Details

analyze11.0ms (1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
0%	0%	50%	50%	0%	0%	0%	1
50%	25%	25%	50%	0%	0%	0%	2
50%	25%	25%	50%	0%	0%	0%	3
75%	37.5%	12.5%	50%	0%	0%	0%	4
75%	37.5%	12.5%	50%	0%	0%	0%	5
87.5%	43.7%	6.2%	50%	0%	0%	0%	6
87.5%	43.7%	6.2%	50%	0%	0%	0%	7
93.8%	46.8%	3.1%	50%	0%	0%	0%	8
93.8%	46.8%	3.1%	50%	0%	0%	0%	9
96.9%	48.4%	1.6%	50%	0%	0%	0%	10
96.9%	48.4%	1.6%	50%	0%	0%	0%	11
98.4%	49.2%	0.8%	50%	0%	0%	0%	12

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample722.0ms (63.8%)

Results

710.0ms

8256×

body

256

valid

Bogosity

preprocess4.0ms (0.4%)

Algorithm

2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

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

Outputs
(atan.f64 (/.f64 y x))
(atan.f64 (/.f64 x y))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify11.0ms (0.9%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

Outputs
(atan.f64 (/.f64 y x))

eval0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(atan.f64 (/.f64 y x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize5.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (/.f64 y x))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

6 calls:

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

rewrite50.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1454×	`add-sqr-sqrt`
1442×	`*-un-lft-identity`
1334×	`add-cube-cbrt`
1316×	`add-cbrt-cube`
1302×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	141	11
2	1777	11

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

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

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

Outputs

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

simplify57.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

1288×	`associate-*r/`
938×	`*-commutative`
868×	`associate-*l/`
614×	`associate-r`
500×	`log-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	391
1	75	289
2	367	187
3	1698	187
4	3968	187
5	5969	187

Stop Event

1×	node limit

Counts

17 → 20

Calls

Call 1

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

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

eval3.0ms (0.2%)

Compiler: Compiled 151 to 54 computations (64.2% saved)

prune3.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	2	21

Error

Counts

21 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.0b	(exp.f64 (log.f64 (atan.f64 (/.f64 y x))))
✓	0.0b	(atan.f64 (/.f64 y x))

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize9.0ms (0.8%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(atan.f64 (/.f64 y x))
✓	1.3b	(exp.f64 (log.f64 (atan.f64 (/.f64 y x))))
✓	6.9b	(log.f64 (atan.f64 (/.f64 y x)))

Compiler

Compiled 22 to 6 computations (72.7% saved)

series90.0ms (8%)

Counts

2 → 24

Calls

12 calls:

Time	Variable		Point	Expression
25.0ms	x	@	-inf	(log.f64 (atan.f64 (/.f64 y x)))
22.0ms	y	@	0	(log.f64 (atan.f64 (/.f64 y x)))
15.0ms	y	@	inf	(log.f64 (atan.f64 (/.f64 y x)))
13.0ms	y	@	-inf	(log.f64 (atan.f64 (/.f64 y x)))
10.0ms	x	@	inf	(log.f64 (atan.f64 (/.f64 y x)))

rewrite63.0ms (5.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1592×	`add-sqr-sqrt`
1580×	`*-un-lft-identity`
1460×	`add-cube-cbrt`
1440×	`add-cbrt-cube`
1424×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	170	26
2	1968	26

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

Inputs
(log.f64 (atan.f64 (/.f64 y x)))
(exp.f64 (log.f64 (atan.f64 (/.f64 y x))))

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

Outputs

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

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

simplify51.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1392×	`associate-r`
1058×	`associate-l`
920×	`*-commutative`
808×	`associate-+r+`
782×	`associate-+l+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	76	1045
1	149	865
2	747	865
3	4285	865

Stop Event

1×	node limit

Counts

63 → 43

Calls

Call 1

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

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

eval8.0ms (0.7%)

Compiler: Compiled 586 to 215 computations (63.3% saved)

prune8.0ms (0.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	63	2	65

Error

Counts

65 → 2

Alt Table

Click to see full alt table

Status	Error	Program
✓	28.0b	(exp.f64 (log.f64 (atan.f64 (/.f64 y x))))
✓	0.0b	(atan.f64 (/.f64 y x))

Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes14.0ms (1.2%)

Accuracy

Total -28.0b remaining (-716886.2%)

Threshold costs -28.0b (-716886.2%)

Counts

2 → 1

Calls

Call 1

Inputs
(atan.f64 (/.f64 y x))
(exp.f64 (log.f64 (atan.f64 (/.f64 y x))))

Outputs
(atan.f64 (/.f64 y x))

Calls

4 calls:

5.0ms	(atan.f64 (/.f64 y x))
3.0ms	x
3.0ms	y
3.0ms	(/.f64 y x)

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(atan.f64 (/.f64 y x))`
0.0b	1	`(/.f64 y x)`

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify3.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11

Stop Event

1×	done
1×	saturated

Calls

Call 1

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

Outputs
(atan.f64 (/.f64 y x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

soundness0.0ms (0%)

end18.0ms (1.6%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

Details

analyze11.0ms (1%)

sample722.0ms (63.8%)

preprocess4.0ms (0.4%)

simplify11.0ms (0.9%)

eval0.0ms (0%)

prune1.0ms (0.1%)

localize5.0ms (0.5%)

series1.0ms (0%)

rewrite50.0ms (4.4%)

simplify57.0ms (5.1%)

eval3.0ms (0.2%)

prune3.0ms (0.3%)

localize9.0ms (0.8%)

series90.0ms (8%)

rewrite63.0ms (5.5%)

simplify51.0ms (4.5%)

eval8.0ms (0.7%)

prune8.0ms (0.7%)

regimes14.0ms (1.2%)

simplify3.0ms (0.3%)

soundness0.0ms (0%)

end18.0ms (1.6%)

Profiling