Details

analyze85.0ms (2.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
25%	68.7%	6.3%	6
34.3%	53.1%	12.6%	7
46.8%	39%	14.1%	8
53.1%	28.9%	18%	9
60.1%	20.7%	19.2%	10
63.6%	15%	21.4%	11
67.3%	10.6%	22%	12

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.1s (30.4%)

Results

1.0s	8256×	body	256	valid
26.0ms	328×	body	256	invalid

preprocess47.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(sqrt.f64 (+.f64 (*.f64 y y) x))

Outputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(sqrt.f64 (fma.f64 x x y))
(sqrt.f64 (+.f64 (*.f64 y y) x))
(sqrt.f64 (fma.f64 y y x))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	8	7

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (*.f64 x x) y))

Outputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(sqrt.f64 (fma.f64 x x y))

eval0.0ms (0%)

Compiler: Compiled 13 to 7 computations (46.2% saved)

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

24.5b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	24.5b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 8 to 5 computations (37.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 x x) y)
✓	22.8b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 18 to 5 computations (72.2% saved)

series7.0ms (0.2%)

Counts

2 → 40

Calls

12 calls:

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

rewrite58.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

662×	`pow1_binary64`
619×	`add-log-exp_binary64`
619×	`log1p-expm1-u_binary64`
619×	`expm1-log1p-u_binary64`
602×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	130	11
2	1751	11

Stop Event

1×	node limit

Counts

2 → 62

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (*.f64 x x) y))
(+.f64 (*.f64 x x) y)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (hypot.f64 x (sqrt.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (sqrt.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (hypot.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x y)) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 x x y) 1/4) (pow.f64 (fma.f64 x x y) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (sqrt.f64 (-.f64 (.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (sqrt.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x y) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 y) x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 y))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x y)) (.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (fma.f64 x x y) 1/4) (.f64 (pow.f64 (fma.f64 x x y) 1/4) (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (/.f64 1 (-.f64 (.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (hypot.f64 x (sqrt.f64 y)) (pow.f64 (fma.f64 x x y) 1/4)) (pow.f64 (fma.f64 x x y) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (hypot.f64 x (sqrt.f64 y)) (cbrt.f64 (fma.f64 x x y))) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))) (+.f64 (pow.f64 x 6) (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (pow.f64 x 4) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (.f64 y y) (-.f64 (pow.f64 x 4) (.f64 (.f64 x x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (.f64 y y)) (-.f64 (.f64 x x) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (.f64 y (-.f64 y (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (.f64 y y))) (neg.f64 (-.f64 (.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 y y) (pow.f64 x 4)) (-.f64 y (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x y) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (*.f64 x x))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (hypot.f64 x (sqrt.f64 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (cbrt.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x y)) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x y) 1/4) (pow.f64 (fma.f64 x x y) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 (pow.f64 x 4) (*.f64 y y))) (sqrt.f64 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (sqrt.f64 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x y) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x y) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x y) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 y) x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 y))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) (-.f64 (*.f64 x x) y)) (/.f64 (*.f64 y y) (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 y)) (hypot.f64 x (sqrt.f64 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x y)) (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x y)) (*.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 y))) (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x y)) 2) (cbrt.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x y) 1/4) (*.f64 (pow.f64 (fma.f64 x x y) 1/4) (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (/.f64 1 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (/.f64 1 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (hypot.f64 x (sqrt.f64 y)) (pow.f64 (fma.f64 x x y) 1/4)) (pow.f64 (fma.f64 x x y) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (hypot.f64 x (sqrt.f64 y)) (cbrt.f64 (fma.f64 x x y))) (cbrt.f64 (hypot.f64 x (sqrt.f64 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x)))) (+.f64 (pow.f64 x 6) (pow.f64 y 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 x x) y) (-.f64 (pow.f64 x 4) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3)) (+.f64 (*.f64 y y) (-.f64 (pow.f64 x 4) (*.f64 (*.f64 x x) y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 y y)) (-.f64 (*.f64 x x) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 3))) (neg.f64 (+.f64 (pow.f64 x 4) (*.f64 y (-.f64 y (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x 4) (*.f64 y y))) (neg.f64 (-.f64 (*.f64 x x) y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 y y) (pow.f64 x 4)) (-.f64 y (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x y) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 y (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) y)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 y) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (sqrt.f64 y) (*.f64 x x))))))

