Details

analyze118.0ms (3.8%)

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
12.5%	12.5%	87.4%	0.1%	0%	0%	0%	5
26.7%	25%	68.7%	0.1%	0%	6.2%	0%	6
39.3%	34.3%	53.1%	0.1%	0%	12.5%	0%	7
54.5%	46.8%	39%	0.1%	0%	14%	0%	8
64.8%	53.1%	28.9%	0.1%	0%	18%	0%	9
74.4%	60.1%	20.7%	0.1%	0%	19.1%	0%	10
80.9%	63.6%	15%	0.1%	0%	21.3%	0%	11
86.4%	67.3%	10.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.4s (43.7%)

Results

1.2s	8256×	body	256	valid
59.0ms	343×	body	256	invalid

Bogosity

preprocess15.0ms (0.5%)

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)

simplify9.0ms (0.3%)

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))

eval1.0ms (0%)

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

prune1.0ms (0%)

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

21.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	21.0b	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 8 to 5 computations (37.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 x x) y)
✓	19.6b	(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))
1.0ms	y	@	0	(sqrt.f64 (+.f64 (*.f64 x x) y))

rewrite112.0ms (3.6%)

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))))))

simplify95.0ms (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

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)

eval49.0ms (1.6%)

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

prune13.0ms (0.4%)

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
✓	21.0b	(sqrt.f64 (+.f64 (*.f64 x x) y))
▶	42.5b	(neg.f64 x)
▶	40.7b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
	40.6b	x
▶	42.5b	(sqrt.f64 y)
▶	42.6b	(-.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)

localize36.0ms (1.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 9 computations (55% saved)

series4.0ms (0.1%)

Counts

1 → 6

Calls

6 calls:

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

rewrite68.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

902×	`pow1_binary64`
841×	`add-log-exp_binary64`
841×	`log1p-expm1-u_binary64`
841×	`expm1-log1p-u_binary64`
824×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	159	8
2	2248	8

