (neg.f64 (*.f64 1/2 x)) (neg.f64 y))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(/.f64 (/.f64 (*.f64 1/2 x) 1) y)
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(/.f64 (/.f64 (*.f64 1/2 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(/.f64 (/.f64 (*.f64 1/2 x) (sqrt.f64 y)) (sqrt.f64 y))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 (neg.f64 x) 1/2) (neg.f64 y))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 (neg.f64 x)) (neg.f64 y))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(pow.f64 (*.f64 1/2 (/.f64 x y)) 1)
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3) 1/3)
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 3)
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(pow.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(log.f64 (pow.f64 (exp.f64 1/2) (/.f64 x y)))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(cbrt.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(expm1.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y))))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(log1p.f64 (expm1.f64 (*.f64 1/2 (/.f64 x y))))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))
(exp.f64 (log.f64 (*.f64 1/2 (/.f64 x y))))
(+.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) -1)
(+.f64 (*.f64 1/2 (/.f64 x y)) 0)
(*.f64 1/2 (/.f64 x y))

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 10 computations (50% saved)

localize3.0ms (0.1%)

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

eval9.0ms (0.4%)

Compiler: Compiled 390 to 252 computations (35.4% saved)

prune35.0ms (1.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	45	6	51

Error

Counts

51 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	36.9b	(/.f64 1/2 (/.f64 y x))
✓	61.7b	(+.f64 x y)
✓	0b	(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
✓	36.8b	(*.f64 1/2 (/.f64 x y))
	27.3b	1/2
	62.2b	0

Compiler

Compiled 34 to 26 computations (23.5% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1/2 (/.f64 y x))

Compiler

Compiled 13 to 6 computations (53.8% saved)

series1.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite67.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

699×	`pow1_binary64`
652×	`add-log-exp_binary64`
652×	`log1p-expm1-u_binary64`
652×	`expm1-log1p-u_binary64`
639×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	134	7
2	1770	7

Stop Event

1×	node limit

Counts

1 → 26

Calls

Call 1

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

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 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1/2 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 (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 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) (sqrt.f64 (*.f64 1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (/.f64 1 (/.f64 (neg.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 y) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (neg.f64 y)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1/2 y) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1/2 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1/2 y) (sqrt.f64 x)) (sqrt.f64 x))))) (#(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 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3) 1/3)))) (#(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 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 y x) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.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 log1p.f64 (expm1.f64 (*.f64 1/2 (/.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/2 (/.f64 x y))))))))

simplify34.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

423×	`associate-/r*_binary64`
391×	`fma-def_binary64`
390×	`associate-/l/_binary64`
369×	`distribute-rgt-in_binary64`
341×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	355
1	158	355
2	583	355
3	2453	352

Stop Event

1×	node limit

Counts

50 → 29

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 y))
(*.f64 x (/.f64 1/2 y))
(.f64 (.f64 1/2 (/.f64 x y)) 1)
(.f64 1 (.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 (pow.f64 (cbrt.f64 (.f64 1/2 (/.f64 x y))) 2) (cbrt.f64 (*.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 1 (/.f64 (neg.f64 y) x)))
(*.f64 (/.f64 x y) 1/2)
(*.f64 (/.f64 1/2 y) x)
(*.f64 (/.f64 1/2 (neg.f64 y)) (neg.f64 x))
(.f64 (.f64 (/.f64 1/2 y) 1) x)
(.f64 (.f64 (/.f64 1/2 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 (.f64 (/.f64 1/2 y) (sqrt.f64 x)) (sqrt.f64 x))
(pow.f64 (*.f64 1/2 (/.f64 x y)) 1)
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3) 1/3)
(pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 3)
(pow.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)
(pow.f64 (*.f64 (/.f64 y x) 2) -1)
(sqrt.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)))
(log.f64 (pow.f64 (exp.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))))
(log1p.f64 (expm1.f64 (*.f64 1/2 (/.f64 x y))))
(exp.f64 (log.f64 (*.f64 1/2 (/.f64 x y))))