simplify96.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

759×	`times-frac_binary64`
599×	`associate-/l*_binary64`
502×	`unswap-sqr_binary64`
498×	`fma-neg_binary64`
427×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	454
1	161	416
2	444	416
3	1586	414
4	5763	414

Stop Event

1×	node limit

Counts

102 → 88

Calls

Call 1

Inputs
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))
(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y)))
(+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6))) (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(*.f64 -1 x)
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 y x)) (+.f64 (.f64 -1 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(+.f64 (.f64 -1/2 (/.f64 y x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 -1 x) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))
(+.f64 y (pow.f64 x 2))

Outputs
(sqrt.f64 y)
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))
(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (sqrt.f64 y))
(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y)))
(fma.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4)) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (*.f64 x x)) (sqrt.f64 y)))
(fma.f64 (sqrt.f64 (/.f64 1 y)) (.f64 1/2 (.f64 x x)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (*.f64 -1/8 (pow.f64 x 4)) (sqrt.f64 y)))
(+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6))) (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (pow.f64 x 2))) (sqrt.f64 y))))
(fma.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (pow.f64 x 6)) (fma.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (pow.f64 x 4)) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (sqrt.f64 y))))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 1/16 (pow.f64 x 6)) (fma.f64 (sqrt.f64 (/.f64 1 y)) (.f64 1/2 (.f64 x x)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 -1/8 (pow.f64 x 4)) (sqrt.f64 y))))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 3))) (.f64 -1/8 (pow.f64 x 4)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 y 5))) (.f64 1/16 (pow.f64 x 6)) (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x x)) (sqrt.f64 y))))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(fma.f64 1/2 (/.f64 y x) x)
(+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) x))
(fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) (fma.f64 1/2 (/.f64 y x) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x)))
(fma.f64 1/2 (/.f64 y x) (fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x)))
(fma.f64 1/2 (/.f64 y x) (fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) (fma.f64 1/2 (/.f64 y x) x)))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1/2 (/.f64 y x)) (.f64 -1 x))
(fma.f64 -1/2 (/.f64 y x) (neg.f64 x))
(-.f64 (*.f64 (/.f64 y x) -1/2) x)
(+.f64 (.f64 -1/2 (/.f64 y x)) (+.f64 (.f64 -1 x) (*.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3)))))
(fma.f64 -1/2 (/.f64 y x) (fma.f64 -1 x (.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) 1/8)))
(fma.f64 (/.f64 y x) -1/2 (-.f64 (*.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8) x))
(-.f64 (fma.f64 (/.f64 y x) -1/2 (*.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8)) x)
(-.f64 (.f64 (/.f64 y x) (+.f64 -1/2 (.f64 (/.f64 y x) (/.f64 1/8 x)))) x)
(fma.f64 (/.f64 y x) (+.f64 -1/2 (*.f64 (/.f64 y x) (/.f64 1/8 x))) (neg.f64 x))
(+.f64 (.f64 -1/2 (/.f64 y x)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 -1 x) (.f64 1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))))))
(fma.f64 -1/2 (/.f64 y x) (fma.f64 -1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1 x (.f64 (/.f64 (.f64 y y) (pow.f64 x 3)) 1/8))))
(fma.f64 (/.f64 y x) -1/2 (fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -1/16 (-.f64 (*.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8) x)))
(fma.f64 (/.f64 y x) -1/2 (fma.f64 (/.f64 y (/.f64 (pow.f64 x 3) y)) 1/8 (-.f64 (/.f64 (*.f64 (pow.f64 y 3) -1/16) (pow.f64 x 5)) x)))
(fma.f64 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) -1/16 (-.f64 (.f64 (/.f64 y x) (+.f64 -1/2 (.f64 (/.f64 y x) (/.f64 1/8 x)))) x))
(fma.f64 (pow.f64 y 3) (/.f64 -1/16 (pow.f64 x 5)) (fma.f64 (/.f64 y x) (+.f64 -1/2 (*.f64 (/.f64 y x) (/.f64 1/8 x))) (neg.f64 x)))
x
(+.f64 (*.f64 1/2 (/.f64 y x)) x)
(fma.f64 1/2 (/.f64 y x) x)
(+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x))
(fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) x))
(fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) (fma.f64 1/2 (/.f64 y x) x))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5))) (+.f64 (.f64 1/2 (/.f64 y x)) (+.f64 (*.f64 -1/8 (/.f64 (pow.f64 y 2) (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 (*.f64 y y) (pow.f64 x 3)) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 1/2 (/.f64 y x) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x)))
(fma.f64 1/2 (/.f64 y x) (fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (/.f64 y (/.f64 (pow.f64 x 3) y)) x)))
(fma.f64 1/2 (/.f64 y x) (fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) x)))
(fma.f64 1/16 (/.f64 (pow.f64 y 3) (pow.f64 x 5)) (fma.f64 -1/8 (*.f64 y (/.f64 y (pow.f64 x 3))) (fma.f64 1/2 (/.f64 y x) x)))
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
y
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)
(+.f64 y (pow.f64 x 2))
(+.f64 y (*.f64 x x))
(fma.f64 x x y)