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 1/2 (/.f64 y x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (pow.f64 (/.f64 y x) 2) 1/4) (-.f64 (.f64 1/2 (/.f64 y x)) x)) (/.f64 (.f64 x x) (-.f64 (.f64 1/2 (/.f64 y x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 1/2 (/.f64 y x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 1/2 (/.f64 y x) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 1/2 (/.f64 y x) x)) (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 y x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 y x) x)) 2) (cbrt.f64 (fma.f64 1/2 (/.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 1/2 (/.f64 y x) x)) (sqrt.f64 (fma.f64 1/2 (/.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 (pow.f64 (/.f64 y x) 3) 1/8) (pow.f64 x 3)) (/.f64 1 (+.f64 (.f64 (pow.f64 (/.f64 y x) 2) 1/4) (.f64 x (-.f64 x (.f64 1/2 (/.f64 y x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 (pow.f64 (/.f64 y x) 2) 1/4) (.f64 x x)) (/.f64 1 (-.f64 (.f64 1/2 (/.f64 y x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (.f64 (pow.f64 (/.f64 y x) 2) 1/4) (.f64 x (-.f64 x (.f64 1/2 (/.f64 y x))))) (+.f64 (.f64 (pow.f64 (/.f64 y x) 3) 1/8) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (.f64 1/2 (/.f64 y x)) x) (-.f64 (.f64 (pow.f64 (/.f64 y x) 2) 1/4) (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (pow.f64 (/.f64 y x) 3) 1/8) (pow.f64 x 3)) (+.f64 (.f64 (pow.f64 (/.f64 y x) 2) 1/4) (.f64 x (-.f64 x (.f64 1/2 (/.f64 y x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (pow.f64 (/.f64 y x) 3) 1/8) (pow.f64 x 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (pow.f64 (/.f64 y x) 2) 1/4) (.f64 1/2 (.f64 (/.f64 y x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (pow.f64 (/.f64 y x) 2) 1/4) (.f64 x x)) (-.f64 (.f64 1/2 (/.f64 y x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (.f64 (pow.f64 (/.f64 y x) 3) 1/8) (pow.f64 x 3))) (neg.f64 (+.f64 (.f64 (pow.f64 (/.f64 y x) 2) 1/4) (.f64 x (-.f64 x (.f64 1/2 (/.f64 y x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (/.f64 y x) 2) 1/4) (.f64 x x))) (neg.f64 (-.f64 (.f64 1/2 (/.f64 y x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 x x) (.f64 (pow.f64 (/.f64 y x) 2) 1/4)) (-.f64 x (.f64 1/2 (/.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 (/.f64 y x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 (/.f64 y x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 y x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 y x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 y x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/2 (/.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 y x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/2 (/.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/2 (/.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (/.f64 y x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 y x) 1/2 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (.f64 1/2 (/.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 1/2 (/.f64 y x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 y x) 2) 1/4)) (cbrt.f64 (.f64 1/2 (/.f64 y x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (.f64 1/2 (/.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 1/2 (/.f64 y x))) (sqrt.f64 (.f64 1/2 (/.f64 y x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 1/2 (/.f64 y x)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 1/2 (/.f64 y x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 (/.f64 y x) 2) 1/4) (-.f64 (*.f64 1/2 (/.f64 y x)) x)) (/.f64 (*.f64 x x) (-.f64 (*.f64 1/2 (/.f64 y x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/2 (/.f64 y x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/2 (/.f64 y x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 y x) x)) (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 y x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 y x) x)) 2) (cbrt.f64 (fma.f64 1/2 (/.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 y x) x)) (sqrt.f64 (fma.f64 1/2 (/.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 (/.f64 y x) 3) 1/8) (pow.f64 x 3)) (/.f64 1 (+.f64 (*.f64 (pow.f64 (/.f64 y x) 2) 1/4) (*.f64 x (-.f64 x (*.f64 1/2 (/.f64 y x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 (/.f64 y x) 2) 1/4) (*.f64 x x)) (/.f64 1 (-.f64 (*.f64 1/2 (/.f64 y x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 (pow.f64 (/.f64 y x) 2) 1/4) (*.f64 x (-.f64 x (*.f64 1/2 (/.f64 y x))))) (+.f64 (*.f64 (pow.f64 (/.f64 y x) 3) 1/8) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 1/2 (/.f64 y x)) x) (-.f64 (*.f64 (pow.f64 (/.f64 y x) 2) 1/4) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 (/.f64 y x) 3) 1/8) (pow.f64 x 3)) (+.f64 (*.f64 (pow.f64 (/.f64 y x) 2) 1/4) (*.f64 x (-.f64 x (*.f64 1/2 (/.f64 y x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 (/.f64 y x) 3) 1/8) (pow.f64 x 3)) (+.f64 (*.f64 x x) (-.f64 (*.f64 (pow.f64 (/.f64 y x) 2) 1/4) (*.f64 1/2 (*.f64 (/.f64 y x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 (/.f64 y x) 2) 1/4) (*.f64 x x)) (-.f64 (*.f64 1/2 (/.f64 y x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 (/.f64 y x) 3) 1/8) (pow.f64 x 3))) (neg.f64 (+.f64 (*.f64 (pow.f64 (/.f64 y x) 2) 1/4) (*.f64 x (-.f64 x (*.f64 1/2 (/.f64 y x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 (/.f64 y x) 2) 1/4) (*.f64 x x))) (neg.f64 (-.f64 (*.f64 1/2 (/.f64 y x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 (/.f64 y x) 2) 1/4)) (-.f64 x (*.f64 1/2 (/.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 (/.f64 y x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 (/.f64 y x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2 (/.f64 y x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 y x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 y x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/2 (/.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 (/.f64 y x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/2 (/.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/2 (/.f64 y x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (/.f64 y x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 y x) 1/2 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 1/2 (/.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/2 (/.f64 y x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 y x) 2) 1/4)) (cbrt.f64 (*.f64 1/2 (/.f64 y x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 1/2 (/.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/2 (/.f64 y x))) (sqrt.f64 (*.f64 1/2 (/.f64 y x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 1/2 (/.f64 y x)))))))

simplify13.0ms (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	24
1	9	24
2	13	24
3	17	24
4	18	24

Stop Event

1×

saturated

Counts

41 → 37

Calls

Call 1

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

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

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

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

rewrite173.0ms (5.5%)

Algorithm

1×	batch-egg-rewrite

Rules

907×	`pow1_binary64`
847×	`add-log-exp_binary64`
847×	`log1p-expm1-u_binary64`
847×	`expm1-log1p-u_binary64`
830×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	159	10
2	2241	10