Outputs
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(-.f64 (+.f64 1 (*.f64 1/2 (/.f64 x y))) 1)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 x (/.f64 1/2 y))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(.f64 (.f64 1/2 (/.f64 x y)) 1)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(.f64 1 (.f64 1/2 (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 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 (*.f64 1/2 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 1/2 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 (*.f64 1/2 x) y)
(*.f64 -1/2 (/.f64 1 (/.f64 (neg.f64 y) x)))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 (/.f64 x y) 1/2)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 (/.f64 1/2 y) x)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(*.f64 (/.f64 1/2 (neg.f64 y)) (neg.f64 x))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(.f64 (.f64 (/.f64 1/2 y) 1) x)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(.f64 (.f64 (/.f64 1/2 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(.f64 (.f64 (/.f64 1/2 y) (sqrt.f64 x)) (sqrt.f64 x))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(pow.f64 (*.f64 1/2 (/.f64 x y)) 1)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(pow.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3) 1/3)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(pow.f64 (cbrt.f64 (*.f64 1/2 (/.f64 x y))) 3)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(pow.f64 (sqrt.f64 (*.f64 1/2 (/.f64 x y))) 2)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(pow.f64 (*.f64 (/.f64 y x) 2) -1)
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(sqrt.f64 (/.f64 1/4 (pow.f64 (/.f64 y x) 2)))
(sqrt.f64 (pow.f64 (/.f64 (*.f64 1/2 x) y) 2))
(fabs.f64 (/.f64 (*.f64 1/2 x) y))
(log.f64 (pow.f64 (exp.f64 1/2) (/.f64 x y)))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(cbrt.f64 (pow.f64 (*.f64 1/2 (/.f64 x y)) 3))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(expm1.f64 (log1p.f64 (*.f64 1/2 (/.f64 x y))))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(log1p.f64 (expm1.f64 (*.f64 1/2 (/.f64 x y))))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)
(exp.f64 (log.f64 (*.f64 1/2 (/.f64 x y))))
(*.f64 1/2 (/.f64 x y))
(/.f64 (*.f64 1/2 x) y)

eval5.0ms (0.2%)

Compiler: Compiled 232 to 143 computations (38.4% saved)

prune33.0ms (1.5%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	28	7	35

Error

Counts

35 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	36.9b	(/.f64 1/2 (/.f64 y x))
✓	61.7b	(+.f64 x y)
✓	0b	(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
▶	36.9b	(*.f64 (/.f64 1/2 y) x)
✓	36.8b	(*.f64 1/2 (/.f64 x y))
	27.3b	1/2
	62.2b	0

Compiler

Compiled 41 to 31 computations (24.4% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1/2 y) x)

Compiler

Compiled 13 to 8 computations (38.5% saved)

series1.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite68.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

617×	`pow1_binary64`
573×	`add-log-exp_binary64`
573×	`log1p-expm1-u_binary64`
573×	`expm1-log1p-u_binary64`
562×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1560	7

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

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

simplify37.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

691×	`log-prod_binary64`
427×	`associate-l_binary64`
401×	`associate-r_binary64`
355×	`distribute-rgt-neg-out_binary64`
317×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	315
1	138	315
2	492	315
3	3887	315

Stop Event

1×	node limit

Counts

45 → 24

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

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

eval4.0ms (0.2%)

Compiler: Compiled 170 to 106 computations (37.6% saved)

prune5.0ms (0.3%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	2	2
Picked	0	1	1
Done	0	4	4
Total	24	7	31

Error

Counts

31 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	36.9b	(/.f64 1/2 (/.f64 y x))
✓	61.7b	(+.f64 x y)
✓	0b	(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
✓	36.9b	(*.f64 (/.f64 1/2 y) x)
✓	36.8b	(*.f64 1/2 (/.f64 x y))
	27.3b	1/2
	62.2b	0

Compiler

Compiled 41 to 31 computations (24.4% saved)

regimes45.0ms (2.1%)

Counts

8 → 1

Calls

Call 1

Inputs
0
1/2
(+.f64 x y)
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 1/2 y) x)
(/.f64 1/2 (/.f64 y x))
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(/.f64 (+.f64 x y) (+.f64 y y))

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

Calls

4 calls:

28.0ms	(/.f64 (+.f64 x y) (+.f64 y y))
7.0ms	x
5.0ms	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))`
0b	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 60 to 34 computations (43.3% saved)

regimes84.0ms (3.9%)