eval22.0ms (0.6%)

Compiler: Compiled 1056 to 523 computations (50.5% saved)

prune73.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	6	89

Error

Counts

89 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	24.5b	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	42.4b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
▶	44.6b	(sqrt.f64 y)
▶	38.9b	(neg.f64 x)
	42.3b	x
▶	38.9b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)

Compiler

Compiled 37 to 25 computations (32.4% saved)

localize3.0ms (0.1%)

Compiler: Compiled 5 to 3 computations (40% saved)

localize3.0ms (0.1%)

Compiler: Compiled 5 to 3 computations (40% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 9 computations (55% saved)

series4.0ms (0.1%)

Counts

1 → 0

Calls

6 calls:

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

rewrite56.0ms (1.5%)

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 y x))

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

Outputs

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

simplify31.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

20 → 20

Calls

Call 1

Inputs

Outputs

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 9 computations (55% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite104.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

655×	`pow1_binary64`
608×	`add-log-exp_binary64`
608×	`log1p-expm1-u_binary64`
608×	`expm1-log1p-u_binary64`
596×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	127	7
2	1614	7

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`
1×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	9	168
2	13	168
3	17	168
4	18	168

Stop Event

1×

saturated

Counts

45 → 22

Calls

Call 1

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

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

eval10.0ms (0.3%)

Compiler: Compiled 396 to 229 computations (42.2% saved)

prune9.0ms (0.2%)

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	1	1
Picked	0	1	1
Done	0	4	4
Total	40	8	48

Error

Counts

48 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	24.5b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	42.4b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
▶	42.4b	(+.f64 (/.f64 1/2 (/.f64 x y)) x)
✓	38.9b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	44.6b	(sqrt.f64 y)
✓	38.9b	(neg.f64 x)
▶	38.9b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
	42.3b	x

Compiler

Compiled 55 to 37 computations (32.7% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 1/2 (/.f64 x y))

Compiler

Compiled 20 to 9 computations (55% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite60.0ms (1.6%)

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 x y))

Outputs

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

simplify43.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`
1×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	9	168
2	13	168
3	17	168
4	18	168

Stop Event

1×

saturated

Counts

50 → 26

Calls

Call 1

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

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

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 -1/2 (/.f64 x y))

Compiler

Compiled 20 to 9 computations (55% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite64.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