Stop Event

1×	node limit

Counts

1 → 37

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 y x) -1/2) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 y x) -1/2) (*.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x) (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x) (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x) (fma.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 x) (*.f64 (/.f64 y x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (*.f64 (/.f64 y x) -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x)) (pow.f64 (cbrt.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x)) 2) (cbrt.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x)) (sqrt.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 -1/8 (pow.f64 (/.f64 y x) 3)) (pow.f64 x 3)) (/.f64 1 (+.f64 (*.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 x (fma.f64 (/.f64 y x) -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 x x)) (/.f64 1 (fma.f64 (/.f64 y x) -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (*.f64 (/.f64 y x) -1/2)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (*.f64 (/.f64 y x) -1/2)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 x (fma.f64 (/.f64 y x) -1/2 x))) (-.f64 (*.f64 -1/8 (pow.f64 (/.f64 y x) 3)) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (/.f64 y x) -1/2 x) (-.f64 (*.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 -1/8 (pow.f64 (/.f64 y x) 3)) (pow.f64 x 3)) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 x (fma.f64 (/.f64 y x) -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 x x)) (fma.f64 (/.f64 y x) -1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 -1/8 (pow.f64 (/.f64 y x) 3)) (pow.f64 x 3))) (neg.f64 (+.f64 (*.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 x (fma.f64 (/.f64 y x) -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 x x))) (neg.f64 (fma.f64 (/.f64 y x) -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 -1/8 (pow.f64 (/.f64 y x) 3)) (pow.f64 (neg.f64 x) 3)) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 y x) 2)) (-.f64 (*.f64 (neg.f64 x) (neg.f64 x)) (*.f64 (*.f64 (/.f64 y x) -1/2) (neg.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 1/4 (pow.f64 (/.f64 y x) 2)) (*.f64 (neg.f64 x) (neg.f64 x))) (-.f64 (*.f64 (/.f64 y x) -1/2) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (*.f64 (/.f64 y x) -1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 y x) -1/2 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/2 (/.f64 y x) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (/.f64 y x) -1/2) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/4 (pow.f64 (/.f64 y x) 2))) (cbrt.f64 (*.f64 (/.f64 y x) -1/2)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (/.f64 y x) -1/2)) (sqrt.f64 (*.f64 (/.f64 y x) -1/2)) (neg.f64 x))))))

simplify150.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-neg_binary64`
410×	`fma-def_binary64`
292×	`associate-/l*_binary64`
253×	`div-sub_binary64`
192×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	210
1	16	210
2	26	210
3	35	210
4	58	210
5	102	210
6	197	210
7	352	210
8	542	210
9	834	210
10	1840	210
11	3052	210
12	3598	210
13	3798	210
14	3895	210
15	3927	210
16	3951	210
17	3951	210

Stop Event

1×

saturated

Counts

61 → 43

Calls

Call 1

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

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

eval27.0ms (0.9%)

Compiler: Compiled 1128 to 597 computations (47.1% saved)

prune28.0ms (0.9%)

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	1	1
Picked	0	1	1
Done	0	4	4
Total	78	8	86

Error

Counts

86 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	21.0b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	42.5b	(neg.f64 x)
✓	40.7b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
	40.6b	x
✓	42.5b	(sqrt.f64 y)
▶	62.2b	(*.f64 1/2 (/.f64 y x))
✓	42.6b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
▶	62.2b	(/.f64 y (/.f64 x -1/2))

Compiler

Compiled 51 to 35 computations (31.4% saved)

localize5.0ms (0.2%)

Compiler: Compiled 13 to 6 computations (53.8% saved)

localize9.0ms (0.3%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	6	6
Total	8	8

Error

Counts

8 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	21.0b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	42.5b	(neg.f64 x)
✓	40.7b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
	40.6b	x
✓	42.5b	(sqrt.f64 y)
✓	62.2b	(*.f64 1/2 (/.f64 y x))
✓	42.6b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	62.2b	(/.f64 y (/.f64 x -1/2))

Compiler

Compiled 51 to 35 computations (31.4% saved)

eval0.0ms (0%)

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

prune3.0ms (0.1%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	7	7
Total	8	8