Counts

6 → 5

Calls

Call 1

Inputs
0
1/2
(+.f64 x y)
(*.f64 1/2 (/.f64 x y))
(*.f64 (/.f64 1/2 y) x)
(/.f64 1/2 (/.f64 y x))

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

Calls

2 calls:

46.0ms	y
36.0ms	x

Results

Error	Segments	Branch
15.4b	5	`x`
17.8b	5	`y`

Compiler

Compiled 28 to 18 computations (35.7% saved)

bsearch107.0ms (5%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
22.0ms	126362877181.60814	353122855271540.1
34.0ms	-1.9902872293470404e-122	-5.559654842073379e-126
12.0ms	-1.5075051912891288e-55	-6.589430331536466e-59
38.0ms	-1.4784357365567313e+55	-2.0394225819188432e+48

Results

100.0ms	528×	body	256	valid
1.0ms	7×	body	256	infinite

Compiler

Compiled 410 to 339 computations (17.3% saved)

regimes7.0ms (0.3%)

Accuracy

Total -35.5b remaining (-129.8%)

Threshold costs -35.5b (-129.8%)

Counts

3 → 1

Calls

Call 1

Inputs
0
1/2
(+.f64 x y)

Outputs
1/2

Calls

2 calls:

3.0ms	y
3.0ms	x

Results

Error	Segments	Branch
27.3b	1	`x`
27.3b	1	`y`

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	59
1	23	59

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(if (<=.f64 x -67999999999999999539024509856590702399396174052196352) (.f64 1/2 (/.f64 x y)) (if (<=.f64 x -7463162001623895/113078212145816597093331040047546785012958969400039613319782796882727665664) 1/2 (if (<=.f64 x -7256757823367339/372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872) (.f64 1/2 (/.f64 x y)) (if (<=.f64 x 23000000000000) 1/2 (*.f64 1/2 (/.f64 x y))))))
1/2
0

Outputs
(+.f64 1/2 (*.f64 1/2 (/.f64 x y)))
(if (<=.f64 x -67999999999999999539024509856590702399396174052196352) (.f64 1/2 (/.f64 x y)) (if (<=.f64 x -7463162001623895/113078212145816597093331040047546785012958969400039613319782796882727665664) 1/2 (if (<=.f64 x -7256757823367339/372141426839350727961253789638658321589064376671906846864122981980487315514059736743009817965446945567110411062408283101969716033850703872) (.f64 1/2 (/.f64 x y)) (if (<=.f64 x 23000000000000) 1/2 (*.f64 1/2 (/.f64 x y))))))
1/2
0

Compiler

Compiled 50 to 36 computations (28% saved)

soundness0.0ms (0%)

end47.0ms (2.2%)

Compiler: Compiled 44 to 29 computations (34.1% saved)

Details

analyze70.0ms (3.2%)

sample1.1s (51%)

preprocess16.0ms (0.8%)

simplify6.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

localize30.0ms (1.4%)

series4.0ms (0.2%)

rewrite43.0ms (2%)

simplify169.0ms (7.8%)

eval10.0ms (0.5%)

prune11.0ms (0.5%)

localize5.0ms (0.2%)

series4.0ms (0.2%)

rewrite43.0ms (2%)

simplify33.0ms (1.5%)

localize7.0ms (0.3%)

localize3.0ms (0.1%)

eval9.0ms (0.4%)

prune35.0ms (1.6%)

localize5.0ms (0.2%)

series1.0ms (0.1%)

rewrite67.0ms (3.1%)

simplify34.0ms (1.6%)

eval5.0ms (0.2%)

prune33.0ms (1.5%)

localize5.0ms (0.3%)

series1.0ms (0.1%)

rewrite68.0ms (3.2%)

simplify37.0ms (1.7%)

eval4.0ms (0.2%)

prune5.0ms (0.3%)

regimes45.0ms (2.1%)

regimes84.0ms (3.9%)

bsearch107.0ms (5%)

regimes7.0ms (0.3%)

simplify4.0ms (0.2%)

soundness0.0ms (0%)

end47.0ms (2.2%)

Profiling