697×	`pow1_binary64`
651×	`add-log-exp_binary64`
650×	`log1p-expm1-u_binary64`
650×	`expm1-log1p-u_binary64`
638×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	134	7
2	1769	7

Stop Event

1×	node limit

Counts

1 → 26

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

simplify19.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`
1×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	9	168
2	13	168
3	17	168
4	18	168

Stop Event

1×

saturated

Counts

50 → 26

Calls

Call 1

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

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

eval12.0ms (0.3%)

Compiler: Compiled 528 to 303 computations (42.6% saved)

prune16.0ms (0.4%)

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	1	1
Picked	0	1	1
Done	0	6	6
Total	50	10	60

Error

Counts

60 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	24.5b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	42.4b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	42.4b	(+.f64 (/.f64 1/2 (/.f64 x y)) x)
✓	38.9b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	44.6b	(sqrt.f64 y)
✓	38.9b	(neg.f64 x)
✓	38.9b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
	42.3b	x
▶	38.9b	(-.f64 (*.f64 (/.f64 -1/2 x) y) x)
▶	42.4b	(+.f64 (*.f64 (/.f64 1/2 x) y) x)

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize72.0ms (1.9%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 12 computations (40% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite58.0ms (1.5%)

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 x) y)

Outputs

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

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`
1×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	9	168
2	13	168
3	17	168
4	18	168

Stop Event

1×

saturated

Counts

45 → 22

Calls

Call 1

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

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

localize13.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 12 computations (40% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite60.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

615×	`pow1_binary64`
572×	`add-log-exp_binary64`
571×	`log1p-expm1-u_binary64`
571×	`expm1-log1p-u_binary64`
561×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1559	7

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify15.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`
1×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	9	168
2	13	168
3	17	168
4	18	168

Stop Event

1×

saturated

Counts

45 → 22

Calls

Call 1

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

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

eval10.0ms (0.3%)

Compiler: Compiled 406 to 236 computations (41.9% saved)

prune13.0ms (0.3%)

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	1	1
Picked	0	1	1
Done	0	8	8
Total	44	10	54

Error

Counts

54 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	24.5b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	42.4b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
✓	42.4b	(+.f64 (/.f64 1/2 (/.f64 x y)) x)
✓	38.9b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	44.6b	(sqrt.f64 y)
✓	38.9b	(neg.f64 x)
✓	38.9b	(-.f64 (/.f64 -1/2 (/.f64 x y)) x)
	42.3b	x
✓	38.9b	(-.f64 (*.f64 (/.f64 -1/2 x) y) x)
✓	42.4b	(+.f64 (*.f64 (/.f64 1/2 x) y) x)

Compiler

Compiled 73 to 49 computations (32.9% saved)

regimes225.0ms (6%)

Counts

10 → 3

Calls

Call 1

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

Outputs
(neg.f64 x)
(sqrt.f64 (+.f64 (*.f64 x x) y))
x

Calls

6 calls:

72.0ms	x
50.0ms	y
27.0ms	(*.f64 x x)
26.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
24.0ms	(+.f64 (*.f64 x x) y)

Results

Error	Segments	Branch
0b	3	`x`
18.9b	4	`y`
11.0b	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
11.0b	2	`(+.f64 (*.f64 x x) y)`
11.0b	2	`(*.f64 x x)`
11.0b	2	`(*.f64 x x)`

Compiler

Compiled 86 to 48 computations (44.2% saved)

bsearch70.0ms (1.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	2.866490898790862e+86	5.644761073401985e+87
52.0ms	-4.762588464129226e+155	-2.3799592869988644e+146

Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes228.0ms (6%)

Counts

9 → 3

Calls

Call 1

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

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

Calls

2 calls:

113.0ms	y
113.0ms	x

Results

Error	Segments	Branch
4.5b	3	`x`
23.9b	8	`y`

Compiler

Compiled 55 to 30 computations (45.5% saved)

bsearch185.0ms (4.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
88.0ms	2.3856078559307772e-108	1.368885169624852e-83
98.0ms	-9.150103934683944e-70	-5.326949788663265e-82