Error

Counts

8 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	21.0b	(sqrt.f64 (+.f64 (*.f64 x x) y))
✓	42.5b	(neg.f64 x)
✓	40.7b	(+.f64 (*.f64 1/2 (/.f64 y x)) x)
	40.6b	x
✓	42.5b	(sqrt.f64 y)
✓	62.2b	(*.f64 1/2 (/.f64 y x))
✓	42.6b	(-.f64 (*.f64 (/.f64 y x) -1/2) x)
✓	62.2b	(/.f64 y (/.f64 x -1/2))

Compiler

Compiled 51 to 35 computations (31.4% saved)

regimes193.0ms (6.2%)

Counts

8 → 3

Calls

Call 1

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

66.0ms	x
57.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
31.0ms	y
18.0ms	(+.f64 (*.f64 x x) y)
10.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0b	3	`x`
17.7b	4	`y`
10.2b	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
10.2b	2	`(+.f64 (*.f64 x x) y)`
10.2b	2	`(*.f64 x x)`
10.2b	2	`(*.f64 x x)`

Compiler

Compiled 68 to 38 computations (44.1% saved)

bsearch46.0ms (1.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
21.0ms	6.654830687358151e+111	2.2232716341031476e+119
25.0ms	-3.854195111584589e+154	-1.757443979442241e+152

Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes62.0ms (2%)

Counts

7 → 3

Calls

Call 1

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

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

Calls

2 calls:

45.0ms	y
15.0ms	x

Results

Error	Segments	Branch
5.9b	3	`x`
23.8b	8	`y`

Compiler

Compiled 37 to 20 computations (45.9% saved)

bsearch66.0ms (2.1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
34.0ms	2.90015381197954e-53	3.491199937032416e-41
31.0ms	-2.3199410670106397e-90	-2.5261665795732223e-106

Compiler

Compiled 313 to 229 computations (26.8% saved)

regimes52.0ms (1.7%)

Counts

6 → 2

Calls

Call 1

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

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

Calls

2 calls:

39.0ms	y
9.0ms	x

Results

Error	Segments	Branch
19.8b	2	`x`
31.9b	8	`y`

Compiler

Compiled 35 to 19 computations (45.7% saved)

bsearch43.0ms (1.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
43.0ms	-8.286663666931702e-227	-1.3696605850404348e-244

Compiler

Compiled 153 to 109 computations (28.8% saved)

regimes87.0ms (2.8%)

Counts

5 → 2

Calls

Call 1

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

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

Calls

2 calls:

72.0ms	y
11.0ms	x

Results

Error	Segments	Branch
19.9b	2	`x`
31.9b	8	`y`

Compiler

Compiled 28 to 16 computations (42.9% saved)

bsearch24.0ms (0.8%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
23.0ms	1.9965662890362107e-245	5.4930359286370086e-244

Compiler

Compiled 118 to 86 computations (27.1% saved)

regimes44.0ms (1.4%)

Accuracy

Total -43.5b remaining (-218.7%)

Threshold costs -43.5b (-218.7%)

Counts

4 → 2

Calls

Call 1

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

Outputs
(neg.f64 x)
x

Calls

2 calls:

33.0ms	y
10.0ms	x

Results

Error	Segments	Branch
19.9b	2	`x`
31.9b	8	`y`

Compiler

Compiled 21 to 13 computations (38.1% saved)

bsearch35.0ms (1.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
35.0ms	-1.1674446852536664e-297	7.159053673263853e-308

Compiler

Compiled 103 to 79 computations (23.3% saved)

simplify9.0ms (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	37	107
1	45	107
2	48	107
3	49	107

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 x -38541951115845889929289602617537491438613208918848961447774650979815254336089754407687126916512356807891850460064549649352386358645279770270572310943498240) (neg.f64 x) (if (<=.f64 x 6654830687358151013850556393340510161256364083131752608987874531720048627194386982673802126443030438759530233856) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -2685539873210385/10328999512347634358623676688012047497318823171316894051322637426162590488067364778518581413120551325743612687890989973504) (-.f64 (.f64 (/.f64 y x) -1/2) x) (if (<=.f64 x 6362547413447551/215679573337205118357336120696157045389097155380324579848828881993728) (sqrt.f64 y) (+.f64 (.f64 1/2 (/.f64 y x)) x)))
(if (<=.f64 x -8748434935938369/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016) (-.f64 (*.f64 (/.f64 y x) -1/2) x) x)
(if (<=.f64 x 4151356505655847/7687697232696013035490465480201479025983241823794691621558168976140934720122093268938148043346259333988919315645138393722043075242293497100043735968399262883880680368733084239192707430286484902215659282347932289182034267181757047930126964620533348010060414976) (neg.f64 x) (+.f64 (*.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x 0) (neg.f64 x) x)
x