Compiler

Compiled 328 to 240 computations (26.8% saved)

regimes108.0ms (2.9%)

Counts

8 → 2

Calls

Call 1

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

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

Calls

2 calls:

55.0ms	y
26.0ms	x

Results

Error	Segments	Branch
17.8b	2	`x`
32.7b	5	`y`

Compiler

Compiled 53 to 29 computations (45.3% saved)

bsearch83.0ms (2.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
82.0ms	-7.320739349505657e-293	-3.9397333623430687e-305

Compiler

Compiled 213 to 149 computations (30% saved)

regimes125.0ms (3.3%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

2 calls:

72.0ms	y
51.0ms	x

Results

Error	Segments	Branch
17.9b	2	`x`
32.8b	5	`y`

Compiler

Compiled 18 to 11 computations (38.9% saved)

bsearch35.0ms (0.9%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
35.0ms	-6.041014762875264e-223	-3.3276611139155913e-227

Compiler

Compiled 125 to 89 computations (28.8% saved)

regimes48.0ms (1.3%)

Accuracy

Total -45.2b remaining (-251.1%)

Threshold costs -45.2b (-251.1%)

Counts

2 → 2

Calls

Call 1

Inputs
x
(neg.f64 x)

Outputs
(neg.f64 x)
x

Calls

2 calls:

40.0ms	y
7.0ms	x

Results

Error	Segments	Branch
18.0b	2	`x`
32.9b	5	`y`

Compiler

Compiled 11 to 7 computations (36.4% saved)

bsearch104.0ms (2.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
104.0ms	-2.966601328103765e-308	1.073146088879102e-298

Compiler

Compiled 103 to 79 computations (23.3% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	114
1	46	114
2	49	114
3	50	114

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 x -476258846412922608139175456357510264840553418783176435748370574053665803873491413783938469241973209498108147919984832273959768485619954018573598452009140224) (neg.f64 x) (if (<=.f64 x 286649089879086222214038391971323022530297689179622965849488744617610065131079544602624) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -2349585739513001/4271974071841820164790043412339104229205409044713305539894083215644439451561281100045924173873152) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (if (<=.f64 x 406152787224728768/169230328010303641331690318856389386196071598838855992136870091590247882556495704531248437872567112920983350278405979725889536) (sqrt.f64 y) (+.f64 (.f64 (/.f64 1/2 x) y) x)))
(if (<=.f64 x -12943390571008674/179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (+.f64 (.f64 (/.f64 1/2 x) y) x))
(if (<=.f64 x -4000808659727912448/6668014432879854274079851790721257797144758322315908160396257811764037237817632071521432200871554290742929910593433240445888801654119365080363356052330830046095157579514014558463078285911814024728965016135886601981690748037476461291163877376) (-.f64 (*.f64 (/.f64 -1/2 x) y) x) x)
(if (<=.f64 x 0) (neg.f64 x) x)
x