Outputs
(if (<=.f64 x -38541951115845889929289602617537491438613208918848961447774650979815254336089754407687126916512356807891850460064549649352386358645279770270572310943498240) (neg.f64 x) (if (<=.f64 x 6654830687358151013850556393340510161256364083131752608987874531720048627194386982673802126443030438759530233856) (sqrt.f64 (+.f64 (*.f64 x x) y)) x))
(if (<=.f64 x -2685539873210385/10328999512347634358623676688012047497318823171316894051322637426162590488067364778518581413120551325743612687890989973504) (-.f64 (.f64 (/.f64 y x) -1/2) x) (if (<=.f64 x 6362547413447551/215679573337205118357336120696157045389097155380324579848828881993728) (sqrt.f64 y) (+.f64 (.f64 1/2 (/.f64 y x)) x)))
(if (<=.f64 x -2685539873210385/10328999512347634358623676688012047497318823171316894051322637426162590488067364778518581413120551325743612687890989973504) (-.f64 (.f64 (/.f64 y x) -1/2) x) (if (<=.f64 x 6362547413447551/215679573337205118357336120696157045389097155380324579848828881993728) (sqrt.f64 y) (+.f64 x (.f64 (/.f64 y x) 1/2))))
(if (<=.f64 x -8748434935938369/106688230926077668385277628651540124754316133157054530566340124988224595805082113144342915213944868651886878569494931847134220826465909841285813696837293280737522521272224232935409252574589024395663440258174185631707051968599623380658622038016) (-.f64 (*.f64 (/.f64 y x) -1/2) x) x)
(if (<=.f64 x 4151356505655847/7687697232696013035490465480201479025983241823794691621558168976140934720122093268938148043346259333988919315645138393722043075242293497100043735968399262883880680368733084239192707430286484902215659282347932289182034267181757047930126964620533348010060414976) (neg.f64 x) (+.f64 (*.f64 1/2 (/.f64 y x)) x))
(if (<=.f64 x 4151356505655847/7687697232696013035490465480201479025983241823794691621558168976140934720122093268938148043346259333988919315645138393722043075242293497100043735968399262883880680368733084239192707430286484902215659282347932289182034267181757047930126964620533348010060414976) (neg.f64 x) (+.f64 x (*.f64 (/.f64 y x) 1/2)))
(if (<=.f64 x 0) (neg.f64 x) x)
x

Compiler

Compiled 86 to 55 computations (36% saved)

soundness82.0ms (2.6%)

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)

end59.0ms (1.9%)

Compiler: Compiled 76 to 41 computations (46.1% saved)

Details

analyze118.0ms (3.8%)

sample1.4s (43.7%)

preprocess15.0ms (0.5%)

simplify9.0ms (0.3%)

eval1.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series7.0ms (0.2%)

rewrite112.0ms (3.6%)

simplify95.0ms (3%)

eval49.0ms (1.6%)

prune13.0ms (0.4%)

localize3.0ms (0.1%)

localize3.0ms (0.1%)

localize36.0ms (1.2%)

series4.0ms (0.1%)

rewrite68.0ms (2.2%)

simplify13.0ms (0.4%)

localize8.0ms (0.2%)

series2.0ms (0.1%)

rewrite173.0ms (5.5%)

simplify150.0ms (4.8%)

eval27.0ms (0.9%)

prune28.0ms (0.9%)

localize5.0ms (0.2%)

localize9.0ms (0.3%)

eval0.0ms (0%)

prune3.0ms (0.1%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes193.0ms (6.2%)

bsearch46.0ms (1.5%)

regimes62.0ms (2%)

bsearch66.0ms (2.1%)

regimes52.0ms (1.7%)

bsearch43.0ms (1.4%)

regimes87.0ms (2.8%)

bsearch24.0ms (0.8%)

regimes44.0ms (1.4%)

bsearch35.0ms (1.1%)

simplify9.0ms (0.3%)

soundness82.0ms (2.6%)

end59.0ms (1.9%)

Profiling