Outputs
(if (<=.f64 x -476258846412922608139175456357510264840553418783176435748370574053665803873491413783938469241973209498108147919984832273959768485619954018573598452009140224) (neg.f64 x) (if (<=.f64 x 286649089879086222214038391971323022530297689179622965849488744617610065131079544602624) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -2349585739513001/4271974071841820164790043412339104229205409044713305539894083215644439451561281100045924173873152) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (if (<=.f64 x 406152787224728768/169230328010303641331690318856389386196071598838855992136870091590247882556495704531248437872567112920983350278405979725889536) (sqrt.f64 y) (+.f64 (.f64 (/.f64 1/2 x) y) x)))
(if (<=.f64 x -2349585739513001/4271974071841820164790043412339104229205409044713305539894083215644439451561281100045924173873152) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (if (<=.f64 x 6346137300386387/2644223875160994395807661232131084159313618731857124877138595181097623164945245383300756841758861139390364848100093433217024) (sqrt.f64 y) (+.f64 x (.f64 y (/.f64 1/2 x)))))
(if (<=.f64 x -12943390571008674/179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216) (-.f64 (.f64 (/.f64 -1/2 x) y) x) (+.f64 (.f64 (/.f64 1/2 x) y) x))
(if (<=.f64 x -6471695285504337/89884656743115795386465259539451236680898848947115328636715040578866337902750481566354238661203768010560056939935696678829394884407208311246423715319737062188883946712432742638151109800623047059726541476042502884419075341171231440736956555270413618581675255342293149119973622969239858152417678164812112068608) (-.f64 (.f64 y (/.f64 -1/2 x)) x) (+.f64 x (.f64 y (/.f64 1/2 x))))
(if (<=.f64 x -4000808659727912448/6668014432879854274079851790721257797144758322315908160396257811764037237817632071521432200871554290742929910593433240445888801654119365080363356052330830046095157579514014558463078285911814024728965016135886601981690748037476461291163877376) (-.f64 (*.f64 (/.f64 -1/2 x) y) x) x)
(if (<=.f64 x -7814079413531079/13023465689218465379062210528752456635048356098273258125773941038601635230112562639690297267327254474107284981627799297745876565730701884922584679789708652433779604647488309684498199777171511767048759797140403519495489742260696213459304448) (-.f64 (*.f64 y (/.f64 -1/2 x)) x) x)
(if (<=.f64 x 0) (neg.f64 x) x)
x

Compiler

Compiled 91 to 59 computations (35.2% saved)

soundness87.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

759×	`times-frac_binary64`
599×	`associate-/l*_binary64`
502×	`unswap-sqr_binary64`
498×	`fma-neg_binary64`
427×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	454
1	161	416
2	444	416
3	1586	414
4	5763	414

Stop Event

1×	node limit

Compiler

Compiled 9 to 7 computations (22.2% saved)

end171.0ms (4.5%)

Compiler: Compiled 81 to 48 computations (40.7% saved)

Details

analyze85.0ms (2.2%)

sample1.1s (30.4%)

preprocess47.0ms (1.2%)

simplify7.0ms (0.2%)

eval0.0ms (0%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series7.0ms (0.2%)

rewrite58.0ms (1.5%)

simplify96.0ms (2.5%)

eval22.0ms (0.6%)

prune73.0ms (1.9%)

localize3.0ms (0.1%)

localize3.0ms (0.1%)

localize8.0ms (0.2%)

series4.0ms (0.1%)

rewrite56.0ms (1.5%)

simplify31.0ms (0.8%)

localize8.0ms (0.2%)

series2.0ms (0.1%)

rewrite104.0ms (2.7%)

simplify14.0ms (0.4%)

eval10.0ms (0.3%)

prune9.0ms (0.2%)

localize9.0ms (0.2%)

series2.0ms (0%)

rewrite60.0ms (1.6%)

simplify43.0ms (1.1%)

localize8.0ms (0.2%)

series2.0ms (0.1%)

rewrite64.0ms (1.7%)

simplify19.0ms (0.5%)

eval12.0ms (0.3%)

prune16.0ms (0.4%)

localize72.0ms (1.9%)

series2.0ms (0%)

rewrite58.0ms (1.5%)

simplify14.0ms (0.4%)

localize13.0ms (0.3%)

series2.0ms (0.1%)

rewrite60.0ms (1.6%)

simplify15.0ms (0.4%)

eval10.0ms (0.3%)

prune13.0ms (0.3%)

regimes225.0ms (6%)

bsearch70.0ms (1.9%)

regimes228.0ms (6%)

bsearch185.0ms (4.9%)

regimes108.0ms (2.9%)

bsearch83.0ms (2.2%)

regimes125.0ms (3.3%)

bsearch35.0ms (0.9%)

regimes48.0ms (1.3%)

bsearch104.0ms (2.7%)

simplify11.0ms (0.3%)

soundness87.0ms (2.3%)

end171.0ms (4.5%)

Profiling